arXiv:2501.06164v5 Announce Type: replace-cross 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). What nuances do we miss, however, when we fail to causally probe the representations? Do the dangers of cause vs. correlation exist in comparative representational analyses? In this work, we introduce a method for connecting neural representational similarity to behavior through causal interventions. The method learns orthogonal transformations that find an aligned subspace in which behavioral information from multiple distributed networks' representations can be isolated and interchanged. We first show that the method can be used to transfer the behavior from one frozen Neural Network (NN) to another in a manner similar to model stitching, and we show how the method can complement correlative similarity measures like RSA. We then introduce an efficient subspace orthogonalization technique using the Gram-Schmidt process -- that can also be used for Distributed Alignment Search (DAS) -- allowing us to perform analyses on larger models. Next, we empirically and theoretically show how our method can be equivalent to model stitching when desired, or it can take a form that is more restrictive to causal information, and in both cases, it reduces the number of required matrices for a comparison of n models from quadratic to linear in n. We then show how we can augment the loss objective with an auxiliary loss to train causally relevant alignments even when we can only read the representations from one of the two networks during training (like with biological networks). Lastly, we use number representations as a case study to explore how our method can be used to compare specific types of representational information across tasks and models.
