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Full-Text Articles in Physical Sciences and Mathematics
Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva
Deep Learning (Partly) Demystified, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Successes of deep learning are partly due to appropriate selection of activation function, pooling functions, etc. Most of these choices have been made based on empirical comparison and heuristic ideas. In this paper, we show that many of these choices -- and the surprising success of deep learning in the first place -- can be explained by reasonably simple and natural mathematics.
Softmax And Mcfadden's Discrete Choice Under Interval (And Other) Uncertainty, Bartłomiej Jacek Kubica, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Softmax And Mcfadden's Discrete Choice Under Interval (And Other) Uncertainty, Bartłomiej Jacek Kubica, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the important steps in deep learning is softmax, when we select one of the alternatives with a probability depending on its expected gain. A similar formula describes human decision making: somewhat surprisingly, when presented with several choices with different expected equivalent monetary gain, we do not just select the alternative with the largest gain; instead, we make a random choice, with probability decreasing with the gain -- so that it is possible that we will select second highest and even third highest value. Both formulas assume that we know the exact value of the expected gain for each …