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• W2999571325 abstract "Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a conventional neuron is replaced with a quadratic function. The resultant quadratic neuron enjoys an enhanced expressive capability over the conventional neuron. However, how quadratic neurons improve the expressing capability of a deep quadratic network has not been studied up to now, preferably in relation to that of a conventional neural network. Specifically, we ask four basic questions in this paper: (1) for the one-hidden-layer network structure, is there any function that a quadratic network can approximate much more efficiently than a conventional network? (2) for the same multi-layer network structure, is there any function that can be expressed by a quadratic network but cannot be expressed with conventional neurons in the same structure? (3) Does a quadratic network give a new insight into universal approximation? (4) To approximate the same class of functions with the same error bound, could a quantized quadratic network have a lower number of weights than a quantized conventional network? Our main contributions are the four interconnected theorems shedding light upon these four questions and demonstrating the merits of a quadratic network in terms of expressive efficiency, unique capability, compact architecture and computational capacity respectively." @default.
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• W2999571325 date "2020-04-01" @default.
• W2999571325 modified "2023-09-25" @default.
• W2999571325 title "Universal approximation with quadratic deep networks" @default.
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• W2999571325 doi "https://doi.org/10.1016/j.neunet.2020.01.007" @default.
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