Abstract: A system for determining the frequency coefficients of a one or multi-dimensional signal that is sparse in the frequency domain includes determining the locations of the non-zero frequency coefficients, and then determining values of the coefficients using the determined locations. If N is total number of frequency coefficients across the one or more dimension of the signal, and if R is an upper bound of the number of non-zero ones of these frequency coefficients, the systems requires up to (O(Rlog(R) (N))) samples and has a computation complexity of up to O(Rlog2(R) log (N). The system and the processing technique are stable to low-level noise and can exhibit only a small probability of failure. The frequency coefficients can be real and positive or they can be complex numbers.

Abstract: A processor-implemented method includes approximating an optimization problem for training an artificial neural network as a nested polynomial optimization problem. The method also includes dividing the nested polynomial optimization problem into a sequence of sub-problems. The method further includes hierarchically solving the sequence of sub-problems to train the artificial neural network.

Abstract: A processor-implemented method includes receiving as input, a global polynomial optimization problem that approximates a training problem of a neural network. The method also includes relaxing the global polynomial optimization problem including polynomial constraints with multiple semi-definite programs. The method further includes solving the semi-definite programs based on a pre-defined structure and outputting a solution indicating a location of a global optimum of the optimization problem. The method includes performing inference with the neural network based on the solution.

Abstract: A processor-implemented method includes receiving, as input, an array of values characterizing a polynomial feasibility problem representing a physical system for solving a computational problem. The method also includes reducing dimensions of the polynomial feasibility problem by transforming the polynomial feasibility problem into a high-dimensional linear feasibility problem and a non-linear feasibility problem. The method further includes solving the high-dimensional linear feasibility problem to obtain a first set of interim solutions. The method includes solving the non-linear feasibility problem based on the first set of interim solutions to obtain a result of the non-linear feasibility problem. The method also includes outputting parameters characterizing the physical system, with a ground state corresponding to an output solution of the computational problem based on the result obtained from solving the non-linear feasibility problem.

Abstract: A technique for measuring properties of a material includes measuring the electromagnetic radiation scattered by one or more scattering points associated with the material, and adjusting the radiation according to the respective sensitivities of the scattering points to changes in material properties at that scattering point for several pairs of radiation sources and receivers. The material properties are determined using the updated measurements and corresponding simulated measurements.

Abstract: A system for determining the frequency coefficients of a one or multi-dimensional signal that is sparse in the frequency domain includes determining the locations of the non-zero frequency coefficients, and then determining values of the coefficients using the determined locations. If N is total number of frequency coefficients across the one or more dimension of the signal, and if R is an upper bound of the number of non-zero ones of these frequency coefficients, the systems requires up to (O (R log(R) (N))) samples and has a computation complexity of up to O (R log2(R) log (N). The system and the processing technique are stable to low-level noise and can exhibit only a small probability of failure. The frequency coefficients can be real and positive or they can be complex numbers.

Abstract: A signal pre-compensation system analyzes one or more properties of a communication medium and, taking advantage of the locality of propagation, generates using sparse fast Fourier transform (sFFT) a sparse kernel based on the medium properties. The system models propagation of data signals through the medium as a fixed-point iteration based on the sparse kernel, and determines initial amplitudes for the data symbol(s) to be transmitted using different communication medium modes. Fixed-point iterations are performed using the sparse kernel to iteratively update the initial amplitudes. If the iterations converge, a subset of the finally updated amplitudes is used as launch amplitudes for the data symbol(s). The data symbol(s) can be modulated using these launch amplitudes such that upon propagation of the pre-compensated data symbol(s) through the communication medium, they would resemble the original data symbols at a receiver, despite any distortion and/or cross-mode interference in the communication medium.

Abstract: A signal pre-compensation system analyzes one or more properties of a communication medium and, taking advantage of the locality of propagation, generates using sparse fast Fourier transform (sFFT) a sparse kernel based on the medium properties. The system models propagation of data signals through the medium as a fixed-point iteration based on the sparse kernel, and determines initial amplitudes for the data symbol(s) to be transmitted using different communication medium modes. Fixed-point iterations are performed using the sparse kernel to iteratively update the initial amplitudes. If the iterations converge, a subset of the finally updated amplitudes is used as launch amplitudes for the data symbol(s). The data symbol(s) can be modulated using these launch amplitudes such that upon propagation of the pre-compensated data symbol(s) through the communication medium, they would resemble the original data symbols at a receiver, despite any distortion and/or cross-mode interference in the communication medium.