相关论文: Uniformity is weaker than semi-uniformity for some…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
We show that two related classes of algorithms, stable algorithms and Boolean circuits with bounded depth, cannot produce an approximate sample from the uniform measure over the set of solutions to the symmetric binary perceptron model at…
Access to quantum computing is steadily increasing each year as the speed advantage of quantum computers solidifies with the growing number of usable qubits. However, the inherent noise encountered when running these systems can lead to…
As supercomputers' complexity has grown, the traditional boundaries between processor, memory, network, and accelerators have blurred, making a homogeneous computer model, in which the overall computer system is modeled as a continuous…
This paper consists of three parts. The first part provides a unified programming model for heterogeneous computing with CPU and accelerator (like GPU, FPGA, Google TPU, Atos QPU, and more) technologies. To some extent, this new programming…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Bounds on their performance, derived in the…
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
Probabilistic circuits are a unifying representation of functions as computation graphs of weighted sums and products. Their primary application is in probabilistic modeling, where circuits with non-negative weights (monotone circuits) can…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
Membranes are of great technological and biological as well as theoretical interest. Two main classes of membranes can be distinguished: Fluid membranes and polymerized, tethered membranes. Here, we review progress in the theoretical…
Neural networks are capable of superposition -- representing more features than there are dimensions. Recent work considers the analogous concept for computation instead of storage, proposing theoretical constructions. But there has been…
In present day technology, storing and processing of information occur on physically distinct regions of space. Not only does this result in space limitations; it also translates into unwanted delays in retrieving and processing of relevant…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
Quantization has emerged as a mainstream method for compressing Large Language Models (LLMs), reducing memory requirements and accelerating inference without architectural modifications. While existing research primarily focuses on…
We introduce a new category of non-archimedean analytic spaces over a complete discretely valued field. These spaces, which we call uniformly rigid, may be viewed as classical rigid-analytic spaces together with an additional uniform…
Despite excellent performance on many tasks, NLP systems are easily fooled by small adversarial perturbations of inputs. Existing procedures to defend against such perturbations are either (i) heuristic in nature and susceptible to stronger…
Recent work has shown that the input-output behavior of some machine learning systems can be captured symbolically using Boolean expressions or tractable Boolean circuits, which facilitates reasoning about the behavior of these systems.…
Recent developments in lipid membrane models for simulations are reviewed. To reduce computational costs, various coarse-grained molecular models have been proposed. Among them, implicit solvent (solvent-free) molecular models are…