Learning through Internalization

2026-06-18

AI Summary

This work investigates how neural networks internalize explicit computational procedures into their weights through chain-of-thought (CoT) supervision and examines the implications of this internalization for out-of-distribution generalization. Focusing on the parity learning task, the study provides the first provable analysis of internalization: a single-layer simplified Transformer, guided by CoT, first learns the target function and subsequently internalizes it autoregressively as CoT tokens are gradually removed, enabling direct computation of the parity function. Both theoretical and empirical results demonstrate that the task is nearly impossible to learn from data alone without CoT supervision. While internalization preserves in-distribution performance, it substantially degrades out-of-distribution generalization, revealing an intrinsic trade-off between internalization and robustness to distributional shift.

Abstract

We study internalization processes, by which neural-network-based systems absorb an explicit computational procedure into their own weights, and how they facilitate learning. We investigate how transformers internalize the simulation of semiautomata by internalizing chain-of-thought (CoT) tokens, which classes of semiautomata are harder to internalize, and expose the flip side of internalization, that is, a progressive degradation of out-of-distribution performance. We then provide the first provable analysis of successful internalization: for the task of learning parities, we show that a simplified one-layer transformer provably first learns the target with explicit CoT supervision and then internalizes the autoregressive generation as CoT tokens are progressively removed, learning to directly compute the parity. This task is computationally hard to learn from data without CoT supervision. Finally, we discuss how learning through internalization relates to the \textit{Positive Distribution Shift} phenomenon recently introduced by~\citet{Med+26}.

Problem

• internalization
• transformers
• semiautomata
• chain-of-thought
• out-of-distribution performance

Innovation

• internalization
• chain-of-thought
• transformer
• parity learning
• out-of-distribution degradation