Sparse Autoencoders

A sparse autoencoder (SAE) is a wide, sparsely-activated autoencoder trained on the internal activations of a transformer . Given a residual-stream or MLP activation , the SAE learns:

where the feature dimension of is much wider than — typically to — and a sparsity constraint forces only a small number of features to be non-zero per token. The reconstruction loss pushes ; the sparsity constraint pushes the network to use as few features as possible to do it.

The payoff is interpretability. Each row of corresponds to a feature direction in the original activation space, and — empirically, when training works — those directions are monosemantic: each one fires for a single, human-understandable concept.

The superposition hypothesis

Why are raw transformer neurons such a mess? The current best answer is superposition: the model has more features it wants to represent than it has dimensions to represent them in, so it packs features into non-orthogonal directions and accepts the interference. A single neuron ends up firing for a long list of unrelated concepts — “DNA sequences”, “C++ pointer code”, “Russian text”, and “names of bridges” might all activate the same neuron at different strengths.

SAEs are dictionary learning applied to this problem. By projecting activations into a wider sparse space, the network can give each feature its own direction without having to share. The sparsity penalty is what makes the directions disentangle — without it the SAE just learns an over-parameterized identity.

The two recipes

Feature splitting

One of the more conceptually interesting findings: as you make the SAE wider, features split into more specific sub-features. A small SAE might have a single feature for “Golden Gate Bridge”. A wider SAE on the same model decomposes that into “Golden Gate Bridge in fog”, “Golden Gate Bridge in photographs”, “Golden Gate Bridge in tourist contexts”, and so on.

This implies there isn’t a single canonical feature dictionary — there’s a hierarchy of features at different granularities, and the SAE width is the knob that selects how fine-grained the decomposition is. Choosing the width is a research decision, not a configuration detail.

The reconstruction-interpretability trade-off

There’s a hard trade-off between how well the SAE reconstructs the original activations and how interpretable its features are. Push sparsity hard ( low, high) and you get a small number of very clean features, but the reconstruction loses fidelity — the model running through the SAE-reconstructed activations performs noticeably worse than the original. Loosen sparsity and the reconstruction is faithful, but features start to merge and lose their monosemanticity.

The standard metric is “loss recovered”: how much of the original model’s loss does running through the SAE preserve, vs the floor of zeroing the activation entirely? Modern SAEs hit 90%+ loss recovery with ~50-200 active features per token at residual-stream widths of 4096-16384 against base widths of 768-4096.

Why this matters

For ten years, the standard answer to “what does this neuron do?” was “it fires for a lot of things, none of them especially clean”. SAEs change that. With a trained SAE you can take any token, list its top active features, and read off a human-understandable description of what the model is representing at that position. You can clamp specific features to high values and watch the model’s behavior shift in predictable ways (Anthropic’s Golden Gate Claude demo). You can compare features across layers and start to describe how representations evolve through the network.

It’s the most tractable “open the black box” recipe the field has produced. Not solved — feature splitting, dead features, and reconstruction-interpretability trade-offs all remain open — but a foothold where there used to be a wall.