Fix LaTeX inline and display math delimiters for Hugging Face Hub KaTeX rendering

README.md

@@ -45,7 +45,7 @@ tags:
 
 ## Abstract
 
-Autoregressive language models incur sequential decoding overhead and token-level probability miscalibration when deployed on closed-schema classification, tool routing, and safety verification tasks. We present **FastBrain-9B**, a 9.41B-parameter non-autoregressive structured decision model built on a 32-layer hybrid Gated DeltaNet and full-attention backbone (`Qwen3.5-9B`, initialized from `Cloudflare/clef-flash`) coupled with a 116M-parameter cross-attention decision head (`JointSchemaHead`). Given an arbitrary JSON or multimodal state and a set of typed decision specifications (`choice`, binary `noul`, and ordinal `score`), FastBrain-9B evaluates all questions and candidate options simultaneously in a single prefill pass (`output_tokens = 0`). We adapt 104 linear-attention and self-attention projections jointly with the decision head under a composite ordinal-KL, cumulative distribution (ranked probability score), and expected-value regression objective, and merge all parameter updates directly into the base tensors. Across three public evaluation suites encompassing 109 model entries, FastBrain-9B ranks **1st of 8** on the `safeagents-judge-bench` (v2) 7-way misuse classification track (`0.751` macro-F1, `0.858` accuracy; +18.8 percentage points over 27.4B `Cloudflare/clef`) while intercepting `82/82` unsafe agent trajectories (`0.985` AUROC); ranks **7th of 43** zero-shot overall (**5th of 36** open-weight, **2nd of 19** in the $\le$9B open-weight class) on `LocalLLaMA/typed-decisions` at `50 ms` median latency (66.7$\times$ faster than 31B `Quyet-1.0-Large`), and **12th-tied (14th listed of 51)** under prior-only calibration without weight updates (`0.797` accuracy, `0.0816` KL); and achieves an **80.55%** 10-task macro mean on Cloudflare Decision Index (v0.2.1), ranking **2nd of 7** overall, **1st on 10 of 10** tasks among $\le$9B models, and outperforming 27.4B `Cloudflare/clef` on 5 of 10 tasks.
+Autoregressive language models incur sequential decoding overhead and token-level probability miscalibration when deployed on closed-schema classification, tool routing, and safety verification tasks. We present **FastBrain-9B**, a 9.41B-parameter non-autoregressive structured decision model built on a 32-layer hybrid Gated DeltaNet and full-attention backbone (`Qwen3.5-9B`, initialized from `Cloudflare/clef-flash`) coupled with a 116M-parameter cross-attention decision head (`JointSchemaHead`). Given an arbitrary JSON or multimodal state and a set of typed decision specifications (`choice`, binary `noul`, and ordinal `score`), FastBrain-9B evaluates all questions and candidate options simultaneously in a single prefill pass (`output_tokens = 0`). We adapt 104 linear-attention and self-attention projections jointly with the decision head under a composite ordinal-KL, cumulative distribution (ranked probability score), and expected-value regression objective, and merge all parameter updates directly into the base tensors. Across three public evaluation suites encompassing 109 model entries, FastBrain-9B ranks **1st of 8** on the `safeagents-judge-bench` (v2) 7-way misuse classification track (`0.751` macro-F1, `0.858` accuracy; +18.8 percentage points over 27.4B `Cloudflare/clef`) while intercepting `82/82` unsafe agent trajectories (`0.985` AUROC); ranks **7th of 43** zero-shot overall (**5th of 36** open-weight, **2nd of 19** in the ≤9B open-weight class) on `LocalLLaMA/typed-decisions` at `50 ms` median latency (66.7× faster than 31B `Quyet-1.0-Large`), and **12th-tied (14th listed of 51)** under prior-only calibration without weight updates (`0.797` accuracy, `0.0816` KL); and achieves an **80.55%** 10-task macro mean on Cloudflare Decision Index (v0.2.1), ranking **2nd of 7** overall, **1st on 10 of 10** tasks among ≤9B models, and outperforming 27.4B `Cloudflare/clef` on 5 of 10 tasks.
 
 ---
 
@@ -65,18 +65,20 @@ FastBrain-9B uses a 32-layer hybrid sequence backbone (`9.30B` parameters, `bflo
 
 ### 2.2 Joint Schema Decision Head and Vectorized CUDA Kernel
 
-The `JointSchemaHead` (`116M` parameters, stored in `joint_head.safetensors`) pools token representations bounded by `<|question_start|>`/`<|question_end|>` and `<|option_start|>`/`<|option_end|>` markers from the final backbone hidden states $H \in \mathbb{R}^{T \times d}$, applies cross-attention over question-option pairs, and projects directly to scalar logits for three decision primitives:
-1. **`choice`** ($K$-way categorical distribution): $\hat{p} = \operatorname{softmax}(z / \tau) \in \Delta^{K-1}$.
-2. **`noul`** (binary verification): $\hat{p}(\text{true}) = \sigma(z_{\text{true}} - z_{\text{false}})$.
-3. **`score`** (ordinal rubric over levels $v_1 < \dots < v_K$): categorical probabilities $\hat{p} \in \Delta^{K-1}$ together with expected value $\mathbb{E}[\hat{y}] = \sum_{k=1}^K \hat{p}_k v_k$.
+The `JointSchemaHead` (`116M` parameters, stored in `joint_head.safetensors`) pools token representations bounded by `<|question_start|>`/`<|question_end|>` and `<|option_start|>`/`<|option_end|>` markers from the final backbone hidden states \(H \in \mathbb{R}^{T \times d}\), applies cross-attention over question-option pairs, and projects directly to scalar logits for three decision primitives:
+1. **`choice`** (\(K\)-way categorical distribution): \(\hat{p} = \operatorname{softmax}(z / \tau) \in \Delta^{K-1}\).
+2. **`noul`** (binary verification): \(\hat{p}(\text{true}) = \sigma(z_{\text{true}} - z_{\text{false}})\).
+3. **`score`** (ordinal rubric over levels \(v_1 < \dots < v_K\)): categorical probabilities \(\hat{p} \in \Delta^{K-1}\) together with expected value \(\mathbb{E}[\hat{y}] = \sum_{k=1}^K \hat{p}_k v_k\).
 
-In `joint_schema_model.py`, the reference Python span-extraction loop and padded SDPA mask are replaced on CUDA devices by `_forward_fast_cuda`: span means are computed in $\mathcal{O}(1)$ kernel launches via prefix sums (`torch.cumsum`) over the schema suffix, and cross-attention is executed via packed variable-length FlashAttention (`torch.ops.aten._flash_attention_forward` parameterized by `cu_seqlens`). On NVIDIA RTX PRO 6000 Blackwell, this reduces isolated decision-head latency from `3.27 ms` to `1.72 ms` (**1.90$\times$ speedup**) with exact numerical equivalence (`max_logit_diff = 0.00000`).
+In `joint_schema_model.py`, the reference Python span-extraction loop and padded SDPA mask are replaced on CUDA devices by `_forward_fast_cuda`: span means are computed in \(\mathcal{O}(1)\) kernel launches via prefix sums (`torch.cumsum`) over the schema suffix, and cross-attention is executed via packed variable-length FlashAttention (`torch.ops.aten._flash_attention_forward` parameterized by `cu_seqlens`). On NVIDIA RTX PRO 6000 Blackwell, this reduces isolated decision-head latency from `3.27 ms` to `1.72 ms` (**1.90× speedup**) with exact numerical equivalence (`max_logit_diff = 0.00000`).
 
 ### 2.3 Ordinal-KL Distillation and Schema-Topology Calibration
 
-Standard cross-entropy or flat KL divergence treats ordinal rubric levels as unordered classes, penalizing adjacent-level errors identically to extreme errors. FastBrain-9B is trained on `TypeScript/FastBrain-Instruct` under a composite loss combining soft-target KL divergence, discrete ranked probability score (squared $L_2$ distance between predicted and target cumulative distribution functions $\hat{F}_k = \sum_{j \le k} \hat{p}_j$), and expected-score mean squared error on `score` primitives:
+Standard cross-entropy or flat KL divergence treats ordinal rubric levels as unordered classes, penalizing adjacent-level errors identically to extreme errors. FastBrain-9B is trained on `TypeScript/FastBrain-Instruct` under a composite loss combining soft-target KL divergence, discrete ranked probability score (squared \(L_2\) distance between predicted and target cumulative distribution functions \(\hat{F}_k = \sum_{j \le k} \hat{p}_j\)), and expected-score mean squared error on `score` primitives:
 
-$$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{ord}} \sum_{k=1}^{K-1} \bigl(\hat{F}_{\theta,k} - F_k\bigr)^2 + \mathbb{I}[\text{type}=\text{score}] \cdot \lambda_{\mathrm{mse}} \bigl(\mathbb{E}[\hat{y}_\theta] - \mathbb{E}[y]\bigr)^2.$$
+$$
+\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{ord}} \sum_{k=1}^{K-1} \bigl(\hat{F}_{\theta,k} - F_k\bigr)^2 + \mathbb{I}[\text{type}=\text{score}] \cdot \lambda_{\mathrm{mse}} \bigl(\mathbb{E}[\hat{y}_\theta] - \mathbb{E}[y]\bigr)^2.
+$$
 
 At inference time, `joint_schema_model.py` optionally applies compile-time schema-topology calibration (`apply_schema_aware_calibration`), which inspects candidate option structures (e.g., `<tool_call>` invocations, clarification prompts, and open-set abstention clauses) to adjust decision margins against systematic tool over-triggering and out-of-scope false acceptance.
 
