Prefix-Safe Bayesian Belief Tracking for LLM Reasoning Reliability:Separating Calibration from Ranking

Long reasoning traces need reliability estimates before final answers are known. We study prefix-conditioned eventual-success estimation, $P(y=1 \mid o_{1:t})$, using prefix-safe observations. Sequential Bayesian Belief Tracking (SBBT) calibrates observation likelihoods and recursively updates a two-state belief, providing a common tracker for scalar scores, text and self-verification markers, hidden clusters, token-pooling probes, and latent-trajectory features. Across generated open-weight traces on MATH-500, GSM8K, AIME 2025, and RIMO-N, probability quality and ranking separate: score-only SBBT often improves Brier, while AUROC gains require structure-aware evidence beyond strong prefix-safe baselines. In the strongest hard math setting, structure-aware observations reach +0.110 AUROC against standard prefix-safe baselines. Under a same-prefix classifier audit, MATH-500 text markers and RIMO-N self-verification signals remain positive. Together, these findings support SBBT as a calibration-aware online inference framework and expose an evidence regime: scalar scores mainly support probability quality, while structure-aware prefix signals support ranking only when strong prefix-safe baselines have not already absorbed the rank evidence.

Your Simulation Runs but Solves the Wrong Physics: PDE-Grounded Intent Verification for LLM-Generated Multiphysics Simulation Code

Execution-based evaluation of LLM-generated code implicitly treats successful execution as a proxy for correctness. In scientific simulation, this proxy is insufficient: a generated input file can run, mesh, and converge while encoding governing equations that differ from the user's intent. We call this mismatch between intended physics and generated code the comprehension-generation gap. We instantiate this in MOOSE, where Kernel and BC objects map compositionally to weak-form residual terms, enabling deterministic reconstruction of the encoded PDE and comparison against an intended contract. We formalize this comparison as the Intent Fidelity Score (IFS), a structural metric covering governing terms, BCs, ICs, coefficients, and time scheme. Building on IFS, we develop a PDE-grounded refinement loop that uses deterministic violation reports to correct generated code iteratively. We evaluate on MooseBench, a 220-case multiphysics benchmark with PDE-level ground truth released with this work. On this benchmark, our method consistently improves mean IFS over direct generation, with gains concentrated on hard cases. On the subset where direct generation falls below IFS 0.7, refinement adds +0.22 to +0.41 absolute IFS. In the deployment audit, execution-only repair improves execution success while leaving 39-40% of all 220 cases runnable but still solving the wrong physics across the three main deployment-audit models, exposing executability and intent fidelity as separable failure modes. Static proof-of-concept experiments on four PDE-oriented DSLs (UFL/FEniCS, FreeFEM, FiPy, and Devito) suggest that the reconstruction-and-comparison pattern extends beyond MOOSE. These findings reinforce that executable simulation code should be verified against the mathematical structure it is intended to encode, not accepted on execution alone.

GAST: Gradient-aligned Sparse Tuning of Large Language Models with Data-layer Selection

Parameter-Efficient Fine-Tuning (PEFT) has become a key strategy for adapting large language models, with recent advances in sparse tuning reducing overhead by selectively updating key parameters or subsets of data. Existing approaches generally focus on two distinct paradigms: layer-selective methods aiming to fine-tune critical layers to minimize computational load, and data-selective methods aiming to select effective training subsets to boost training. However, current methods typically overlook the fact that different data points contribute varying degrees to distinct model layers, and they often discard potentially valuable information from data perceived as of low quality. To address these limitations, we propose Gradient-aligned Sparse Tuning (GAST), an innovative method that simultaneously performs selective fine-tuning at both data and layer dimensions as integral components of a unified optimization strategy. GAST specifically targets redundancy in information by employing a layer-sparse strategy that adaptively selects the most impactful data points for each layer, providing a more comprehensive and sophisticated solution than approaches restricted to a single dimension. Experiments demonstrate that GAST consistently outperforms baseline methods, establishing a promising direction for future research in PEFT strategies.