aiqbench analysis
This paper rigorously formalizes the Linear Representation Hypothesis by introducing group actions to define precise equivalence classes for neural representations, addressing ambiguity in current interpretability metrics. By distinguishing between different structural assumptions across analysis stages, it provides a necessary framework for auditing claims that generalize beyond specific trained models. This theoretical advancement is critical for establishing robust, architecture-agnostic standards in representation learning and model interpretation.
The Linear Representation Hypothesis Needs a Group Action
arXiv:2609.27158v1 Announce Type: cross Abstract: To make claims about representations that generalize beyond a particular trained model, we need to specify when two representations should count as equivalent. The Linear Representation Hypothesis is often discussed without making this equivalence explicit. Different notions of equivalence preserve different structures, so metrics, probes, and interventions that appear to study the same representation may in fact correspond to different hypotheses. We therefore argue that the Linear Representation Hypothesis is not one hypothesis but a family of claims distinguished by representation equivalence. We formalize this idea using group actions, specifying the representation object, the procedure that produces it, and the property ultimately asserted, while accounting for equivalences imposed by the model architecture. This framework clarifies how assumptions can change across metrics, reading points, and analysis stages, and we use it to audit common representation quantities and recent interpretability analyses.
Abstract:To make claims about representations that generalize beyond a particular trained model, we need to specify when two representations should count as equivalent. The Linear Representation Hypothesis is often discussed without making this equivalence explicit. Different notions of equivalence preserve different structures, so metrics, probes, and interventions that appear to study the same representation may in fact correspond to different hypotheses. We therefore argue that the Linear Representation Hypothesis is not one hypothesis but a family of claims distinguished by representation equivalence. We formalize this idea using group actions, specifying the representation object, the procedure that produces it, and the property ultimately asserted, while accounting for equivalences imposed by the model architecture. This framework clarifies how assumptions can change across metrics, reading points, and analysis stages, and we use it to audit common representation quantities and recent interpretability analyses.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
arXiv:2609.27158 [cs.LG]
(or arXiv:2609.27158v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.27158 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 240 words