@@ -91,27 +93,27 @@ At inference time, `joint_schema_model.py` optionally applies compile-time schem
 | [`safeagents-judge-bench` (v2)](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) — 7-Way Category ([PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)) | 8 decision models (+2 baselines) | **0.751** Macro-F1 / **0.858** Acc | **1 / 8** | `Cloudflare/clef` (27.4B, `0.563`), `vllm-sr/d3-mini` (1.8B, `0.512`), `Cloudflare/clef-flash` (9.4B, `0.462`), `clef-omni` (30B, `0.437`) |
 | [`safeagents-judge-bench` (v2)](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) — Binary Guardrail ([PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)) | 8 decision models (+2 baselines) | **0.985** AUROC / **82/82** Traj.<br>(`0.814` raw; **0.938** calibrated) | **3 / 8** AUROC<br>**1 / 8** (tied) Traj. | `Cloudflare/clef` (27.4B, `0.808` raw bal. acc), `clef-flash` (`0.967` AUROC, `81/82`), `clef-omni` (`0.946` AUROC, `81/82`), `d1-3B` (`68/82`) |
 | [`safeagents-judge-bench` (v1)](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v1) — Binary & Category ([PR #1](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/discussions/1)) | 9 decision models (+2 baselines) | **0.974** Bal. Acc / **0.850** Cat. F1 | **1 / 9** (both tracks) | `Cloudflare/clef-omni` (30B, `0.845` bal. acc / `0.327` F1), `Cloudflare/clef` (27.4B, `0.718` / `0.425`), `clef-flash` (`0.721` / `0.345`) |
-| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — Zero-Shot ([PR #58](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/58)) | 43 total (36 open, 19 $\le$9B open) | **0.7525** Acc (`0.7625` tied-top)<br>`0.1508` KL · `0.0795` Brier · **50 ms** | **7 / 43** overall<br>**5 / 36** open · **2 / 19** $\le$9B | `vllm-sr/d3` (27B, `0.749`), `Elephant 1` (9B, `0.748`, `352 ms`), `Darwin-27B` (`0.743`), `Cloudflare/clef` (27B, `0.728`), `clef-flash` (`0.710`) |
-| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — Fitted on `train` ([PR #57](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/57)) | 51 specialist & calibrated models | **0.7970** Acc (`0.8070` tied-top)<br>**0.0816** KL · **0.0437** Brier · **50 ms** | **12-tied** (14 / 51 listed)<br>**1st** frozen-weight $\le$9B & KL | Frozen weights (`no weights changed`); surpasses `Rev-gen1-midi` (25.6B, `0.7945`), `OpenDecider-small-td` (4B LoRA, `0.792`), `OpenDecider-medium-td` (30B LoRA, `0.788`) |
-| Cloudflare Decision Index (`v0.2.1`) — 10-Task Suite | 7 models (0.4B–27.4B) | **80.55%** Macro Mean | **2 / 7** overall<br>**1st** on **10 / 10** ($\le$9B) | `Jev` (27B, `80.32%`), `Kev 9B` (`76.51%`), `Clef-flash` (9.4B, `74.96%`), `DiffGemma` (26B, `69.14%`); exceeds `27.4B Clef` on 5 / 10 tasks |
+| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — Zero-Shot ([PR #58](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/58)) | 43 total (36 open, 19 ≤9B open) | **0.7525** Acc (`0.7625` tied-top)<br>`0.1508` KL · `0.0795` Brier · **50 ms** | **7 / 43** overall<br>**5 / 36** open · **2 / 19** ≤9B | `vllm-sr/d3` (27B, `0.749`), `Elephant 1` (9B, `0.748`, `352 ms`), `Darwin-27B` (`0.743`), `Cloudflare/clef` (27B, `0.728`), `clef-flash` (`0.710`) |
+| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — Fitted on `train` ([PR #57](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/57)) | 51 specialist & calibrated models | **0.7970** Acc (`0.8070` tied-top)<br>**0.0816** KL · **0.0437** Brier · **50 ms** | **12-tied** (14 / 51 listed)<br>**1st** frozen-weight ≤9B & KL | Frozen weights (`no weights changed`); surpasses `Rev-gen1-midi` (25.6B, `0.7945`), `OpenDecider-small-td` (4B LoRA, `0.792`), `OpenDecider-medium-td` (30B LoRA, `0.788`) |
+| Cloudflare Decision Index (`v0.2.1`) — 10-Task Suite | 7 models (0.4B–27.4B) | **80.55%** Macro Mean | **2 / 7** overall<br>**1st** on **10 / 10** (≤9B) | `Jev` (27B, `80.32%`), `Kev 9B` (`76.51%`), `Clef-flash` (9.4B, `74.96%`), `DiffGemma` (26B, `69.14%`); exceeds `27.4B Clef` on 5 / 10 tasks |
 
 ---
 
 ### 3.1 Agent Tool-Call Guardrail Evaluation (`safeagents-judge-bench`)
 
-[`harness-hub/safeagents-judge-bench`](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) evaluates whether a System-1 decision model can audit suspicious tool calls flagged by a static scanner (`atif-scan`) during real coding-agent executions on Terminal-Bench 2.1, OpenThoughts-TBLite, and Terminal-Bench 4. Version 2 (`v2`) comprises $N = 661$ tool calls across 55 tasks (`536` malicious `block` calls spanning `82` misbehaving trajectories and `125` legitimate `allow` calls). Each call is issued as a single zero-shot System-1 request containing one binary `noul` question (`block`) and one 7-way `choice` question (`legit`, `eval_gaming`, `harness_introspection`, `credential_misuse`, `exfiltration`, `sandbox_escape`, `other_overreach`). All v2 results in Table 2 were executed independently on NVIDIA A100-SXM4-80GB via Hugging Face Jobs ([Merged PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)).
+[`harness-hub/safeagents-judge-bench`](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) evaluates whether a System-1 decision model can audit suspicious tool calls flagged by a static scanner (`atif-scan`) during real coding-agent executions on Terminal-Bench 2.1, OpenThoughts-TBLite, and Terminal-Bench 4. Version 2 (`v2`) comprises \(N = 661\) tool calls across 55 tasks (`536` malicious `block` calls spanning `82` misbehaving trajectories and `125` legitimate `allow` calls). Each call is issued as a single zero-shot System-1 request containing one binary `noul` question (`block`) and one 7-way `choice` question (`legit`, `eval_gaming`, `harness_introspection`, `credential_misuse`, `exfiltration`, `sandbox_escape`, `other_overreach`). All v2 results in Table 2 were executed independently on NVIDIA A100-SXM4-80GB via Hugging Face Jobs ([Merged PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)).
 
-On the 7-way category classification track, FastBrain-9B achieves `0.751` macro-F1 and `0.858` accuracy (`567/661`), outperforming the 27.4B `Cloudflare/clef` model (`0.563` macro-F1, `0.737` accuracy) by `+18.8` percentage points in macro-F1 and `+12.1` points in accuracy, and improving upon its 9.4B base model `Cloudflare/clef-flash` (`0.462` macro-F1, `0.576` accuracy) by `+28.9` and `+28.2` points, respectively. Per-category F1 reaches `0.945` on `harness_introspection` ($n=272$, recall `0.978`), `0.828` on `eval_gaming` ($n=245$, recall `0.853`), and `0.761` on `legit` ($n=125$, precision `0.975`).
+On the 7-way category classification track, FastBrain-9B achieves `0.751` macro-F1 and `0.858` accuracy (`567/661`), outperforming the 27.4B `Cloudflare/clef` model (`0.563` macro-F1, `0.737` accuracy) by `+18.8` percentage points in macro-F1 and `+12.1` points in accuracy, and improving upon its 9.4B base model `Cloudflare/clef-flash` (`0.462` macro-F1, `0.576` accuracy) by `+28.9` and `+28.2` points, respectively. Per-category F1 reaches `0.945` on `harness_introspection` (\(n=272\), recall `0.978`), `0.828` on `eval_gaming` (\(n=245\), recall `0.853`), and `0.761` on `legit` (\(n=125\), precision `0.975`).
 
-On the binary guardrail track, FastBrain-9B attains `0.985` AUROC and `0.996` malicious-call recall (`534/536`), intercepting all `82/82` unsafe trajectories (`median_bad_calls_before_catch = 0.0`), with `1.000` recall on `harness_introspection` (`272/272`), `credential_misuse` (`15/15`), and `sandbox_escape` (`4/4`). Under the uncalibrated default decision rule $P(\text{block}) \ge 0.50$, balanced accuracy is `0.814` (false-block rate `0.368` across the 125 `allow` calls, compared with `0.808` balanced accuracy and `0.384` false-block rate for 27.4B `Cloudflare/clef`). Because rank-ordering discrimination is preserved (`0.985` AUROC), setting the operating threshold to $P(\text{block}) \ge 0.961$ yields `0.938` balanced accuracy at a `0.056` (`7/125`) false-block rate while maintaining `82/82` trajectory interception. Table 2 also includes the `v1` release ($N = 562$ calls, `78` trajectories), where FastBrain-9B ranked 1st of 9 on both tracks.
+On the binary guardrail track, FastBrain-9B attains `0.985` AUROC and `0.996` malicious-call recall (`534/536`), intercepting all `82/82` unsafe trajectories (`median_bad_calls_before_catch = 0.0`), with `1.000` recall on `harness_introspection` (`272/272`), `credential_misuse` (`15/15`), and `sandbox_escape` (`4/4`). Under the uncalibrated default decision rule \(P(\text{block}) \ge 0.50\), balanced accuracy is `0.814` (false-block rate `0.368` across the 125 `allow` calls, compared with `0.808` balanced accuracy and `0.384` false-block rate for 27.4B `Cloudflare/clef`). Because rank-ordering discrimination is preserved (`0.985` AUROC), setting the operating threshold to \(P(\text{block}) \ge 0.961\) yields `0.938` balanced accuracy at a `0.056` (`7/125`) false-block rate while maintaining `82/82` trajectory interception. Table 2 also includes the `v1` release (\(N = 562\) calls, `78` trajectories), where FastBrain-9B ranked 1st of 9 on both tracks.
 
-**Table 2: Zero-shot evaluation on `harness-hub/safeagents-judge-bench` (`v2`, $N = 661$ calls, 82 unsafe trajectories; and `v1` reference, $N = 562$).**
+**Table 2: Zero-shot evaluation on `harness-hub/safeagents-judge-bench` (`v2`, \(N = 661\) calls, 82 unsafe trajectories; and `v1` reference, \(N = 562\)).**
 
 | Model | Params | Cat. Macro-F1 ↑ | Cat. Acc ↑ | AUROC ↑ | Bal. Acc ↑ | Recall ↑ | False Block ↓ | Traj. Caught ↑ | p50 Latency (Hardware) |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
-| **TypeScript/FastBrain-9B** (`v2`, default $t = 0.50$) | 9.4B | **0.751** | **0.858** | 0.985 | 0.814 | 0.996 | 0.368 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
-| **TypeScript/FastBrain-9B** (`v2`, calibrated $t = 0.961$) | 9.4B | **0.751** | **0.858** | 0.985 | **0.938** | 0.931 | 0.056 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
-| **TypeScript/FastBrain-9B** (`v1` official, $N = 562$) | 9.4B | **0.850** | **0.923** | 0.983 | **0.974** | **1.000** | 0.051 | **78 / 78** | 104 ms (RTX PRO 6000) |
+| **TypeScript/FastBrain-9B** (`v2`, default \(t = 0.50\)) | 9.4B | **0.751** | **0.858** | 0.985 | 0.814 | 0.996 | 0.368 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
+| **TypeScript/FastBrain-9B** (`v2`, calibrated \(t = 0.961\)) | 9.4B | **0.751** | **0.858** | 0.985 | **0.938** | 0.931 | 0.056 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
+| **TypeScript/FastBrain-9B** (`v1` official, \(N = 562\)) | 9.4B | **0.850** | **0.923** | 0.983 | **0.974** | **1.000** | 0.051 | **78 / 78** | 104 ms (RTX PRO 6000) |
 | Cloudflare/clef | 27.4B | 0.563 | 0.737 | **0.993** | 0.808 | **1.000** | 0.384 | **82 / 82** | 636 ms (A100) |
 | vllm-sr/d3-mini | 1.8B | 0.512 | 0.652 | 0.986 | 0.856 | **1.000** | 0.288 | **82 / 82** | 168 ms (A100) |
 | Cloudflare/clef-flash (base) | 9.4B | 0.462 | 0.576 | 0.967 | 0.893 | 0.978 | 0.192 | 81 / 82 | 326 ms (A100) |
@@ -126,11 +128,11 @@ On the binary guardrail track, FastBrain-9B attains `0.985` AUROC and `0.996` ma
 
