Daily Papers

This paper introduces and operationalizes summarization bias: a proposed systematic tendency of large language models (LLMs) to represent narrative meaning as an abstract summary label rather than as the reconstructable inferential structure that produces it. Within the Bulut Doctrine, narrative effect is theorized along a told-shown axis: in told mode, emotional and informational content is declared explicitly and requires little reader reconstruction; in shown mode, that content is suppressed at the surface and must be reconstructed from physical cues and indirection (Objective Projection). Shown mode is the higher-load condition the doctrine is designed to measure. The claim is that LLMs fail along this axis in a specific direction. Summarization bias is hypothesized to operate in two regimes: (i) a generative regime, in which a model asked to render an emotion through Objective Projection defaults to declaring it instead; and (ii) an evaluative regime, in which a model judging narrative quality rewards told-mode explicitness and under-detects shown-mode suppression. The evaluative regime is the more consequential, since LLMs increasingly serve as judges and reward models, and a directional bias toward told mode would impose a selection pressure degrading prose toward flat declaration. This report does not claim the bias is validated. It defines the construct, situates it against LLM-as-judge biases, rereads a completed independent reliability study as directional evidence consistent with it, and pre-registers a two-regime test with decision rules under which the construct would be abandoned.

Domain Generalization (DG) aims to learn representations robust to distribution shifts. Recent geometric alignment methods, such as CPCANet, extract domain-invariant structures through batch-wise Common Principal Component Analysis (CPCA). However, CPCANet suffers from rank-deficient covariance estimation due to the small-sample-size issue in mini-batch training. To address this limitation, we propose Projection Pursuit CPCANet (PP-CPCANet), a covariance-free framework that learns a global orthogonal basis on the Stiefel manifold and jointly optimizes it with network parameters via the Cayley transform. We further introduce a symmetry-breaking detached-median PP dispersion objective to extract common principal components (CPCs) with dense and robust optimization signals. Experiments on four DG benchmarks show that PP-CPCANet achieves SOTA performance while maintaining stable training.

Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and does not explicitly force different class features to be well-separated. Motivated by the observation that ground-truth class representations in CE loss are orthogonal (one-hot encoded vectors), we develop a novel loss function termed `Orthogonal Projection Loss' (OPL) which imposes orthogonality in the feature space. OPL augments the properties of CE loss and directly enforces inter-class separation alongside intra-class clustering in the feature space through orthogonality constraints on the mini-batch level. As compared to other alternatives of CE, OPL offers unique advantages e.g., no additional learnable parameters, does not require careful negative mining and is not sensitive to the batch size. Given the plug-and-play nature of OPL, we evaluate it on a diverse range of tasks including image recognition (CIFAR-100), large-scale classification (ImageNet), domain generalization (PACS) and few-shot learning (miniImageNet, CIFAR-FS, tiered-ImageNet and Meta-dataset) and demonstrate its effectiveness across the board. Furthermore, OPL offers better robustness against practical nuisances such as adversarial attacks and label noise. Code is available at: https://github.com/kahnchana/opl.

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise Policy Optimization (LPO) to explicitly conduct the target-projection, which demystifies the implicit target by restricting the proximal RL objective to the response simplex, and then projects the policy via exact divergence minimization. This framework provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step. On diverse reasoning tasks and LLM backbones, LPO consistently improves training performance over typical policy gradient baselines under matched targets, while intrinsically preserving optimization stability and response diversity.

Media compression standards have reached a plateau in terms of the rate-distortion-complexity trade-off, limiting the ability to offload expensive AI perception to the cloud in applications like robotics, wearables, and remote sensing. DNN-based codecs improve compression efficiency, but at a cost: they cannot easily adapt to large changes in available bitrate, and real-time encoding requires expensive, power-hungry GPUs that prohibit use on low-cost or resource-constrained platforms. To address these limitations, we propose a novel autoencoding framework (FRAPPE) that uses the Full input to predict the Residual output via a Projection Pursuit Encoder. FRAPPE's encoding objective naturally sorts latent channels by importance, allowing zero-overhead variable-rate coding. Unlike RNN-based learned codecs, whose encoder consumes the previous reconstruction's residual, or RVQ-style codecs, whose codebooks must be applied sequentially, FRAPPE's analysis path is an embarrassingly parallel DAG of independent input projections. Using FRAPPE, we build a variable-rate RGB image codec (FRAPPE-Image), and evaluate its rate-distortion-complexity trade-off against standard image codecs. At high compression ratios (approx. 0.1 bpp) FRAPPE-Image provides higher perceptual quality than AVIF with 47 times faster encoding, making it capable of real-time 1080p, 30fps CPU-only encoding. Our code and pre-trained models are available: https://github.com/UT-SysML/FRAPPE .

Recently, learning-based models have enhanced the performance of single-image super-resolution (SISR). However, applying SISR successively to each video frame leads to a lack of temporal coherency. Convolutional neural networks (CNNs) outperform traditional approaches in terms of image quality metrics such as peak signal to noise ratio (PSNR) and structural similarity (SSIM). However, generative adversarial networks (GANs) offer a competitive advantage by being able to mitigate the issue of a lack of finer texture details, usually seen with CNNs when super-resolving at large upscaling factors. We present iSeeBetter, a novel GAN-based spatio-temporal approach to video super-resolution (VSR) that renders temporally consistent super-resolution videos. iSeeBetter extracts spatial and temporal information from the current and neighboring frames using the concept of recurrent back-projection networks as its generator. Furthermore, to improve the "naturality" of the super-resolved image while eliminating artifacts seen with traditional algorithms, we utilize the discriminator from super-resolution generative adversarial network (SRGAN). Although mean squared error (MSE) as a primary loss-minimization objective improves PSNR/SSIM, these metrics may not capture fine details in the image resulting in misrepresentation of perceptual quality. To address this, we use a four-fold (MSE, perceptual, adversarial, and total-variation (TV)) loss function. Our results demonstrate that iSeeBetter offers superior VSR fidelity and surpasses state-of-the-art performance.

This paper focuses on the problem of constrained stochastic optimization. A zeroth order Frank-Wolfe algorithm is proposed, which in addition to the projection-free nature of the vanilla Frank-Wolfe algorithm makes it gradient free. Under convexity and smoothness assumption, we show that the proposed algorithm converges to the optimal objective function at a rate Oleft(1/T^{1/3}right), where T denotes the iteration count. In particular, the primal sub-optimality gap is shown to have a dimension dependence of Oleft(d^{1/3}right), which is the best known dimension dependence among all zeroth order optimization algorithms with one directional derivative per iteration. For non-convex functions, we obtain the Frank-Wolfe gap to be Oleft(d^{1/3}T^{-1/4}right). Experiments on black-box optimization setups demonstrate the efficacy of the proposed algorithm.

The modeling of turn-taking in dialog can be viewed as the modeling of the dynamics of voice activity of the interlocutors. We extend prior work and define the predictive task of Voice Activity Projection, a general, self-supervised objective, as a way to train turn-taking models without the need of labeled data. We highlight a theoretical weakness with prior approaches, arguing for the need of modeling the dependency of voice activity events in the projection window. We propose four zero-shot tasks, related to the prediction of upcoming turn-shifts and backchannels, and show that the proposed model outperforms prior work.

KV cache has become a de facto technique for the inference of large language models (LLMs), where tensors of shape (layer number, head number, sequence length, feature dimension) are introduced to cache historical information for self-attention. As the size of the model and data grows, the KV cache can quickly become a bottleneck within the system in both storage and memory transfer. To address this, prior studies usually focus on the first three axes of the cache tensors for compression. This paper supplements them, focusing on the feature dimension axis, by utilizing low-rank projection matrices to transform the cache features into spaces with reduced dimensions. We begin by investigating the canonical orthogonal projection method for data compression through principal component analysis (PCA). We observe the issue with PCA projection where significant performance degradation is observed at low compression rates. To bridge the gap, we propose to directly tune the orthogonal projection matrices with a distillation objective using an elaborate Matryoshka training strategy. After training, we adaptively search for the optimal compression rates for various layers and heads given varying compression budgets. Compared to previous works, our method can easily embrace pre-trained LLMs and hold a smooth tradeoff between performance and compression rate. We empirically witness the high data efficiency of our training procedure and find that our method can sustain over 90% performance with an average KV cache compression rate of 60% (and up to 75% in certain extreme scenarios) for popular LLMs like LLaMA2-7B-base and Mistral-7B-v0.3-base.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

On-policy Reinforcement Learning (RL) with PPO-like clip objectives has become the standard choice for reward-based fine-tuning of large language models (LLMs). Although recent work has explored improved estimators of advantages and normalization, the clipping mechanism itself has remained untouched. Originally introduced as a proxy for principled KL-based trust regions, clipping is a crude approximation that often causes unstable updates and suboptimal performance. We replace the clip objective with a novel discrete differentiable trust region projection, which provides principled token-level KL constraints. The projection operates on a sparse subset of the model's most important token logits to balance computational cost and projection effectiveness. Our approach, Trust Region Optimization for Large Language Models (TROLL), serves as a direct replacement for PPO-like clipping during training and does not alter the model's inference behavior. Across datasets, model families, and advantage-estimation methods, TROLL consistently outperforms PPO-like clipping in terms of training speed, stability, and final success rates.

Autoregressive video diffusion enables efficient streaming and long-horizon video generation, but repeatedly reusing generated latents as causal context can amplify temporal errors, resulting in flickering, motion jitter, and structural drift. In this paper, we investigate this failure mode from a spectral kinematic perspective and identify discrete latent acceleration as an effective signal for revealing unstable high-frequency temporal perturbations. To this end, we propose SAGA, a training-free \textit{s}table \textit{a}cceleration \textit{g}uidance approach for \textit{a}utoregressive video generation. SAGA integrates an acceleration domain spectral guidance objective based on finite-window Slepian projections with a structured autoregressive noise initialization strategy that suppresses short-range temporal correlations while preserving long-range motion structure. Without retraining or modifying the backbone, SAGA can be directly applied to existing chunk-wise autoregressive diffusion models, which is the prevalent setting for high-quality generation. Extensive experiments show that SAGA consistently improves temporal quality across multiple autoregressive diffusion models. On Self-Forcing, SAGA improves Temporal Quality from 97.30 to 97.91 and Image Quality from 69.60 to 70.51. Moreover, spectral analysis and human preference studies demonstrate that SAGA reduces temporal instability while maintaining visual fidelity.

Long-context language modeling remains central to modern sequence modeling, but the quadratic cost of Transformer attention makes scaling computationally prohibitive. Linear recurrent models address this bottleneck by compressing the context into a fixed-size state, making the rule that forgets, writes, and edits information a central design problem. To address state maintenance, Gated DeltaNet (GDN) combines gated state decay with delta-rule residual writes, using a learnable coefficient to balance forgetting and update magnitude. However, this coefficient is learned empirically rather than derived from the underlying objective, which can lead to suboptimal update magnitudes. We revisit the online-regression objective underlying GDN and, inspired by the Kaczmarz projection method, derive the key-norm-normalized dynamic step size β_t = η_t / (|k_t|_2^2 + ε) for residual updates. We propose Kaczmarz Linear Attention (KLA), a one-scalar modification of GDN that preserves the state shape, gates, linear recurrence, and chunkwise parallel algorithm. At the 0.4B scale with a 1B-token budget, KLA achieves the lowest validation perplexity among evaluated linear-time baselines, 8.09 versus 8.50 for GDN, and remains stable up to 65K tokens. On controlled tasks, KLA reaches 100% on single-needle-in-a-haystack retrieval, improves 8x multi-query associative recall by 7.03 points over GDN, and delivers 2.1x higher decode throughput at 32K context. These results suggest that the key-norm-normalized Kaczmarz coefficient is a first-order design axis for delta-rule sequence models: it improves accuracy, extrapolation, and decoding efficiency without changing the recurrent state or hardware kernel.

Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.

As part of a series on first-principles modeling of cognitive functions, this paper attempts to provide a mathematical formulation of thinking and perception. It formally derives slow thinking or more generally, active perception, and encompasses the design, training and inference of slow thinking large language models. Our starting point is the lifting and projection of probability distributions on the observable and latent spaces, with the objective of representing complex data distributions by simple function families such as neural networks. A theory called "active lifting" is proposed, based on the sampling of latent sequences and an intrinsic drive to reduce uncertainty with maximum rate. It derives a large design space, containing the slow thinking models in a subspace that we call the static theory. These models are positioned on the representation hierarchy and sampler hierarchy induced by the static theory, and can be upgraded by climbing the two hierarchies. Active lifting further derives an inference process with an internal time axis, and a training objective that resembles minimum-length coding as well as the invention of languages. Thus, it characterizes the agency of perception, including the emergence of the slow thinking formats. Technical by-products of this theory include a three-stage pathway for improving slow thinking models, a unified approach to constructing encoders and generative models for all data modalities, a priori formation of human-like visual representations, and a possible solution to policy collapse.

