Are LLM Uncertainty and Correctness Encoded by the Same Features? A Functional Dissociation via Sparse Autoencoders

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.

Large language models (LLMs) generate not only reasoning text, but also token-level confidence trajectories that record how uncertainty evolves during inference. Whether these trajectories are relevant to reasoning correctness remains unclear. Here we show that confidence trajectories encode a content-agnostic confidence geometry associated with trace-level final-answer correctness. Using only token-level confidence values, without access to the input question, reasoning text, hidden states, or external verifiers, we find that low-dimensional representations of confidence trajectories separate correct from incorrect reasoning traces. Across GSM8K, MATH, and MMLU, this geometric separation is quantitatively linked to downstream predictability: stronger clustering of correct and incorrect traces, measured by the Davies--Bouldin index, consistently corresponds to higher correctness-discrimination AUC. We further show that correctness-related information is enriched in the tail of reasoning, suggesting that late-stage confidence dynamics carry key correctness signals. We propose NeuralConf, a lightweight estimator that learns from confidence trajectories for correctness evaluation. Under a fixed trace budget, NeuralConf-derived scores improve confidence-weighted answer aggregation over majority voting, tail confidence, and other static baselines. These results reveal that LLMs expose trace-intrinsic statistical signals of correctness through their own confidence dynamics, offering a route to improve inference using information already present within generation.

Sparse Autoencoders (SAEs) decompose large language model representations into interpretable features, but how these features interact under uncertainty remains poorly understood. We introduce Feature Rivalry -- negatively correlated SAE feature pairs -- and study whether rivalry serves as a mechanistic signature of model uncertainty in Gemma-2-2B using Gemma Scope SAEs. Through a controlled within-domain experiment on PopQA split by response entropy, we find that high-entropy questions produce significantly stronger feature rivalry at layers 0 and 12 relative to low-entropy questions (p=5.3x10^-26 and p=5.8x10^-5 respectively), localizing uncertainty to specific processing stages in the residual stream. We then test whether rivalry is causally upstream of model outputs via activation steering along rivalry axes -- finding that steering along the rivalry direction (vec_A - vec_B) causes more output changes than random directions at low steering multipliers across 15 of 20 rival feature pairs. Finally, a per-prompt rivalry score derived from pairwise cosine similarities of active SAE feature decoder vectors predicts answer correctness (AUROC=0.689), approaching but not matching softmax confidence (AUROC=0.808).