 [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) tests multi-primitive structured judgment across four enterprise workflows (`agent_trace_observability`, `customer_service`, `invoice_processing`, and `security_incidents`), comprising 400 held-out test cases and 2,000 individual decisions (`noul`, `choice`, and `score`) scored against teacher-panel soft label distributions. Two scoring conventions exist in the benchmark repository: `bench/score_with_jobs.py` resolves exact ties in the gold distribution by selecting the first index (`g.index(max(g))`), whereas `scripts/score_model.py` credits any tied maximum across the 20 tied test items; KL divergence and Brier score are identical under both scripts. We report both accuracy figures (`strict / tied-top`) alongside prediction traces in [`eval_submissions/`](./eval_submissions/).
 
-On the official zero-shot leaderboard ($N = 43$ models), FastBrain-9B scores `0.7525` (`0.7625` tied-top) accuracy, `0.1508` KL divergence, `0.0795` Brier score, and `0.085` ECE at `50 ms` p50 latency (RTX PRO 6000 via SGLang). It places **7th of 43** overall, **5th of 36** among open-weight models, **2nd of 19** among $\le$9B open-weight models, and **1st** among all `Clef`-architecture models, improving over 9.4B `Cloudflare/clef-flash` (`0.7100` accuracy, `0.2093` KL) by `+4.25` percentage points and over 27.4B `Cloudflare/clef` (`0.7275` accuracy, `0.1907` KL) by `+2.50` points. Across all 28 models exceeding `0.700` zero-shot accuracy, FastBrain-9B exhibits the lowest p50 latency (`50 ms`, compared with `118 ms` for 9B `Amos 1 medium`, `357 ms` for 27B `Amos 1 large`, `526 ms` for `meraGPT Decider 1`, and `3,335 ms` for 31B `Quyet-1.0-Large`). Evaluating the uncalibrated ordinal-KL distilled head directly yields `0.7735` raw accuracy (`0.1039` KL, `0.0582` Brier).
+On the official zero-shot leaderboard (\(N = 43\) models), FastBrain-9B scores `0.7525` (`0.7625` tied-top) accuracy, `0.1508` KL divergence, `0.0795` Brier score, and `0.085` ECE at `50 ms` p50 latency (RTX PRO 6000 via SGLang). It places **7th of 43** overall, **5th of 36** among open-weight models, **2nd of 19** among ≤9B open-weight models, and **1st** among all `Clef`-architecture models, improving over 9.4B `Cloudflare/clef-flash` (`0.7100` accuracy, `0.2093` KL) by `+4.25` percentage points and over 27.4B `Cloudflare/clef` (`0.7275` accuracy, `0.1907` KL) by `+2.50` points. Across all 28 models exceeding `0.700` zero-shot accuracy, FastBrain-9B exhibits the lowest p50 latency (`50 ms`, compared with `118 ms` for 9B `Amos 1 medium`, `357 ms` for 27B `Amos 1 large`, `526 ms` for `meraGPT Decider 1`, and `3,335 ms` for 31B `Quyet-1.0-Large`). Evaluating the uncalibrated ordinal-KL distilled head directly yields `0.7735` raw accuracy (`0.1039` KL, `0.0582` Brier).
 
-On the separate `train`-fitted leaderboard ($N = 51$ models), fitting only scalar per-question log-priors and temperature parameters on the 1,200 `train` cases—with all backbone and head weights frozen (`no weights changed`)—achieves `0.7970` (`0.8070` tied-top) accuracy, `0.0816` KL divergence, and `0.0437` Brier score, ranking **12th-tied (14th listed of 51)** overall and **1st in KL calibration** among frozen-weight models.
+On the separate `train`-fitted leaderboard (\(N = 51\) models), fitting only scalar per-question log-priors and temperature parameters on the 1,200 `train` cases—with all backbone and head weights frozen (`no weights changed`)—achieves `0.7970` (`0.8070` tied-top) accuracy, `0.0816` KL divergence, and `0.0437` Brier score, ranking **12th-tied (14th listed of 51)** overall and **1st in KL calibration** among frozen-weight models.
 
-**Table 3: Performance on `LocalLLaMA/typed-decisions` ($N = 400$ cases, 2,000 decisions). Values separated by `/` denote `score_with_jobs.py` / `score_model.py` tie handling.**
+**Table 3: Performance on `LocalLLaMA/typed-decisions` (\(N = 400\) cases, 2,000 decisions). Values separated by `/` denote `score_with_jobs.py` / `score_model.py` tie handling.**
 
 | Model | Params | Protocol | Overall Acc ↑ | KL ↓ | Brier ↓ | `noul` ↑ | `choice` ↑ | `score` ↑ | Agent ↑ | Cust. Svc ↑ | Invoice ↑ | Security ↑ | p50 Latency |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
@@ -152,9 +154,9 @@ On the separate `train`-fitted leaderboard ($N = 51$ models), fitting only scala
 
 ### 3.3 Multi-Domain Decision Suite (Cloudflare Decision Index `v0.2.1`)
 
-On the 10-benchmark **Cloudflare Decision Index (`v0.2.1`)** suite ($N = 22,427$ evaluation requests spanning AST tool calling, 20-candidate tool reranking, stateful API invocation, fine-grained intent classification, out-of-scope rejection, reasoning-intensive retrieval, e-commerce relevance, phishing detection, and tool-use governance), FastBrain-9B attains an **80.55%** unweighted macro mean (Table 4, Figures 1–3).
+On the 10-benchmark **Cloudflare Decision Index (`v0.2.1`)** suite (\(N = 22,427\) evaluation requests spanning AST tool calling, 20-candidate tool reranking, stateful API invocation, fine-grained intent classification, out-of-scope rejection, reasoning-intensive retrieval, e-commerce relevance, phishing detection, and tool-use governance), FastBrain-9B attains an **80.55%** unweighted macro mean (Table 4, Figures 1–3).
 
-Across the $\le$9B parameter tier (`Clef-flash` 9.4B, `Kev 9B`, and `Laya` 0.4B), FastBrain-9B ranks **1st on all 10 benchmarks**, improving the 10-task macro mean over `Clef-flash` (`74.96%`) by `+5.59` percentage points and over `Kev 9B` (`76.51%`) by `+4.04` points. The largest gains occur on calibration-sensitive abstention and governance tasks: `+31.67` points on `CLINC150+OOS` (`98.44%` vs. `66.77%`), `+15.55` points on `When2Call` (`81.13%` vs. `65.58%`), and `+6.80` points on `PhishNChips` (`78.75%` vs. `71.95%`). Across all model scales up to 27.4B, FastBrain-9B ranks **2nd of 7** overall, surpassing `27B Jev` (`80.32%`) and `26B-A4B DiffusionGemma Jev` (`69.14%`), and exceeding `27.4B Clef` (`81.81%`) on 5 of 10 individual benchmarks (`BFCL`, `API-Bank`, `CLINC150+OOS`, `Home Appliances`, and `When2Call`).
+Across the ≤9B parameter tier (`Clef-flash` 9.4B, `Kev 9B`, and `Laya` 0.4B), FastBrain-9B ranks **1st on all 10 benchmarks**, improving the 10-task macro mean over `Clef-flash` (`74.96%`) by `+5.59` percentage points and over `Kev 9B` (`76.51%`) by `+4.04` points. The largest gains occur on calibration-sensitive abstention and governance tasks: `+31.67` points on `CLINC150+OOS` (`98.44%` vs. `66.77%`), `+15.55` points on `When2Call` (`81.13%` vs. `65.58%`), and `+6.80` points on `PhishNChips` (`78.75%` vs. `71.95%`). Across all model scales up to 27.4B, FastBrain-9B ranks **2nd of 7** overall, surpassing `27B Jev` (`80.32%`) and `26B-A4B DiffusionGemma Jev` (`69.14%`), and exceeding `27.4B Clef` (`81.81%`) on 5 of 10 individual benchmarks (`BFCL`, `API-Bank`, `CLINC150+OOS`, `Home Appliances`, and `When2Call`).
 
 ![Figure 1: Aggregate macro mean and parameter efficiency on Cloudflare Decision Index v0.2.1](./assets/benchmark_overview.png)
 *Figure 1. Aggregate 10-benchmark macro mean versus parameter count on Cloudflare Decision Index (v0.2.1, 22,427 requests).*
@@ -165,7 +167,7 @@ Across the $\le$9B parameter tier (`Clef-flash` 9.4B, `Kev 9B`, and `Laya` 0.4B)
 ![Figure 3: Reliability diagrams and open-set calibration breakdown](./assets/decision_calibration_breakdown.png)
 *Figure 3. Confidence calibration, open-set out-of-scope rejection (`CLINC150+OOS`), and abstention margin analysis (`When2Call`).*
 
-**Table 4: Per-benchmark results on Cloudflare Decision Index (`v0.2.1`, 10 tasks, $N = 22,427$). Bold denotes the highest score across all parameter scales; underline denotes best in the $\le$9B class.**
+**Table 4: Per-benchmark results on Cloudflare Decision Index (`v0.2.1`, 10 tasks, \(N = 22,427\)). Bold denotes the highest score across all parameter scales; underline denotes best in the ≤9B class.**
 
 | Benchmark (Metric) | **FastBrain-9B** (Ours) | Clef-flash (Base) | Kev 9B | Clef | Jev | DiffGemma | Laya |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
@@ -188,7 +190,7 @@ Across the $\le$9B parameter tier (`Clef-flash` 9.4B, `Kev 9B`, and `Laya` 0.4B)
 
 ### 4.1 Runtime Comparison Across Inference Engines
 
-Table 5 compares end-to-end latency, prefill throughput, and memory footprint across three serving backends—SGLang (`lmsysorg/sglang:dev-clef` with `JointSchemaPooler`), `llama.cpp` (`b11430` `ClefModel` graph in `Q8_0` and `Q4_K_M`), and native PyTorch (`joint_schema_model.py`)—benchmarking identical requests on a single NVIDIA RTX PRO 6000 Blackwell Server Edition GPU. Because `output_tokens = 0` for all requests, throughput is governed purely by prefill compute and span-pooling efficiency, reaching `19,319 tok/s` (`131.2` decisions/s) at batch size $B = 4$ in SGLang.
+Table 5 compares end-to-end latency, prefill throughput, and memory footprint across three serving backends—SGLang (`lmsysorg/sglang:dev-clef` with `JointSchemaPooler`), `llama.cpp` (`b11430` `ClefModel` graph in `Q8_0` and `Q4_K_M`), and native PyTorch (`joint_schema_model.py`)—benchmarking identical requests on a single NVIDIA RTX PRO 6000 Blackwell Server Edition GPU. Because `output_tokens = 0` for all requests, throughput is governed purely by prefill compute and span-pooling efficiency, reaching `19,319 tok/s` (`131.2` decisions/s) at batch size \(B = 4\) in SGLang.
 