Looped Transformers provide a parameter-efficient approach to depth scaling by repeatedly applying shared Transformer blocks. Recent reasoning models have likewise highlighted the value of scaling test-time computation through longer computation trajectories. However, the principles for designing effective loop transitions remain poorly understood. We view the looped hidden state as a fast weight that is updated throughout the depth. We formulate loop transitions as local gradient-based updates, with recurrent blocks predicting implicit targets at each depth. Our framework derives loop transitions in closed form from a projection, a local objective and an optimizer update rule. Mapping representative loop transitions into this framework reveals mismatches between their transitions and projections. We first align the input maps of existing transitions. We then derive OperLoop, which combines explicit weight decay, adaptive step size and a delta objective. The aligned variants reduce training loss and improve average commonsense accuracy. OperLoop improves average generative performance over the compared looped and non-looped baselines under matched training FLOPs. These results support the framework's usefulness for loop design. We extend the analysis to additional loop models and outline a roadmap for future loop transition design.

Statistical whitening transformations play a fundamental role in many computational systems, and may also play an important role in biological sensory systems. Existing neural circuit models of adaptive whitening operate by modifying synaptic interactions; however, such modifications would seem both too slow and insufficiently reversible. Motivated by the extensive neuroscience literature on gain modulation, we propose an alternative model that adaptively whitens its responses by modulating the gains of individual neurons. Starting from a novel whitening objective, we derive an online algorithm that whitens its outputs by adjusting the marginal variances of an overcomplete set of projections. We map the algorithm onto a recurrent neural network with fixed synaptic weights and gain-modulating interneurons. We demonstrate numerically that sign-constraining the gains improves robustness of the network to ill-conditioned inputs, and a generalization of the circuit achieves a form of local whitening in convolutional populations, such as those found throughout the visual or auditory systems.

Foundation models are increasingly being pursued in particle and nuclear physics, but existing approaches remain strongly tied to individual experiments through detector-specific architectures or pre-training objectives, limiting their reuse across sensing modalities. We show that a point cloud self-distillation framework yields a substantially more general sensor-level pre-training recipe. We show that the same refined architecture and objective can be independently pre-trained with minimal changes on three qualitatively different detector modalities: liquid argon time projection chamber (LArTPC), collider TPC, and water Cherenkov. Using 1,000 labeled images for downstream task adaptation, Panda V2 matches or exceeds specialized foundation-model baselines trained with orders of magnitude more supervision, matching state-of-the-art particle-clustering performance with 70x fewer labeled events on sPHENIX while substantially improving particle identification, and on LArTPC data matching Panda (arXiv:2512.01324) particle reconstruction with up to 1,000x fewer labels. Beyond reconstruction, simple linear probes reveal physically meaningful latent structure associated with particle causality and track curvature.

Shared embedding spaces are widely used for multimodal search and data curation. In practice, two problems often limit how well this works. First, embeddings can reflect modality more than meaning, so examples cluster by input type even when the underlying content matches. Second, the paired supervision used to train these spaces is often noisy. When we blend many heterogeneous, human-labeled datasets, these issues reinforce each other and degrade cross-modal retrieval. We present a framework that improves alignment by acting on both the training pairs and the embedding model. Symmetric Nucleus Subsampling (SNS) refines training pairs by trimming raw inputs and annotations to the portions that best support each other. Expert Embedding Engine (EEE) combines complementary embedding experts using a learned projection network, together with a bias-aware objective that reduces modality-driven separation in the embedding space. We demonstrate that this approach collapses the modality gap by over 90% on average vs base embedding experts and is a strong data curator, with datablends from our method outperforming stratified sampling and traditional curation baselines in downstream model performance.

Small language models trained on a single local machine leave little room for architectural trial and error. Kairos combines bidirectional gated-DeltaNet linear attention and sliding-window attention over shared projections (LiZAttention2), block-wise Attention-Residual aggregation, a sparse Mixture-of-Experts (MoE) feed-forward layer and a multi-scale byte-level codec, trained with a uniform-noise denoising objective over one byte space shared by text, image, audio, video, lidar and control streams; this report asks whether the combination optimizes at all before asking whether it is useful. We give code-derived algorithms for each component, including a cross-session recurrent-state memory gate, then run convergence sanity checks: overfittinga single 440-byte sentence at 1--15M parameters, text only, with three seeds for codec and attention choices and single-run sweeps for seven further factors. The two attention variants tested at 3\,000 steps (LiZAttention2 and window attention alone) reach a minimum loss near 10^{-3}. After 600 steps, the mean minimum loss ranges from 0.018 (patch codec) to 0.354 (depthwise convolutional codec) with an identical ranking on three seeds. An apparent advantage of shared over separate attention projections closes with more steps or more diverse data and reverses when the projections are frozen: it is a convergence-speed effect, not a capacity effect. These checks suggest that the implementation optimizes; they say nothing about generalization, multimodal training or comparison with existing models, which a planned pretraining run is meant to address. The Discussion sizes a 200M-total/25M-active target analytically; none of its throughput figures is measured. Code is available at https://github.com/fabienfrfr/Kairos . Python package at https://pypi.org/project/kairos-fm/ .

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so far. However, we show that even with a perfect approximation to the joint loss, these approaches still suffer from temporary but substantial forgetting when starting to train on a new task. Motivated by this 'stability gap', we propose that continual learning strategies should focus not only on the optimization objective, but also on the way this objective is optimized. While there is some continual learning work that alters the optimization trajectory (e.g., using gradient projection techniques), this line of research is positioned as alternative to improving the optimization objective, while we argue it should be complementary. To evaluate the merits of our proposition, we plan to combine replay-approximated joint objectives with gradient projection-based optimization routines to test whether the addition of the latter provides benefits in terms of (1) alleviating the stability gap, (2) increasing the learning efficiency and (3) improving the final learning outcome.

The static ``train then deploy" paradigm fundamentally limits Large Language Models (LLMs) from dynamically adapting their weights in response to continuous streams of new information inherent in real-world tasks. Test-Time Training (TTT) offers a compelling alternative by updating a subset of model parameters (fast weights) at inference time, yet its potential in the current LLM ecosystem is hindered by critical barriers including architectural incompatibility, computational inefficiency and misaligned fast weight objectives for language modeling. In this work, we introduce In-Place Test-Time Training (In-Place TTT), a framework that seamlessly endows LLMs with Test-Time Training ability. In-Place TTT treats the final projection matrix of the ubiquitous MLP blocks as its adaptable fast weights, enabling a ``drop-in" enhancement for LLMs without costly retraining from scratch. Furthermore, we replace TTT's generic reconstruction objective with a tailored, theoretically-grounded objective explicitly aligned with the Next-Token-Prediction task governing autoregressive language modeling. This principled objective, combined with an efficient chunk-wise update mechanism, results in a highly scalable algorithm compatible with context parallelism. Extensive experiments validate our framework's effectiveness: as an in-place enhancement, it enables a 4B-parameter model to achieve superior performance on tasks with contexts up to 128k, and when pretrained from scratch, it consistently outperforms competitive TTT-related approaches. Ablation study results further provide deeper insights on our design choices. Collectively, our results establish In-Place TTT as a promising step towards a paradigm of continual learning in LLMs.

Deep metric learning objectives (e.g., triplet loss) require storing and comparing high-dimensional embeddings, making the per-batch loss buffer scale as O(Scdot D), where S is the number of samples in a batch and D is the feature dimension, thus limiting training on memory-constrained hardware. We propose Shadow Loss, a proxy-free, parameter-free objective that measures similarity via scalar projections onto the anchor direction, reducing the loss-specific buffer from O(Scdot D) to O(S) while preserving the triplet structure. We analyze gradients, provide a Lipschitz continuity bound, and show that Shadow Loss penalizes trivial collapse for stable optimization. Across fine-grained retrieval (CUB-200, CARS196), large-scale product retrieval (Stanford Online Products, In-Shop Clothes), and standard/medical benchmarks (CIFAR-10/100, Tiny-ImageNet, HAM-10K, ODIR-5K), Shadow Loss consistently outperforms recent objectives (Triplet, Soft-Margin Triplet, Angular Triplet, SoftTriple, Multi-Similarity). It also converges in approx 1.5-2times fewer epochs under identical backbones and mining. Furthermore, it improves representation separability as measured by higher silhouette scores. The design is architecture-agnostic and vectorized for efficient implementation. By decoupling discriminative power from embedding dimensionality and reusing batch dot-products, Shadow Loss enables memory-linear training and faster convergence, making deep metric learning practical on both edge and large-scale systems.

Recent research on sequence labelling has been exploring different strategies to mitigate the lack of manually annotated data for the large majority of the world languages. Among others, the most successful approaches have been based on (i) the cross-lingual transfer capabilities of multilingual pre-trained language models (model-transfer), (ii) data translation and label projection (data-transfer) and (iii), prompt-based learning by reusing the mask objective to exploit the few-shot capabilities of pre-trained language models (few-shot). Previous work seems to conclude that model-transfer outperforms data-transfer methods and that few-shot techniques based on prompting are superior to updating the model's weights via fine-tuning. In this paper, we empirically demonstrate that, for Argument Mining, a sequence labelling task which requires the detection of long and complex discourse structures, previous insights on cross-lingual transfer or few-shot learning do not apply. Contrary to previous work, we show that for Argument Mining data transfer obtains better results than model-transfer and that fine-tuning outperforms few-shot methods. Regarding the former, the domain of the dataset used for data-transfer seems to be a deciding factor, while, for few-shot, the type of task (length and complexity of the sequence spans) and sampling method prove to be crucial.

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales, these biases imply a parameter underallocation corresponding to 6.5% of the 3.8times10^{25} FLOP training budget and \1.4M (90% CI: 412K-\2.9M) in unnecessary compute at 50% H100 MFU. Simulated multimodal model misallocations show even greater opportunity costs due to higher loss surface asymmetry. Three sources of this error are examined: IsoFLOP sampling grid width (Taylor approximation accuracy), uncentered IsoFLOP sampling, and loss surface asymmetry (α\neq β$). Chinchilla Approach 3 largely eliminates these biases but is often regarded as less data-efficient, numerically unstable, prone to local minima, and harder to implement. Each concern is shown to be unfounded or addressable, especially when the partially linear structure of the objective is exploited via Variable Projection, enabling unbiased inference on all five loss surface parameters through a two-dimensional optimization that is well-conditioned, analytically differentiable, and amenable to dense, or even exhaustive, grid search. It may serve as a more convenient replacement for Approach 2 or a more scalable alternative for adaptations of Approach 3 to richer scaling law formulations.

Recent studies have made notable progress in video representation learning by transferring image-pretrained models to video tasks, typically with complex temporal modules and video fine-tuning. However, fine-tuning heavy modules may compromise inter-video semantic separability, i.e., the essential ability to distinguish objects across videos. While reducing the tunable parameters hinders their intra-video temporal consistency, which is required for stable representations of the same object within a video. This dilemma indicates a potential trade-off between the intra-video temporal consistency and inter-video semantic separability during image-to-video transfer. To this end, we propose the Consistency-Separability Trade-off Transfer Learning (Co-Settle) framework, which applies a lightweight projection layer on top of the frozen image-pretrained encoder to adjust representation space with a temporal cycle consistency objective and a semantic separability constraint. We further provide a theoretical support showing that the optimized projection yields a better trade-off between the two properties under appropriate conditions. Experiments on eight image-pretrained models demonstrate consistent improvements across multiple levels of video tasks with only five epochs of self-supervised training. The code is available at https://github.com/yafeng19/Co-Settle.

We introduce JuRe (Just Repair), a minimal denoising network for time series anomaly detection that exposes a central finding: architectural complexity is unnecessary when the training objective correctly implements the manifold-projection principle. JuRe consists of a single depthwise-separable convolutional residual block with hidden dimension 128, trained to repair corrupted time series windows and scored at inference by a fixed, parameter-free structural discrepancy function. Despite using no attention, no latent variable, and no adversarial component, JuRe ranks second on the TSB-AD multivariate benchmark (AUC-PR 0.404, 180 series, 17 datasets) and second on the UCR univariate archive by AUC-PR (0.198, 250 series), leading all neural baselines on AUC-PR and VUS-PR. Component ablation on TSB-AD identifies training-time corruption as the dominant factor (ΔAUC-PR = 0.047 on removal), confirming that the denoising objective, not network capacity, drives detection quality. Pairwise Wilcoxon signed-rank tests establish statistical significance against 21 of 25 baselines on TSB-AD. Code is available at the URL https://github.com/iis-esslingen/JuRe.

