Paper
Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalisation
Authors
Vitória Barin Pacela, Shruti Joshi, Isabela Camacho, Simon Lacoste-Julien, David Klindt
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 -- not the inference procedure -- as the binding constraint: 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 reframe the SAE failure as a dictionary learning challenge, not an amortisation problem, and point to scalable dictionary learning as the key open problem for sparse inference under superposition.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.28744v1</id>\n <title>Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalisation</title>\n <updated>2026-03-30T17:52:16Z</updated>\n <link href='https://arxiv.org/abs/2603.28744v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.28744v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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 -- not the inference procedure -- as the binding constraint: 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 reframe the SAE failure as a dictionary learning challenge, not an amortisation problem, and point to scalable dictionary learning as the key open problem for sparse inference under superposition.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-03-30T17:52:16Z</published>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Vitória Barin Pacela</name>\n </author>\n <author>\n <name>Shruti Joshi</name>\n </author>\n <author>\n <name>Isabela Camacho</name>\n </author>\n <author>\n <name>Simon Lacoste-Julien</name>\n </author>\n <author>\n <name>David Klindt</name>\n </author>\n </entry>"
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