MonoLoss: A Training Objective for Interpretable Monosemantic Representations

TL;DR

MonoLoss introduces a new training objective that enhances the interpretability of neural representations by directly encouraging monosemantic features, significantly improving class purity and efficiency in evaluation.

Contribution

The paper proposes MonoLoss, a novel, efficient training objective that directly optimizes monosemanticity in neural representations, enabling more interpretable features and improved performance.

Findings

MonoLoss increases MonoScore across various models and features.

MonoLoss significantly improves class purity of latent representations.

MonoLoss yields up to 0.6% accuracy gains on ImageNet-1K.

Abstract

Sparse autoencoders (SAEs) decompose polysemantic neural representations, where neurons respond to multiple unrelated concepts, into monosemantic features that capture single, interpretable concepts. However, standard training objectives only weakly encourage this decomposition, and existing monosemanticity metrics require pairwise comparisons across all dataset samples, making them inefficient during training and evaluation. We study a recent MonoScore metric and derive a single-pass algorithm that computes exactly the same quantity, but with a cost that grows linearly, rather than quadratically, with the number of dataset images. On OpenImagesV7, we achieve up to a 1200x speedup wall-clock speedup in evaluation and 159x during training, while adding only ~4% per-epoch overhead. This allows us to treat MonoScore as a training signal: we introduce the Monosemanticity Loss (MonoLoss), a plug-in objective that directly rewards semantically consistent activations for learning interpretable monosemantic representations. Across SAEs trained on CLIP, SigLIP2, and pretrained ViT features, using BatchTopK, TopK, and JumpReLU SAEs, MonoLoss increases MonoScore for most latents. MonoLoss also consistently improves class purity (the fraction of a latent's activating images belonging to its dominant class) across all encoder and SAE combinations, with the largest gain raising baseline purity from 0.152 to 0.723. Used as an auxiliary regularizer during ResNet-50 and CLIP-ViT-B/32 finetuning, MonoLoss yields up to 0.6\% accuracy gains on ImageNet-1K and monosemantic activating patterns on standard benchmark datasets. The code is publicly available at https://github.com/AtlasAnalyticsLab/MonoLoss.