Self-supervised learning (SSL) is standard for speech representation learning, but mainstream models are designed around single-speaker audio, limiting their usefulness in multi-speakers scenarios. We present SepRQ, an open-source SSL framework that replaces masked prediction with a pseudo-source-separation objective over frozen random-projection codebooks. By adopting a novel mask-free, multiresolution approach, SepRQ achieves state-of-the-art performance in Speaker Diarization and Speech Separation on the SUPERB benchmark, surpassing WavLM and other cocktail-party derived SSLs at both Base and Large scales, while requiring only 85.68M inference parameters. SepRQ also demonstrates strong performance across target-speaker tasks requiring enrollment (such as Target-Speaker Automatic Speech Recognition), and on the challenging multi-domain DIHARD 3 diarization dataset. Notably, we report strong separation capabilities on three-speaker mixtures (WSJ0-3Mix), where current SSL literature struggles. While cocktail-party SSLs remain scarce and closed-source, limited to C-HuBERT and the enrollment-based SA-WavLM, we open-source SepRQ to the community.

An application of the POCS-based clustering algorithm (POCS stands for Projection Onto Convex Set), a novel clustering technique, for feature embedding clustering problems is proposed in this paper. The POCS-based clustering algorithm applies the POCS's convergence property to clustering problems and has shown competitive performance when compared with that of other classical clustering schemes in terms of clustering error and execution speed. Specifically, the POCS-based clustering algorithm treats each data point as a convex set and applies a parallel projection operation from every cluster prototype to corresponding data members in order to minimize the objective function and update the prototypes. The experimental results on the synthetic embedding datasets extracted from the 5 Celebrity Faces and MNIST datasets show that the POCS-based clustering algorithm can perform with favorable results when compared with those of other classical clustering schemes such as the K-Means and Fuzzy C-Means algorithms in feature embedding clustering problems.

Transferable adversarial attacks are arguably the most practical black-box threat model. Under the same perturbation budget, stronger transfer attacks attain higher attack success rate (ASR), yet their imperceptibility also tends to degrade. Under such a fixed-budget protocol, transferability and imperceptibility therefore appear to trade off against each other. We argue that this conflict is an artifact of fixed-budget evaluation, not an intrinsic trade-off. When attacks are compared on the ASR--imperceptibility Pareto frontier obtained by sweeping ε, stronger transfer attacks already attain better imperceptibility at matched ASR than weaker ones. To exploit this latent advantage, we introduce the stealthy transfer attack ST, a plug-in primal-dual wrapper that adds an L_infty saturation regularizer to the standard constrained objective and resolves it through a two-step primal-dual update: a projected primal step on the perturbation coupled with an L_1-ball projection on a dual variable that absorbs the regularizer through Fenchel duality, requiring no auxiliary models or handcrafted perceptual priors. Empirically, ST extends the Pareto frontier across different base attacks and additional surrogate architectures. At ε{=}16/255, average imperceptibility gains over each base attack are 17% on LPIPS and 14% on NIQE while ASR is preserved or improved. At matched high-ASR levels, the strongest ST variants further Pareto-dominate dedicated stealth-oriented transfer attacks, confirming that the latent imperceptibility advantage of strong transfer attacks can be unlocked by a primal-dual optimization wrapper without sacrificing transferability. Code will be made available at https://github.com/AndssY/ST.

We present BioMatrix, the first multimodal foundation model that natively integrates sequences, structures, and natural language for both molecules and proteins within a single decoder-only architecture. Existing biological foundation models pursue native multimodality and broad entity coverage separately: those that fuse multiple modalities under a shared objective remain confined to a single entity type, while those spanning multiple entity types either omit explicit structural modeling or rely on adapter-based designs in which the model cannot natively generate the very modalities it can read. BioMatrix closes this gap by mapping molecular sequences (supporting both SMILES and SELFIES notations), molecular structures, protein sequences, protein structures, and natural language into a shared discrete token space through a unified tokenization scheme, so that all modalities are consumed and produced uniformly under a single next-token prediction objective -- without external encoders, projection adapters, or modality-specific output heads. Built upon the Qwen3 language model (1.7B and 4B), BioMatrix is continually pretrained on 304.4 billion tokens spanning general and domain-specific text, sequence and structure views of molecules and proteins, and cross-modal corpora that interleave biomolecular entities with scientific text and link distinct entities through molecule-protein and protein-protein interaction data. After tuning on a comprehensive suite of downstream applications covering 80 tasks across 6 categories -- encompassing single-entity and multi-entity understanding and generation tasks across and within modalities -- BioMatrix achieves state-of-the-art or competitive performance on 77 out of 80 tasks, demonstrating that a single, natively multimodal generalist model can effectively match or surpass specialized approaches across a wide range of biological tasks.

Diffusion prior-based methods have shown impressive results in real-world image super-resolution (ISR), yet two key challenges persist: balancing pixel-level fidelity with semantic quality, and adapting to diverse degradations. Existing dual-branch approaches freeze the pixel module during semantic training, but the semantic branch can still expand capacity within the pixel subspace, precluding genuine perceptual improvement. Moreover, using a single static adapter cannot generalize across heterogeneous real-world corruptions. To address both issues, we propose FreqOrtho-SR, which comprises: Frequency-guided Mixture of LoRA Experts (FreqMoE), it routes inputs to specialized experts via a non-parametric FFT-based degradation-feature extractor that encodes frequency-domain signatures, enabling stable and interpretable specialization across corruption types; and Orthogonal Gradient Projection (OGP), which reframes the dual-objective optimization as a subspace-constrained problem: by extracting the pixel-fidelity subspace via SVD on combined expert weight deltas and projecting semantic gradients onto its null space, OGP guarantees orthogonality between the two objectives, enabling genuinely complementary learning without mutual interference. Experiments show that FreqOrtho-SR achieves competitive overall performance and a strong fidelity-perception trade-off across multiple benchmarks with efficient single-step inference. The source code of our method can be found at https://github.com/sonhm3029/FreqOrtho-SR{sonhm3029/FreqOrtho-SR}.

Merging multiple expert models offers a promising approach for performing multi-task learning without accessing their original data. Existing methods attempt to alleviate task conflicts by sparsifying task vectors or promoting orthogonality among them. However, they overlook the fundamental target of model merging: the merged model performs as closely as possible to task-specific models on respective tasks. We find these methods inevitably discard task-specific information that, while causing conflicts, is crucial for performance. Based on our findings, we frame model merging as a constrained optimization problem (i.e., minimizing the gap between the merged model and individual models, subject to the constraint of retaining shared knowledge) and solve it via adaptive projective gradient descent. Specifically, we align the merged model with individual models by decomposing and reconstituting the loss function, alleviating conflicts through data-free optimization of task vectors. To retain shared knowledge, we optimize this objective by projecting gradients within a shared subspace spanning all tasks. Moreover, we view merging coefficients as adaptive learning rates and propose a task-aware, training-free strategy. Experiments show that our plug-and-play approach consistently outperforms previous methods, achieving state-of-the-art results across diverse architectures and tasks in both vision and NLP domains.

Latent world models are judged by how well they predict, so when planning fails at long horizons the natural reading is that the predictor degrades. On a reproduction of LeWorldModel on TwoRoom we show the binding constraint is the planner's objective instead. The predictor is not the limit: its imagined state seventy-five environment steps ahead is still only 0.189 as wrong as assuming the world froze, while the planner never imagines beyond twenty-five. The objective is. Cross-entropy-method planning minimises squared latent distance, which tracks true distance at r = 0.426, saturates by about eighty arena units and decreases beyond a hundred and twenty, so moving away from the goal can lower the cost. The information is present throughout: a ridge probe recovers position from the frozen embedding at R^2 0.9922. The pathology is the method's, not one reimplementation's. It is present in the authors' released weights, and across four checkpoints long-horizon success rank-orders exactly with metric quality and inversely with prediction accuracy. Replacing only the objective, with nothing retrained and no GPU, lifts goals reached at offset 100 from 26.0% to 98.0%, equals the 98.0% at offset 25, and reaches 92.0% under a third of the budget: planning stops depending on the horizon. The best cost is not the most accurate. A head learned from frame separation alone predicts spatial distance worse than a position probe (r = 0.819 against 0.9897) yet plans better, charging 24% more to cross the environment's dividing wall where squared latent distance charges 4% less. It has learned reachability, not proximity.

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Current LLM unlearning methods face a critical security vulnerability that undermines their fundamental purpose: while they appear to successfully remove sensitive or harmful knowledge, this ``forgotten" information remains precariously recoverable through relearning attacks. We identify that the root cause is that conventional methods optimizing the forgetting loss at individual data points will drive model parameters toward sharp minima in the loss landscape. In these unstable regions, even minimal parameter perturbations can drastically alter the model's behaviors. Consequently, relearning attacks exploit this vulnerability by using just a few fine-tuning samples to navigate the steep gradients surrounding these unstable regions, thereby rapidly recovering knowledge that was supposedly erased. This exposes a critical robustness gap between apparent unlearning and actual knowledge removal. To address this issue, we propose StableUN, a bi-level feedback-guided optimization framework that explicitly seeks more stable parameter regions via neighborhood-aware optimization. It integrates forgetting feedback, which uses adversarial perturbations to probe parameter neighborhoods, with remembering feedback to preserve model utility, aligning the two objectives through gradient projection. Experiments on WMDP and MUSE benchmarks demonstrate that our method is significantly more robust against both relearning and jailbreaking attacks while maintaining competitive utility performance.

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information for object-oriented exploration. On the other hand, end-to-end learning methods alleviate manual map design and predict actions using implicit representations. Such methods, however, lack an explicit notion of geometry and may have limited ability to encode navigation history. In this work, we propose an implicit spatial map for object goal navigation. Our implicit map is recursively updated with new observations at each step using a transformer. To encourage spatial reasoning, we introduce auxiliary tasks and train our model to reconstruct explicit maps as well as to predict visual features, semantic labels and actions. Our method significantly outperforms the state of the art on the challenging MP3D dataset and generalizes well to the HM3D dataset. We successfully deploy our model on a real robot and achieve encouraging object goal navigation results in real scenes using only a few real-world demonstrations. Code, trained models and videos are available at https://www.di.ens.fr/willow/research/onav_rim/.

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

Projection-based appearance editing changes selected visual attributes of a physical object through projection mapping (PM). To display a desired appearance, PM typically uses projector compensation, which computes a projector input that counteracts the geometric and photometric distortions of the scene. Compensation can only approximate this appearance within the available projection range, and it cannot revise the appearance itself. Pretrained LLM-based image editors provide a direct way to produce the desired appearance from a text prompt or reference image; projector compensation can then attempt to reproduce the edited result through projection. However, these editors do not have an accurate measure of the scene geometry or scene response. Therefore, their outputs may contain geometric misalignment, inconsistent shading, or changes outside the available projection range, which downstream projector compensation cannot correct. To address this problem, we introduce SREdit, an efficient response-guided framework for projection-based appearance editing. SREdit estimates a scene response map from the reconstructed scene that reflects how strongly projected illumination can affect different surface regions. SREdit uses the source appearance to constrain the early sampling process and preserve registration with the fixed physical object, while the scene response map adapts the amount of editing across surface regions. Experiments across two pretrained image editors show that SREdit improves projected appearance quality and reproduction fidelity. It adds less than one second per image with negligible VRAM overhead. Participants also consistently preferred the results produced with SREdit in our user study.

Designing learnable information-theoretic objectives for robot exploration remains challenging. Such objectives aim to guide exploration toward data that reduces uncertainty in model parameters, yet it is often unclear what information the collected data can actually reveal. Although reinforcement learning (RL) can optimize a given objective, constructing objectives that reflect parametric learnability is difficult in high-dimensional robotic systems. Many parameter directions are weakly observable or unidentifiable, and even when identifiable directions are selected, omitted directions can still influence exploration and distort information measures. To address this challenge, we propose Quasi-Optimal Experimental Design (Q{\footnotesize OED}), an adaptive information objective grounded in optimal experimental design. Q{\footnotesize OED} (i) performs eigenspace analysis of the Fisher information matrix to identify an observable subspace and select identifiable parameter directions, and (ii) modifies the exploration objective to emphasize these directions while suppressing nuisance effects from non-critical parameters. Under bounded nuisance influence and limited coupling between critical and nuisance directions, Q{\footnotesize OED} provides a constant-factor approximation to the ideal information objective that explores all parameters. We evaluate Q{\footnotesize OED} on simulated and real-world navigation and manipulation tasks, where identifiable-direction selection and nuisance suppression yield performance improvements of 35.23{\percent} and 21.98{\percent}, respectively. When integrated as an exploration objective in model-based policy optimization, Q{\footnotesize OED} further improves policy performance over established RL baselines.

