Abstract: Certain aspects of the present disclosure provide techniques and apparatus for executing a workload on a computing device based on an approximation of a target function. An example method generally includes generating a plurality of sample points from a multi-dimensional space representing domain of a target function. A plurality of sparse matrices is generated from the plurality of sample points, each respective sparse matrix being generated based on known non-zero coefficients of the target function. A plurality of transformed sparse matrices representing a relationship between Chebyshev coefficients of the target function and the plurality of sample points after applying lower dimensional cosine transformations are generated. An approximation of the target function is generated based on the plurality of transformed sparse matrices. An output of at least a portion of a neural network may be generated based on the approximation of the target function.

Abstract: A processor-implemented method for simultaneously tracking one or more objects includes receiving, via a dynamical system with a set of sensors, a first set of unlabeled measurements from one or more objects. Each of the measurements is a function of time. A set of candidate tracks is determined for the one or more objects. Probabilities of each of the first set of unlabeled measurements being assigned to each of the set of candidate tracks are computed. A track from the set of candidate tracks is determined for each of the one or more objects based on a joint probability distribution of track attributes and the probabilistic assignment of each of the first set of unlabeled measurements to each of the set of candidate tracks.

Abstract: Methods, systems, and media for solving quadratic optimization problems are disclosed herein. In some embodiments, a method may involve receiving, by one or more processors, a first quadratic optimization problem comprising an objective and a set of inequality constraints. The method may involve obtaining an initial solution to the first quadratic optimization problem subject to the set of inequality constraints. The method may involve identifying a subset of the set of inequality constraints that are active constraints with respect to an optimal solution. The method may involve obtaining an updated solution to the first quadratic optimization problem by solving a second quadratic optimization problem that corresponds to optimizing the objective subject to the active constraints. The method may involve determining an accuracy and precision associated with the updated solution.

Abstract: A processor-implemented method for simultaneously tracking one or more objects includes receiving, via a dynamical system with a set of sensors, a first set of unlabeled measurements from one or more objects. Each of the measurements is a function of time. A set of candidate tracks is determined for the one or more objects. Probabilities of each of the first set of unlabeled measurements being assigned to each of the set of candidate tracks are computed. A track from the set of candidate tracks is determined for each of the one or more objects based on a joint probability distribution of track attributes and the probabilistic assignment of each of the first set of unlabeled measurements to each of the set of candidate tracks.

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.