Your Model Diversity, Not Method, Determines Reasoning Strategy

Compute scaling for LLM reasoning requires allocating budget between exploring solution approaches ($breadth$) and refining promising solutions ($depth$). Most methods implicitly trade off one for the other, yet why a given trade-off works remains unclear, and validation on a single model obscures the role of the model itself. We argue that $\textbf{the optimal strategy depends on the model's diversity profile, the spread of probability mass across solution approaches, and that this must be characterized before any exploration strategy is adopted.}$ We formalize this through a theoretical framework decomposing reasoning uncertainty and derive conditions under which tree-style depth refinement outperforms parallel sampling. We validate it on Qwen-3 4B and Olmo-3 7B families, showing that lightweight signals suffice for depth-based refinement on low-diversity aligned models while yielding limited utility for high-diversity base models, which we hypothesize require stronger compensation for lower exploration coverage.

SPEAR-MM: Selective Parameter Evaluation and Restoration via Model Merging for Efficient Financial LLM Adaptation

Large language models (LLMs) adapted to financial domains often suffer from catastrophic forgetting of general reasoning capabilities essential for customer interactions and complex financial analysis. We introduce Selective Parameter Evaluation and Restoration via Model Merging (SPEAR-MM), a practical framework that preserves critical capabilities while enabling domain adaptation. Our method approximates layer-wise impact on external benchmarks through post-hoc analysis, then selectively freezes or restores transformer layers via spherical interpolation merging. Applied to LLaMA-3.1-8B for financial tasks, SPEAR-MM achieves 91.2% retention of general capabilities versus 69.7% for standard continual pretraining, while maintaining 94% of domain adaptation gains. The approach provides interpretable trade-off control and reduces computational costs by 90% crucial for resource-constrained financial institutions.

Optimizing Reasoning Efficiency through Prompt Difficulty Prediction

Reasoning language models perform well on complex tasks but are costly to deploy due to their size and long reasoning traces. We propose a routing approach that assigns each problem to the smallest model likely to solve it, reducing compute without sacrificing accuracy. Using intermediate representations from s1.1-32B, we train lightweight predictors of problem difficulty or model correctness to guide routing across a pool of reasoning models. On diverse math benchmarks, routing improves efficiency over random assignment and matches s1.1-32B's performance while using significantly less compute. Our results demonstrate that difficulty-aware routing is effective for cost-efficient deployment of reasoning models.

Critique-Guided Distillation: Improving Supervised Fine-tuning via Better Distillation

Supervised fine-tuning (SFT) using expert demonstrations often suffer from the imitation problem, where the model learns to reproduce the correct responses without \emph{understanding} the underlying rationale. To address this limitation, we propose \textsc{Critique-Guided Distillation (CGD)}, a novel multi-stage framework that integrates teacher model generated \emph{explanatory critiques} and \emph{refined responses} into the SFT process. A student model is then trained to map the triplet of prompt, teacher critique, and its own initial response to the corresponding refined teacher response, thereby learning both \emph{what} to imitate and \emph{why}. Using entropy-based analysis, we show that \textsc{CGD} reduces refinement uncertainty and can be interpreted as a Bayesian posterior update. We perform extensive empirical evaluation of \textsc{CGD}, on variety of benchmark tasks, and demonstrate significant gains on both math (AMC23 +17.5%) and language understanding tasks (MMLU-Pro +6.3%), while successfully mitigating the format drift issues observed in previous critique fine-tuning (CFT) techniques.