Joint-embedding self-supervised learning typically combines an invariance objective across augmented views with additional mechanisms to prevent representational collapse. These objectives are often applied after a projection head, while downstream tasks use the backbone representation before the projector. We find that this mismatch does not necessarily prevent dimensional collapse in the backbone, which can retain low effective rank and potentially limit downstream transfer. To address this, we introduce SACReg, a spectral anti-collapse regularizer motivated by an analysis of λ-balance, which captures the relative scale of weight matrices across layers. In a two-layer linear network, we show that (i) λ-balance prevents collapse, and (ii) our regularizer applied to the backbone induces λ-balance. In the nonlinear case, this regularizer leads to anti-collapse as well and, in realistic architectures on ImageNet100, it empirically increases the representations' ranks. We apply SACReg to JEPA and propose λ-JEPA, which improves over LeJEPA and VISReg on ImageNet-1k classification and in average linear-probe transfer performance across eight downstream image datasets. On video self-supervised learning, λ-JEPA improves over LeVJEPA and V-JEPA 2 on the Something-Something-v2 and Kinetics-400 benchmarks. Code is available at https://github.com/berkerdemirel/lambda-jepa.

Deep learning problems rarely involve objectives that are equal in importance. A primary objective defines the goal, whilst secondary objectives, such as sparsity, compression, or robustness constrain the solution. While existing multi-objective methods have proven effective in practice, they have a clear symmetry problem and neglect the inherent objective hierarchy built into these objective spaces. We introduce Priority-Constrained Descent (PCD), a gradient-based optimization framework designed to explicitly exploit hierarchical objective structures. PCD preserves the direction of primary descent whilst allowing for the minimal distortion necessary to guarantee progress on secondary objectives, controlled by a single τin [0, 1] that dictates the strength of the distortion. The resulting formulation is invariant to objective scaling and admits exact closed-form solutions for problems with two and three objectives. We evaluate PCD within structured network compression settings, unstructured sparsity and low-rankness, and across a variety of synthetic experiments, showing Pareto dominance and better per-objective performance with secondary progress guarantees over existing methods, further exhibiting the interpretable trade-off that τ provides.

Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex objectives on these domains, utilizing the principles of Sinkhorn matrix scaling and mirror descent. The proposed algorithm is robust to noise, and can be used in an online setting. We provide theoretical guarantees for convex objectives and experimental results showcasing it effectiveness on both synthetic and real-world data.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

Most Bundle Adjustment (BA) solvers like the Levenberg-Marquardt algorithm require a good initialization. Instead, initialization-free BA remains a largely uncharted territory. The under-explored Variable Projection algorithm (VarPro) exhibits a wide convergence basin even without initialization. Coupled with object space error formulation, recent works have shown its ability to solve small-scale initialization-free bundle adjustment problem. To make such initialization-free BA approaches scalable, we introduce Power Variable Projection (PoVar), extending a recent inverse expansion method based on power series. Importantly, we link the power series expansion to Riemannian manifold optimization. This projective framework is crucial to solve large-scale bundle adjustment problems without initialization. Using the real-world BAL dataset, we experimentally demonstrate that our solver achieves state-of-the-art results in terms of speed and accuracy. To our knowledge, this work is the first to address the scalability of BA without initialization opening new venues for initialization-free structure-from-motion.

Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the accuracy and robustness, several researchers have recently demonstrated the benefit of using large field-of-view cameras for such applications. In this paper, we provide an extensive review of existing models for large field-of-view cameras. For each model we provide projection and unprojection functions and the subspace of points that result in valid projection. Then, we propose the Double Sphere camera model that well fits with large field-of-view lenses, is computationally inexpensive and has a closed-form inverse. We evaluate the model using a calibration dataset with several different lenses and compare the models using the metrics that are relevant for Visual Odometry, i.e., reprojection error, as well as computation time for projection and unprojection functions and their Jacobians. We also provide qualitative results and discuss the performance of all models.

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal algorithm with a closed-form projection and proximal operator scheme, thereby affording a more scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer not only results in a better preservation of the class structure in the data but also yields additional robustness to the data geometry, compared to previous regularizers.

We investigate an experiential learning paradigm for acquiring an internal model of intuitive physics. Our model is evaluated on a real-world robotic manipulation task that requires displacing objects to target locations by poking. The robot gathered over 400 hours of experience by executing more than 100K pokes on different objects. We propose a novel approach based on deep neural networks for modeling the dynamics of robot's interactions directly from images, by jointly estimating forward and inverse models of dynamics. The inverse model objective provides supervision to construct informative visual features, which the forward model can then predict and in turn regularize the feature space for the inverse model. The interplay between these two objectives creates useful, accurate models that can then be used for multi-step decision making. This formulation has the additional benefit that it is possible to learn forward models in an abstract feature space and thus alleviate the need of predicting pixels. Our experiments show that this joint modeling approach outperforms alternative methods.

To achieve the highest perceptual quality, state-of-the-art diffusion models are optimized with objectives that typically look very different from the maximum likelihood and the Evidence Lower Bound (ELBO) objectives. In this work, we reveal that diffusion model objectives are actually closely related to the ELBO. Specifically, we show that all commonly used diffusion model objectives equate to a weighted integral of ELBOs over different noise levels, where the weighting depends on the specific objective used. Under the condition of monotonic weighting, the connection is even closer: the diffusion objective then equals the ELBO, combined with simple data augmentation, namely Gaussian noise perturbation. We show that this condition holds for a number of state-of-the-art diffusion models. In experiments, we explore new monotonic weightings and demonstrate their effectiveness, achieving state-of-the-art FID scores on the high-resolution ImageNet benchmark.

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

A popular way to approximate the Koopman operator's action on a finite-dimensional subspace of functions is via orthogonal projections. The quality of the projected model directly depends on the selected subspace, specifically on how close it is to being invariant under the Koopman operator. The notion of invariance proximity provides a tight upper bound on the worst-case relative prediction error of the finite-dimensional model. However, its direct calculation is computationally challenging. This paper leverages the geometric structure behind the definition of invariance proximity to provide a closed-form expression in terms of Jordan principal angles on general inner product spaces. Unveiling this connection allows us to exploit specific isomorphisms to circumvent the computational challenges associated with spaces of functions and enables the use of existing efficient numerical routines to compute invariance proximity.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

We study optimization problems on Hadamard manifolds, motivated by recent advances in geometric approaches to optimization on curved spaces, particularly those involving the structure of Busemann functions. We introduce a projection based variant of the proximal point algorithm, termed the Busemann hybrid projection proximal point algorithm, which replaces Euclidean hyperplanes with horospheres defined via convex Busemann functions. The algorithm performs projections in closed form using the gradients of these functions, resulting in a geometrically intrinsic scheme that requires no tangent space linear solves. We allow for inexact subgradient evaluations and prove global convergence under controlled inexactness, with a relative error level strictly below one. We establish a Fejér type descent and sublinear complexity with a rate proportional to the inverse square root of the iteration count, and show that the exact variant coincides with the classical Riemannian proximal point algorithm. The framework clarifies the role of Busemann based subdifferentials in optimization on spaces of nonpositive curvature.

Continual learning aims to avoid catastrophic forgetting and effectively leverage learned experiences to master new knowledge. Existing gradient projection approaches impose hard constraints on the optimization space for new tasks to minimize interference, which simultaneously hinders forward knowledge transfer. To address this issue, recent methods reuse frozen parameters with a growing network, resulting in high computational costs. Thus, it remains a challenge whether we can improve forward knowledge transfer for gradient projection approaches using a fixed network architecture. In this work, we propose the Restricted Orthogonal Gradient prOjection (ROGO) framework. The basic idea is to adopt a restricted orthogonal constraint allowing parameters optimized in the direction oblique to the whole frozen space to facilitate forward knowledge transfer while consolidating previous knowledge. Our framework requires neither data buffers nor extra parameters. Extensive experiments have demonstrated the superiority of our framework over several strong baselines. We also provide theoretical guarantees for our relaxing strategy.

Machine learning systems often experience a distribution shift between training and testing. In this paper, we introduce a simple variational objective whose optima are exactly the set of all representations on which risk minimizers are guaranteed to be robust to any distribution shift that preserves the Bayes predictor, e.g., covariate shifts. Our objective has two components. First, a representation must remain discriminative for the task, i.e., some predictor must be able to simultaneously minimize the source and target risk. Second, the representation's marginal support needs to be the same across source and target. We make this practical by designing self-supervised objectives that only use unlabelled data and augmentations to train robust representations. Our objectives give insights into the robustness of CLIP, and further improve CLIP's representations to achieve SOTA results on DomainBed.

Generative world models provide rich predictions of how manipulation scenes may evolve toward task objectives, yet those futures do not directly expose the compact task variables required by control. When training supervises future prediction alone, terminal goal accuracy is not an explicit learning objective, even when geometric recovery is available. We present Entity-Level Goal Readout, a learned prediction-to-execution interface that makes the executable terminal goal an explicit output of a 3D trace world model. It combines object-centric pose prediction with translation grounded in observed depth to produce a compact goal in SE(3). A shared Pose-Native Executor consumes this fixed goal with online object-pose feedback for closed-loop control without rerunning the world model. Across five manipulation tasks, the pipeline achieves a mean success rate of 79.69%. Goal diagnostics directly measure terminal goal accuracy, while controlled translation perturbations characterize how execution degrades under goal error. Zero-shot deployment on a Franka arm achieves 73.33% success on nominal StackCube, 66.67% with distractors, and 75.00% on PickPlate with a target unseen during policy training. These results support treating the prediction-to-execution interface as an explicit learned component of world-model planning rather than incidental post-processing in the control pipeline itself. Project page: https://claire0730.github.io/executable-goals/

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Beyond minimizing a single training loss, many deep learning estimation pipelines rely on an auxiliary objective to quantify and encourage desirable properties of the model (e.g. performance on another dataset, robustness, agreement with a prior). Although the simplest approach to incorporating an auxiliary loss is to sum it with the training loss as a regularizer, recent works have shown that one can improve performance by blending the gradients beyond a simple sum; this is known as gradient surgery. We cast the problem as a constrained minimization problem where the auxiliary objective is minimized among the set of minimizers of the training loss. To solve this bilevel problem, we follow a parameter update direction that combines the training loss gradient and the orthogonal projection of the auxiliary gradient to the training gradient. In a setting where gradients come from mini-batches, we explain how, using a moving average of the training loss gradients, we can carefully maintain this critical orthogonality property. We demonstrate that our method, Bloop, can lead to much better performances on NLP and vision experiments than other gradient surgery methods without EMA.

The goal of predictive data attribution is to estimate how adding or removing a given set of training datapoints will affect model predictions. In convex settings, this goal is straightforward (i.e., via the infinitesimal jackknife). In large-scale (non-convex) settings, however, existing methods are far less successful -- current methods' estimates often only weakly correlate with ground truth. In this work, we present a new data attribution method (MAGIC) that combines classical methods and recent advances in metadifferentiation to (nearly) optimally estimate the effect of adding or removing training data on model predictions.

Model-based reinforcement learning (MBRL) has been shown to be a powerful framework for data-efficiently learning control of continuous tasks. Recent work in MBRL has mostly focused on using more advanced function approximators and planning schemes, with little development of the general framework. In this paper, we identify a fundamental issue of the standard MBRL framework -- what we call the objective mismatch issue. Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized. In the context of MBRL, we characterize the objective mismatch between training the forward dynamics model w.r.t.~the likelihood of the one-step ahead prediction, and the overall goal of improving performance on a downstream control task. For example, this issue can emerge with the realization that dynamics models effective for a specific task do not necessarily need to be globally accurate, and vice versa globally accurate models might not be sufficiently accurate locally to obtain good control performance on a specific task. In our experiments, we study this objective mismatch issue and demonstrate that the likelihood of one-step ahead predictions is not always correlated with control performance. This observation highlights a critical limitation in the MBRL framework which will require further research to be fully understood and addressed. We propose an initial method to mitigate the mismatch issue by re-weighting dynamics model training. Building on it, we conclude with a discussion about other potential directions of research for addressing this issue.

Test-time alignment of Large Language Models (LLMs) to human preferences offers a flexible way to generate responses aligned to diverse objectives without extensive retraining of LLMs. Existing methods achieve alignment to multiple objectives simultaneously (e.g., instruction-following, helpfulness, conciseness) by optimizing their corresponding reward functions. However, they often rely on predefined weights or optimize for averages, sacrificing one objective for another and leading to unbalanced outcomes. To address this, we introduce Robust Multi-Objective Decoding (RMOD), a novel inference-time algorithm that optimizes for improving worst-case rewards. RMOD formalizes the robust decoding problem as a maximin two-player game between reward weights and the sampling policy, solving for the Nash equilibrium. We show that the game reduces to a convex optimization problem to find the worst-case weights, while the best response policy can be computed analytically. We also introduce a practical RMOD variant designed for efficient decoding with contemporary LLMs, incurring minimal computational overhead compared to non-robust Multi-Objective Decoding (MOD) methods. Our experimental results showcase the effectiveness of RMOD in generating responses equitably aligned with diverse objectives, outperforming baselines up to 20%.

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.