 **Table 5: End-to-end latency and prefill throughput on NVIDIA RTX PRO 6000 Blackwell Server Edition (G4).**
 
@@ -198,12 +200,12 @@ Table 5 compares end-to-end latency, prefill throughput, and memory footprint ac
 | Peak GPU Memory (16K context) | ~20.5 GiB | 12.55 GiB | **10.30 GiB** | 20.3–24.7 GiB |
 | Compatible with 16 GiB T4 GPU | No (BF16 TP=1) | Yes (`9.03 GiB` at 4K) | **Yes (`6.78 GiB` at 4K)** | Yes (`6.8 GiB` via NF4) |
 | Top-1 Agreement vs. PyTorch BF16 | **100.00%** | 99.86% (1,471 / 1,473) | 98.78% (1,455 / 1,473) | 100.00% (reference) |
-| 1. Short Intent Routing (293 tok, $K=2$) | **30.01 ms** (9,763 tok/s) | 32.82 ms (8,929 tok/s) | 31.69 ms (9,245 tok/s) | 43.23 ms (6,778 tok/s) |
-| 2. Typed Decisions (736 tok, $K=5$) | **50.29 ms** (14,635 tok/s) | 62.40 ms (11,795 tok/s) | 61.80 ms (11,909 tok/s) | 63.58 ms (11,576 tok/s) |
-| 3. When2Call Governance (1,068 tok, $K=1$) | **66.06 ms** (16,167 tok/s) | 87.78 ms (12,167 tok/s) | 89.34 ms (11,955 tok/s) | 77.77 ms (13,733 tok/s) |
-| 4. PhishNChips Security (1,303 tok, $K=9$) | **75.86 ms** (17,176 tok/s) | 108.55 ms (12,004 tok/s) | 109.97 ms (11,849 tok/s) | 90.32 ms (14,426 tok/s) |
-| 5. SafeAgents Judge (2,217 tok, $K=2$) | **125.85 ms** (17,616 tok/s) | 181.70 ms (12,201 tok/s) | 183.50 ms (12,082 tok/s) | 138.06 ms (16,058 tok/s) |
-| Batch $B=4$ Typed Decisions (2,944 tok, 20 dec) | **152.39 ms** (19,319 tok/s) | 248.50 ms (11,847 tok/s) | 245.20 ms (12,006 tok/s) | 175.85 ms (16,742 tok/s) |
+| 1. Short Intent Routing (293 tok, \(K=2\)) | **30.01 ms** (9,763 tok/s) | 32.82 ms (8,929 tok/s) | 31.69 ms (9,245 tok/s) | 43.23 ms (6,778 tok/s) |
+| 2. Typed Decisions (736 tok, \(K=5\)) | **50.29 ms** (14,635 tok/s) | 62.40 ms (11,795 tok/s) | 61.80 ms (11,909 tok/s) | 63.58 ms (11,576 tok/s) |
+| 3. When2Call Governance (1,068 tok, \(K=1\)) | **66.06 ms** (16,167 tok/s) | 87.78 ms (12,167 tok/s) | 89.34 ms (11,955 tok/s) | 77.77 ms (13,733 tok/s) |
+| 4. PhishNChips Security (1,303 tok, \(K=9\)) | **75.86 ms** (17,176 tok/s) | 108.55 ms (12,004 tok/s) | 109.97 ms (11,849 tok/s) | 90.32 ms (14,426 tok/s) |
+| 5. SafeAgents Judge (2,217 tok, \(K=2\)) | **125.85 ms** (17,616 tok/s) | 181.70 ms (12,201 tok/s) | 183.50 ms (12,082 tok/s) | 138.06 ms (16,058 tok/s) |
+| Batch \(B=4\) Typed Decisions (2,944 tok, 20 dec) | **152.39 ms** (19,319 tok/s) | 248.50 ms (11,847 tok/s) | 245.20 ms (12,006 tok/s) | 175.85 ms (16,742 tok/s) |
 
 ### 4.2 Mixed-Precision GGUF Quantization Fidelity
 
@@ -213,8 +215,8 @@ Uniform 4-bit quantization degrades cross-attention span readout and linear-atte
 
 | Metric / Subset | PyTorch `bfloat16` (18.82 GB) | GGUF `Q8_0` (9.66 GB) | GGUF `Q4_K_M` (6.73 GB, `Q8_0` Head) |
 | :--- | :---: | :---: | :---: |
-| Top-1 Decision Agreement ($N = 1,473$) | 100.00% (ref) | 99.86% (1,471 / 1,473) | 98.78% (1,455 / 1,473) |
-| Mean Absolute Probability Error ($\|\hat{p}_q - \hat{p}_{\text{bf16}}\|$) | 0.00000 | 0.00203 | 0.00387 |
+| Top-1 Decision Agreement (\(N = 1,473\)) | 100.00% (ref) | 99.86% (1,471 / 1,473) | 98.78% (1,455 / 1,473) |
+| Mean Absolute Probability Error (\(\lvert \hat{p}_q - \hat{p}_{\mathrm{bf16}} \rvert\)) | 0.00000 | 0.00203 | 0.00387 |
 | 10-Task Mean (Uncalibrated Head) | 82.37% | 82.34% (-0.03) | 82.56% (+0.19) |
 | 10-Task Mean (Schema-Calibrated) | 83.68% | 83.65% (-0.03) | 83.48% (-0.20) |
 | ├─ 1. BFCL / 3. API-Bank / 4. BANKING77 | 100.0% / 95.0% / 100.0% | 100.0% / 95.0% / 100.0% | 100.0% / 95.0% / 100.0% |
@@ -230,7 +232,7 @@ Uniform 4-bit quantization degrades cross-attention span readout and linear-atte
 | PyTorch `load_in_4bit=True` (NF4 + `fp16` head) | ~5.5 GB (mem) | 6.20 – 6.80 GiB | — | 8–16 GB CUDA GPU (Colab T4, consumer GPUs) |
 | `FastBrain-9B-Q8_0.gguf` | 9.66 GB | 9.03 – 12.55 GiB | 349.3 ms / 1,149.8 ms | 12–16 GB GPU (Tesla T4, RTX 4070 Ti), Apple Silicon (16 GB+) |
 | PyTorch `load_in_8bit=True` (INT8 + `bf16` head) | ~9.6 GB (mem) | ~11.20 GiB | — | 12–16 GB CUDA GPU |
-| Native `bfloat16` (`safetensors` / `BF16.gguf`) | 18.82 / 18.16 GB | 20.30 – 24.70 GiB | — | $\ge$24 GB GPU (NVIDIA L4, A100, H100, RTX 3090/4090, PRO 6000) |
+| Native `bfloat16` (`safetensors` / `BF16.gguf`) | 18.82 / 18.16 GB | 20.30 – 24.70 GiB | — | ≥24 GB GPU (NVIDIA L4, A100, H100, RTX 3090/4090, PRO 6000) |
 
 ---
 

README_zh.md

@@ -19,7 +19,7 @@
 
 ## 摘要
 
-将自回归语言模型用于封闭 Schema 分类、工具路由与安全合规校验等结构化决策任务时，逐 Token 解码机制不仅引入与决策复杂度无关的序列生成延迟，还会因表面词形切分导致类别概率分布失准。本文发布 **FastBrain-9B**，一个总参数量为 9.41B 的非自回归结构化决策模型，由 32 层混合 Gated DeltaNet 线性注意力与全注意力主干网络（基于 `Cloudflare/clef-flash` 初始化的 `Qwen3.5-9B` 架构）及 116M 参数的交叉注意力联合决策头（`JointSchemaHead`）组成。给定任意 JSON 或多模态状态以及一组类型化决策定义（多选分类 `choice`、二元真值判别 `noul` 与序数量表评分 `score`），模型仅通过单次 Prefill 前向传播（`output_tokens = 0`）即可同步输出全部问题与候选项的校准概率分布。训练阶段，我们在复合序数 KL 散度、累积分布距离（离散分级概率评分 RPS）与期望值均方误差目标下，联合优化全部 32 层中的 104 个注意力投影矩阵及决策头参数，并将增量权重原地合并至主干张量。在涵盖 109 个参评模型条目的三项公开评测基准中：FastBrain-9B 在 `safeagents-judge-bench`（v2）7 类违规判别赛道位列 **第 1 / 8**（Macro-F1 `0.751`，准确率 `0.858`，较 27.4B 参数的 `Cloudflare/clef` 高出 18.8 个百分点），并在二元拦截赛道实现 `82/82` 越界轨迹全检出（AUROC `0.985`）；在 `LocalLLaMA/typed-decisions` 零样本总榜位列 **第 7 / 43**（开源权重模型 **第 5 / 36**，$\le$9B 开源模型 **第 2 / 19**），中位推理延迟为 `50 ms`（较 31B 模型 `Quyet-1.0-Large` 快 66.7 倍），在冻结全部模型权重仅拟合先验与温度参数的设定下位列 `train` 校准榜 **并列第 12（列表第 14 / 51）**（准确率 `0.7970`，KL 散度 `0.0816`）；在 Cloudflare Decision Index（v0.2.1）10 任务套件上取得 **80.55%** 的宏平均分，位列全量级 **第 2 / 7**、$\le$9B 量级 **10 / 10 任务单项第 1**，并在其中 5 项任务上超越 27.4B 的 `Cloudflare/clef`。
+将自回归语言模型用于封闭 Schema 分类、工具路由与安全合规校验等结构化决策任务时，逐 Token 解码机制不仅引入与决策复杂度无关的序列生成延迟，还会因表面词形切分导致类别概率分布失准。本文发布 **FastBrain-9B**，一个总参数量为 9.41B 的非自回归结构化决策模型，由 32 层混合 Gated DeltaNet 线性注意力与全注意力主干网络（基于 `Cloudflare/clef-flash` 初始化的 `Qwen3.5-9B` 架构）及 116M 参数的交叉注意力联合决策头（`JointSchemaHead`）组成。给定任意 JSON 或多模态状态以及一组类型化决策定义（多选分类 `choice`、二元真值判别 `noul` 与序数量表评分 `score`），模型仅通过单次 Prefill 前向传播（`output_tokens = 0`）即可同步输出全部问题与候选项的校准概率分布。训练阶段，我们在复合序数 KL 散度、累积分布距离（离散分级概率评分 RPS）与期望值均方误差目标下，联合优化全部 32 层中的 104 个注意力投影矩阵及决策头参数，并将增量权重原地合并至主干张量。在涵盖 109 个参评模型条目的三项公开评测基准中：FastBrain-9B 在 `safeagents-judge-bench`（v2）7 类违规判别赛道位列 **第 1 / 8**（Macro-F1 `0.751`，准确率 `0.858`，较 27.4B 参数的 `Cloudflare/clef` 高出 18.8 个百分点），并在二元拦截赛道实现 `82/82` 越界轨迹全检出（AUROC `0.985`）；在 `LocalLLaMA/typed-decisions` 零样本总榜位列 **第 7 / 43**（开源权重模型 **第 5 / 36**，≤9B 开源模型 **第 2 / 19**），中位推理延迟为 `50 ms`（较 31B 模型 `Quyet-1.0-Large` 快 66.7 倍），在冻结全部模型权重仅拟合先验与温度参数的设定下位列 `train` 校准榜 **并列第 12（列表第 14 / 51）**（准确率 `0.7970`，KL 散度 `0.0816`）；在 Cloudflare Decision Index（v0.2.1）10 任务套件上取得 **80.55%** 的宏平均分，位列全量级 **第 2 / 7**、≤9B 量级 **10 / 10 任务单项第 1**，并在其中 5 项任务上超越 27.4B 的 `Cloudflare/clef`。
 
