From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit

• URL: http://arxiv.org/abs/2506.03093v1
• Date: Tue, 03 Jun 2025 17:24:55 GMT
• Title: From Flat to Hierarchical: Extracting Sparse Representations with Matching Pursuit
• Authors: Valérie Costa, Thomas Fel, Ekdeep Singh Lubana, Bahareh Tolooshams, Demba Ba,
• Abstract summary: We show that MP-SAE unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features.<n>We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time.
• Score: 16.996218963146788
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuits (MP) algorithm from sparse coding to design MP-SAE -- an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

Related papers

• Evaluating Sparse Autoencoders: From Shallow Design to Matching Pursuit [16.996218963146788]
  Sparse autoencoders (SAEs) have recently become central tools for interpretability.<n>This paper evaluates SAEs in a controlled setting using MNIST.<n>We introduce a multi-iteration SAE by unrolling Matching Pursuit (MP-SAE)
  arXiv  Detail & Related papers  (2025-06-05T16:57:58Z)
• Sparsification and Reconstruction from the Perspective of Representation Geometry [10.834177456685538]
  Sparse Autoencoders (SAEs) have emerged as a predominant tool in mechanistic interpretability.<n>This study explains the principles of sparsity from the perspective of representational geometry.<n>Specifically emphasizes the necessity of understanding representations and incorporating representational constraints.
  arXiv  Detail & Related papers  (2025-05-28T15:54:33Z)
• The Origins of Representation Manifolds in Large Language Models [52.68554895844062]
  We show that cosine similarity in representation space may encode the intrinsic geometry of a feature through shortest, on-manifold paths.<n>The critical assumptions and predictions of the theory are validated on text embeddings and token activations of large language models.
  arXiv  Detail & Related papers  (2025-05-23T13:31:22Z)
• I Predict Therefore I Am: Is Next Token Prediction Enough to Learn Human-Interpretable Concepts from Data? [76.15163242945813]
  Large language models (LLMs) have led many to conclude that they exhibit a form of intelligence.<n>We introduce a novel generative model that generates tokens on the basis of human-interpretable concepts represented as latent discrete variables.
  arXiv  Detail & Related papers  (2025-03-12T01:21:17Z)
• "Principal Components" Enable A New Language of Images [79.45806370905775]
  We introduce a novel visual tokenization framework that embeds a provable PCA-like structure into the latent token space.<n>Our approach achieves state-of-the-art reconstruction performance and enables better interpretability to align with the human vision system.
  arXiv  Detail & Related papers  (2025-03-11T17:59:41Z)
• Interpretability as Compression: Reconsidering SAE Explanations of Neural Activations with MDL-SAEs [0.0]
  We present an information-theoretic framework for interpreting SAEs as lossy compression algorithms. We argue that using MDL rather than sparsity may avoid potential pitfalls with naively maximising sparsity.
  arXiv  Detail & Related papers  (2024-10-15T01:38:03Z)
• Semantic Loss Functions for Neuro-Symbolic Structured Prediction [74.18322585177832]
  We discuss the semantic loss, which injects knowledge about such structure, defined symbolically, into training. It is agnostic to the arrangement of the symbols, and depends only on the semantics expressed thereby. It can be combined with both discriminative and generative neural models.
  arXiv  Detail & Related papers  (2024-05-12T22:18:25Z)
• Labeling Neural Representations with Inverse Recognition [25.867702786273586]
  Inverse Recognition (INVERT) is a scalable approach for connecting learned representations with human-understandable concepts. In contrast to prior work, INVERT is capable of handling diverse types of neurons, exhibits less computational complexity, and does not rely on the availability of segmentation masks. We demonstrate the applicability of INVERT in various scenarios, including the identification of representations affected by spurious correlations.
  arXiv  Detail & Related papers  (2023-11-22T18:55:25Z)
• A Recursive Bateson-Inspired Model for the Generation of Semantic Formal Concepts from Spatial Sensory Data [77.34726150561087]
  This paper presents a new symbolic-only method for the generation of hierarchical concept structures from complex sensory data. The approach is based on Bateson's notion of difference as the key to the genesis of an idea or a concept. The model is able to produce fairly rich yet human-readable conceptual representations without training.
  arXiv  Detail & Related papers  (2023-07-16T15:59:13Z)
• Nonlinear ISA with Auxiliary Variables for Learning Speech Representations [51.9516685516144]
  We introduce a theoretical framework for nonlinear Independent Subspace Analysis (ISA) in the presence of auxiliary variables. We propose an algorithm that learns unsupervised speech representations whose subspaces are independent.
  arXiv  Detail & Related papers  (2020-07-25T14:53:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.