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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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.