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Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoning

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Chain-of-thought training and analysis · 0 citations (OpenAlex)

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Argues CoT training enables compositional generalization in transformers, with information-theoretic bounds decomposing error into ID/OOD KL terms and a logit-lens/causal-tracing analysis showing a two-stage circuit, validated on synthetic two-hop fact tasks.

Problem

Why and how chain-of-thought training improves generalization to both in-distribution and out-of-distribution compositional reasoning, and how this is realized internally in transformers.

Approach

Frames CoT training as teaching models to compose simpler learned skills; derives an information-theoretic generalization bound that splits into ID and OOD KL-divergence terms, and uses logit lens and causal tracing to show CoT-trained models form a two-stage circuit where intermediate results are resolved at shallower layers.

Key results

• Training with CoT reaches near-perfect ID two-hop accuracy within about 4,000 steps, whereas training without CoT shows delayed grokking on ID and no OOD generalization even after millions of steps.
• CoT-trained models resolve the bridge entity at layer 3 for ID and layer 5 for OOD, while non-CoT models resolve it at layer 5 for ID.
• Noise injected only into the second hop degrades ID and OOD accuracy, with small noise (ratio below 0.2) having little effect, while noise in both hops has a much stronger suppressive effect.

Surprising findings

• A smaller two-hop/one-hop ratio can expedite OOD generalization under CoT training.
• Scaling model size does not qualitatively change generalization; larger models only converge in fewer steps.

Limitations

• Main evidence comes from controlled synthetic fact-composition tasks with a small GPT-2-style model; real-world validation is limited in scope.
• The notion of simpler learned skills is hard to delineate in real-world tasks.
• The OOD bound relies on assumptions such as disjoint-support mixtures and linear combining rules.

Experimental setup

Datasets: synthetic atomic and two-hop fact dataset math word problems

Benchmarks: synthetic ID two-hop test synthetic OOD two-hop test math word problems

Metrics: accuracy

Baselines: training without CoT

Builds on: information-theoretic generalization bounds grokking logit lens causal tracing

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