EvalQReason: A Framework for Step-Level Reasoning Evaluation in Large Language Models

TL;DR

EvalQReason presents a fully automated, probability-based framework to evaluate LLM reasoning at the step level by analyzing step-by-step logit-derived distributions. It introduces Consecutive Step Divergence (CSD) for local coherence and Step-to-Final Convergence (SFC) for global convergence, quantified via $KL$, $JS$, Hellinger, Cosine Similarity, and Entropy Difference, and demonstrates strong, annotation-free discrimination of correctness, especially in mathematical domains. Across math and medicine, results show domain-specific dynamics: mathematical reasoning exhibits clear divergence-based discrimination between correct and incorrect solutions, while medical reasoning yields weaker signals, highlighting different inference mechanisms. Classical ML and sequential models using these features achieve high accuracy, with sequential architectures delivering substantial gains; EvalQReason also outperforms existing, annotation-dependent evaluation methods, offering scalable, trustworthy AI evaluation.

Abstract

Large Language Models (LLMs) are increasingly deployed in critical applications requiring reliable reasoning, yet their internal reasoning processes remain difficult to evaluate systematically. Existing methods focus on final-answer correctness, providing limited insight into how reasoning unfolds across intermediate steps. We present EvalQReason, a framework that quantifies LLM reasoning quality through step-level probability distribution analysis without requiring human annotation. The framework introduces two complementary algorithms: Consecutive Step Divergence (CSD), which measures local coherence between adjacent reasoning steps, and Step-to-Final Convergence (SFC), which assesses global alignment with final answers. Each algorithm employs five statistical metrics to capture reasoning dynamics. Experiments across mathematical and medical datasets with open-source 7B-parameter models demonstrate that CSD-based features achieve strong predictive performance for correctness classification, with classical machine learning models reaching F1=0.78 and ROC-AUC=0.82, and sequential neural models substantially improving performance (F1=0.88, ROC-AUC=0.97). CSD consistently outperforms SFC, and sequential architectures outperform classical machine learning approaches. Critically, reasoning dynamics prove domain-specific: mathematical reasoning exhibits clear divergence-based discrimination patterns between correct and incorrect solutions, while medical reasoning shows minimal discriminative signals, revealing fundamental differences in how LLMs process different reasoning types. EvalQReason enables scalable, process-aware evaluation of reasoning reliability, establishing probability-based divergence analysis as a principled approach for trustworthy AI deployment.

Figures (11)

• Figure 1: EvalQReason framework architecture.
• Figure 2: Comparison of five statistical metrics for CSD computation on AIME (Qwen2.5-7B). (a) KL Divergence, (b) JS Divergence, (c) Hellinger Distance, (d) Cosine Similarity, and (e) Entropy Difference. Shaded regions: ±1 SD.
• Figure 3: CSD analysis across difficulty levels for the AIME dataset using Qwen2.5-7B with KL Divergence. Panels correspond to Level 1 (Easy), Level 2 (Medium), and Level 3 (Hard).
• Figure 4: Consecutive Step Divergence (CSD) patterns across step-length categories for the Math-500 dataset using Qwen2.5-7B with KL Divergence. Step-length categories are defined by total reasoning steps: Short ($\leq 6$ steps), Medium ($7$--$10$ steps), Long ($\geq 11$ steps).
• Figure 5: Comparison of Consecutive Step Divergence (CSD) and Step-to-Final Convergence (SFC) using KL Divergence across five difficulty levels in the Math-500 dataset with Mathstral-7B. (a) CSD measures local coherence with varying correctness separation. (b) SFC measures global convergence toward the final answer with minimal correctness separation.