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Neural Collapse is a phenomenon recently discovered in deep classifiers where the last layer activations collapse onto their class means, while the means and last layer weights take on the structure of dual equiangular tight frames. In this paper we present results showing the role of weight decay in the emergence of Neural Collapse in deep homogeneous networks. We show that certain near-interpolating minima of deep networks satisfy the Neural Collapse condition, and this can be derived from the gradient flow on the regularized square loss.

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The recent trend in regularization methods for inverse problems is to replace handcrafted sparsifying operators with data-driven approaches. Although using such machine learning techniques often improves image reconstruction methods, the results can depend significantly on the learning methodology. This paper compares two supervised learning methods. First, the paper considers a transform learning approach and, to learn the transform, introduces a variant on the Procrustes method for wide matrices with orthogonal rows. Second, we consider a bilevel convolutional filter learning approach.

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In this paper we consider a joint detection, mapping and navigation problem by an unmanned aerial vehicle (UAV) with real-time learning capabilities. We formulate this problem as a Markov decision process (MDP), where the UAV is equipped with a THz radar capable to electronically scan the environment with high accuracy and to infer its probabilistic occupancy map. The navigation task amounts to maximizing the desired mapping accuracy and coverage and to decide whether targets (e.g., people carrying radio devices) are present or not.

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Backpropagation has revolutionized neural network training however, its biological plausibility remains questionable. Hebbian learning, a completely unsupervised and feedback free learning technique is a strong contender for a biologically plausible alternative. However, so far, it has neither achieved high accuracy performance vs. backprop, nor is the training procedure simple. In this work, we introduce a new Hebbian learning based neural network, called Hebb-Net.

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