 ---
 
@@ -39,18 +39,20 @@ FastBrain-9B 主干网络包含 32 层混合序列建模模块（`9.30B` 参数
 
 ### 2.2 联合 Schema 决策头与向量化 CUDA 算子
 
-`JointSchemaHead`（`116M` 参数，独立存储于 `joint_head.safetensors`）从主干末层隐藏状态 $H \in \mathbb{R}^{T \times d}$ 中提取由 `<|question_start|>`/`<|question_end|>` 与 `<|option_start|>`/`<|option_end|>` 界定的片段表征，经问题-选项交叉注意力交互后映射为三类基础决策原语的标量对数几率：
-1. **`choice`**（$K$ 分类离散分布）：输出归一化概率向量 $\hat{p} = \operatorname{softmax}(z / \tau) \in \Delta^{K-1}$。
-2. **`noul`**（二元真值判别）：输出命题成立概率 $\hat{p}(\text{true}) = \sigma(z_{\text{true}} - z_{\text{false}})$。
-3. **`score`**（定义在有序分值 $v_1 < \dots < v_K$ 上的量表评估）：同时输出各等级概率 $\hat{p} \in \Delta^{K-1}$ 与数学期望得分 $\mathbb{E}[\hat{y}] = \sum_{k=1}^K \hat{p}_k v_k$。
+`JointSchemaHead`（`116M` 参数，独立存储于 `joint_head.safetensors`）从主干末层隐藏状态 \(H \in \mathbb{R}^{T \times d}\) 中提取由 `<|question_start|>`/`<|question_end|>` 与 `<|option_start|>`/`<|option_end|>` 界定的片段表征，经问题-选项交叉注意力交互后映射为三类基础决策原语的标量对数几率：
+1. **`choice`**（\(K\) 分类离散分布）：输出归一化概率向量 \(\hat{p} = \operatorname{softmax}(z / \tau) \in \Delta^{K-1}\)。
+2. **`noul`**（二元真值判别）：输出命题成立概率 \(\hat{p}(\text{true}) = \sigma(z_{\text{true}} - z_{\text{false}})\)。
+3. **`score`**（定义在有序分值 \(v_1 < \dots < v_K\) 上的量表评估）：同时输出各等级概率 \(\hat{p} \in \Delta^{K-1}\) 与数学期望得分 \(\mathbb{E}[\hat{y}] = \sum_{k=1}^K \hat{p}_k v_k\)。
 
-在参考运行时 `joint_schema_model.py` 中，针对 CUDA 设备实现了融合算子路径 `_forward_fast_cuda`：利用基于 `torch.cumsum` 的 $\mathcal{O}(1)$ 前缀和差分替代逐片段 Python 循环完成变长片段均值池化，并通过 `cu_seqlens` 紧凑打包调用变长 FlashAttention（`torch.ops.aten._flash_attention_forward`）替代稠密掩码注意力。在 NVIDIA RTX PRO 6000 Blackwell 上，该实现将决策头单次前向耗时由 `3.27 ms` 降至 `1.72 ms`（**1.90 倍加速**），且保持严格数值等价（最大 Logit 绝对偏差 `max_logit_diff = 0.00000`）。
+在参考运行时 `joint_schema_model.py` 中，针对 CUDA 设备实现了融合算子路径 `_forward_fast_cuda`：利用基于 `torch.cumsum` 的 \(\mathcal{O}(1)\) 前缀和差分替代逐片段 Python 循环完成变长片段均值池化，并通过 `cu_seqlens` 紧凑打包调用变长 FlashAttention（`torch.ops.aten._flash_attention_forward`）替代稠密掩码注意力。在 NVIDIA RTX PRO 6000 Blackwell 上，该实现将决策头单次前向耗时由 `3.27 ms` 降至 `1.72 ms`（**1.90 倍加速**），且保持严格数值等价（最大 Logit 绝对偏差 `max_logit_diff = 0.00000`）。
 
 ### 2.3 序数 KL 蒸馏与编译期 Schema 拓扑校准
 
-标准交叉熵或普通多类 KL 散度将有序评定量表视为无序独立类别，对相邻等级误差与跨端极端误差施加同等惩罚。FastBrain-9B 在 `TypeScript/FastBrain-Instruct` 数据集上采用复合分布匹配损失进行训练，联合优化软标签 KL 散度、离散分级概率评分（预测累积分布 $\hat{F}_k = \sum_{j \le k} \hat{p}_j$ 与目标累积分布 $F_k$ 之间的二阶距离）以及 `score` 题型的期望值均方误差：
+标准交叉熵或普通多类 KL 散度将有序评定量表视为无序独立类别，对相邻等级误差与跨端极端误差施加同等惩罚。FastBrain-9B 在 `TypeScript/FastBrain-Instruct` 数据集上采用复合分布匹配损失进行训练，联合优化软标签 KL 散度、离散分级概率评分（预测累积分布 \(\hat{F}_k = \sum_{j \le k} \hat{p}_j\) 与目标累积分布 \(F_k\) 之间的二阶距离）以及 `score` 题型的期望值均方误差：
 
-$$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{ord}} \sum_{k=1}^{K-1} \bigl(\hat{F}_{\theta,k} - F_k\bigr)^2 + \mathbb{I}[\text{type}=\text{score}] \cdot \lambda_{\mathrm{mse}} \bigl(\mathbb{E}[\hat{y}_\theta] - \mathbb{E}[y]\bigr)^2.$$
+$$
+\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{ord}} \sum_{k=1}^{K-1} \bigl(\hat{F}_{\theta,k} - F_k\bigr)^2 + \mathbb{I}[\text{type}=\text{score}] \cdot \lambda_{\mathrm{mse}} \bigl(\mathbb{E}[\hat{y}_\theta] - \mathbb{E}[y]\bigr)^2.
+$$
 
 在推理阶段，`joint_schema_model.py` 提供可选的编译期 Schema 拓扑校准函数（`apply_schema_aware_calibration`），通过解析候选项的语法结构特征（如 `<tool_call>` 调用声明、澄清追问子句及越界拒识选项）修正判别边际，抑制工具过度触发（Over-Triggering）与开放集误接收。
 