Flow matching (FM) generators often face a quality-coverage tradeoff. Inference-time techniques such as classifier-free guidance raise quality, but at the cost of coverage. We hypothesize this limitation stems from a basic property of the objective: an intermediate noisy image could correspond to many clean images, yet the model can only predict a single velocity, at best averaging over the multiple possibilities. To mitigate this, we introduce competition among predictions during training. We achieve this by augmenting the predictor with a randomly drawn low-dimensional conditioning code z. For each training example, we sample K values of z to produce K candidate velocities that compete to explain the target, and apply the loss only to the best-matching candidate. This winner-take-all objective allows different modes to shape different predictions, rather than being averaged into a single compromise. Furthermore, this term naturally enables a new form of guidance, auxiliary conditioning scaling, which complements traditional guidance methods. Together, these two guidance mechanisms show that our method substantially improves the quality-coverage frontier. We validate on ImageNet-256, using two different testbeds, SiT and RAEv2. Given less than 3% of the original SiT pretraining compute for post-training, at the 67% Recall point, our method reduces FD_{r,6} from 19.22 to 5.91. On RAEv2, at the 70% Recall point, it reduces FD_{r,6} from 16.83 to 3.18.

As LLM-based agents continue to advance, their evaluation has become increasingly multifaceted: a capable agent must not only achieve high task completion accuracy but also perform well in interaction quality, safety, and efficiency, raising a central question: can these objectives be optimized simultaneously? Existing methods have considered multiple objectives, but many collapse heterogeneous measurements into a fixed scalar score. Such scalarization depends on metric normalization and preference weights and may discard candidates that represent useful deployment trade-offs. We introduce Multi-Objective Agent Evolution (MOAE), which organizes iterative in-context refinement as a Pareto-preserving evolutionary search over complete agent rollouts. Given a limited rollout budget, MOAE maintains an empirical archive of non-dominated candidates, uses objective-specific diagnostics to guide offspring generation, and applies constraint-aware selection only at deployment. This separates candidate preservation during search from the preference used to return a final solution. The procedure requires no parameter updates and allows each objective to be replaced by any measurable property, which we instantiate as task performance, trajectory quality, and safety. Experiments on TravelPlanner and AgentDojo show that MOAE consistently improves task performance and trajectory quality while maintaining strong safety under matched rollout budgets. Search-behavior analysis further shows that Pareto preservation expands the attainable objective region and increases the frequency of joint improvement. These results demonstrate the potential of Pareto-preserving in-context evolution for optimizing multiple agent properties without committing to a fixed scalarization during search.

We propose LAPIG, a language guided projector image generation method with surface adaptation and stylization. LAPIG consists of a projector-camera system and a target textured projection surface. LAPIG takes the user text prompt as input and aims to transform the surface style using the projector. LAPIG's key challenge is that due to the projector's physical brightness limitation and the surface texture, the viewer's perceived projection may suffer from color saturation and artifacts in both dark and bright regions, such that even with the state-of-the-art projector compensation techniques, the viewer may see clear surface texture-related artifacts. Therefore, how to generate a projector image that follows the user's instruction while also displaying minimum surface artifacts is an open problem. To address this issue, we propose projection surface adaptation (PSA) that can generate compensable surface stylization. We first train two networks to simulate the projector compensation and project-and-capture processes, this allows us to find a satisfactory projector image without real project-and-capture and utilize gradient descent for fast convergence. Then, we design content and saturation losses to guide the projector image generation, such that the generated image shows no clearly perceivable artifacts when projected. Finally, the generated image is projected for visually pleasing surface style morphing effects. The source code and video are available on the project page: https://Yu-chen-Deng.github.io/LAPIG/.

3D Gaussian Splatting (3DGS) provides high-fidelity scenes for large-scale embodied simulation, but constructing large-scale urban assets remains constrained by expensive equipment and delayed quality feedback. Preset surveys can leave complex surfaces insufficiently observed, with defects discovered only after reconstruction, requiring return visits and repeated processing. We present OpenFlyScan, a quality-guided aerial reconstruction system for consumer drones that integrates a GS quality model, a reacquisition planner, and a custom-designed mobile app. The model learns from GS rendering errors to predict regional reconstruction quality. Based on these predictions, the planner then generates complementary reacquisition strips to be executed through the app, which also supports automated oblique surveys and data transfer without additional hardware on board. Across real aerial scenes, the model effectively identifies regions that are likely to be poorly reconstructed. In the Expo West field experiment, targeted reacquisition improves PSNR at additional views by 10.95 dB. With consumer drones, OpenFlyScan integrates capture, targeted reacquisition, and reconstruction to support rapid, low-cost urban asset creation. Code and models will be made publicly available at https://openflyscan.github.io/.

Federated learning (FL) enables collaborative model training across distributed clients without sharing raw data, making it a promising approach for privacy-preserving machine learning. However, ensuring differential privacy (DP) in FL presents challenges due to the trade-off between model utility and privacy protection. Clipping gradients before aggregation is a common strategy to limit privacy loss, but selecting an optimal clipping norm is non-trivial, as excessively high values compromise privacy, while overly restrictive clipping degrades model performance. In this work, we propose an adaptive clipping mechanism that dynamically adjusts the clipping norm using a multi-objective optimization framework. By integrating privacy and utility considerations into the optimization objective, our approach balances privacy preservation with model accuracy. We theoretically analyze the convergence properties of our method and demonstrate its effectiveness through extensive experiments on MNIST, Fashion-MNIST, and CIFAR-10 datasets. Our results show that adaptive clipping consistently outperforms fixed-clipping baselines, achieving improved accuracy under the same privacy constraints. This work highlights the potential of dynamic clipping strategies to enhance privacy-utility trade-offs in differentially private federated learning.

In this study, we investigate the protection offered by federated learning algorithms against eavesdropping adversaries. In our model, the adversary is capable of intercepting model updates transmitted from clients to the server, enabling it to create its own estimate of the model. Unlike previous research, which predominantly focuses on safeguarding client data, our work shifts attention protecting the client model itself. Through a theoretical analysis, we examine how various factors, such as the probability of client selection, the structure of local objective functions, global aggregation at the server, and the eavesdropper's capabilities, impact the overall level of protection. We further validate our findings through numerical experiments, assessing the protection by evaluating the model accuracy achieved by the adversary. Finally, we compare our results with methods based on differential privacy, underscoring their limitations in this specific context.

Data selection for language models is often framed as balancing example quality and diversity. We argue that both are consequences of a more fundamental principle: selected examples should preserve the downstream query space induced by instructions, task signals, or retrieval needs. We present Greedy Information Projection (GIP), a query-aligned method that requires only candidate embeddings and a score signal from LLM judgments, metadata, or intrinsic geometry. GIP greedily selects examples whose embedding span explains the largest residual component of task/query scores, yielding a fast matching-pursuit selector. A Gaussian projection view connects this update to maximizing mutual information, equivalently minimizing the residual volume of the query subspace left unexplained by selected data; this explains how quality and diversity emerge from one objective. Empirically, GIP matches or surpasses full-data fine-tuning using small instruction and reasoning subsets, while pretraining and RAG passage-selection experiments show that the same residual principle transfers beyond supervised fine-tuning.

Diffusion models have greatly advanced instruction-guided image editing, while also raising concerns about unauthorized image manipulation. Image immunization addresses this risk by adding imperceptible perturbations to an input image to disrupt subsequent edits. Since editing requests are unknown at image release, protection should remain effective beyond the instruction used to construct the perturbation. Existing immunization methods either require costly full-trajectory backpropagation or use intermediate objectives whose effects may be weakened by subsequent denoising. Meanwhile, a single inference path provides limited feedback about alternative denoising continuations. To address these challenges, we propose SPIN, a framework for image immunization via one-step projection over local stochastic trajectory neighborhoods. Starting from an early denoising state, SPIN generates stochastic neighboring states under the same instruction and predicts their clean latents through one-step projection without full unrolling. We then optimize a bounded input perturbation to maximize the average deviation of these predictions from a clean-edit reference, encouraging the perturbation to disrupt multiple possible editing outcomes. Experiments on two image editors demonstrate substantial gains in protection performance, with SPIN outperforming compared methods across all six metrics under seen instructions and in the more challenging unseen instruction setting.

Safety post-training can improve the harmfulness and policy compliance of Large Language Models (LLMs), but it may also reduce general utility, a phenomenon often described as the alignment tax. We study this trade-off through the lens of continual learning: sequential alignment stages expose the model to shifted data distributions and objectives, and their gradients may interfere with directions that support previously acquired general capabilities. This view does not claim that all alignment degradation has a single cause; rather, it provides a useful first-order mechanism for mitigating one important source of capability regression. We propose Orthogonal Gradient Projection for Safety Alignment (OGPSA), a lightweight update rule that estimates a low-rank reference subspace from gradients on a small set of general-capability data and removes from each safety gradient the component lying in this subspace. The resulting update is the steepest local safety-descent direction subject to first-order preservation constraints on the reference objectives. OGPSA is compatible with standard post-training pipelines and avoids large-scale replay, although it introduces periodic reference-gradient computation. Across Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and sequential SFTrightarrowDPO settings, OGPSA improves the observed safety--utility trade-off over standard baselines. Under the sequential SFTrightarrowDPO pipeline, the average performance gain increases from 33.98\% to 42.74\% on Qwen2.5-7B-Instruct and from 19.74\% to 32.98\% on Llama3.1-8B-Instruct. We have open sourced our code at https://github.com/SunGL001/OGPSA.

Unlearning concerns the task of removing the influence of a sensitive portion of the training data, such as protected, copyrighted or private text, from a model without retraining it from scratch. While unlearning requests happen continuously during a model's lifetime, the vast majority of LLM unlearning methods are ill-suited for iterated removal, yielding steep decay in forgetting and utility upon sequential unlearning. This decay stems from interference between successive updates, as each new deletion can undo earlier ones or push the model further along directions already degraded by them. To address this, we introduce Continual Orthogonal Projection (COP), a gradient-projection scheme that restricts each update to the orthogonal complement of activation subspaces cached from prior forget sets. This approach provably guarantees first-order non-interference with earlier deletions. COP stores only a low-rank basis per layer, requiring neither past gradients nor previous forget sets, and plugs into unlearning methods that update the model through gradient steps on a differentiable loss without modifying its objective. Experiments on standard LLM unlearning benchmarks (TOFU and RWKU) show that COP preserves utility across sequential requests without weakening forgetting, preventing the collapse of standard objectives and forgetting more effectively than continual-specific baselines.

Multi-teacher on-policy distillation (MOPD) has emerged as a popular post-training paradigm for integrating specialized capabilities in frontier language models. Existing OPD research has primarily focused on optimizing single-task distillation through objective design, distillation scope, and teacher signal construction, whereas MOPD must aggregate multiple capabilities in shared parameters and address the resulting capability seesaw, in which improving one domain suppresses capabilities acquired from another. Inspired by the distinctive update geometry of OPD, we find that parameter updates from different tasks rapidly concentrate in their respective low-dimensional subspaces during MOPD, providing a direct geometric basis for identifying and controlling cross-task interference. We therefore propose PMOPD (Projection-based Multi-Teacher On-Policy Distillation), which constructs subspace memories from the cumulative parameter displacements of different tasks and projects both gradients and optimizer updates to remove components that interfere with protected task directions. We further develop a lightweight conflict probe to characterize task interactions and guide task ordering, together with a cycling strategy that balances subspace estimation and timely task revisitation. Experiments on representative Code, Reason, and Math tasks show that PMOPD improves every evaluated capability over MOPD, raising the average score across the three tasks by 2.54 points on Qwen2.5-7B and 2.09 points on Llama-3.1-8B. These consistent gains establish geometry-aware optimization as an effective and transferable approach to balanced multi-teacher distillation.

Supervised fine-tuning (SFT) is the standard approach for post-training large language models (LLMs), yet it often shows limited generalization. We trace this limitation to its default training objective: negative log likelihood (NLL). While NLL is classically optimal when training from scratch, post-training operates in a different paradigm and could violate its optimality assumptions, where models already encode task-relevant priors and supervision can be long and noisy. To this end, we study a general family of probability-based objectives and characterize their effectiveness under different conditions. Through comprehensive experiments and extensive ablation studies across 7 model backbones, 14 benchmarks, and 3 domains, we uncover a critical dimension that governs objective behavior: the model-capability continuum. Near the model-strong end, prior-leaning objectives that downweight low-probability tokens (e.g., -p, -p^{10}, thresholded variants) consistently outperform NLL; toward the model-weak end, NLL dominates; in between, no single objective prevails. Our theoretical analysis further elucidates how objectives trade places across the continuum, providing a principled foundation for adapting objectives to model capability. Our code is available at https://github.com/GaotangLi/Beyond-Log-Likelihood.

The ability to control for the kinds of information encoded in neural representation has a variety of use cases, especially in light of the challenge of interpreting these models. We present Iterative Null-space Projection (INLP), a novel method for removing information from neural representations. Our method is based on repeated training of linear classifiers that predict a certain property we aim to remove, followed by projection of the representations on their null-space. By doing so, the classifiers become oblivious to that target property, making it hard to linearly separate the data according to it. While applicable for multiple uses, we evaluate our method on bias and fairness use-cases, and show that our method is able to mitigate bias in word embeddings, as well as to increase fairness in a setting of multi-class classification.

