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Strategy Coopetition Explains the Emergence and Transience of In-Context Learning

ICML 2025 · Architectures and efficiency › Attention and transformers · approach: Transformer expressivity and circuits

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Shows that after ICL transience in a 2-layer attention-only transformer, the asymptotic strategy is context-constrained in-weights learning (CIWL), and that ICL emerges via cooperative sharing of Layer 2 circuits with CIWL, explained by a toy model of strategy coopetition.

Problem

Why in-context learning emerges during training if it is not the asymptotically preferred strategy, and what the asymptotic strategy is after ICL transience disappears.

Approach

Identifies a hybrid asymptotic strategy (CIWL) that requires the correct label in context and in-weights knowledge, and shows ICL and CIWL share Layer 2 circuits so that competition (Layer 1) and cooperation (Layer 2) jointly produce transient ICL ("strategy coopetition"); a toy tensor-product loss model reproduces these dynamics and guides a data change (exact context-query matching) that makes I

Key results

• CIWL becomes the asymptotic strategy (CIWL evaluator 98.7% accuracy at end of training, while ICL transiently emerges and fades).
• Layer 1 ablations show V-composition (drop to 59.3%) and K-composition (drop to 57.5%) into Layer 2, while Layer 2 weights are reused across ICL and CIWL.
• Matching context exemplars to the query (exact match in bursty context) makes ICL persist rather than fade in the small setup, and extends to a larger 12-layer setup.

Measured effects reported in the paper

Surprising findings

• ICL emerges more easily when it is not the only viable strategy: training on ICL-only data from scratch struggles, but reusing Layer 2 weights from a bursty-data run enables rapid ICL emergence.
• The asymptotic strategy is a hybrid (context-constrained in-weights) rather than pure in-weights learning, and pure IWL is negligible.

Limitations

• Main analysis uses a small attention-only 2-layer model on a synthetic Omniglot-based task; MLP variants showed different behavior in some settings.
• The mechanistic explanation of superposition and the divot in CIWL formation are speculative and not fully understood.
• Toy model is minimal and only qualitatively matches the transformer dynamics.

Experimental setup

Datasets: Omniglot ImageNet (ResNet18 pretraining)

Benchmarks: ICL evaluator IWL evaluator CIWL evaluator Flip evaluator (synthetic OOD sets on Omniglot)

Metrics: accuracy in-context accuracy attention delta Flip evaluator accuracy

Baselines: Chan et al. 2022 bursty setup standard training without intervention

Builds on: induction heads Omniglot bursty training (Chan et al. 2022) progress measures minimal phase change model (Saxe et al.)

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• What needs to go right for an induction head? A mechanistic study of in-context learning circuits and their formation (ICML 2024 · similarity 0.89)
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