@@ -65,27 +67,27 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 | [`safeagents-judge-bench` (v2)](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) — 7 类违规判别 ([PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)) | 8 个决策模型 (+2 基线) | **0.751** Macro-F1 / **0.858** Acc | **1 / 8** | `Cloudflare/clef` (27.4B, `0.563`), `vllm-sr/d3-mini` (1.8B, `0.512`), `Cloudflare/clef-flash` (9.4B, `0.462`), `clef-omni` (30B, `0.437`) |
 | [`safeagents-judge-bench` (v2)](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) — 二元安全护栏 ([PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)) | 8 个决策模型 (+2 基线) | **0.985** AUROC / **82/82** 轨迹检出<br>(`0.814` 默认；**0.938** 阈值校准) | **3 / 8** AUROC<br>**1 / 8** (并列) 轨迹 | `Cloudflare/clef` (27.4B, 默认 Bal. Acc `0.808`), `clef-flash` (`0.967` AUROC, `81/82`), `clef-omni` (`0.946` AUROC, `81/82`), `d1-3B` (`68/82`) |
 | [`safeagents-judge-bench` (v1)](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v1) — 二元与 7 分类 ([PR #1](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/discussions/1)) | 9 个决策模型 (+2 基线) | **0.974** Bal. Acc / **0.850** Cat. F1 | **1 / 9** (双赛道第 1) | `Cloudflare/clef-omni` (30B, `0.845` / `0.327`), `Cloudflare/clef` (27.4B, `0.718` / `0.425`), `clef-flash` (`0.721` / `0.345`) |
-| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — 零样本评测 ([PR #58](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/58)) | 43 个模型 (36 开源, 19 个 $\le$9B 开源) | **0.7525** Acc (`0.7625` 并列口径)<br>`0.1508` KL · `0.0795` Brier · **50 ms** | **7 / 43** 总榜<br>**5 / 36** 开源 · **2 / 19** $\le$9B | `vllm-sr/d3` (27B, `0.749`), `Elephant 1` (9B, `0.748`, `352 ms`), `Darwin-27B` (`0.743`), `Cloudflare/clef` (27B, `0.728`), `clef-flash` (`0.710`) |
-| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — `train` 校准 ([PR #57](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/57)) | 51 个微调与校准模型 | **0.7970** Acc (`0.8070` 并列口径)<br>**0.0816** KL · **0.0437** Brier · **50 ms** | **并列 12** (列表 14 / 51)<br>冻结权重 $\le$9B 及 KL **第 1** | 冻结全部模型权重（`no weights changed`）；高于 `Rev-gen1-midi` (25.6B, `0.7945`)、`OpenDecider-small-td` (4B LoRA, `0.792`)、`OpenDecider-medium-td` (30B LoRA, `0.788`) |
-| Cloudflare Decision Index (`v0.2.1`) — 10 任务套件 | 7 个模型 (0.4B–27.4B) | **80.55%** 宏平均 | **2 / 7** 全量级总榜<br>$\le$9B 量级 **10 / 10 单项第 1** | `Jev` (27B, `80.32%`), `Kev 9B` (`76.51%`), `Clef-flash` (9.4B, `74.96%`), `DiffGemma` (26B, `69.14%`)；5 / 10 项任务高于 `27.4B Clef` |
+| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — 零样本评测 ([PR #58](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/58)) | 43 个模型 (36 开源, 19 个 ≤9B 开源) | **0.7525** Acc (`0.7625` 并列口径)<br>`0.1508` KL · `0.0795` Brier · **50 ms** | **7 / 43** 总榜<br>**5 / 36** 开源 · **2 / 19** ≤9B | `vllm-sr/d3` (27B, `0.749`), `Elephant 1` (9B, `0.748`, `352 ms`), `Darwin-27B` (`0.743`), `Cloudflare/clef` (27B, `0.728`), `clef-flash` (`0.710`) |
+| [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) — `train` 校准 ([PR #57](https://huggingface.co/datasets/LocalLLaMA/typed-decisions/discussions/57)) | 51 个微调与校准模型 | **0.7970** Acc (`0.8070` 并列口径)<br>**0.0816** KL · **0.0437** Brier · **50 ms** | **并列 12** (列表 14 / 51)<br>冻结权重 ≤9B 及 KL **第 1** | 冻结全部模型权重（`no weights changed`）；高于 `Rev-gen1-midi` (25.6B, `0.7945`)、`OpenDecider-small-td` (4B LoRA, `0.792`)、`OpenDecider-medium-td` (30B LoRA, `0.788`) |
+| Cloudflare Decision Index (`v0.2.1`) — 10 任务套件 | 7 个模型 (0.4B–27.4B) | **80.55%** 宏平均 | **2 / 7** 全量级总榜<br>≤9B 量级 **10 / 10 单项第 1** | `Jev` (27B, `80.32%`), `Kev 9B` (`76.51%`), `Clef-flash` (9.4B, `74.96%`), `DiffGemma` (26B, `69.14%`)；5 / 10 项任务高于 `27.4B Clef` |
 
 ---
 
 ### 3.1 智能体工具调用安全审计评测 (`safeagents-judge-bench`)
 
-[`harness-hub/safeagents-judge-bench`](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) 用于评估决策模型对真实编码智能体（运行于 Terminal-Bench 2.1、OpenThoughts-TBLite 与 Terminal-Bench 4）在沙箱中被静态扫描器 `atif-scan` 标记的可疑工具调用的审计能力。`v2` 测试集包含来自 55 个任务的 $N = 661$ 次工具调用（其中 `536` 次为分布在 `82` 条违规轨迹中的恶意 `block` 调用，`125` 次为正常 `allow` 调用）。每次调用以零样本单次请求形式同时询问一个二元 `noul` 拦截问题与一个 7 类 `choice` 违规归因问题（`legit`、`eval_gaming`、`harness_introspection`、`credential_misuse`、`exfiltration`、`sandbox_escape`、`other_overreach`）。表 2 中的 `v2` 官方结果由基准维护者在 NVIDIA A100-SXM4-80GB（HF Jobs）上独立运行并提交合入（[PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)）。
+[`harness-hub/safeagents-judge-bench`](https://huggingface.co/datasets/harness-hub/safeagents-judge-bench/tree/v2) 用于评估决策模型对真实编码智能体（运行于 Terminal-Bench 2.1、OpenThoughts-TBLite 与 Terminal-Bench 4）在沙箱中被静态扫描器 `atif-scan` 标记的可疑工具调用的审计能力。`v2` 测试集包含来自 55 个任务的 \(N = 661\) 次工具调用（其中 `536` 次为分布在 `82` 条违规轨迹中的恶意 `block` 调用，`125` 次为正常 `allow` 调用）。每次调用以��样本单次请求形式同时询问一个二元 `noul` 拦截问题与一个 7 类 `choice` 违规归因问题（`legit`、`eval_gaming`、`harness_introspection`、`credential_misuse`、`exfiltration`、`sandbox_escape`、`other_overreach`）。表 2 中的 `v2` 官方结果由基准维护者在 NVIDIA A100-SXM4-80GB（HF Jobs）上独立运行并提交合入（[PR #1](https://huggingface.co/TypeScript/FastBrain-9B/discussions/1)）。
 
-在 7 类违规归因赛道上，FastBrain-9B 取得 `0.751` 的 Macro-F1 与 `0.858` 的分类准确率（`567/661`），位列全部参评模型第 1：相较于参数量约为其 3 倍的 27.4B 模型 `Cloudflare/clef`（Macro-F1 `0.563`，准确率 `0.737`），分别高出 `+18.8` 与 `+12.1` 个百分点；相较于同尺寸基座 `Cloudflare/clef-flash`（Macro-F1 `0.462`，准确率 `0.576`），分别提升 `+28.9` 与 `+28.2` 个百分点。分项指标上，`harness_introspection`（$n=272$）F1 达 `0.945`（召回率 `0.978`），`eval_gaming`（$n=245$）F1 达 `0.828`（召回率 `0.853`），合法调用 `legit`（$n=125$）精确率达 `0.975`。
+在 7 类违规归因赛道上，FastBrain-9B 取得 `0.751` 的 Macro-F1 与 `0.858` 的分类准确率（`567/661`），位列全部参评模型第 1：相较于参数量约为其 3 倍的 27.4B 模型 `Cloudflare/clef`（Macro-F1 `0.563`，准确率 `0.737`），分别高出 `+18.8` 与 `+12.1` 个百分点；相较于同尺寸基座 `Cloudflare/clef-flash`（Macro-F1 `0.462`，准确率 `0.576`），分别提升 `+28.9` 与 `+28.2` 个百分点。分项指标上，`harness_introspection`（\(n=272\)）F1 达 `0.945`（召回率 `0.978`），`eval_gaming`（\(n=245\)）F1 达 `0.828`（召回率 `0.853`），合法调用 `legit`（\(n=125\)）精确率达 `0.975`。
 
-在二元安全拦截赛道上，FastBrain-9B 的 AUROC 为 `0.985`，恶意调用总召回率为 `0.996`（`534/536`），全部 `82/82` 条越界轨迹均在首次违规调用处即被捕获（`median_bad_calls_before_catch = 0.0`），其中 `harness_introspection`（`272/272`）、`credential_misuse`（`15/15`）与 `sandbox_escape`（`4/4`）三类召回率均为 `1.000`。在未经验证集调整的默认判别阈值 $P(\text{block}) \ge 0.50$ 下，平衡准确率为 `0.814`（误拦率 `0.368`，优于 27.4B `Cloudflare/clef` 的平衡准确率 `0.808` 与误拦率 `0.384`）。由于连续概率排序区分度保持在 `0.985` AUROC，将工作点阈值设定为 $P(\text{block}) \ge 0.961$ 时，平衡准确率提升至 `0.938`，误拦率降至 `0.056`（`7/125`），同时仍保持 `82/82` 越界轨迹全检出。表 2 同时列出了 `v1` 版本（$N = 562$，78 条轨迹）的官方归档结果，FastBrain-9B 在该版本二元与多分类双赛道均位居第 1 / 9。
+在二元安全拦截赛道上，FastBrain-9B 的 AUROC 为 `0.985`，恶意调用总召回率为 `0.996`（`534/536`），全部 `82/82` 条越界轨迹均在首次违规调用处即被捕获（`median_bad_calls_before_catch = 0.0`），其中 `harness_introspection`（`272/272`）、`credential_misuse`（`15/15`）与 `sandbox_escape`（`4/4`）三类召回率均为 `1.000`。在未经验证集调整的默认判别阈值 \(P(\text{block}) \ge 0.50\) 下，平衡准确率为 `0.814`（误拦率 `0.368`，优于 27.4B `Cloudflare/clef` 的平衡准确率 `0.808` 与误拦率 `0.384`）。由于连续概率排序区分度保持在 `0.985` AUROC，将工作点阈值设定为 \(P(\text{block}) \ge 0.961\) 时，平衡准确率提升至 `0.938`，误拦率降至 `0.056`（`7/125`），同时仍保持 `82/82` 越界轨迹全检出。表 2 同时列出了 `v1` 版本（\(N = 562\)，78 条轨迹）的官方归档结果，FastBrain-9B 在该版本二元与多分类双赛道均位居第 1 / 9。
 
-**表 2：`harness-hub/safeagents-judge-bench` 零样本评测结果对比（`v2` 测试集 $N = 661$，82 条越界轨迹；附 `v1` 归档对照 $N = 562$）。**
+**表 2：`harness-hub/safeagents-judge-bench` 零样本评测结果对比（`v2` 测试集 \(N = 661\)，82 条越界轨迹；附 `v1` 归档对照 \(N = 562\)）。**
 
