Model Alignment Search (2501.06164v5)

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.

• The paper demonstrates a novel framework that identifies causal similarities in neural systems using invertible linear transformations.
• It outperforms correlative methods by robustly aligning key subspaces, enabling consistent causal interventions across diverse neural architectures.
• The study offers theoretical insights and practical tools for advancing cross-model comparisons in machine learning and cognitive sciences.

Overview of Model Alignment Search

The paper "Model Alignment Search" by Satchel Grant introduces a novel framework called Model Alignment Search (MAS), which aims to identify causal similarities between neural systems through the alignment of distributed representations. This method is significant for systems that are seemingly similar in function but differ in their representational mechanisms due to variations in training regimes, structural designs, or other distinct characteristics.

Research Focus and Methodology

The primary question addressed by this research is, "When can we say that two neural systems are the same?" Traditionally, this question is approached using correlative methods like Representational Similarity Analysis (RSA) and Centered Kernel Alignment (CKA). These techniques have been extensively employed to understand structural correlations between different neural architectures. However, they lack causal explanations of representational isomorphism, which MAS aims to address.

MAS operates by learning invertible linear transformations that align subspaces within distributed networks where causally relevant information can be interchanged. The core of MAS lies in determining subsets of representations that allow causal interventions—thereby enabling more definitive statements about the functional equivalences between different neural architectures.

Results and Applications

This paper demonstrates the efficacy of the MAS procedure through several compelling applications. Firstly, it showcases that MAS can effectively transfer specific causal elements such as counting variables between networks trained with varying initialization seeds. This is crucial as it allows for consistent behavior across models trained under different conditions. Secondly, MAS is applied to explore questions in number cognition, particularly focusing on how numeric representations differ or converge when models are trained on structurally distinct tasks.

One of the primary advantages of MAS over existing methods, such as RSA, is its robustness to irrelevant data substitution during causal intervention. The paper provides quantitative analysis indicating that MAS maintains representational integrity where previous causal methods might falter due to unwanted information exchanges.

Furthermore, the authors introduce a counterfactual latent auxiliary loss for shaping causally relevant alignments, even when no causal access is available to one of the networks being compared. This feature is particularly relevant for advancing research on biological neural networks (BNNs), where direct intervention is often not feasible.

Theoretical and Practical Implications

The theoretical implications of MAS are substantial. By focusing on causal, not just correlational, similarities, MAS provides deeper insights into the functional mechanics of neural networks. It suggests a refined approach for examining the interchangeability of information representations, potentially influencing how we understand multi-modal neural processing.

Practically, MAS could have a profound impact on how cross-model similarities are evaluated and exploited, particularly in large-scale machine learning and cognitive sciences. It has the potential to foster advancements in fields such as neural information transfer, systems neuroscience, and robust machine learning models that need to maintain performance across varied datasets and environments.

Future Directions

The introduction of MAS paves the way for future investigations into more granular causal structures within neural network representations. There is a potential for further exploration into its application in models with biological plausibility, enhancing interpretability and synergy between artificial and biological systems. Additionally, this method holds promise for addressing outstanding issues in the fields of transfer learning and domain adaptation by providing a more causally informed lens through which model alignment should be assessed.

In conclusion, this paper presents a significant step forward in understanding the causal interchangeability of neural representations, providing a robust framework that transcends traditional correlative methodologies. It offers both theoretical advancements and practical tools for advancing research across computational and cognitive disciplines.