# Feature Starvation as Geometric Instability in Sparse Autoencoders

arXiv: https://arxiv.org/abs/2605.05341 · HTML: https://mlsanity.com/paper/2605.05341/

## 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 21 of its 38 references that are in the map.
- First posted on arXiv 6 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, 21 of 21)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [A is for Absorption: Studying Feature Splitting and Absorption in Sparse Autoencoders](https://mlsanity.com/paper/2409.14507/) (2024)
- [Learning Multi-Level Features with Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2503.17547/) (2025)
- [OLMoTrace: Tracing Language Model Outputs Back to Trillions of Training Tokens](https://mlsanity.com/paper/2504.07096/) (2025)
- [Optimal ablation for interpretability](https://mlsanity.com/paper/2409.09951/) (2024)
- [Hyperparameter Tuning is All You Need for LISTA](https://mlsanity.com/paper/2110.15900/) (2021)
- [Adaptive Sparse Allocation with Mutual Choice & Feature Choice Sparse Autoencoders](https://mlsanity.com/paper/2411.02124/) (2024)
- [Evaluating and Designing Sparse Autoencoders by Approximating Quasi-Orthogonality](https://mlsanity.com/paper/2503.24277/) (2025)
- [Investigating Neuron Ablation in Attention Heads: The Case for Peak Activation Centering](https://mlsanity.com/paper/2408.17322/) (2024)
- [Attribution-Guided Distillation of Matryoshka Sparse Autoencoders](https://mlsanity.com/paper/2512.24975/) (2025)

## Abstract (arXiv)

Sparse autoencoders (SAEs) are used to disentangle the dense, polysemantic internal representations of large language models (LLMs) into interpretable, monosemantic concepts. However, standard ℓ1-regularized SAEs suffer from feature starvation (dead neurons) and shrinkage bias, often requiring computationally expensive heuristic resampling and nondifferentiable hard-masking methods to bypass these challenges. We argue that feature starvation is not merely an empirical artifact of poor data diversity, but a fundamental optimization-geometric pathology of overcomplete dictionaries: the ℓ1-induced sparse coding map is unstable and fundamentally misaligned with shallow, amortized encoders. To address this structural instability, we introduce adaptive elastic net SAEs (AEN-SAEs), a fully differentiable architecture grounded in classical sparse regression. AEN-SAEs combine an ℓ2 structural term that enforces strong convexity and Lipschitz stability with adaptive ℓ1 reweighting that eliminates shrinkage bias and suppresses spurious features, thereby jointly controlling the curvature and interaction structure of the induced polyhedral geometry. Theoretically, we show that AEN-SAEs yield a Lipschitz-continuous sparse coding map and recover the global feature support under mild assumptions. Empirically, across synthetic settings and LLMs (Pythia 70M, Llama 3.1 8B), AEN-SAEs mitigate feature starvation without auxiliary heuristics while maintaining competitive reconstruction abilities.