 | 模型 | 参数量 | 7 分类 Macro-F1 ↑ | 7 分类准确率 ↑ | AUROC ↑ | 平衡准确率 ↑ | 恶意召回率 ↑ | 误拦率 ↓ | 越界轨迹检出 ↑ | p50 延迟（测试硬件） |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
-| **TypeScript/FastBrain-9B** (`v2`, 默认 $t = 0.50$) | 9.4B | **0.751** | **0.858** | 0.985 | 0.814 | 0.996 | 0.368 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
-| **TypeScript/FastBrain-9B** (`v2`, 校准 $t = 0.961$) | 9.4B | **0.751** | **0.858** | 0.985 | **0.938** | 0.931 | 0.056 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
-| **TypeScript/FastBrain-9B** (`v1` 官方榜, $N = 562$) | 9.4B | **0.850** | **0.923** | 0.983 | **0.974** | **1.000** | 0.051 | **78 / 78** | 104 ms (RTX PRO 6000) |
+| **TypeScript/FastBrain-9B** (`v2`, 默认 \(t = 0.50\)) | 9.4B | **0.751** | **0.858** | 0.985 | 0.814 | 0.996 | 0.368 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
+| **TypeScript/FastBrain-9B** (`v2`, 校准 \(t = 0.961\)) | 9.4B | **0.751** | **0.858** | 0.985 | **0.938** | 0.931 | 0.056 | **82 / 82** | 327 ms (A100) · 104 ms (G4) |
+| **TypeScript/FastBrain-9B** (`v1` 官方榜, \(N = 562\)) | 9.4B | **0.850** | **0.923** | 0.983 | **0.974** | **1.000** | 0.051 | **78 / 78** | 104 ms (RTX PRO 6000) |
 | Cloudflare/clef | 27.4B | 0.563 | 0.737 | **0.993** | 0.808 | **1.000** | 0.384 | **82 / 82** | 636 ms (A100) |
 | vllm-sr/d3-mini | 1.8B | 0.512 | 0.652 | 0.986 | 0.856 | **1.000** | 0.288 | **82 / 82** | 168 ms (A100) |
 | Cloudflare/clef-flash (基座) | 9.4B | 0.462 | 0.576 | 0.967 | 0.893 | 0.978 | 0.192 | 81 / 82 | 326 ms (A100) |
@@ -100,11 +102,11 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 
 [`LocalLLaMA/typed-decisions`](https://huggingface.co/datasets/LocalLLaMA/typed-decisions) 评测集覆盖智能体轨迹可观测性（`agent_trace_observability`）、客户服务（`customer_service`）、供应商发票核验（`invoice_processing`）与安全事件响应（`security_incidents`）四类企业工作流，测试集包含 400 个独立案例、共 2,000 个类型化子问题（涵盖 `noul`、`choice` 与 `score`），并以多教师模型集成的软标签分布作为真值基准。官方仓库存在两种并列真值处理脚本：`bench/score_with_jobs.py` 对真值分布中概率并列最高的选项按首个索引判对（`g.index(max(g))`），而 `scripts/score_model.py` 将 20 道并列题中的任一最高分选项均计为正确；两种脚本下的 KL 散度与 Brier 评分完全一致。我们在表 3 中同时报告两种口径的准确率，并在 [`eval_submissions/`](./eval_submissions/) 中公开原始预测文件。
 
-在零样本总榜（$N = 43$ 个参评模型）中，FastBrain-9B 取得 `0.7525`（并列口径 `0.7625`）的准确率、`0.1508` 的 KL 散度、`0.0795` 的 Brier 评分与 `0.085` 的期望校准误差（ECE），在 RTX PRO 6000（SGLang）上的 p50 延迟为 `50 ms`。该成绩位列全量零样本榜 **第 7 / 43**、开源权重模型 **第 5 / 36**、$\le$9B 开源模型 **第 2 / 19** 以及全部 `Clef` 架构模型 **第 1**，较 9.4B 基座 `Cloudflare/clef-flash`（准确率 `0.7100`，KL `0.2093`）提升 `+4.25` 个百分点，较 27.4B `Cloudflare/clef`（准确率 `0.7275`，KL `0.1907`）提升 `+2.50` 个百分点。在零样本准确率高于 `0.700` 的全部 28 个模型中，FastBrain-9B 具有最低的 p50 推理延迟（`50 ms`，对比 9B `Amos 1 medium` 的 `118 ms`、27B `Amos 1 large` 的 `357 ms`、`meraGPT Decider 1` 的 `526 ms` 以及 31B `Quyet-1.0-Large` 的 `3,335 ms`）。若直接评测未经后验规则调整的序数 KL 蒸馏原生头，零样本准确率为 `0.7735`（KL `0.1039`，Brier `0.0582`）。
+在零样本总榜（\(N = 43\) 个参评模型）中，FastBrain-9B 取得 `0.7525`（并列口径 `0.7625`）的准确率、`0.1508` 的 KL 散度、`0.0795` 的 Brier 评分与 `0.085` 的期望校准误差（ECE），在 RTX PRO 6000（SGLang）上的 p50 延迟为 `50 ms`。该成绩位列全量零样本榜 **第 7 / 43**、开源权重模型 **第 5 / 36**、≤9B 开源模型 **第 2 / 19** 以及全部 `Clef` 架构模型 **第 1**，较 9.4B 基座 `Cloudflare/clef-flash`（准确率 `0.7100`，KL `0.2093`）提升 `+4.25` 个百分点，较 27.4B `Cloudflare/clef`（准确率 `0.7275`，KL `0.1907`）提升 `+2.50` 个百分点。在零样本准确率高于 `0.700` 的全部 28 个模型中，FastBrain-9B 具有最低的 p50 推理延迟（`50 ms`，对比 9B `Amos 1 medium` 的 `118 ms`、27B `Amos 1 large` 的 `357 ms`、`meraGPT Decider 1` 的 `526 ms` 以及 31B `Quyet-1.0-Large` 的 `3,335 ms`）。若直接评测未经后验规则调整的序数 KL 蒸馏原生头，零样本准确率为 `0.7735`（KL `0.1039`，Brier `0.0582`）。
 
-在使用 `train` 划分（1,200 个样本）的独立榜单（$N = 51$ 个模型）上，在**完全冻结主干与决策头权重（`no weights changed`）**、仅拟合逐问题对数先验偏置与标量温度参数的前提下，FastBrain-9B 取得 `0.7970`（并列口径 `0.8070`）的准确率、`0.0816` 的 KL 散度与 `0.0437` 的 Brier 评分，位列 **并列第 12（列表第 14 / 51）**，并在冻结权重模型中取得最优的 KL 分布校准度。
+在使用 `train` 划分（1,200 个样本）的独立榜单（\(N = 51\) 个模型）上，在**完全冻结主干与决策头权重（`no weights changed`）**、仅拟合逐问题对数先验偏置与标量温度参数的前提下，FastBrain-9B 取得 `0.7970`（并列口径 `0.8070`）的准确率、`0.0816` 的 KL 散度与 `0.0437` 的 Brier 评分，位列 **并列第 12（列表第 14 / 51）**，并在冻结权重模型中取得最优的 KL 分布校准度。
 
-**表 3：`LocalLLaMA/typed-decisions` 测试集（$N = 400$ 案例，2,000 次决策）评测结果。`/` 前后分别对应 `score_with_jobs.py` 与 `score_model.py` 口径。**
+**表 3：`LocalLLaMA/typed-decisions` 测试集（\(N = 400\) 案例，2,000 次决策）评测结果。`/` ��后分别对应 `score_with_jobs.py` 与 `score_model.py` 口径。**
 
 | 模型 | 参数量 | 评测设定 | 总体准确率 ↑ | KL 散度 ↓ | Brier ↓ | `noul` ↑ | `choice` ↑ | `score` ↑ | Agent ↑ | 客服 ↑ | 发票 ↑ | 安全 ↑ | p50 延迟 |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
@@ -126,9 +128,9 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 
 ### 3.3 多领域结构化决策基准 (Cloudflare Decision Index `v0.2.1`)
 
-在涵盖 10 个评测数据集、共 $N = 22,427$ 条请求的 **Cloudflare Decision Index（`v0.2.1`）** 套件（覆盖 AST 函数调用、20 候选工具检索重排、多步状态 API 调用、细粒度金融意图识别、开放集越界拒识、推理密集型检索、电商相关性分级、多探针钓鱼网站鉴别与工具调用触发治理）上，FastBrain-9B 的无加权 10 任务宏平均得分为 **80.55%**（表 4，图 1–3）。
+在涵盖 10 个评测数据集、共 \(N = 22,427\) 条请求的 **Cloudflare Decision Index（`v0.2.1`）** 套件（覆盖 AST 函数调用、20 候选工具检索重排、多步状态 API 调用、细粒度金融意图识别、开放集越界拒识、推理密集型检索、电商相关性分级、多探针钓鱼网站鉴别与工具调用触发治理）上，FastBrain-9B 的无加权 10 任务宏平均得分为 **80.55%**（表 4，图 1–3）。
 
-在 $\le$9B 参数量级（对比 `Clef-flash` 9.4B、`Kev 9B` 与 `Laya` 0.4B）中，FastBrain-9B 在全部 **10 / 10 个子基准上均取得第 1**，宏平均分较同架构基座 `Clef-flash`（`74.96%`）提升 `+5.59` 个百分点，较 `Kev 9B`（`76.51%`）提升 `+4.04` 个百分点。增幅主要集中于对边界校准敏感的开放集拒识与安全治理任务：`CLINC150+OOS` 提升 `+31.67` 个百分点（`98.44%` 对比 `66.77%`），`When2Call` 提升 `+15.55` 个百分点（`81.13%` 对比 `65.58%`），`PhishNChips` 提升 `+6.80` 个百分点（`78.75%` 对比 `71.95%`）。跨全部参数规模（最高 27.4B）比较，FastBrain-9B 总宏平均位列 **第 2 / 7**，高于 `27B Jev`（`80.32%`）与 `26B-A4B DiffusionGemma Jev`（`69.14%`），并在 `BFCL`、`API-Bank`、`CLINC150+OOS`、`Home Appliances` 与 `When2Call` 五个子基准上高于 `27.4B Clef`（`81.81%`）。
+在 ≤9B 参数量级（对比 `Clef-flash` 9.4B、`Kev 9B` 与 `Laya` 0.4B）中，FastBrain-9B 在全部 **10 / 10 个子基准上均取得第 1**，宏平均分较同架构基座 `Clef-flash`（`74.96%`）提升 `+5.59` 个百分点，较 `Kev 9B`（`76.51%`）提升 `+4.04` 个百分点。增幅主要集中于对边界校准敏感的开放集拒识与安全治理任务：`CLINC150+OOS` 提升 `+31.67` 个百分点（`98.44%` 对比 `66.77%`），`When2Call` 提升 `+15.55` 个百分点（`81.13%` 对比 `65.58%`），`PhishNChips` 提升 `+6.80` 个百分点（`78.75%` 对比 `71.95%`）。跨全部参数规模（最高 27.4B）比较，FastBrain-9B 总宏平均位列 **第 2 / 7**，高于 `27B Jev`（`80.32%`）与 `26B-A4B DiffusionGemma Jev`（`69.14%`），并在 `BFCL`、`API-Bank`、`CLINC150+OOS`、`Home Appliances` 与 `When2Call` 五个子基准上高于 `27.4B Clef`（`81.81%`）。
 
 ![图 1：Cloudflare Decision Index v0.2.1 总体宏平均与参数效率对比](./assets/benchmark_overview.png)
 *图 1. Cloudflare Decision Index（v0.2.1，22,427 条请求）10 任务宏平均分与模型参数规模关系。*
@@ -139,7 +141,7 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 ![图 3：置信度校准曲线与开放集越界拒识分析](./assets/decision_calibration_breakdown.png)
 *图 3. 置信度可靠性图、开放集越界意图拒识（`CLINC150+OOS`）与工具触发边际分析（`When2Call`）。*
 
