Related papers: Cube-based Isomorph-free Finite Model Finding

While it is trivial to multiply two C-finite sequences (just like integers), it is not quite so trivial to "factorize" them, or to decide whether they are "prime". The former is plain linear algebra, while the latter is heavy-duty…

Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…

This paper presents a novel approach for similarity search with complex filtering capabilities on billion-scale datasets, optimized for CPU inference. Our method extends the classical IVF-Flat index structure to integrate multi-dimensional…

Collaborative filtering (CF), as a fundamental approach for recommender systems, is usually built on the latent factor model with learnable parameters to predict users' preferences towards items. However, designing a proper CF model for a…

The paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used in simulating complex physical processes on supercomputer systems. The proposed methodology is based on…

Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…

In this paper, we propose a two-steps approach to partition instances of the Conjunctive Normal Form (CNF) Syntactic Formula Isomorphism problem (CSFI) into groups of different complexity. First, we build a model, based on the Transformer…

Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…

It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…

Most fair machine learning methods either highly rely on the sensitive information of the training samples or require a large modification on the target models, which hinders their practical application. To address this issue, we propose a…

We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach relies on a multi-scale pruning scheme that is able to…

The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires…

We factor Beamer's push-pull, also known as direction-optimized breadth-first-search (DOBFS) into 3 separable optimizations, and analyze them for generalizability, asymptotic speedup, and contribution to overall speedup. We demonstrate that…

Here we present a very efficient method to search for Liouvillian first integrals of second order rational ordinary differential equations (rational 2ODEs). This new algorithm can be seen as an improvement to the S-function method we have…

We present novel algorithms for design and design space exploration. The designs discovered by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified…

In collaborative filtering (CF) algorithms, the optimal models are usually learned by globally minimizing the empirical risks averaged over all the observed data. However, the global models are often obtained via a performance tradeoff…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

We design and analyze an algorithm for computing solutions with coefficients in a finite field $\mathbb{F}_q$ of underdetermined systems defined over $\mathbb{F}_q$. The algorithm is based on reductions to zero-dimensional searches. The…

Confounders in deep learning are in general detrimental to model's generalization where they infiltrate feature representations. Therefore, learning causal features that are free of interference from confounders is important. Most previous…

We propose a polynomial time $f$-algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over $\mathbb{F}_q$) for computing an isomorphism (if there is any) of a finite dimensional…