{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/projecting-assumptions-the-duality-between","title":"Projecting Assumptions: The Duality Between Sparse Autoencoders and Concept Geometry","arxiv_id":"2503.01822","date":"2025-03-03","proceeding":null,"authors":["Sai Sumedh R. Hindupur","Ekdeep Singh Lubana","Thomas Fel","Demba Ba"],"abstract":"Sparse Autoencoders (SAEs) are widely used to interpret neural networks by identifying meaningful concepts from their representations. However, do SAEs truly uncover all concepts a model relies on, or are they inherently biased toward certain kinds of concepts? We introduce a unified framework that recasts SAEs as solutions to a bilevel optimization problem, revealing a fundamental challenge: each SAE imposes structural assumptions about how concepts are encoded in model representations, which in turn shapes what it can and cannot detect. This means different SAEs are not interchangeable -- switching architectures can expose entirely new concepts or obscure existing ones. To systematically probe this effect, we evaluate SAEs across a spectrum of settings: from controlled toy models that isolate key variables, to semi-synthetic experiments on real model activations and finally to large-scale, naturalistic datasets. Across this progression, we examine two fundamental properties that real-world concepts often exhibit: heterogeneity in intrinsic dimensionality (some concepts are inherently low-dimensional, others are not) and nonlinear separability. We show that SAEs fail to recover concepts when these properties are ignored, and we design a new SAE that explicitly incorporates both, enabling the discovery of previously hidden concepts and reinforcing our theoretical insights. Our findings challenge the idea of a universal SAE and underscores the need for architecture-specific choices in model interpretability. Overall, we argue an SAE does not just reveal concepts -- it determines what can be seen at all.","url_abs":"https://arxiv.org/abs/2503.01822v1","url_pdf":"https://arxiv.org/pdf/2503.01822v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"bilevel-optimization","task_name":"Bilevel Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2503.01822","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2503.01822"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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