When Pruning Breaks Reasoning: Chain-of-Thought Similarity and Faithfulness in Language Models

Pruning large reasoning models for edge deployment degrades performance in ways that standard accuracy metrics systematically fail to detect. We show that the relationship between sparsity and chain-of-thought (CoT) faithfulness is non-monotonic: light pruning ($\leq 5%$) improves reasoning consistency by removing low-magnitude interference, while sparsity beyond $30\%$ triggers catastrophic collapse of logical coherence. To diagnose this behavior, we present ASAND (Adaptive Sparsity-Adjusted Normalized Distance), a geometry-aware similarity metric that jointly models centered weight alignment, structural sparsity, adaptive exponential decay, and weight-distribution volatility. On Qwen-0.5B evaluated across GSM8K and competition-level MATH problems, ASAND achieves PLCC =0.948 and 0.972 respectively, outperforming cosine similarity, $L_1/L_2$ distances, and CKA. These results establish sparsity-aware representational geometry as a necessary lens for safe, reasoning-preserving model compression.