This paper introduces AIM, a collection of vision models pre-trained with an autoregressive objective. These models are inspired by their textual counterparts, i.e., Large Language Models (LLMs), and exhibit similar scaling properties. Specifically, we highlight two key findings: (1) the performance of the visual features scale with both the model capacity and the quantity of data, (2) the value of the objective function correlates with the performance of the model on downstream tasks. We illustrate the practical implication of these findings by pre-training a 7 billion parameter AIM on 2 billion images, that achieves 84.0% on ImageNet-1k with a frozen trunk. Interestingly, even at this scale, we observe no sign of saturation in performance, suggesting that AIM potentially represents a new frontier for training large-scale vision models. The pre-training of AIM is similar to the pre-training of LLMs, and does not require any image-specific strategy to stabilize the training at scale.

Visual Language Navigation foundation models aim to unify deep reasoning for grounded spatial decisions with broad versatility for diverse embodied tasks. Current approaches typically achieve this integration via monolithic policies that map observations directly to actions, yet they often suffer from coordinate drift and poor handling of long-tail semantics. Furthermore, these black-box mappings lack interpretability, hindering the simultaneous achievement of generality, robustness, and transparency. We present ABot-N1, a step toward a general Visual Language Navigation foundation model, that addresses these challenges by decoupling cognition from control via a slow-fast architecture guided by dual visual-language signals. More specifically, a slow vision-language reasoner performs explicit Chain-of-Thought reasoning while producing a pixel goal. This compact set of image-space anchor points serves as a universal interface for diverse tasks, including point-goal, object-goal, poi-goal, instruction-following, and person-following. Subsequently, a fast action expert leverages both the textual cues and the pixel guidance to generate continuous waypoints at the native control frequency. By bridging high-level intents and low-level control through pixel-grounded anchors paired with explicit linguistic traces, our approach ensures robust, generalizable, and interpretable navigation across simulation and real-world benchmarks. ABot-N1 establishes new state-of-the-art records, delivering massive gains specifically in urban-scale navigation: boosting POI arrival by 35.0% (to 77.3%) and achieving 95.4%/92.9% SR in complex indoor and outdoor scenes. It also maintains superior robustness across object-reaching, person-following, and instruction-following tasks. New Point-Goal/POI-Goal benchmarks are released as open source to advance the field of urban-scale navigation.

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of Oleft(T^{-2/3}right). In the sample-based setting, we demonstrate that, with high probability, our algorithm requires mathcal{O}left(ε^{-3.5}right) samples to achieve an ε-FOSP with an approximation error of O(φ_0^{2κ}), where φ_0in (0,1). Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

We aim to develop a goal specification method that is semantically clear, spatially sensitive, and intuitive for human users to guide agent interactions in embodied environments. Specifically, we propose a novel cross-view goal alignment framework that allows users to specify target objects using segmentation masks from their own camera views rather than the agent's observations. We highlight that behavior cloning alone fails to align the agent's behavior with human intent when the human and agent camera views differ significantly. To address this, we introduce two auxiliary objectives: cross-view consistency loss and target visibility loss, which explicitly enhance the agent's spatial reasoning ability. According to this, we develop ROCKET-2, a state-of-the-art agent trained in Minecraft, achieving an improvement in the efficiency of inference 3x to 6x. We show ROCKET-2 can directly interpret goals from human camera views for the first time, paving the way for better human-agent interaction.

In this paper, we propose a general framework for universal zero-shot goal-oriented navigation. Existing zero-shot methods build inference framework upon large language models (LLM) for specific tasks, which differs a lot in overall pipeline and fails to generalize across different types of goal. Towards the aim of universal zero-shot navigation, we propose a uniform graph representation to unify different goals, including object category, instance image and text description. We also convert the observation of agent into an online maintained scene graph. With this consistent scene and goal representation, we preserve most structural information compared with pure text and are able to leverage LLM for explicit graph-based reasoning. Specifically, we conduct graph matching between the scene graph and goal graph at each time instant and propose different strategies to generate long-term goal of exploration according to different matching states. The agent first iteratively searches subgraph of goal when zero-matched. With partial matching, the agent then utilizes coordinate projection and anchor pair alignment to infer the goal location. Finally scene graph correction and goal verification are applied for perfect matching. We also present a blacklist mechanism to enable robust switch between stages. Extensive experiments on several benchmarks show that our UniGoal achieves state-of-the-art zero-shot performance on three studied navigation tasks with a single model, even outperforming task-specific zero-shot methods and supervised universal methods.

Aligning large language models to human preferences is inherently multidimensional, yet most pipelines collapse heterogeneous signals into a single optimizeable objective. We seek to answer what it would take to simultaneously align a model across various domains spanning those with: verifiable rewards (mathematical accuracy), non-verifiable subjective preferences (human values), and complex interactive scenarios (multi-turn AI tutoring dialogues). Such multi-objective reinforcement learning setups are often plagued by the individual objectives being at odds with each other, resulting in inefficient training and little user control during inference. We propose a unified framework that: (i) standardizes {process reward model} (PRM) training across both verifiable and non-verifiable settings to better supervise models' chain-of-thought reasoning; (ii) performs {multi-objective alignment} by training the LLM with our Multi-Action-Head DPO (MAH-DPO) and a vectorized reward where the dimensions of the vector correspond to the various objectives instead of a single scalar; and (iii) demonstrates how such a system provides fine-grained inference-time user control. Experiments across math reasoning, value alignment, and multi-turn dialogue show that our framework improves performance across multiple objectives simultaneously, while minimizing cross-objective trade-offs and enabling flexible inference time user control. The code can be found at https://github.com/pearls-lab/multiobj-align.

Cross-entropy pretraining and preference alignment update the same transformer weights, but leave geometrically distinct traces. We characterise this asymmetry with a relative-subspace-fraction probe that tracks how weight deltas align with residual-stream activation subspaces and with the prediction subspace defined by the unembedding. Alignment deltas concentrate in the read pathway (W_Q, W_K), along principal directions of attention-input activations, while remaining near-isotropic in the write pathway (W_O, W_2) relative to the prediction subspace. We explain this pattern through anisotropic gradient accumulation: updates to a matrix W are sums of outer products δ_t a_t^top, and inherit directional structure from whichever side has concentrated covariance. For read-pathway matrices, this side is the input activation a_t, whose covariance is spiked in trained transformers and therefore produces objective-agnostic concentration. For write-pathway matrices, the relevant side is the upstream gradient δ_t, whose anisotropy depends on the loss. Cross-entropy supplies the canonical sharp per-sample signal, inducing write-pathway prediction geometry during pretraining; alignment objectives typically add little further write-side concentration. We support this explanation with a within-checkpoint trajectory, a graded contrastive-objective control, and a closed-form rank-1 intervention with matched direction controls, providing causal evidence for the proposed weight-space geometry.

A typical human strategy for giving navigation guidance is to sketch route maps based on the environmental layout. Inspired by this, we introduce Sketch map-based visual Navigation (SkeNa), an embodied navigation task in which an agent must reach a goal in an unseen environment using only a hand-drawn sketch map as guidance. To support research for SkeNa, we present a large-scale dataset named SoR, comprising 54k trajectory and sketch map pairs across 71 indoor scenes. In SoR, we introduce two navigation validation sets with varying levels of abstraction in hand-drawn sketches, categorized based on their preservation of spatial scales in the environment, to facilitate future research. To construct SoR, we develop an automated sketch-generation pipeline that efficiently converts floor plans into hand-drawn representations. To solve SkeNa, we propose SkeNavigator, a navigation framework that aligns visual observations with hand-drawn maps to estimate navigation targets. It employs a Ray-based Map Descriptor (RMD) to enhance sketch map valid feature representation using equidistant sampling points and boundary distances. To improve alignment with visual observations, a Dual-Map Aligned Goal Predictor (DAGP) leverages the correspondence between sketch map features and on-site constructed exploration map features to predict goal position and guide navigation. SkeNavigator outperforms prior floor plan navigation methods by a large margin, improving SPL on the high-abstract validation set by 105% relatively. Our code and dataset will be released.

Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood. We develop an ADMM-Inspired Momentum (AIM) framework based on residual-penalty variable splitting, which interprets momentum as a multiplier-like correction driven by the splitting residual. AIM recovers the exponential moving average of gradients from an ADMM-style multiplier update and separates two mechanisms that are usually intertwined in practical optimizers: the residual penalty determines the update geometry, whereas the approximation of the objective-related subproblem determines the acceleration form. Building on AIM, we propose Relativistic Adaptive gradient Descent with Accelerated Residual (RADAR), which combines relativistic adaptive geometry, decoupled residual correction, and second-order momentum filtering to improve the update direction and momentum estimation. We establish stochastic convergence through a variance-perturbed Lyapunov drift analysis. Experiments on supervised vision learning, language modeling, and reinforcement learning show that RADAR achieves consistent improvements over strong adaptive optimizer baselines.

Quite surprisingly, exact maximum a posteriori (MAP) decoding of neural language generators frequently leads to low-quality results. Rather, most state-of-the-art results on language generation tasks are attained using beam search despite its overwhelmingly high search error rate. This implies that the MAP objective alone does not express the properties we desire in text, which merits the question: if beam search is the answer, what was the question? We frame beam search as the exact solution to a different decoding objective in order to gain insights into why high probability under a model alone may not indicate adequacy. We find that beam search enforces uniform information density in text, a property motivated by cognitive science. We suggest a set of decoding objectives that explicitly enforce this property and find that exact decoding with these objectives alleviates the problems encountered when decoding poorly calibrated language generation models. Additionally, we analyze the text produced using various decoding strategies and see that, in our neural machine translation experiments, the extent to which this property is adhered to strongly correlates with BLEU.

Human hands possess the dexterity to interact with diverse objects such as grasping specific parts of the objects and/or approaching them from desired directions. More importantly, humans can grasp objects of any shape without object-specific skills. Recent works synthesize grasping motions following single objectives such as a desired approach heading direction or a grasping area. Moreover, they usually rely on expensive 3D hand-object data during training and inference, which limits their capability to synthesize grasping motions for unseen objects at scale. In this paper, we unify the generation of hand-object grasping motions across multiple motion objectives, diverse object shapes and dexterous hand morphologies in a policy learning framework GraspXL. The objectives are composed of the graspable area, heading direction during approach, wrist rotation, and hand position. Without requiring any 3D hand-object interaction data, our policy trained with 58 objects can robustly synthesize diverse grasping motions for more than 500k unseen objects with a success rate of 82.2%. At the same time, the policy adheres to objectives, which enables the generation of diverse grasps per object. Moreover, we show that our framework can be deployed to different dexterous hands and work with reconstructed or generated objects. We quantitatively and qualitatively evaluate our method to show the efficacy of our approach. Our model, code, and the large-scale generated motions are available at https://eth-ait.github.io/graspxl/.

We study a persistent failure mode in multi-objective alignment for large language models (LLMs): training improves performance on only a subset of objectives while causing others to degrade. We formalize this phenomenon as cross-objective interference and conduct the first systematic study across classic scalarization algorithms, showing that interference is pervasive and exhibits strong model dependence. To explain this phenomenon, we derive a local covariance law showing that an objective improves at first order when its reward exhibits positive covariance with the scalarized score. We extend this analysis to clipped surrogate objectives used in modern alignment, demonstrating that the covariance law remains valid under mild conditions despite clipping. Building on this analysis, we propose Covariance Targeted Weight Adaptation (CTWA), a plug-and-play method that maintains positive covariance between objective rewards and the training signal to effectively mitigate cross-objective interference. Finally, we complement these local improvement conditions with a global convergence analysis under the Polyak--Łojasiewicz condition, establishing when non-convex scalarized optimization achieves global convergence and how cross-objective interference depends on specific model geometric properties.

In our pursuit of advancing multi-modal AI assistants capable of guiding users to achieve complex multi-step goals, we propose the task of "Visual Planning for Assistance (VPA)". Given a succinct natural language goal, e.g., "make a shelf", and a video of the user's progress so far, the aim of VPA is to devise a plan, i.e., a sequence of actions such as "sand shelf", "paint shelf", etc. to realize the specified goal. This requires assessing the user's progress from the (untrimmed) video, and relating it to the requirements of natural language goal, i.e., which actions to select and in what order? Consequently, this requires handling long video history and arbitrarily complex action dependencies. To address these challenges, we decompose VPA into video action segmentation and forecasting. Importantly, we experiment by formulating the forecasting step as a multi-modal sequence modeling problem, allowing us to leverage the strength of pre-trained LMs (as the sequence model). This novel approach, which we call Visual Language Model based Planner (VLaMP), outperforms baselines across a suite of metrics that gauge the quality of the generated plans. Furthermore, through comprehensive ablations, we also isolate the value of each component--language pre-training, visual observations, and goal information. We have open-sourced all the data, model checkpoints, and training code.

