A synthesis of approximation, optimization, and generalization theory arguing that gradient descent's implicit norm control on weight directions explains why overparameterized deep networks generalize.
An Algorithm for Training Polynomial Networks
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abstract
We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the \emph{Basis Learner}. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.
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cs.LG 1years
2019 1verdicts
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Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization
A synthesis of approximation, optimization, and generalization theory arguing that gradient descent's implicit norm control on weight directions explains why overparameterized deep networks generalize.