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We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…

The Burrows-Wheeler Transform (BWT) is among the most influential discoveries in text compression and DNA storage. It is a reversible preprocessing step that rearranges an $n$-letter string into runs of identical characters (by exploiting…

Previous studies dominantly target at self-supervised learning on real-valued networks and have achieved many promising results. However, on the more challenging binary neural networks (BNNs), this task has not yet been fully explored in…

Based on the assumption that there exists a neural network that efficiently represents a set of Boolean functions between all binary inputs and outputs, we propose a process for developing and deploying neural networks whose weight…

Weight binarization has emerged as a promising strategy to reduce the complexity of large language models (LLMs). Existing approaches fall into post-training binarization, which is simple but causes severe performance loss, and…

We extend the recent sparse Fourier transform algorithm of (Lawlor, Christlieb, and Wang, 2013) to the noisy setting, in which a signal of bandwidth N is given as a superposition of k << N frequencies and additive noise. We present two such…

Several well-studied models of access to data samples, including statistical queries, local differential privacy and low-communication algorithms rely on queries that provide information about a function of a single sample. (For example, a…

Pretrained large language models (LLMs) exhibit exceptional general language processing capabilities but come with significant demands on memory and computational resources. As a powerful compression technology, binarization can extremely…

In this paper we present a new algorithm for online (sequential) inference in Bayesian neural networks, and show its suitability for tackling contextual bandit problems. The key idea is to combine the extended Kalman filter (which locally…

This paper introduces a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained and non-binary problems. The algorithm leverages an engineered interference process…

In this paper, a class of linear authentication codes with secrecy are constructed, which have simple encoding rules and are easy to implement. Based on the special Weil sum, the maximum success probabilities of substitution attack and…

We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…

Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized…

Multiple kernel learning algorithms are proposed to combine kernels in order to obtain a better similarity measure or to integrate feature representations coming from different data sources. Most of the previous research on such methods is…

In this paper, we address the design of high spectral-efficiency Barnes-Wall (BW) lattice codes which are amenable to low-complexity decoding in additive white Gaussian noise (AWGN) channels. We propose a new method of constructing complex…

We consider sparse variants of the classical Learning Parities with random Noise (LPN) problem. Our main contribution is a new algorithmic framework that provides learning algorithms against low-noise for both Learning Sparse Parities…

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…

Large Language Models (LLMs) demonstrate promising capabilities in solving scientific problems but often suffer from the issue of hallucination. While integrating LLMs with tools can mitigate this issue, models fine-tuned on tool usage…