# Compositional Generalization

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arXiv Nov 4, 2026
Chain-of-thought solves unseen multi-step tasks by reusing one step predictor, with error growing sublinearly in depth
Chain-of-thought out-of-distribution generalization is framed as compositional generalization: training supplies only single-step atomic transitions, while the target task requires composing many steps. Theory bounds target risk by the sum of step risks times a depth-independent coefficient, and shows that sharing one predictor makes the estimation term shrink as the inverse square root of depth rather than grow linearly. Atom-Task and GSM8K experiments support short-to-long and unseen-combination transfer, and show explicit state tracking is essential.
Chain-of-thought out-of-distribution generalization is framed as compositional generalization: training supplies only single-step atomic transitions, while the target task requires composing many steps. Theory bounds target risk by the sum of step risks times a depth-independent coefficient, and shows that sharing one predictor makes the estimation term shrink as the inverse square root of depth rather than grow linearly. Atom-Task and GSM8K experiments support short-to-long and unseen-combination transfer, and show explicit state tracking is essential.
Nanjing University Singapore Management University
Nuojing Liang（First author）
Chain-of-Thought Out-of-Distribution Generalization Generalization Bounds Compositional Generalization Next-Token Prediction
arXiv Oct 31, 2026
Composed labels beat whole-problem guesses: compositional self-improvement pushes reliable prediction past a model's starting range
Models struggle to generate reliable supervision for harder, out-of-distribution instances, so compositional self-improvement instead predicts simpler subproblems and combines them into labels for full problems, training on those labels repeatedly. Across three controlled algorithmic tasks, composed labels extended reliable prediction beyond the initial range while direct self-improvement gave little or no such extension on addition and grid navigation; program generation and multi-hop reasoning likewise showed composed labels more accurate than direct self-labels, though unreliable components, invalid composition rules and limited coverage cap the gains.
Models struggle to generate reliable supervision for harder, out-of-distribution instances, so compositional self-improvement instead predicts simpler subproblems and combines them into labels for full problems, training on those labels repeatedly. Across three controlled algorithmic tasks, composed labels extended reliable prediction beyond the initial range while direct self-improvement gave little or no such extension on addition and grid navigation; program generation and multi-hop reasoning likewise showed composed labels more accurate than direct self-labels, though unreliable components, invalid composition rules and limited coverage cap the gains.
Changho Shin（First author）
Compositional Self-Improvement Compositional Generalization Reinforcement Learning
arXiv Oct 14, 2026
Language models don't learn in-context all at once: control of the answer flips first, and accuracy catches up trillions of tokens later
Language models do not acquire in-context learning in one step. A controlled diagnostic separates copying the nearest demonstration from composing mappings spread across the prompt; across 17 models about a third prefer the copied answer and the rest the rule-consistent one, and in OLMo-2-7B dependence on the requested value overtakes the conflicting example hundreds of billions of tokens before accuracy rises above chance. Training on synthetic definition-and-query documents flips the preference, while exposure to definitions or suppressing copy-favoring heads does not.
Language models do not acquire in-context learning in one step. A controlled diagnostic separates copying the nearest demonstration from composing mappings spread across the prompt; across 17 models about a third prefer the copied answer and the rest the rule-consistent one, and in OLMo-2-7B dependence on the requested value overtakes the conflicting example hundreds of billions of tokens before accuracy rises above chance. Training on synthetic definition-and-query documents flips the preference, while exposure to definitions or suppressing copy-favoring heads does not.
University of Arizona
Minglai Yang（First author）
In-Context Learning Compositional Generalization Activation Patching Fine-tuning

You’re all caught up

Chain-of-thought solves unseen multi-step tasks by reusing one step predictor, with error growing sublinearly in depth

Composed labels beat whole-problem guesses: compositional self-improvement pushes reliable prediction past a model's starting range

Language models don't learn in-context all at once: control of the answer flips first, and accuracy catches up trillions of tokens later