Feature Rivalry in Sparse Autoencoder Representations: A Mechanistic Study of Uncertainty-Driven Feature Competition in LLMs

Authors: Harshavardhan

arXiv · PDF

Summary

The authors study "feature rivalry"—negatively correlated pairs of SAE (sparse autoencoder) features—as a mechanistic signature of model uncertainty in Gemma-2-2B. They show that high-entropy questions produce significantly stronger rivalry at specific layers than low-entropy questions, and that steering along the rivalry axis (feature A minus feature B) changes outputs more than random directions. A per-prompt rivalry score predicts answer correctness with AUROC 0.689, approaching but not matching softmax confidence at 0.808.

Main takeaways:

• Feature rivalry is defined as negatively correlated SAE feature pairs; stronger rivalry correlates with higher question entropy (model uncertainty) at layers 0 and 12.
• Activation steering along the rivalry direction (vector_A − vector_B) causes more output changes than random directions, suggesting rivalry is causally upstream of outputs.
• A rivalry score computed from pairwise cosine similarities of active SAE features predicts answer correctness (AUROC 0.689 vs. 0.808 for softmax confidence).
• The results localize uncertainty to specific residual-stream processing stages and suggest SAE features encode uncertainty mechanistically, not just statistically.

Relevance

Directly relevant to my persona and activation-steering work—this shows how SAE feature pairs can encode uncertainty and causally influence outputs, which could connect to how personas or markers compete or leak across contexts in my marker-implantation experiments.

Threat model

Potential threat/caveat for clean result "Random obscure Latin 3-grams don't leak Gaperon-1125-1B's hidden pretraining trigger; leakage seen on famous Latin phrases at ~10% doesn't extend to the obscure-vocab neighborhood (MODERATE confidence)": this item discusses negative.

Abstract

arXiv:2605.08149v1 Announce Type: new Abstract: 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).