aiqbench analysis
This study demonstrates that Sparse Autoencoders (SAEs) fail at compositional generalization not due to inference limitations, but because their learned dictionaries misalign with the true latent structure of neural activations under superposition. By replacing amortized encoders with iterative methods like FISTA on a fixed dictionary, researchers can recover latent factors effectively, shifting the core challenge to scalable dictionary learning for real-world LLMs.
Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalisation
arXiv:2603.28744v2 Announce Type: replace Abstract: The linear representation hypothesis states that neural network activations encode high-level concepts as linear mixtures. However, under superposition, this encoding is a projection from a higher-dimensional concept space into a lower-dimensional activation space, and a linear decision boundary in the concept space need not remain linear after projection. In this setting, classical sparse coding methods with per-sample iterative inference leverage compressed sensing guarantees to recover latent factors. Sparse autoencoders (SAEs), on the other hand, amortise sparse inference into a fixed encoder, introducing a systematic gap. We show this amortisation gap persists across training set sizes, latent dimensions, and sparsity levels, causing SAEs to fail under out-of-distribution (OOD) compositional shifts. Through controlled experiments that decompose the failure, we identify dictionary learning as the limiting factor (not the inference procedure): SAE-learned dictionaries point in substantially wrong directions, and replacing the encoder with per-sample FISTA on the same dictionary does not close the gap. An oracle baseline proves the problem is solvable with a good dictionary at all scales tested. Our results, including experiments with real LLM activations (Pythia-70M, Gemma-2-2B) reframe the SAE failure as a dictionary learning challenge, not an inference problem, and point to scalable dictionary learning as the key open problem for sparse inference under superposition.
Abstract:The linear representation hypothesis states that neural network activations encode high-level concepts as linear mixtures. However, under superposition, this encoding is a projection from a higher-dimensional concept space into a lower-dimensional activation space, and a linear decision boundary in the concept space need not remain linear after projection. In this setting, classical sparse coding methods with per-sample iterative inference leverage compressed sensing guarantees to recover latent factors. Sparse autoencoders (SAEs), on the other hand, amortise sparse inference into a fixed encoder, introducing a systematic gap. We show this amortisation gap persists across training set sizes, latent dimensions, and sparsity levels, causing SAEs to fail under out-of-distribution (OOD) compositional shifts. Through controlled experiments that decompose the failure, we identify dictionary learning as the limiting factor (not the inference procedure): SAE-learned dictionaries point in substantially wrong directions, and replacing the encoder with per-sample FISTA on the same dictionary does not close the gap. An oracle baseline proves the problem is solvable with a good dictionary at all scales tested. Our results, including experiments with real LLM activations (Pythia-70M, Gemma-2-2B) reframe the SAE failure as a dictionary learning challenge, not an inference problem, and point to scalable dictionary learning as the key open problem for sparse inference under superposition.
Accepted for publication at UAI 2026. This is a slightly updated version of the published manuscript; see Corrigendum at the end of the paper
Machine Learning (cs.LG)
arXiv:2603.28744 [cs.LG]
(or arXiv:2603.28744v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.28744 Focus to learn more arXiv-issued DOI via DataCite
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