# MonoLoss: A Training Objective for Interpretable Monosemantic Representations

arXiv: https://arxiv.org/abs/2602.12403 · HTML: https://mlsanity.com/paper/2602.12403/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in SAE features and their applications, one of 13 directions in Mechanistic interpretability.
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Placed in

- Mechanistic interpretability / [SAE features and their applications](https://mlsanity.com/mechinterp/sae-features-and-their-applications/)

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [BatchTopK Sparse Autoencoders](https://mlsanity.com/paper/2412.06410/) (2024)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [Sparse Autoencoders Learn Monosemantic Features in Vision-Language Models](https://mlsanity.com/paper/2504.02821/) (2025)
- [Sparse autoencoders reveal selective remapping of visual concepts during adaptation](https://mlsanity.com/paper/2412.05276/) (2024)
- [Efficient Dictionary Learning with Switch Sparse Autoencoders](https://mlsanity.com/paper/2410.08201/) (2024)
- [Disentangling Neuron Representations with Concept Vectors](https://mlsanity.com/paper/2304.09707/) (2023)
- [Residual Stream Analysis with Multi-Layer SAEs](https://mlsanity.com/paper/2409.04185/) (2024)
- [Capturing Polysemanticity with PRISM: A Multi-Concept Feature Description Framework](https://mlsanity.com/paper/2506.15538/) (2025)
- [Measuring and Guiding Monosemanticity](https://mlsanity.com/paper/2506.19382/) (2025)
- [SPARC: Concept-Aligned Sparse Autoencoders for Cross-Model and Cross-Modal Interpretability](https://mlsanity.com/paper/2507.06265/) (2025)
- [AdaptiveK: Complexity-Driven Sparse Autoencoders for Interpretable Language Model Representations](https://mlsanity.com/paper/2508.17320/) (2025)

## Built on by (most cited first, 1 of 1)

- [Size Doesn't Matter: Cosine-Scored Sparse Autoencoders](https://mlsanity.com/paper/2606.15054/) (2026)

## Abstract (arXiv)

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.