Probing the Origins of Reasoning Performance: Representational Quality for Mathematical Problem-Solving in RL vs. SFT Fine-Tuned Models

Large reasoning models trained via reinforcement learning (RL) have been increasingly shown to outperform their supervised fine-tuned (SFT) counterparts on mathematical reasoning tasks; Yet the mechanistic basis for this advantage remains unclear. We therefore ask, what internal representational differences enable RL models' superior performance? Our work presents two converging lines of evidence: First, linear probes trained on layer-wise hidden states reveal that RL models tend to achieve higher accuracy in predicting answer correctness compared to SFT models, indicating more linearly separable and structured representations. Second, mean ablation studies show that RL models develop a hierarchical architecture where deeper layers become progressively more critical, whereas SFT models distribute importance uniformly across layers. Together, these findings demonstrate that RL training fundamentally restructures how models represent and process reasoning problems. Finally, we analyze token-count variability under repeated sampling across problems to assess adaptive compute allocation. While we observe higher variability in some RL-tuned models than in their SFT counterparts, we see strong consistency in others, suggesting that token allocation may depend more on the overall training pipeline than on RL versus SFT alone. We believe this token-allocation variability reveals the spread of plausible on-policy reasoning, highlighting which models exhibit stable policies versus those that are under-determined, potentially non-identifiable solution behaviour.

LegalHalluLens: Typed Hallucination Auditing and Calibrated Multi-Agent Debate for Trustworthy Legal AI

AI systems deployed in legal workflows hallucinate at rates that aggregate metrics report at ~52%, but this average conceals where errors concentrate and in which direction they run, leaving compliance officers without an actionable signal for trustworthy deployment. We present LegalHalluLens, an auditing framework with three components: typed hallucination profiles across four legally-motivated claim categories (numeric, temporal, obligation/entitlement, factual) over CUAD (Hendrycks et al., 2021); a Risk Direction Index (RDI) that reduces omission-versus-invention bias to a single deployment-comparable scalar; and a typed debate pipeline calibrated to both magnitudes and directions. Across 510 contracts and 249,252 clause-level instances we measure a within-model gap of approximately 38-40 pp between obligation/numeric and temporal claims that aggregate reporting hides, and show that two systems with matched 52% rates can carry opposite RDIs. The debate pipeline reduces fabricated detections by 45% with per-category gains tracking the diagnosis, matching commercial APIs with a substantially smaller backbone (4B active parameters). Typed profiles and RDI surface failure modes that aggregate metrics hide; we further show these diagnostics serve as calibration inputs for multi-agent debate pipelines, where Skeptic challenges and asymmetric gates targeted at measured failure modes outperform generically-tuned debate. The framework supports direction-aware procurement, accountability, and agent design for legal AI deployed in the wild.