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In this paper, we focus on the problem of integrating Energy-based Models (EBM) as guiding priors for motion optimization. EBMs are a set of neural networks that can represent expressive probability density distributions in terms of a Gibbs…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
Energy-Based Models (EBMs) offer a versatile framework for modeling complex data distributions. However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method for…
We show a new algorithm and its implementation for multiplying bit-polynomials of large degrees. The algorithm is based on evaluating polynomials at a specific set comprising a natural set for evaluation with additive FFT and a high order…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional…
We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dimension three that parametrize rational conformal motions.…
This work explores the novel idea of learning a submodular scoring function to improve the specificity/selectivity of existing feature attribution methods. Submodular scores are natural for attribution as they are known to accurately model…
We present efficient algorithms to calculate the color factors for the $SU(N)$ gauge group and to evaluate $\gamma$ traces. The aim of these notes is to give a self-contained, proved account of the basic results with particular emphasis on…
Instrumental variable analysis is a powerful tool for estimating causal effects when randomization or full control of confounders is not possible. The application of standard methods such as 2SLS, GMM, and more recent variants are…
Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
We describe a combinatorial algorithm which, given a monotone and consistent symmetric set function d on a finite set V in the sense of Rizzi, constructs a non trivial set S minimizing d(S,V-S). This includes the possibility for the…
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
Submodular functions are set functions mapping every subset of some ground set of size $n$ into the real numbers and satisfying the diminishing returns property. Submodular minimization is an important field in discrete optimization theory…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…
Community detection is a fundamental task in graph analysis, with methods often relying on fitting models like the Stochastic Block Model (SBM) to observed networks. While many algorithms can accurately estimate SBM parameters when the…
We present the first mini-batch algorithm for maximizing a non-negative monotone decomposable submodular function, $F=\sum_{i=1}^N f^i$, under a set of constraints. We consider two sampling approaches: uniform and weighted. We first show…