Evidence for feature-specific error correction in LLMs

2026-06-23

AI Summary

This study investigates whether large language models implement feature-specific error correction along privileged directions in their superposition representations to support high-dimensional feature computation. By perturbing residual stream activations, constructing contrastive prompts to isolate pure feature directions, and analyzing perturbation effects through MELBO and SAE decoders in relation to Lᵖ norm decomposition, the work provides the first empirical evidence that genuine feature directions in multiple mainstream large models exhibit robust responses with p > 2—distinct from control directions, which conform to p ≈ 2. This finding indicates a model-intrinsic protective mechanism for critical features, challenging the theoretical limitations of conventional L²-norm-based analyses that fail to account for such privileged high-dimensional representations. The validity of the approach is further corroborated in toy models containing ground-truth features.

Abstract

Understanding the features of large language models (LLMs) is a central goal of interpretability. LLMs are commonly assumed to use superposition to represent more features than they have dimensions. They may not only represent features in superposition but also perform computation in superposition. Theory predicts that computing in superposition requires error correction that privileges feature directions over generic ones, but this prediction has not been tested empirically. We propose an empirical test of error correction in LLMs based on activation perturbations. Perturbing residual-stream activations, we find that they are robust to small perturbations--forming activation plateaus consistent with error correction--but less robust along candidate feature directions ("pure" directions, constructed from contrastive prompt pairs) than along mixtures of two such directions, indicating that the pure directions are privileged. We quantify this privilegedness by modeling the perturbation effect as a function of the $L^p$-norm of its decomposition into feature components. For $p=2$ the response is a quadratic form with at most as many nonzero eigenvalues as the residual-stream dimension, which cannot privilege the many feature directions superposition requires. $p>2$ lifts this constraint and is consistent with feature-specific error correction. We find $p>2$ for contrastive, MELBO, and SAE-decoder directions, and $p\approx2$ for random and PCA directions (controls). These results replicate across Gemma-2-9B, Qwen3-1.7B, Llama-3.1-8B, Mistral-7B-v0.3, Aya-Expanse-8B, and Yi-1.5-9B. We further validate our method on a toy model of error correction with known ground-truth features, recovering $p>2$ for true feature directions, degrading toward $2$ as we rotate away from them.

Problem

• feature-specific error correction
• superposition
• large language models
• activation perturbations
• interpretability

Innovation

• feature-specific error correction
• superposition
• activation perturbation
• L^p-norm analysis
• interpretability