Evidence for feature-specific error correction in LLMs

This paper investigates whether large language models (LLMs) perform computation in superposition—a theoretical framework suggesting that models represent more features than they have dimensions. A key prediction of this theory is that models must implement error correction to prevent interference between these overlapping features. The authors hypothesize that this error correction should be "feature-specific," meaning the model should be more sensitive to perturbations along specific feature directions than to generic mixtures of those directions.

To test this, the researchers developed an empirical method based on activation perturbations. They perturbed the residual-stream activations of several LLMs and measured the downstream impact. By comparing the model's sensitivity to single "pure" candidate feature directions versus mixtures of two such directions, they quantified the model's selectivity. They modeled the response as a function of the Lp-norm of the perturbation's decomposition into these directions, where p > 2 indicates that pure directions are privileged over mixtures.

The authors found consistent evidence of feature-specific error correction across six different LLMs (Gemma-2-9B, Qwen3-1.7B, Llama-3.1-8B, Mistral-7B-v0.3, Aya-Expanse-8B, and Yi-1.5-9B). Specifically, candidate feature directions—including those derived from contrastive prompt pairs, MELBO, and sparse autoencoder (SAE) decoders—consistently yielded exponents of p > 2. In contrast, control directions such as random vectors and PCA components yielded p ≈ 2, indicating no such privileging. The researchers also validated this methodology using a toy model with known ground-truth features, confirming that the exponent degrades toward 2 as directions become misaligned with the true features.

This work provides the first empirical evidence for the existence of feature-specific error correction in LLMs, supporting the hypothesis that these models perform computation in superposition. By demonstrating that the geometry of the model's activation plateaus encodes information about its internal features, the authors provide a new, unsupervised tool for interpretability. This approach allows researchers to identify candidate features without requiring extensive labeled data, offering a deeper understanding of how LLMs manage information within their limited dimensional space.