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Moving Horizon Estimation~(MHE) is essentially an optimization-based approach designed to estimate the states of dynamic systems within a moving time horizon. Traditional MHE solutions become computationally prohibitive due to the…

The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…

A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…

In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DLP) into a system of equations. These…

Large Language Models (LLMs) are powerful but incur high memory and computation costs. Quantization is an effective solution, with INT weights and FP activations being widely adopted to preserve accuracy. Prior works further reduce FP…

We formalize and interpret the geometric structure of $d$-dimensional fully connected ReLU layers in neural networks. The parameters of a ReLU layer induce a natural partition of the input domain, such that the ReLU layer can be…

The low-rank approximation properties of Randomly Pivoted LU (RPLU), a variant of Gaussian elimination where pivots are sampled proportional to the squared entries of the Schur complement, are analyzed. It is shown that the RPLU iterates…

Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…

We consider the problem of learning an arbitrarily-biased ReLU activation (or neuron) over Gaussian marginals with the squared loss objective. Despite the ReLU neuron being the basic building block of modern neural networks, we still do not…

Vision-language models (VLMs) enable open-ended visual question answering but remain prone to hallucinations. We present HEDGE, a unified framework for hallucination detection that combines controlled visual perturbations, semantic…

This paper introduces efficient modifications to neural network-based sequence processing approaches, laying new grounds for scalable privacy-preserving machine learning under Fully Homomorphic Encryption (FHE). Transformers are now…

In the steady-state contingency analysis, the traditional Newton-Raphson method suffers from non-convergence issues when solving post-outage power flow problems, which hinders the integrity and accuracy of security assessment. In this…

Model quantization is a widely used technique to compress and accelerate deep neural network (DNN) inference. Emergent DNN hardware accelerators begin to support mixed precision (1-8 bits) to further improve the computation efficiency,…

We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…

One common function class in machine learning is the class of ReLU neural networks. ReLU neural networks induce a piecewise linear decomposition of their input space called the canonical polyhedral complex. It has previously been…

Quantum fully homomorphic encryption (QFHE) promises secure delegated quantum computation but has been impeded by the prohibitive quantum resource demands of existing constructions. This paper introduces a unified framework that achieves an…

Gaussian Error Linear Unit (GELU) is a widely used smooth alternative to Rectifier Linear Unit (ReLU), yet many deployment, compression, and analysis toolchains are most naturally expressed for piecewise-linear (ReLU-type) networks. We…

The low-degree polynomial framework has emerged as a powerful tool for providing evidence of statistical-computational gaps in high-dimensional inference. For detection problems, the standard approach bounds the low-degree advantage through…

A large variety of real-world Reinforcement Learning (RL) tasks is characterized by a complex and heterogeneous structure that makes end-to-end (or flat) approaches hardly applicable or even infeasible. Hierarchical Reinforcement Learning…

The Learning-With-Errors (LWE) problem is a fundamental computational challenge with implications for post-quantum cryptography and computational learning theory. Here we propose a quantum-classical hybrid algorithm with Ising model to…