SAE Limitations and Crosscoders

Sparse autoencoders became the standard interpretability tool on a specific promise: train a wide, sparsely-activating dictionary on a model's activations and the learned directions will be the model's own features, decomposed out of superposition. The promise carries two claims, atomicity and completeness, and both have now been tested directly.

Neither survived intact. This is a case where the field revised a widely held belief within about eighteen months, and the revision is more instructive than the original claim.

Feature absorption

Increase an SAE's width and features split: a "math" direction becomes "algebra", "geometry", and so on. That was read as a resolution improvement. Chanin and colleagues showed the split is not clean.

A latent that appears monosemantic, say one that fires on words beginning with the letter S, systematically fails to fire on some inputs it should, because a more specific child latent has absorbed that case and taken over the parent's role for it. The cause is structural rather than incidental: optimising for sparsity whenever the underlying features form a hierarchy creates pressure to route the parent's activation through the child, since the child alone is cheaper than parent-plus-child. Validated across hundreds of SAEs, and neither larger dictionaries nor different sparsity levels resolve it (Chanin et al., NeurIPS 2025, arXiv:2409.14507).

The practical consequence is severe for any downstream use. A latent used as a classifier or a steering handle has silent, input-dependent holes, and the holes are invisible to the usual interpretability dashboards, which display where a latent fires and not where it should have.

Not atomic, not complete

Leask and colleagues attacked the two claims directly with two constructions. SAE stitching inserts latents from a larger SAE into a smaller one and finds novel latents carrying information the smaller SAE simply lacks, which falsifies completeness at any fixed width. Meta-SAEs, trained on the decoder matrix of another SAE, find that individual latents decompose into combinations of latents from a smaller SAE, which falsifies atomicity; their illustrative example is an "Einstein" latent decomposing into "scientist", "Germany", and "famous person" (Leask et al., ICLR 2025, arXiv:2502.04878).

There is no privileged width. The dictionary you get is a function of the dictionary size you chose, and the honest reading is that SAE width is a resolution setting selected for a purpose, not a discovery of the model's true vocabulary.

The utility question was then asked directly. In a sparse-probing case study, SAEs occasionally beat baselines on individual datasets, but no ensemble combining SAEs with baselines consistently beat ensembles of baselines alone; promising results on spurious-correlation detection and dataset-quality problems were also reproducible with simple non-SAE methods (Kantamneni et al., 2025, arXiv:2502.16681).

Crosscoders: features that live across layers

One structural assumption behind per-layer SAEs is that a feature belongs to a layer. In a residual-stream transformer that is doubtful: the stream is linear and additive, and a feature written at layer 8 is still readable at layer 20, so a per-layer dictionary re-discovers the same feature repeatedly and cannot represent anything genuinely spread across depth.

Crosscoders read from and write to multiple layers at once, producing a shared feature set across depth. Three consequences follow: cross-layer superposition becomes representable rather than an artefact; circuit analysis simplifies because duplicate per-layer copies of one feature collapse into a single latent, letting analysis skip uninteresting identity connections; and because the dictionary can be shared between two models, they enable model diffing, comparing a base model against its fine-tune or two independently trained models (Lindsey et al., Anthropic, October 2024).

That work was published as preliminary research at a lower rigour bar than a full paper, and the compute cost is higher than per-layer SAEs. It addresses the layer-locality assumption; it does not address absorption or non-atomicity, which are properties of the sparsity objective itself.

When it breaks

Interpretability illusions. A latent with a compelling human-readable label may still be an artefact of the dictionary size, absorbed on a subset of its domain, or decomposable into finer parts. Confidence should come from causal interventions, ablate it, steer with it, and measure the downstream effect, not from a legible activation pattern.

Reconstruction error is not the right metric, and neither is loss recovered. Both measure how much of the activation the dictionary captures, and neither measures whether the pieces correspond to anything the model computes with. A dictionary can reconstruct well and decompose wrongly.

Downstream tasks need strong baselines. The sparse-probing result generalises as methodology: an interpretability method should be compared against linear probes, difference-in-means directions, and other cheap alternatives on a task with a real metric, because those baselines are often competitive.

None of this makes SAEs useless. They remain the best available tool for open-ended discovery of what a model represents, and attribution-graph work builds on them productively. What has failed is the strong claim that they recover a canonical basis, which matters most for arguments that lean on completeness, of the form "we looked at the features and found no deceptive one".