# Interpretability-Guided Layer Selection over Subspace Projection: SAEs as Stethoscopes, Not Scalpels, for Raw Task Vector Model Editing

arXiv: https://arxiv.org/abs/2605.28649 · HTML: https://mlsanity.com/paper/2605.28649/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 18 of 18)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [Open Problems in Mechanistic Interpretability](https://mlsanity.com/paper/2501.16496/) (2025)
- [Llama Scope: Extracting Millions of Features from Llama-3.1-8B with Sparse Autoencoders](https://mlsanity.com/paper/2410.20526/) (2024)
- [Are Sparse Autoencoders Useful? A Case Study in Sparse Probing](https://mlsanity.com/paper/2502.16681/) (2025)
- [Localize-and-Stitch: Efficient Model Merging via Sparse Task Arithmetic](https://mlsanity.com/paper/2408.13656/) (2024)
- [Into the Rabbit Hull: From Task-Relevant Concepts in DINO to Minkowski Geometry](https://mlsanity.com/paper/2510.08638/) (2025)
- [Priors in Time: Missing Inductive Biases for Language Model Interpretability](https://mlsanity.com/paper/2511.01836/) (2025)
- [Subspace-Boosted Model Merging](https://mlsanity.com/paper/2506.16506/) (2025)
- [Joint Localization and Activation Editing for Low-Resource Fine-Tuning](https://mlsanity.com/paper/2502.01179/) (2025)

## Abstract (arXiv)

LLMs increasingly require surgical model editing to enhance domain-specific capabilities without incurring the computational cost or catastrophic forgetting associated with full fine-tuning. Sparse Autoencoders (SAEs) have emerged as a promising tool in this setting, in principle allowing for feature-level identification of where to intervene. In this work, we rigorously evaluate an SAE-guided editing pipeline for mathematical reasoning on Gemma-3-4B-IT and uncover a fundamental failure mode: the intuitively appealing approach of projecting task vectors onto SAE feature subspaces acts as an information bottleneck that discards approximately 97% of the modification energy, yielding no statistically significant improvements across seven math subjects. We show that this failure stems from a geometric misalignment between activation-space SAE directions and weight-space task vectors. We then propose a shift in perspective: SAE as a Stethoscope, Not a Scalpel, where SAEs are used for layer-level diagnosis rather than intervention-level filtering. By injecting unfiltered raw task vectors only into layers identified by an SAE-derived specificity score, we improve Number Theory accuracy from 29.6% to 39.4% (z=+3.41, p=0.0007) on the Minerva Math benchmark; 5 of 7 math subjects significantly improved and none significantly degraded. Our method is fully deterministic, requires no additional inference cost, and provides a principled framework for interpretability-guided model editing.