In neuroscience, the similarity matrix of neural activity patterns in response to different sensory stimuli or under different cognitive states reflects the structure of neural representational space. Existing methods derive point estimations of neural activity patterns from noisy neural imaging data, and the similarity is calculated from these point estimations. We show that this approach translates structured noise from estimated patterns into spurious bias structure in the resulting similarity matrix, which is especially severe when signal-to-noise ratio is low and experimental conditions cannot be fully randomized in a cognitive task. We propose an alternative Bayesian framework for computing representational similarity in which we treat the covariance structure of neural activity patterns as a hyper-parameter in a generative model of the neural data, and directly estimate this covariance structure from imaging data while marginalizing over the unknown activity patterns. Converting the estimated covariance structure into a correlation matrix offers a much less biased estimate of neural representational similarity. Our method can also simultaneously estimate a signal-to-noise map that informs where the learned representational structure is supported more strongly, and the learned covariance matrix can be used as a structured prior to constrain Bayesian estimation of neural activity patterns.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Here we provide more experimental results. Specifically, we evaluate the representational similarity using the CKA value of the same layer from the model (ResNet-32) with different sparsity at each epoch and compare them with the final model. In our work, we evaluate four different types of freezing schemes (Sec. Inthis case, we can keep the single-shot & resume has the same FLOPs reduction asthe single-shot scheme, and the entire network can be fine-tuned at the end of training with a small learningrate. For the periodically freezing scheme, we let the selected layers freeze periodically with a given frequency so that all the layers/blocks are able to be updated at different stages of the training process.

Analyzing representational similarity among neural networks (NNs) is essential for interpreting or transferring deep models. In application scenarios where numerous NN models are learned, it becomes crucial to assess model similarities in computationally efficient ways. In this paper, we propose a new paradigm for reducing NN representational similarity to filter subspace distance. Specifically, when convolutional filters are decomposed as a linear combination of a set of filter subspace elements, denoted as filter atoms, and have those decomposed atom coefficients shared across networks, NN representational similarity can be significantly simplified as calculating the cosine distance among respective filter atoms, to achieve millions of times computation reduction over popular probing-based methods. We provide both theoretical and empirical evidence that such simplified filter subspace-based similarity preserves a strong linear correlation with other popular probing-based metrics, while being significantly more efficient to obtain and robust to probing data. We further validate the effectiveness of the proposed method in various application scenarios where numerous models exist, such as federated and continual learning as well as analyzing training dynamics. We hope our findings can help further explorations of real-time large-scale representational similarity analysis in neural networks.

Despite impressive performance on numerous visual tasks, Convolutional Neural Networks (CNNs) --- unlike brains --- are often highly sensitive to small perturbations of their input, e.g.