We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...
Locally correctable codes (LCCs) are error correcting codes C : \Sigmak \rightarrow \Sigman which admit local algorithms that correct any individual symbol of a corrupted codeword via a minuscule number of queries. For systematic codes, this notion is stro ...
We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...
The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...
Neural networks have become indispensable for a wide range of applications, but they suffer from high computational- and memory-requirements, requiring optimizations from the algorithmic description of the network to the hardware implementation. Moreover, ...
