Model Alignment Search

When can we say that two neural systems are the same? What nuances do we miss when we fail to causally probe the representations of the systems? In this work, we introduce a method for connecting neural representational similarity to behavior through causal interventions. The method learns transformations that find an aligned subspace in which behavioral information can be interchanged between multiple distributed networks' representations. 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 differ from correlative similarity measures like Representational Similarity Analysis. Next, we empirically and theoretically show how the method can be equivalent to model stitching when desired, or it can take a form that has a more restrictive focus to shared causal information; in both forms, it reduces the number of required matrices for a comparison of n models to be linear in n. We then present a case study on number-related tasks showing that the method can be used to examine specific subtypes of causal information, and we present another case study showing that the method can reveal toxicity in fine-tuned DeepSeek-r1-Qwen-1.5B models. Lastly, we show how to augment the loss with a counterfactual latent auxiliary objective to improve causal relevance when one of the two networks is causally inaccessible (as is often the case in comparisons with biological networks). We use our results to encourage the use of causal methods in neural similarity analyses and to suggest future explorations of network similarity methodology for model misalignment.