When Are Two Networks the Same? Tensor Similarity for Mechanistic Interpretability
Mechanistic interpretability research has long struggled with a fundamental problem: determining whether two neural network components actually compute the same function, or merely produce similar outputs by accident. This paper introduces tensor similarity, a weight-space metric that survives the symmetries inherent in neural architectures, enabling researchers to track whether learned mechanisms remain functionally equivalent across training phases. The work matters because it bridges the gap between behavioral similarity (which misses out-of-distribution failures) and parameter-level analysis (which gets confused by weight-space rotations). Early results show the metric captures phenomena like grokking and backdoor insertion more reliably than existing approaches, potentially accelerating the pace at which interpretability researchers can validate mechanistic claims about model internals.
Modelwire context
ExplainerThe deeper issue tensor similarity addresses is that mechanistic interpretability has largely been a qualitative discipline: researchers identify circuits and claim functional equivalence without a principled way to verify that claim holds across model variants or training checkpoints. This paper is an attempt to put a number on that.
Most of Modelwire's recent coverage has clustered around agent evaluation and retrieval, but this paper belongs to a quieter thread: the infrastructure problem underneath alignment and interpretability research. The closest thematic neighbor in recent coverage is FutureSim, which also targets a measurement gap, specifically whether agents can update beliefs as facts arrive. Both papers are making the same structural argument: the field has been building on evaluation foundations that are less rigorous than they appear. Where FutureSim exposes that gap in agent benchmarking, tensor similarity exposes it in mechanistic claims about model internals. Neither paper ships a product; both are trying to give researchers better instruments.
The real test is whether a major interpretability group, Anthropic's or DeepMind's interpretability teams being the obvious candidates, adopts tensor similarity as a standard diagnostic in a published circuit analysis within the next twelve months. Adoption by one credible lab would signal the metric is practically useful rather than theoretically tidy.
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