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Dual Operating Modes of In-Context Learning

ICML 2024 · Large language models › Language, safety and interpretability · approach: In-context learning analysis · 1 citations (OpenAlex)

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Proposes a Gaussian-mixture pretraining-data model for linear-regression ICL that yields closed-form Bayes-optimal predictions, explaining task retrieval vs. task learning, the early-ascent phenomenon, and bounded efficacy of biased-label/zero-shot ICL.

Problem

Existing theoretical models of in-context learning cannot fully explain its dual operating modes (task retrieval vs. task learning), the early-ascent risk curve, or the bounded efficacy of biased-label ICL.

Approach

Model pretraining tasks as a Gaussian mixture over linear-regression parameters (with task-dependent input distributions), so the Bayes-optimal next-token predictor has a closed-form Gaussian-mixture posterior; ICL then decomposes into component re-weighting (retrieval) and component shifting (learning).

Key results

• Transformer trained on the Gaussian mixture prior approximates Bayes-optimal prediction across noise levels, component counts and dimensions.
• GPT-4 error on biased addition rises from 33.9% at k=2 to 85.1% (correct-for-biased) at k=16 ... error for biased task drops to 16.8% at k=16 while addition error rises from 33.9% to 85.1%, showing bounded efficacy.
• Predicts and observes bounded efficacy of random-label ICL in larger-context LLMs (Mistral 7B, Mixtral 8x7B, Llama 2, GPT-4) when k exceeds 32.

Measured effects reported in the paper

Surprising findings

• Early ascent: ICL risk first increases then decreases with more in-context examples when the in-context task is misleadingly close to a wrong prior component.
• Zero-shot ICL with random labels shows bounded efficacy: performance degrades at larger numbers of in-context examples, contrary to prior claims that random labels do not matter for k up to 32.

Limitations

• Analysis assumes pretraining tasks are noisy linear regression, not the non-linear, categorical tasks of real LLMs.
• In-context labels are assumed noiseless.
• Assumes an optimally trained next-token predictor on infinite pretraining data, without considering architecture or training statistics.

Experimental setup

Datasets: synthetic linear regression pretraining data from the Gaussian mixture model

Benchmarks: synthetic linear regression ICL biased addition task (GPT-4) random-label ICL in LLMs

Metrics: ICL risk (squared loss) error rate

Baselines: ridge regression Bayes-optimal predictor

Builds on: Garg et al. in-context learning of linear functions Xie et al. implicit Bayesian inference in ICL Min et al. rethinking role of demonstrations

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