Related papers: Dandelion: Certified Approximations of Elementary …
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
A large body of work in machine learning has focused on the problem of learning a close approximation to an underlying combinatorial function, given a small set of labeled examples. However, for real-valued functions, cardinal labels might…
The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension,…
Outsourcing deep neural networks (DNNs) inference tasks to an untrusted cloud raises data privacy and integrity concerns. While there are many techniques to ensure privacy and integrity for polynomial-based computations, DNNs involve…
We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps >…
We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
Usual termination proofs for a functional program require to check all the possible reduction paths. Due to an exponential gap between the height and size of such the reduction tree, no naive formalization of termination proofs yields a…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions…
Rectified Linear Units (ReLUs) are among the most widely used activation function in a broad variety of tasks in vision. Recent theoretical results suggest that despite their excellent practical performance, in various cases, a substitution…
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…
As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical…
We introduce a computationally efficient screening for the Coulomb potential that also allows calculating approximated long-range exact exchange contributions with an accuracy similar to an explicit full-range evaluation of the exact…
We give two approximation algorithms solving the Stochastic Boolean Function Evaluation (SBFE) problem for symmetric Boolean functions. The first is an $O(\log n)$-approximation algorithm, based on the submodular goal-value approach of…
We study algorithms for average-cost reinforcement learning problems with value function approximation. Our starting point is the recently proposed POLITEX algorithm, a version of policy iteration where the policy produced in each iteration…