Perspective projection has been extensively utilized in monocular 3D object detection methods. It introduces geometric priors from 2D bounding boxes and 3D object dimensions to reduce the uncertainty of depth estimation. However, due to depth errors originating from the object's visual surface, the height of the bounding box often fails to represent the actual projected central height, which undermines the effectiveness of geometric depth. Direct prediction for the projected height unavoidably results in a loss of 2D priors, while multi-depth prediction with complex branches does not fully leverage geometric depth. This paper presents a Transformer-based monocular 3D object detection method called MonoDGP, which adopts perspective-invariant geometry errors to modify the projection formula. We also try to systematically discuss and explain the mechanisms and efficacy behind geometry errors, which serve as a simple but effective alternative to multi-depth prediction. Additionally, MonoDGP decouples the depth-guided decoder and constructs a 2D decoder only dependent on visual features, providing 2D priors and initializing object queries without the disturbance of 3D detection. To further optimize and fine-tune input tokens of the transformer decoder, we also introduce a Region Segment Head (RSH) that generates enhanced features and segment embeddings. Our monocular method demonstrates state-of-the-art performance on the KITTI benchmark without extra data. Code is available at https://github.com/PuFanqi23/MonoDGP.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

When artificial agents are jointly trained to perform collaborative tasks using a communication channel, they develop opaque goal-oriented communication protocols. Good task performance is often considered sufficient evidence that meaningful communication is taking place, but existing empirical results show that communication strategies induced by common objectives can be counterintuitive whilst solving the task nearly perfectly. In this work, we identify a goal-agnostic prerequisite to meaningful communication, which we term semantic consistency, based on the idea that messages should have similar meanings across instances. We provide a formal definition for this idea, and use it to compare the two most common objectives in the field of emergent communication: discrimination and reconstruction. We prove, under mild assumptions, that semantically inconsistent communication protocols can be optimal solutions to the discrimination task, but not to reconstruction. We further show that the reconstruction objective encourages a stricter property, spatial meaningfulness, which also accounts for the distance between messages. Experiments with emergent communication games validate our theoretical results. These findings demonstrate an inherent advantage of distance-based communication goals, and contextualize previous empirical discoveries.

Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear averaging, task vectors, and related rules operate on Euclidean coordinates, even though the desired goal is to merge functionality, i.e., predictive behaviors across tasks. Second, when the source checkpoints are farther apart or more heterogeneous, Euclidean blends often trigger representation collapse, manifested as activation variance shrinkage and effective-rank degradation, which sharply degrades accuracy. Third, many geometry-inspired methods are most natural for two-model interpolation and do not extend cleanly to merging N>2 experts with a principled objective. We address these issues by formulating model merging as computing a weighted Karcher mean on the Fisher--Rao manifold, which is locally equivalent to minimizing a KL-based function distance between predictive distributions. We derive a practical fixed-point algorithm using a lightweight spherical proxy that preserves norms and generalizes directly to multi-expert merging. Across various benchmarks and collapse diagnostics, our method remains stable as the number and heterogeneity of merged models increase, consistently outperforming prior baselines.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

Autonomous high-fidelity object reconstruction is fundamental for creating digital assets and bridging the simulation-to-reality gap in robotics. We present ObjSplat, an active reconstruction framework that leverages Gaussian surfels as a unified representation to progressively reconstruct unknown objects with both photorealistic appearance and accurate geometry. Addressing the limitations of conventional opacity or depth-based cues, we introduce a geometry-aware viewpoint evaluation pipeline that explicitly models back-face visibility and occlusion-aware multi-view covisibility, reliably identifying under-reconstructed regions even on geometrically complex objects. Furthermore, to overcome the limitations of greedy planning strategies, ObjSplat employs a next-best-path (NBP) planner that performs multi-step lookahead on a dynamically constructed spatial graph. By jointly optimizing information gain and movement cost, this planner generates globally efficient trajectories. Extensive experiments in simulation and on real-world cultural artifacts demonstrate that ObjSplat produces physically consistent models within minutes, achieving superior reconstruction fidelity and surface completeness while significantly reducing scan time and path length compared to state-of-the-art approaches. Project page: https://li-yuetao.github.io/ObjSplat-page/ .

Vision-Language-Action (VLA) models map observations to actions with no objective that accounts for how the world responds, so their robustness is bounded primarily by data coverage. World models carry precisely that missing objective and are better grounded for it, yet rolling the future forward costs seconds per decision and rules them out of the control loop. We show the two can be separated. What a world model knows about physical scenes lives in its internal features; generating the future is merely the objective that produced them, so the grounding can be inherited while the generative machinery is left behind. We add one feature-alignment term to ordinary VLA training: a frozen world model is run over the training frames once and cached, and the student learns to agree with that cache. No teacher is loaded during training, the projector is discarded after it, and the deployed policy is identical to the undistilled baseline, running in 32~ms and 1.86~GB on a consumer RTX~5090, so every gain is attributable to the representation rather than to added capacity or test-time compute. A 0.8B student reaches 97.9% on LIBERO, improves from 48.2% to 50.5% on RoboCasa-GR1 humanoid manipulation, and the same objective carries over to real hardware, on both a single-arm and a bimanual platform. The gain survives changes of student scale, backbone, alignment layer, and teacher, indicating a broad representational prior rather than a fragile alignment between two particular networks. Project page: https://thaw-vla.trung-dt.com/.

An effective technique for obtaining high-quality representations is adding a projection head on top of the encoder during training, then discarding it and using the pre-projection representations. Despite its proven practical effectiveness, the reason behind the success of this technique is poorly understood. The pre-projection representations are not directly optimized by the loss function, raising the question: what makes them better? In this work, we provide a rigorous theoretical answer to this question. We start by examining linear models trained with self-supervised contrastive loss. We reveal that the implicit bias of training algorithms leads to layer-wise progressive feature weighting, where features become increasingly unequal as we go deeper into the layers. Consequently, lower layers tend to have more normalized and less specialized representations. We theoretically characterize scenarios where such representations are more beneficial, highlighting the intricate interplay between data augmentation and input features. Additionally, we demonstrate that introducing non-linearity into the network allows lower layers to learn features that are completely absent in higher layers. Finally, we show how this mechanism improves the robustness in supervised contrastive learning and supervised learning. We empirically validate our results through various experiments on CIFAR-10/100, UrbanCars and shifted versions of ImageNet. We also introduce a potential alternative to projection head, which offers a more interpretable and controllable design.

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or unitarily invariant, i.e., they depend only on the eigenvalues or singular values of the matrix. This paper investigates how spectral matrix cones -- cones defined from epigraphs and perspectives of spectral or unitarily invariant functions -- can be used to enhance first-order conic solvers for semidefinite programs. Our main result shows that projecting a matrix can be reduced to projecting its eigenvalues or singular values, which we demonstrate can be done at a negligible cost compared to the eigenvalue or singular value decomposition itself. We have integrated support for spectral matrix cone projections into the Splitting Conic Solver (SCS). Numerical experiments show that SCS with this enhancement can achieve speedups of up to an order of magnitude for solving semidefinite programs arising in experimental design, robust principal component analysis, and graph partitioning.

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

Latent world models learn action-conditioned dynamics in representation space and often score candidate actions by Euclidean distance to a goal representation. Joint training typically regularizes the representation to prevent collapse, but the resulting representation geometry also determines how terminal errors are weighted during planning. We show that accurate prediction and noncollapsed representations do not guarantee a task-aligned latent planning cost: isotropic Gaussian regularization can induce a geometry that ranks feasible outcomes differently from the task cost. To address this mismatch, we introduce AnisoWM with ΛReg, which replaces the fixed isotropic Gaussian target with a learnable diagonal covariance under fixed-trace and anisotropy constraints. The prediction objective, predictor architecture, and Euclidean planner remain unchanged; the target is used only during training. Our analysis characterizes the prediction-driven allocation of target variance, its dependence on the training distribution, and the conditions under which the induced metric reduces planning regret. Across four visual control environments, AnisoWM improves planning success over LeWorldModel in all four. Its latent planning cost also shows better agreement with task outcomes. Project website: https://rkdrn79.github.io/AnisoWM-page/

Domain adaptation (DA) attempts to transfer the knowledge from a labeled source domain to an unlabeled target domain that follows different distribution from the source. To achieve this, DA methods include a source classification objective to extract the source knowledge and a domain alignment objective to diminish the domain shift, ensuring knowledge transfer. Typically, former DA methods adopt some weight hyper-parameters to linearly combine the training objectives to form an overall objective. However, the gradient directions of these objectives may conflict with each other due to domain shift. Under such circumstances, the linear optimization scheme might decrease the overall objective value at the expense of damaging one of the training objectives, leading to restricted solutions. In this paper, we rethink the optimization scheme for DA from a gradient-based perspective. We propose a Pareto Domain Adaptation (ParetoDA) approach to control the overall optimization direction, aiming to cooperatively optimize all training objectives. Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification. To improve target-prediction accuracy to support the mimicking, we propose a target-prediction refining mechanism which exploits domain labels via Bayes' theorem. On the other hand, since prior knowledge of weighting schemes for objectives is often unavailable to guide optimization to approach the optimal solution on the target domain, we propose a dynamic preference mechanism to dynamically guide our cooperative optimization by the gradient of the surrogate loss on a held-out unlabeled target dataset. Extensive experiments on image classification and semantic segmentation benchmarks demonstrate the effectiveness of ParetoDA

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each vertex in the graph is a continuous decision variable constrained in a convex set, and the length of an edge is a convex function of the position of its endpoints. Problems of this form arise naturally in many areas, from motion planning of autonomous vehicles to optimal control of hybrid systems. The price for such a wide applicability is the complexity of this problem, which is easily seen to be NP-hard. Our main contribution is a strong and lightweight mixed-integer convex formulation based on perspective operators, that makes it possible to efficiently find globally optimal paths in large graphs and in high-dimensional spaces.

We revisit the problem of Object-Goal Navigation (ObjectNav). In its simplest form, ObjectNav is defined as the task of navigating to an object, specified by its label, in an unexplored environment. In particular, the agent is initialized at a random location and pose in an environment and asked to find an instance of an object category, e.g., find a chair, by navigating to it. As the community begins to show increased interest in semantic goal specification for navigation tasks, a number of different often-inconsistent interpretations of this task are emerging. This document summarizes the consensus recommendations of this working group on ObjectNav. In particular, we make recommendations on subtle but important details of evaluation criteria (for measuring success when navigating towards a target object), the agent's embodiment parameters, and the characteristics of the environments within which the task is carried out. Finally, we provide a detailed description of the instantiation of these recommendations in challenges organized at the Embodied AI workshop at CVPR 2020 http://embodied-ai.org .

Reinforcement learning (RL) with group-relative advantages has become the de facto standard for post-training language model reasoners. However, when optimizing multiple reward objectives, existing methods typically scalarize the reward vector with a fixed weighted sum before group-wise standardization. We show that this design leads to two fundamental problems: rollouts with distinct reward profiles can receive identical advantages, and all objectives are optimized with fixed relative weights regardless of their current level of saturation. As a result, training continues to allocate gradient budget to already-solved objectives instead of focusing on those with greater remaining headroom. We introduce Saturation Aware Advantage Reweighting for Multi-Reward Policy Optimization (SA-MRPO), which standardizes each reward objective independently and adaptively discounts its contribution according to a batch-level estimate of objective saturation. This dynamically reallocates optimization effort toward under-optimized objectives while empirically maintaining performance on those that are already well satisfied. We further show that saturation-aware reweighting can reverse the sign of an update, rather than merely rescale its magnitude. Across mathematical reasoning with two- and three-objective reward combinations, SA-MRPO improves the harder correctness objective over GDPO in 12 of 15 benchmark comparisons, with gains of up to 5% on AIME24. On adaptive reasoning it improves accuracy on all five benchmarks, by 3.8% on average and up to 9.2 % on AMC23, and on coding benchmarks it improves pass rate by up to 2.3%, while in all settings maintaining the easier objectives near their already satisfied levels.

