5 research outputs found
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Larger bases and mixed analog/digital neural nets
The paper overviews results dealing with the approximation capabilities of neural networks, and bounds on the size of threshold gate circuits. Based on an explicit numerical algorithm for Kolmogorov`s superpositions the authors show that minimum size neural networks--for implementing any Boolean function--have the identity function as the activation function. Conclusions and several comments on the required precision are ending the paper
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Implementing size-optimal discrete neural networks require analog circuitry
This paper starts by overviewing results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on a constructive solution for Kolmogorov`s superpositions the authors show that implementing Boolean functions can be done using neurons having an identity transfer function. Because in this case the size of the network is minimized, it follows that size-optimal solutions for implementing Boolean functions can be obtained using analog circuitry. Conclusions and several comments on the required precision are ending the paper
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On automatic synthesis of analog/digital circuits
The paper builds on a recent explicit numerical algorithm for Kolmogorov`s superpositions, and will show that in order to synthesize minimum size (i.e., size-optimal) circuits for implementing any Boolean function, the nonlinear activation function of the gates has to be the identity function. Because classical and--or implementations, as well as threshold gate implementations require exponential size, it follows that size-optimal solutions for implementing arbitrary Boolean functions can be obtained using analog (or mixed analog/digital) circuits. Conclusions and several comments are ending the paper
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2D neural hardware versus 3D biological ones
This paper will present important limitations of hardware neural nets as opposed to biological neural nets (i.e. the real ones). The author starts by discussing neural structures and their biological inspirations, while mentioning the simplifications leading to artificial neural nets. Going further, the focus will be on hardware constraints. The author will present recent results for three different alternatives of implementing neural networks: digital, threshold gate, and analog, while the area and the delay will be related to neurons' fan-in and weights' precision. Based on all of these, it will be shown why hardware implementations cannot cope with their biological inspiration with respect to their power of computation: the mapping onto silicon lacking the third dimension of biological nets. This translates into reduced fan-in, and leads to reduced precision. The main conclusion is that one is faced with the following alternatives: (1) try to cope with the limitations imposed by silicon, by speeding up the computation of the elementary silicon neurons; (2) investigate solutions which would allow one to use the third dimension, e.g. using optical interconnections
A Constructive Approach to Calculating Lower Entropy Bounds
This paper presents a constructive approach to estimating the size of a neural network necessary to solve a given classification problem. The results are derived using an information entropy approach in the context of limited precision integer weights. Such weights are particularly suited for hardware implementations since the area they occupy is limited, and the computations performed with them can be efficiently implemented in hardware. The considerations presented use an information entropy perspective and calculate lower bounds on the number of bits needed in order to solve a given classification problem. These bounds are obtained by approximating the classification hypervolumes with the volumes of several regular (i.e. highly symmetric) n-dimensional bodies. The bounds given here allow the user to choose the appropriate size of a neural network such that: (i) the given classification problem can be solved, and (ii) the network architecture is not oversized. All considerations pres..