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Deep learning, computational neuroscience, and cognitive science have overlapping goals related to understanding intelligence such that perc… (see more)eption and behaviour can be simulated in computational systems. In neuroimaging, machine learning methods have been used to test computational models of sensory information processing. Recently, these model comparison techniques have been used to evaluate deep neural networks (DNNs) as models of sensory information processing. However, the interpretation of such model evaluations is muddied by imprecise statistical conclusions. Here, we make explicit the types of conclusions that can be drawn from these existing model comparison techniques and how these conclusions change when the model in question is a DNN. We discuss how DNNs are amenable to new model comparison techniques that allow for stronger conclusions to be made about the computational mechanisms underlying sensory information processing.
While a lot of progress has been made in recent years, the dynamics of learning in deep nonlinear neural networks remain to this day largely… (see more) misunderstood. In this work, we study the case of binary classification and prove various properties of learning in such networks under strong assumptions such as linear separability of the data. Extending existing results from the linear case, we confirm empirical observations by proving that the classification error also follows a sigmoidal shape in nonlinear architectures. We show that given proper initialization, learning expounds parallel independent modes and that certain regions of parameter space might lead to failed training. We also demonstrate that input norm and features' frequency in the dataset lead to distinct convergence speeds which might shed some light on the generalization capabilities of deep neural networks. We provide a comparison between the dynamics of learning with cross-entropy and hinge losses, which could prove useful to understand recent progress in the training of generative adversarial networks. Finally, we identify a phenomenon that we baptize \textit{gradient starvation} where the most frequent features in a dataset prevent the learning of other less frequent but equally informative features.