Regression-based RL for flow models mandates sampling without classifier-free guidance (CFG) to align the rectification target with the reference marginal velocity. Extending Advantage-Weighted Rectification (AWR), which dynamically scales this regression target based on reward, to video generation encounters a cold-start pathology: unguided rollouts collapse into low-fidelity regions where intra-group reward gaps remain wide but no longer track perceptual quality, rendering the optimization target arbitrary. Conversely, utilizing guided rollouts to restore fidelity, while keeping the regression target tied to the guided sampling distribution, provably triggers a geometric guidance blow-up under exponential-moving-average (EMA) updates. We propose VideoAWR, which resolves this tension by untying sampling from the optimization anchor. An EMA reference policy generates guided rollouts to restore reward separability, while the trainable policy is rectified against the unguided conditional anchor. We prove this decoupled objective is mathematically exact: the centered advantage cancels the anchor in expectation, filtering out the reward-neutral guidance offset and retaining only the reward-correlated covariance increment. Consequently, inference runs single-branch and CFG-free, yet inference-time CFG preserves its original semantics. Furthermore, we introduce Decoupled Timestep Rectification, supervising each rollout at an independently sampled timestep without bias to improve sample efficiency. Experiments on Wan2.1-1.3B and 14B demonstrate stable optimization and superior visual and motion quality in both CFG-free and CFG-enabled regimes. Code is available at \pdfstartlink attr{/Border [0 0 0]} user{/Subtype /Link /A << /S /URI /URI (https://github.com/Fuzm7/FlowAWR) >>}% pearDark{VideoAWR}\pdfendlink.

LeWorldModel trains a latent world model with a prediction loss and a single anti-collapse regulariser, and reports approximately 87% of goals reached on TwoRoom, its simplest diagnostic environment. We reproduce that result by independent reimplementation on roughly $25 of rented compute, with all evaluation on one laptop CPU. We reach 94.0% at the repository's evaluation goal offset, against 84.0% for the authors' own released checkpoint measured under our protocol on identical episodes, and we reproduce the reported representation result directly (position probe Pearson r = 0.9988 against a reported 0.996). Reaching that point required four conventions that determine the outcome and appear in no released configuration file: dense action gathering across a frameskip block, a programmatically-set action-encoder width, ImageNet pixel normalisation, and action z-scoring. A reproducer following the released configurations alone obtains a model whose predictor cannot converge. The evaluation protocol is itself contested by the released material. The paper's appendix and the repository's configuration specify different goal offsets and step budgets; on the authors' own weights these yield 14.0% and 84.0%, and only the configuration's values reproduce the reported figure. On fifty identical episodes, changing nothing but how the goal is constructed moves that checkpoint from 84.0% to 8.0%. Two findings generalise. One-step prediction accuracy does not predict long-horizon planning success: across three checkpoints spanning a sevenfold range in prediction error, including the authors' own, it orders short-horizon success monotonically and fails to order long-horizon success at all. And a batch normalisation layer inflated our reported validation loss by up to a factor of 300, concealing a training loss that was flat throughout.

Health economic evaluations are sensitive to the choice of analytical perspective (e.g., health system vs. societal). While guidelines often recommend specific perspectives, the uncertainty associated with this choice - and the potential decision discordance it creates - is rarely quantified. We present vop_poc_nz, a Python package that implements a framework for Distributional Cost-Effectiveness Analysis (DCEA) and operationalizes the quantification of perspective uncertainty through the Value of Perspective (VoP) metric. The package provides tools for Markov modeling, probabilistic sensitivity analysis, value of information analysis, and equity impact assessment. Unlike existing tools that treat perspective as a fixed input, vop_poc_nz allows for the simultaneous evaluation of multiple perspectives. This enables decision-makers to estimate the opportunity cost of perspective misalignment. We demonstrate the package's capabilities using case studies from Aotearoa New Zealand.

Reinforcement learning (RL) has become a standard post-training method for diffusion models, but most RL objectives roll out the current policy at every iteration, and with a many-step sampler these rollouts typically dominate the cost of training. Few-step models cut this cost, yet they model an average velocity over an interval, whereas existing RL objectives are built for an instantaneous velocity with a many-step sampler. We adapt RL objectives to few-step models systematically in three phases, namely a transformation, a decomposition and an adaptation. The transformation to x-space expresses each objective we consider through a common policy prediction, at the clean end by default and at an explicitly marked level for transition or flow-map objectives, so that objectives stated over densities, velocities or rewards become comparable. The decomposition writes the gradient of each of these objectives as the sum of a self-regression toward a reference and a reward augmentation, so that a method reduces, at the gradient level, to a choice of anchors and weights. The adaptation computes each anchor from a few-step model at the end of its transport or along its tangent, with the instantaneous velocity recovered from the network itself or from an auxiliary network. This yields few-step versions of FlowGRPO, AWM, DiffusionNFT, DiffusionOPSD and ReFL in one modular codebase. In our experiments, reward-gradient-based methods are the most effective when the reward is differentiable and its gradient is affordable; otherwise DiffusionNFT-style methods generally reach high rewards in relatively few iterations despite a sometimes higher per-iteration cost. Extra inference steps show no systematic aggregate benefit in our experiments, although selected outputs visibly improve with two to four times as many sampling steps as in training.

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.

Point cloud registration is an essential step for free-form blade reconstruction in industrial measurement. Nonetheless, measuring defects of the 3D acquisition system unavoidably result in noisy and incomplete point cloud data, which renders efficient and accurate registration challenging. In this paper, we propose a novel global registration method that is based on the minimum potential energy (MPE) method to address these problems. The basic strategy is that the objective function is defined as the minimum potential energy optimization function of the physical registration system. The function distributes more weight to the majority of inlier points and less weight to the noise and outliers, which essentially reduces the influence of perturbations in the mathematical formulation. We decompose the solution into a globally optimal approximation procedure and a fine registration process with the trimmed iterative closest point algorithm to boost convergence. The approximation procedure consists of two main steps. First, according to the construction of the force traction operator, we can simply compute the position of the potential energy minimum. Second, to find the MPE point, we propose a new theory that employs two flags to observe the status of the registration procedure. We demonstrate the performance of the proposed algorithm on four types of blades. The proposed method outperforms the other global methods in terms of both accuracy and noise resistance.

Some security-development settings require local models that map an objective to an ordered, checkable plan. We present a low-rank decomposition adapter and release a case-disjoint corpus with 24 authored decompositions and 83 derived next-step examples across 24 satellite-security cases. To prevent reference-plan leakage, prompts contain one objective and eight shuffled SPARTA candidates. The evaluation candidate sets are constructed with oracle inclusion of every reference technique, so this study measures selection from a controlled set, not retrieval. On six fixed cases and five decoding seeds, mean scores vary across adapters and prompted Qwen2.5 baselines; a separate greedy check over three adapter training seeds shows non-negligible training variance. A 24-fold greedy leave-one-case-out control at the two compact sizes likewise shows tradeoffs: at 1.5B, adapter precision is 0.583 against 0.480 for two-shot prompting, while recall is 0.586 against 0.660. Case-resampling intervals for adapter precision relative to the strongest prompted baseline cross zero at 1.5B and 7B. The adapter is also substantially more format-compliant, which prevents attributing all score differences to selection. Autoregressive next-step accuracy is 0.08, 0.06, and 0.29 at 0.5B, 1.5B, and 7B. We therefore offer the formulation, leakage-controlled dataset, reproducibility package, and descriptive analysis as a proof of concept, not evidence of a reliable stand-alone decomposition system or a general adapter advantage. A separate diagnostic tests contract reuse.

We present a generalization of the proximal operator defined through a convex combination of convex objectives, where the coefficients are updated in a minimax fashion. We prove that this new operator is Bregman firmly nonexpansive with respect to a Bregman divergence that combines Euclidean and information geometries.

Object-Goal Navigation (ObjectNav) requires an agent to autonomously explore an unknown environment and navigate toward target objects specified by a semantic label. While prior work has primarily studied zero-shot ObjectNav under 2D locomotion, extending it to aerial platforms with 3D locomotion capability remains underexplored. Aerial robots offer superior maneuverability and search efficiency, but they also introduce new challenges in spatial perception, dynamic control, and safety assurance. In this paper, we propose AION for vision-based aerial ObjectNav without relying on external localization or global maps. AION is an end-to-end dual-policy reinforcement learning (RL) framework that decouples exploration and goal-reaching behaviors into two specialized policies. We evaluate AION on the AI2-THOR benchmark and further assess its real-time performance in IsaacSim using high-fidelity drone models. Experimental results show that AION achieves superior performance across comprehensive evaluation metrics in exploration, navigation efficiency, and safety. The video can be found at https://youtu.be/TgsUm6bb7zg, code and model checkpoints are available at https://github.com/Zichen-Yan/AION.

Optimisation problems often have multiple conflicting objectives that can be computationally and/or financially expensive. Mono-surrogate Bayesian optimisation (BO) is a popular model-based approach for optimising such black-box functions. It combines objective values via scalarisation and builds a Gaussian process (GP) surrogate of the scalarised values. The location which maximises a cheap-to-query acquisition function is chosen as the next location to expensively evaluate. While BO is an effective strategy, the use of GPs is limiting. Their performance decreases as the problem input dimensionality increases, and their computational complexity scales cubically with the amount of data. To address these limitations, we extend previous work on BO by density-ratio estimation (BORE) to the multi-objective setting. BORE links the computation of the probability of improvement acquisition function to that of probabilistic classification. This enables the use of state-of-the-art classifiers in a BO-like framework. In this work we present MBORE: multi-objective Bayesian optimisation by density-ratio estimation, and compare it to BO across a range of synthetic and real-world benchmarks. We find that MBORE performs as well as or better than BO on a wide variety of problems, and that it outperforms BO on high-dimensional and real-world problems.

As Learning-to-Rank (LTR) approaches primarily seek to improve ranking quality, their output scores are not scale-calibrated by design. This fundamentally limits LTR usage in score-sensitive applications. Though a simple multi-objective approach that combines a regression and a ranking objective can effectively learn scale-calibrated scores, we argue that the two objectives are not necessarily compatible, which makes the trade-off less ideal for either of them. In this paper, we propose a practical regression compatible ranking (RCR) approach that achieves a better trade-off, where the two ranking and regression components are proved to be mutually aligned. Although the same idea applies to ranking with both binary and graded relevance, we mainly focus on binary labels in this paper. We evaluate the proposed approach on several public LTR benchmarks and show that it consistently achieves either best or competitive result in terms of both regression and ranking metrics, and significantly improves the Pareto frontiers in the context of multi-objective optimization. Furthermore, we evaluated the proposed approach on YouTube Search and found that it not only improved the ranking quality of the production pCTR model, but also brought gains to the click prediction accuracy. The proposed approach has been successfully deployed in the YouTube production system.

Prior works in multi-objective reinforcement learning typically use linear reward scalarization with fixed weights, which provably fail to capture non-convex Pareto fronts and thus yield suboptimal results. This limitation becomes especially critical in online preference alignment for large language models. Here, stochastic trajectories generated by parameterized policies create highly non-linear and non-convex mappings from parameters to objectives that no single static weighting scheme can find optimal trade-offs. We address this limitation by introducing dynamic reward weighting, which adaptively adjusts reward weights during the online reinforcement learning process. Unlike existing approaches that rely on fixed-weight interpolation, our dynamic weighting continuously balances and prioritizes objectives in training, facilitating effective exploration of Pareto fronts in objective space. We introduce two approaches of increasing sophistication and generalizability: (1) hypervolume-guided weight adaptation and (2) gradient-based weight optimization, offering a versatile toolkit for online multi-objective alignment. Our extensive experiments demonstrate their compatibility with commonly used online reinforcement learning algorithms (including GRPO, REINFORCE, and RLOO), effectiveness across multiple mathematical reasoning datasets, and applicability to different model families, consistently achieving Pareto dominant solutions with fewer training steps than fixed-weight linear scalarization baselines.

Off-policy evaluation (OPE) is a method for estimating the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In some cases, there may be unmeasured variables that can confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded Markov decision processes (MDPs). Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Furthermore, we propose an efficient and robust value estimator and illustrate its effectiveness through extensive simulations and analysis of real data from a world-leading short-video platform.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices lauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices truell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ell_1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.

Machine learning models trained on Earth observation data, such as satellite imagery, have demonstrated significant promise in predicting household-level wealth indices, enabling the creation of high-resolution wealth maps that can be leveraged across multiple causal trials. However, because standard training objectives prioritize overall predictive accuracy, these predictions inherently suffer from shrinkage toward the mean, leading to attenuated estimates of causal treatment effects and limiting their utility in policy. Existing debiasing methods, such as Prediction-Powered Inference, can handle this attenuation bias but require additional fresh ground-truth data at the downstream stage of causal inference, which restricts their applicability in data-scarce environments. Here, we introduce and evaluate two correction methods -- linear calibration correction and Tweedie's correction -- that substantially reduce prediction bias without relying on newly collected labeled data. Linear calibration corrects bias through a straightforward linear transformation derived from held-out calibration data, whereas Tweedie's correction leverages empirical Bayes principles to directly address shrinkage-induced biases by exploiting score functions derived from the model's learning patterns. Through analytical exercises and experiments using Demographic and Health Survey data, we demonstrate that the proposed methods meet or outperform existing approaches that either require (a) adjustments to training pipelines or (b) additional labeled data. These approaches may represent a promising avenue for improving the reliability of causal inference when direct outcome measures are limited or unavailable, enabling a "one map, many trials" paradigm where a single upstream data creation team produces predictions usable by many downstream teams across diverse ML pipelines.