# Where Decoder Cosine Similarity Fails for SAE Feature Flow Discovery

arXiv: https://arxiv.org/abs/2609.12591 · HTML: https://mlsanity.com/paper/2609.12591/

## 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 11 of its 13 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Sparse Autoencoders Trained on the Same Data Learn Different Features](https://mlsanity.com/paper/2501.16615/) (2025)
- [Overcoming Sparsity Artifacts in Crosscoders to Interpret Chat-Tuning](https://mlsanity.com/paper/2504.02922/) (2025)
- [Evolution of SAE Features Across Layers in LLMs](https://mlsanity.com/paper/2410.08869/) (2024)
- [Position: Mechanistic Interpretability Should Prioritize Feature Consistency in SAEs](https://mlsanity.com/paper/2505.20254/) (2025)
- [Analyze Feature Flow to Enhance Interpretation and Steering in Language Models](https://mlsanity.com/paper/2502.03032/) (2025)

## Abstract (arXiv)

Foundation models are increasingly adapted through fine-tuning, model editing, and alignment procedures while retaining previously acquired capabilities. Understanding the internal computations that support these adaptations is therefore becoming increasingly important for continual model evolution. Sparse autoencoders (SAEs) provide interpretable feature dictionaries for residual-stream activations and sublayer outputs, but it remains unclear how state features and update features interact to produce downstream residual features. In this work, we focus on MLP updates as a first test case. We construct a transition atlas of triples sk + uj rightarrow tℓ, where a residual-state feature and an MLP-update feature jointly predict a target residual feature, and validate candidate triples by ablating the decoded update feature. In a 20M-token Pythia-160M L7 rightarrow L8 run, we find 38,125 strong ablation-effect transitions, but 88.0% have both state-target and update-target decoder cosine similarity below 0.7. As a preliminary cross-model check, a run of 20M-token Gemma-3-4B L21 rightarrow L22 causally validates only the top 30,000 ranked candidate triples by ablating the decoded update feature, and 53.6% of strong-effect triples have both state-target and update-target decoder cosine similarity below 0.7. The Gemma result is directionally consistent with Pythia, but weaker, since update-target cosine recovers many of the strongest Gemma effects and the run is not a full-atlas causal validation. Ultimately, our results suggest that feature flow atlases can serve as diagnostics of representation-update mechanisms and thereby inform tools for steering model updates. Future work will validate more complex patterns across layers, models, and SAE families.