When Are Two Networks the Same? Tensor Similarity for Mechanistic Interpretability

2026-05-14 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Researchers have introduced "tensor similarity," a novel weight-based metric designed for mechanistic interpretability in tensor-based models. This metric addresses limitations of existing similarity measures, which either focus on empirical behavior (failing out-of-distribution) or basis-dependent parameters (ignoring weight-space symmetries). Tensor similarity is invariant to these symmetries, capturing global functional equivalence and accounting for cross-layer mechanisms through an efficient recursive algorithm. Empirical evaluations demonstrate that this new metric tracks functional training dynamics, including phenomena like grokking and backdoor insertion, with greater fidelity compared to current alternatives. This approach transforms the problem of measuring network similarity and verifying faithfulness from an empirical approximation task into a solved algebraic problem.

Key takeaway

For research scientists focused on mechanistic interpretability, this new tensor similarity metric provides a robust method to verify that two network parts implement the same computation. You should consider integrating this algebraic approach to assess functional equivalence, especially when analyzing out-of-distribution behaviors or complex cross-layer mechanisms, thereby moving beyond empirical approximations.

Key insights

Tensor similarity offers a weight-based, symmetry-invariant metric for comparing neural network components functionally.

Principles

• Functional equivalence requires symmetry-invariant weight comparison.
• Cross-layer mechanisms demand recursive similarity evaluation.

Method

Tensor similarity uses an efficient recursive algorithm to compare tensor-based model components, ensuring invariance to weight-space symmetries and capturing global functional equivalence across layers.

In practice

• Verify model component equivalence algebraically.
• Track functional training dynamics more accurately.

Topics

• Mechanistic Interpretability
• Tensor Similarity
• Weight-Based Metrics
• Functional Equivalence
• Training Dynamics

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.