Model Alignment Search

Satchel Grant

Track: long paper (up to 10 pages)

Domain: cognitive science

Abstract: When can we say that two neural systems are the same? The answer to this question is goal-dependent, and it is often addressed through correlative methods such as Representational Similarity Analysis (RSA) and Centered Kernel Alignment (CKA). We find ourselves chiefly interested in the relationship between representations and behavior, asking ourselves how we can isolate specific functional aspects of representational similarity to relate our measures to behavior––avoiding cause vs. correlation pitfalls in the process. In this work, we introduce Model Alignment Search (MAS), a method for causally exploring distributed representational similarity as it relates to behavior. The method learns invertible linear transformations that find an aligned subspace between two distributed networks' representations where functional information can be isolated and manipulated. We first show that the method can be used to transfer values of specific causal variables––such as the number of items in a counting task––between networks with different training seeds and different architectures. We then explore open questions in number cognition by comparing different types of numeric representations in models trained on structurally different tasks, we explore differences between MAS and preexisting functional similarity methods, and lastly, we introduce a counterfactual latent auxiliary loss that helps shape functionally relevant alignments even in cases where we do not have causal access to one of the two models for training.

Submission Number: 25