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The representations of neural networks are often compared to those ofbiological systems by performing regression between the neural networkresponses and those measured from biological systems. Many differentstate-of-the-art deep neural networks yield similar neural predictions, but itremains unclear how to differentiate among models that perform equally well atpredicting neural responses. To gain insight into this, we use a recenttheoretical framework that relates the generalization error from regression tothe spectral properties of the model and the target. We apply this theory tothe case of regression between model activations and neural responses anddecompose the neural prediction error in terms of the model eigenspectra,alignment of model eigenvectors and neural responses, and the training setsize. Using this decomposition, we introduce geometrical measures to interpretthe neural prediction error. We test a large number of deep neural networksthat predict visual cortical activity and show that there are multiple types ofgeometries that result in low neural prediction error as measured viaregression. The work demonstrates that carefully decomposing representationalmetrics can provide interpretability of how models are capturing neuralactivity and points the way towards improved models of neural activity.

A Spectral Theory of Neural Prediction and Alignment