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Shapley and Banzhaf interactions capture the complex dynamics inherent in modern machine learning applications. However, current estimators for these higher-order interactions trade off between speed and accuracy. To overcome this…

We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…

We study the natural question of constructing pseudorandom generators (PRGs) for low-degree polynomial threshold functions (PTFs). We give a PRG with seed-length log n/eps^{O(d)} fooling degree d PTFs with error at most eps. Previously, no…

It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibly even transcendental) numbers. In this paper, we prove that…

In this work, we argue that the implications of Pseudo and Quantum Random Number Generators (PRNG and QRNG) inexplicably affect the performances and behaviours of various machine learning models that require a random input. These…

We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…

True random number generator (TRNG) plays a vital role in a variety of security applications and protocols. The security and privacy of an asset rely on the encryption, which solely depends on the quality of random numbers. Memory chips are…

In this work it is shown how 128 bit SSE2 multimedia extension registers, present in Pentium IV class 32 bit processors, may be used to generate random numbers at several times greater speed then when regular general purpose registers are…

A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…

It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…

The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…

We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every…

The ever-increasing need for random numbers is clear in many areas of computer science, from neural networks to optimization. As such, most common programming language provide easy access to Pseudorandom Number Generators. However, these…

In \cite{Castoldi}, $q^t \by (q+1)t$ ordered orthogonal arrays (OOAs) of strength $t$ over the alphabet $\FF_q$ were constructed using linear feedback shift register sequences (LFSRs) defined by {\em primitive} polynomials in $\FF_q[x]$. In…

The Graphcore Intelligence Processing Unit contains an original pseudorandom number generator (PRNG) called xoroshiro128aox, based on the F2-linear generator xoroshiro128. It is designed to be cheap to implement in hardware and provide…

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…

We illustrate a process that constructs martingales from raw material that arises naturally from the theory of sampling without replacement.The usefulness of the new martingales is illustrated by the development of maximal inequalities for…

A high-speed random number generator (RNG) circuit based on magnetoresistive random-access memory (MRAM) using an error-correcting code (ECC) post processing circuit is presented. ECC post processing increases the quality of randomness by…

Random number generation is fundamental for many modern applications including cryptography, simulations and machine learning. Traditional pseudo-random numbers may offer statistical unpredictability, but are ultimately deterministic. On…

We present an application of invariant polynomials in machine learning. Using the methods developed in previous work, we obtain two types of generators of the Lorentz- and permutation-invariant polynomials in particle momenta; minimal…