Related papers: Characterizing Small Circuit Classes from FAC^0 to…

Let $\mathscr{F}_{n,d}$ be the class of all functions $f:\{-1,1\}^n\to[-1,1]$ on the $n$-dimensional discrete hypercube of degree at most $d$. In the first part of this paper, we prove that any (deterministic or randomized) algorithm which…

This paper presents a new causal network learning algorithm (FSNN, Feedback System Neural Network) based on the construction and analysis of a non-linear system of Ordinary Differential Equations (ODEs). The constructed system provides…

Given an autonomous system of ordinary differential equations (ODE), we consider developing practical models for the deterministic, slow/coarse behavior of the ODE system. Two types of coarse variables are considered. The first type…

Linear models, such as force constant (FC) and cluster expansions, play a key role in physics and materials science. While they can in principle be parametrized using regression and feature selection approaches, the convergence behavior of…

We numerically study the crossing symmetry constraints in 4D CFTs, using previously introduced algorithms based on semidefinite programming. We study bounds on OPE coefficients of tensor operators as a function of their scaling dimension…

The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…

We consider the problem of efficiently enumerating the satisfying assignments to $\AC^0$ circuits. We give a zero-error randomized algorithm which takes an $\AC^0$ circuit as input and constructs a set of restrictions which partition…

We extend in this paper the definition of Caputo derivatives of order in $(0,1)$ to a certain class of locally integrable functions using a convolution group. Our strategy is to define a fractional calculus for a certain class of…

We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…

Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…

The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is…

We aim to identify the generating, ordinary differential equation (ODE) from a set of trajectories of a partially observed system. Our approach does not need prescribed basis functions to learn the ODE model, but only a rich set of Neural…

Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale. We employ an agent-based model to describe the microscopic…

Recently classes of conic and discrete conic functions were introduced. In this paper we use the term convic instead conic. The class of convic functions properly includes the classes of convex functions, strictly quasiconvex functions and…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs).…

We consider boolean circuits computing n-operators f:{0,1}^n --> {0,1}^n. As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes…