Measuring chain-of-thought causality by scrambling step order beat the usual perturbation metrics
AspireAI community · arXiv (cs.CL, cs.AI)
RLVR rewards answer correctness, which does not guarantee the chain of thought causally contributed to that answer. Existing causality metrics perturb the CoT by deleting steps or injecting errors, but those perturbations also change the information inside each step, so a high score can reflect sensitivity to injected information rather than true causality. Using such metrics as training rewards also degrades behaviour, producing less informative CoTs and less exploration and self-correction. CRoS perturbs the order of reasoning steps without altering content, preserving information within each step. On Reasoning Gym with Gemma-3-4B, CRoS reaches 46.8 percent accuracy on five unseen logic and games datasets against 43.8 percent for the strongest baseline, and improves chain-of-thought faithfulness, with a hint-acknowledgment score of 34.0 against 20.2 percent. The experiments are on a single 4B model and one reasoning benchmark family.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.