When and why representations learned by different deep neural networks are similar is an active research topic. We choose to address these questions from the perspective of identifiability theory, which suggests that a measure of representational similarity should be invariant to transformations that leave the model distribution unchanged. Focusing on a model family which includes several popular pre-training approaches, e.g., autoregressive language models, we explore when models which generate distributions that are close have similar representations. We prove that a small Kullback--Leibler divergence between the model distributions does not guarantee that the corresponding representations are similar. This has the important corollary that models with near-maximum data likelihood can still learn dissimilar representations---a phenomenon mirrored in our experiments with models trained on CIFAR-10. We then define a distributional distance for which closeness implies representational similarity, and in synthetic experiments, we find that wider networks learn distributions which are closer with respect to our distance and have more similar representations. Our results thus clarify the link between closeness in distribution and representational similarity.

Deep neural networks (DNNs) are widely used models for investigating biological visual representations. However, existing DNNs are mostly designed to analyze neural responses to static images, relying on feedforward structures and lacking physiological neuronal mechanisms. There is limited insight into how the visual cortex represents natural movie stimuli that contain context-rich information. To address these problems, this work proposes the long-range feedback spiking network (LoRaFB-SNet), which mimics top-down connections between cortical regions and incorporates spike information processing mechanisms inherent to biological neurons. Taking into account the temporal dependence of representations under movie stimuli, we present Time-Series Representational Similarity Analysis (TSRSA) to measure the similarity between model representations and visual cortical representations of mice. LoRaFB-SNet exhibits the highest level of representational similarity, outperforming other well-known and leading alternatives across various experimental paradigms, especially when representing long movie stimuli. We further conduct experiments to quantify how temporal structures (dynamic information) and static textures (static information) of the movie stimuli influence representational similarity, suggesting that our model benefits from long-range feedback to encode context-dependent representations just like the brain. Altogether, LoRaFB-SNet is highly competent in capturing both dynamic and static representations of the mouse visual cortex and contributes to the understanding of movie processing mechanisms of the visual system.

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.