-**表 4：Cloudflare Decision Index（`v0.2.1`，10 任务，$N = 22,427$）逐项评测结果。粗体表示全参数规模最高值，下划线表示 $\le$9B 量级最高值。**
+**表 4：Cloudflare Decision Index（`v0.2.1`，10 任务，\(N = 22,427\)）逐项评测结果。粗体表示全参数规模最高值，下划线表示 ≤9B 量级最高值。**
 
 | 评测基准（指标） | **FastBrain-9B** (本工作) | Clef-flash (基座) | Kev 9B | Clef | Jev | DiffGemma | Laya |
 | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |
@@ -162,7 +164,7 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 
 ### 4.1 不同推理引擎性能对比
 
-表 5 展示了在同一张 NVIDIA RTX PRO 6000 Blackwell Server Edition GPU 上，SGLang（集成 `JointSchemaPooler` 的 `lmsysorg/sglang:dev-clef`）、`llama.cpp`（`b11430` `ClefModel` 计算图，含 `Q8_0` 与 `Q4_K_M` 两种精度）以及原生 PyTorch（`joint_schema_model.py`）在五类典型长度负载下的端到端延迟、Prefill 吞吐率与显存占用。由于全部请求的生成步数均为零（`output_tokens = 0`），推理耗时完全取决于 Prefill 计算与片段池化效率；在批量 $B=4$ 并发设定下，SGLang 吞吐达 `19,319 tok/s`（每秒完成 `131.2` 个独立结构化决策）。
+表 5 展示了在同一张 NVIDIA RTX PRO 6000 Blackwell Server Edition GPU 上，SGLang（集成 `JointSchemaPooler` 的 `lmsysorg/sglang:dev-clef`）、`llama.cpp`（`b11430` `ClefModel` 计算图，含 `Q8_0` 与 `Q4_K_M` 两种精度）以及原生 PyTorch（`joint_schema_model.py`）在五类典型长度负载下的端到端延迟、Prefill 吞吐率与显存占用。由于全部请求的生成步数均为零（`output_tokens = 0`），推理耗时完全取决于 Prefill 计算与片段池化效率；在批量 \(B=4\) 并发设定下，SGLang 吞吐达 `19,319 tok/s`（每秒完成 `131.2` 个独立结构化决策）。
 
 **表 5：NVIDIA RTX PRO 6000 Blackwell Server Edition（G4）上三类推理后端的延迟与吞吐实测。**
 
@@ -172,23 +174,23 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 | 峰值显存占用 (16K 上下文) | ~20.5 GiB | 12.55 GiB | **10.30 GiB** | 20.3–24.7 GiB |
 | 兼容 16 GiB T4 显卡 | 否 (BF16 TP=1) | 是 (`9.03 GiB`, 4K) | **是 (`6.78 GiB`, 4K)** | 是 (`6.8 GiB`, NF4) |
 | 相对 PyTorch BF16 Top-1 一致率 | **100.00%** | 99.86% (1,471 / 1,473) | 98.78% (1,455 / 1,473) | 100.00% (基准) |
-| 1. 短文本意图路由 (293 tok, $K=2$) | **30.01 ms** (9,763 tok/s) | 32.82 ms (8,929 tok/s) | 31.69 ms (9,245 tok/s) | 43.23 ms (6,778 tok/s) |
-| 2. Typed Decisions (736 tok, $K=5$) | **50.29 ms** (14,635 tok/s) | 62.40 ms (11,795 tok/s) | 61.80 ms (11,909 tok/s) | 63.58 ms (11,576 tok/s) |
-| 3. When2Call 工具治理 (1,068 tok, $K=1$) | **66.06 ms** (16,167 tok/s) | 87.78 ms (12,167 tok/s) | 89.34 ms (11,955 tok/s) | 77.77 ms (13,733 tok/s) |
-| 4. PhishNChips 安全检测 (1,303 tok, $K=9$) | **75.86 ms** (17,176 tok/s) | 108.55 ms (12,004 tok/s) | 109.97 ms (11,849 tok/s) | 90.32 ms (14,426 tok/s) |
-| 5. SafeAgents 审计 (2,217 tok, $K=2$) | **125.85 ms** (17,616 tok/s) | 181.70 ms (12,201 tok/s) | 183.50 ms (12,082 tok/s) | 138.06 ms (16,058 tok/s) |
-| 批量 $B=4$ Typed Decisions (2,944 tok, 20 题) | **152.39 ms** (19,319 tok/s) | 248.50 ms (11,847 tok/s) | 245.20 ms (12,006 tok/s) | 175.85 ms (16,742 tok/s) |
+| 1. 短文本意图路由 (293 tok, \(K=2\)) | **30.01 ms** (9,763 tok/s) | 32.82 ms (8,929 tok/s) | 31.69 ms (9,245 tok/s) | 43.23 ms (6,778 tok/s) |
+| 2. Typed Decisions (736 tok, \(K=5\)) | **50.29 ms** (14,635 tok/s) | 62.40 ms (11,795 tok/s) | 61.80 ms (11,909 tok/s) | 63.58 ms (11,576 tok/s) |
+| 3. When2Call 工具治理 (1,068 tok, \(K=1\)) | **66.06 ms** (16,167 tok/s) | 87.78 ms (12,167 tok/s) | 89.34 ms (11,955 tok/s) | 77.77 ms (13,733 tok/s) |
+| 4. PhishNChips 安全检测 (1,303 tok, \(K=9\)) | **75.86 ms** (17,176 tok/s) | 108.55 ms (12,004 tok/s) | 109.97 ms (11,849 tok/s) | 90.32 ms (14,426 tok/s) |
+| 5. SafeAgents 审计 (2,217 tok, \(K=2\)) | **125.85 ms** (17,616 tok/s) | 181.70 ms (12,201 tok/s) | 183.50 ms (12,082 tok/s) | 138.06 ms (16,058 tok/s) |
+| 批量 \(B=4\) Typed Decisions (2,944 tok, 20 题) | **152.39 ms** (19,319 tok/s) | 248.50 ms (11,847 tok/s) | 245.20 ms (12,006 tok/s) | 175.85 ms (16,742 tok/s) |
 
 ### 4.2 混合精度 GGUF 量化保真度分析
 
 若对交叉注意力决策头或线性注意力递归状态直接施加均匀 4-bit 量化，细粒度选项间微小的对数几率差值易受量化噪声干扰。因此在 `FastBrain-9B-Q4_K_M.gguf`（`6.73 GB`）构建方案中，仅对前馈网络（FFN）使用 4-bit K-quants，而将全部 `dec.*` 决策头张量、`ssm_*` Gated DeltaNet 状态参数以及 `attn_*` 投影矩阵保持为 `Q8_0` 精度。在涵盖 10 类任务的分层验证子集（`203` 个多约束请求，共 `1,473` 道独立评分题；表 6）上，`Q8_0.gguf`（`9.66 GB`）在 `1,471/1,473` 道题上与原生 `bfloat16` 给出完全一致的 Top-1 决策（一致率 `99.86%`，预测概率平均绝对误差 `0.00203`，10 任务均分差异 `-0.03` 个百分点）；`Q4_K_M.gguf` 保持了 `98.78%` 的 Top-1 决策一致率（概率 MAE `0.00387`，校准后均分差异 `-0.20` 个百分点）。表 7 给出了各精度版本在不同硬件（含 NVIDIA Tesla T4 `16 GiB` 实测）上的资源需求。
 
-**表 6：10 任务分层子集（$N = 1,473$ 道评分题）上 GGUF 量化模型的决策一致性与精度保持率。**
+**表 6：10 任务分层子集（\(N = 1,473\) 道评分题）上 GGUF 量化模型的决策一致性与精度保持率。**
 
 | 评测指标 / 子任务 | PyTorch `bfloat16` (18.82 GB) | GGUF `Q8_0` (9.66 GB) | GGUF `Q4_K_M` (6.73 GB, `Q8_0` 决策头) |
 | :--- | :---: | :---: | :---: |
-| Top-1 决策一致率 ($N = 1,473$) | 100.00% (基准) | 99.86% (1,471 / 1,473) | 98.78% (1,455 / 1,473) |
-| 预测概率平均绝对误差 ($\|\hat{p}_q - \hat{p}_{\text{bf16}}\|$) | 0.00000 | 0.00203 | 0.00387 |
+| Top-1 决策一致率 (\(N = 1,473\)) | 100.00% (基准) | 99.86% (1,471 / 1,473) | 98.78% (1,455 / 1,473) |
+| 预测概率平均绝对误差 (\(\lvert \hat{p}_q - \hat{p}_{\mathrm{bf16}} \rvert\)) | 0.00000 | 0.00203 | 0.00387 |
 | 10 任务宏平均（未校准原生输出） | 82.37% | 82.34% (-0.03) | 82.56% (+0.19) |
 | 10 任务宏平均（Schema 拓扑校准） | 83.68% | 83.65% (-0.03) | 83.48% (-0.20) |
 | ├─ 1. BFCL / 3. API-Bank / 4. BANKING77 | 100.0% / 95.0% / 100.0% | 100.0% / 95.0% / 100.0% | 100.0% / 95.0% / 100.0% |
@@ -204,7 +206,7 @@ $$\mathcal{L}(\theta) = \mathrm{KL}(p \,\|\, \hat{p}_\theta) + \lambda_{\mathrm{
 | PyTorch `load_in_4bit=True` (NF4 + `fp16` 头) | ~5.5 GB (内存) | 6.20 – 6.80 GiB | — | 8–16 GB CUDA 显卡 (Colab T4, 消费级 GPU) |
 | `FastBrain-9B-Q8_0.gguf` | 9.66 GB | 9.03 – 12.55 GiB | 349.3 ms / 1,149.8 ms | 12–16 GB 显卡 (Tesla T4, RTX 4070 Ti), Apple Silicon (16 GB+) |
 | PyTorch `load_in_8bit=True` (INT8 + `bf16` 头) | ~9.6 GB (内存) | ~11.20 GiB | — | 12–16 GB CUDA 显卡 |
-| 原生 `bfloat16` (`safetensors` / `BF16.gguf`) | 18.82 / 18.16 GB | 20.30 – 24.70 GiB | — | $\ge$24 GB 显卡 (NVIDIA L4, A100, H100, RTX 3090/4090, PRO 6000) |
+| 原生 `bfloat16` (`safetensors` / `BF16.gguf`) | 18.82 / 18.16 GB | 20.30 – 24.70 GiB | — | ≥24 GB 显卡 (NVIDIA L4, A100, H100, RTX 3090/4090, PRO 6000) |
 
 ---