Dynamical similarity analysis can identify compositional dynamics developing in RNNs (2410.24070v4)

Abstract: Methods for analyzing representations in neural systems have become a popular tool in both neuroscience and mechanistic interpretability. Having measures to compare how similar activations of neurons are across conditions, architectures, and species, gives us a scalable way of learning how information is transformed within different neural networks. In contrast to this trend, recent investigations have revealed how some metrics can respond to spurious signals and hence give misleading results. To identify the most reliable metric and understand how measures could be improved, it is going to be important to identify specific test cases which can serve as benchmarks. Here we propose that the phenomena of compositional learning in recurrent neural networks (RNNs) allows us to build a test case for dynamical representation alignment metrics. By implementing this case, we show it enables us to test whether metrics can identify representations which gradually develop throughout learning and probe whether representations identified by metrics are relevant to computations executed by networks. By building both an attractor- and RNN-based test case, we show that the new Dynamical Similarity Analysis (DSA) is more noise robust and identifies behaviorally relevant representations more reliably than prior metrics (Procrustes, CKA). We also show how test cases can be used beyond evaluating metrics to study new architectures. Specifically, results from applying DSA to modern (Mamba) state space models, suggest that, in contrast to RNNs, these models may not exhibit changes to their recurrent dynamics due to their expressiveness. Overall, by developing test cases, we show DSA's exceptional ability to detect compositional dynamical motifs, thereby enhancing our understanding of how computations unfold in RNNs.

• The paper introduces Dynamical Similarity Analysis (DSA) to capture the evolving state representations in RNNs.
• DSA outperforms Procrustes analysis and CKA by demonstrating superior noise robustness and ratio-like behavior.
• The study aligns neural representation development with task learning, offering deeper insights into dynamic computational processes.

Analysis of Computational Dynamics in RNNs Through Dynamical Similarity Analysis

The paper "Dynamical similarity analysis uniquely captures how computations develop in RNNs" by Quentin Guilhot et al. presents an in-depth examination of interpretability metrics utilized to understand computational processes in recurrent neural networks (RNNs). The paper introduces and evaluates the efficacy of Dynamical Similarity Analysis (DSA) in comparison to established metrics such as Procrustes analysis and Centered Kernel Alignment (CKA). By constructing a detailed analytical framework, the authors aim to advance our understanding of representation development within varying neural architectures.

Context and Motivation

As tasks faced by neural networks become increasingly complex, there is a growing necessity for refined tools that allow comparative analysis across different conditions and architectures. Existing metrics focus primarily on static representations; however, they fall short in addressing the temporal dynamics within neural networks, especially in networks such as RNNs that are inherently temporal. The authors propose DSA as a specialized metric that considers the dynamic evolution of state representations as tasks are learned and computations develop over time.

Methodology and Experiments

The authors undertake a rigorous comparison across three metrics: Procrustes, CKA, and the newly introduced DSA. Initially, they evaluate these metrics against simulated attractor dynamics to establish a baseline for interpretability. Here, the focus is on assessing noise robustness and the metrics' ability to discern compositionalities within combined dynamics. DSA exhibited superior noise robustness and a more ratio-like behavior compared to the others.

Subsequently, the paper transitions to a test case involving RNNs and a series of computational tasks designed to tease out the subtasks' influence on the RNN's learning dynamics. By examining how representations emerging within RNNs relate to their computational capabilities, the paper provides valuable insights into the temporal alignment of neural representations. Only DSA successfully captured the gradual development of neural representations, aligning closely with task learning and improved behavior prediction.

Implications and Future Directions

The research underscores DSA's potential as a reliable metric, distinguishing it in terms of efficacy when studying dynamical representations that span various architectures and task conditions. This is particularly pertinent for RNNs dealing with compositional tasks, where traditional metrics might fail to capture the nuances of dynamic learning processes.

Furthermore, the paper suggests that applying DSA in contemporary models such as Mamba SSMs can yield insights into architectural learning mechanisms. In these models, the paper demonstrated that Mamba's expressive hidden states might substitute for dynamic recurrent transformation. This indicates a broader applicability of DSA beyond RNNs, extending into analyzing state space models whose expressive capabilities are yet to be fully understood.

Conclusion

This analysis introduces significant advancements in the domain of neural networks' mechanistic interpretability, providing a nuanced approach to quantify and track how computations develop within RNNs. The development and validation of DSA represent an invaluable tool for researchers aiming to dissect neural dynamics at scale. Future work could explore cross-validation of DSA with empirical neural data, potentially broadening its applicability to more complex neural systems beyond artificial architectures.