We investigate how the population nonlinearities resulting from lateral inhibition and thresholding in sparse coding networks influence neural response selectivity and robustness. We show that when compared to pointwise nonlinear models, such population nonlinearities improve the selectivity to a preferred stimulus and protect against adversarial perturbations of the input. These findings are predicted from the geometry of the single-neuron iso-response surface, which provides new insight into the relationship between selectivity and adversarial robustness. Inhibitory lateral connections curve the iso-response surface outward in the direction of selectivity. Since adversarial perturbations are orthogonal to the iso-response surface, adversarial attacks tend to be aligned with directions of selectivity. Consequently, the network is less easily fooled by perceptually irrelevant perturbations to the input. Together, these findings point to benefits of integrating computational principles found in biological vision systems into artificial neural networks.

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Sparse coding models have been widely used to decompose monocular images into linear combinations of small numbers of basis vectors drawn from an overcomplete set. However, little work has examined sparse coding in the context of stereopsis. In this paper, we demonstrate that sparse coding facilitates better depth inference with sparse activations than comparable feed-forward networks of the same size. This is likely due to the noise and redundancy of feed-forward activations, whereas sparse coding utilizes lateral competition to selectively encode image features within a narrow band of depths.

While deep learning has proven to be successful for various tasks in the field of computer vision, there are several limitations of deep-learning models when compared to human performance. Specifically, human vision is largely robust to noise and distortions, whereas deep learning performance tends to be brittle to modifications of test images, including being susceptible to adversarial examples. Additionally, deep-learning methods typically require very large collections of training examples for good performance on a task, whereas humans can learn to perform the same task with a much smaller number of training examples. In this dissertation, I investigate whether the use of a biologically informed, unsupervised sparse coding algorithm can help to alleviate these shortcomings within classification networks. I find that (1) the non-linear encoding scheme of convolutional sparse coding, as opposed to the dictionary learned, contributes to classification performance when used within a model. In addition, (2) sparse coding helps classification models trained on clean images to be more robust to adversarial examples and images corrupted with high frequency noise. Finally, (3) sparse coding helps alleviate the number of human-annotated training labels needed for classification on stereo-video data. Overall, using unsupervised sparse coding within supervised models can help alleviate various shortcomings of traditional deep neural networks. i List of Figures .