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- W2022088560 abstract "Abstract Owing to their generalization-and-approximation capability, humans can recognize an object world such as a motion picture film by perceiving an appropriate finite set of points selected from among objects such as picture frames. This paper mathematically constructs a specific minimal layer network of a continuous type loaded with minimal finite samples that can simulate the human generalization-and-approximation capability. First, it formulates a Generalization-and-Approximation Problem (GAP) mathematically rigorously. It is to find a minimal pair of 〈sample, structure〉 that can generalize-and-approximate any given smooth mapping from an object world to another. Here, a structure of the network is comprised of unit sizes, synapse weights and biases. In addition, the pair 〈sample, structure〉 is minimal if the number of samples and the unit sizes are both minimum. Next, it reduces the GAP into a Standard Restricted Version (SRV-GAP) where solution construction techniques are restricted to those through polynomials. This is because of our aim to construct a practically feasible GAP solution that is calculable by almost all computers. Finally, the paper constructs a solution to the SRV-GAP rigorously, which constitutes its main results. It argues additionally that the solution also yields a useful practical version of the current universal approximation theorem that ensures an approximator network of a continuous mapping from one Euclidean space to another." @default.
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- W2022088560 date "1997-07-01" @default.
- W2022088560 modified "2023-09-25" @default.
- W2022088560 title "Simulating human generalization-and-approximation capability by minimal layer networks loaded with minimal samples" @default.
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- W2022088560 doi "https://doi.org/10.1016/s0925-2312(97)89422-2" @default.
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