Computing optimal discrete readout weights in reservoir computing is NP-hard
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We show NP-hardness of a generalized quadratic programming problem, which we called Unconstrained N-ary Quadratic Programming (UNQP). This problem has recently become practically relevant in the context of novel memristor-based neuromorphic microchip designs, where solving the UNQP is a key operation for on-chip training of the neural network implemented on the chip. UNQP is the problem of finding a vector v∈ S^N which minimizes v^T Q v +v^T c , where S = {s_1, ..., s_n}⊂Z is a given set of eligible parameters for v, Q ∈Z^N × N is positive semi-definite, and c∈Z^N. In memristor-based neuromorphic hardware, S is physically given by a finite (and small) number of possible memristor states. The proof of NP-hardness is by reduction from the Unconstrained Binary Quadratic Programming problem, which is a special case of UNQP where S = {0, 1} and which is known to be NP-hard.
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