Problem
Research questions and friction points this paper is trying to address.
Linear Representation Hypothesis
representation equivalence
group actions
The Linear Representation Hypothesis Needs a Group Action
🤖 AI Summary
本文通过引入群作用来明确表示等价性，解决线性表示假设在不同模型中的一致性问题，从而统一了对表示学习的分析方法。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Linear Representation Hypothesis
Group Action
Equivalence of Representations
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