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The Direction of Ignorance: LLMs Encode and Temper a Unigram Prior

AspireAI community · arXiv
A single direction in the unembedding matrix encodes the unigram distribution of the training corpus, acting as the Bayesian prior a model falls back on when context is thin. The authors report this structure across Llama, Qwen, Gemma and Pythia from 0.4B to 405B parameters, and show that projecting the final prediction state onto it yields a per-token prior loading factor that declines as context becomes more informative. The same projection decomposes the prediction state into a unigram prior and a context-driven likelihood, and the authors use that factor as an inference-time control: reducing it improves Llama-3.2-3B-Instruct on GSM8K, while amplifying it, or applying matched perturbations along random directions, degrades performance. The paper's v2 retitled the work and expanded the analysis, so earlier figures quoted under the old title should be read against the current version.
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