Exploring Neural Network Representational Similarity using Filter Subspaces

Wei Chen, Zichen Miao, Qiang Qiu

Abstract: Analyzing representational similarity in neural networks is crucial to numerous tasks, such as interpreting or transferring deep models. One typical approach is to input probing data into convolutional neural networks (CNNs) as stimuli to reveal their deep representation for model similarity analysis. Those methods are often computationally expensive and stimulus-dependent. By representing filter subspace in a CNN as a set of filter atoms, previous work has reported competitive performance in continual learning by learning a different set of filter atoms for each task while sharing common atom coefficients across tasks. Inspired by this observation, in this paper, we propose a new paradigm for reducing representational similarity analysis in CNNs to filter subspace distance assessment. Specifically, when filter atom coefficients are shared across networks, model representational similarity can be significantly simplified as calculating the cosine distance among respective filter atoms, to achieve \textit{millions of times} computation reduction. We provide both theoretical and empirical evidence that this simplified filter subspace-based similarity preserves a strong linear correlation with other popular stimulus-based metrics, while being significantly more efficient and robust to probing data. We further validate the effectiveness of the proposed method in various applications, such as analyzing training dynamics as well as in federated and continual learning. We hope our findings can help further explorations of real-time large-scale representational similarity analysis in neural networks.

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