ICML 2025

Sparse Autoencoders, Again?
Yin Lu 1 Xuening Zhu 1 Tong He 2 David Wipf 2
Abstract
Is there really much more to say about sparse au-
toencoders (SAEs)? Autoencoders in general, and
SAEs in particular, represent deep architectures
that are capable of modeling low-dimensional la-
tent structure in data. Such structure could re-
flect, among other things, correlation patterns
in large language model activations, or complex
natural image manifolds. And yet despite the
wide-ranging applicability, there have been rel-
atively few changes to SAEs beyond the origi-
nal recipe from decades ago, namely, standard
deep encoder/decoder layers trained with a classi-
cal/deterministic sparse regularizer applied within
the latent space. One possible exception is the
variational autoencoder (VAE), which adopts a
stochastic encoder module capable of producing
sparse representations when applied to manifold
data. In this work we formalize underappreciated
weaknesses with both canonical SAEs, as well as
analogous VAEs applied to similar tasks, and pro-
pose a hybrid alternative model that circumvents
these prior limitations. In terms of theoretical sup-
port, we prove that global minima of our proposed
model recover certain forms of structured data
spread across a union of manifolds. Meanwhile,
empirical evaluations on synthetic and real-world
datasets substantiate the efficacy of our approach
in accurately estimating underlying manifold di-
mensions and producing sparser latent representa-
tions without compromising reconstruction error.
In general, we are able to exceed the performance
of equivalent-capacity SAEs and VAEs, as well as
recent diffusion models where applicable, within
domains such as images and language model acti-
vation patterns. A link to the code is here.
1School of Data Science, Fudan University 2Amazon Web Services.
Correspondence
to:
Yin
Lu
<yinlu23@m.fudan.edu.cn>,
Xuening
Zhu
<xueningzhu@fudan.edu.cn>,
Tong
He
<htong@amazon.com>, David Wipf <davidwipf@gmail.com...

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