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Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to…
This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…
Link prediction is a cornerstone of the Web ecosystem, powering applications from recommendation and search to knowledge graph completion and collaboration forecasting. However, large-scale networks present unique challenges: they contain…
We present an application of the tensor network generator-enhanced optimization (TN-GEO) framework to address the traveling salesman problem (TSP), a fundamental combinatorial optimization challenge. Our approach employs a tensor network…
Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, long-horizon…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
Transition path sampling (TPS), which involves finding probable paths connecting two points on an energy landscape, remains a challenge due to the complexity of real-world atomistic systems. Current machine learning approaches use…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations,…
This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems beyond the case of free fermions. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the…
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. In…
We present the Temporal Graph Benchmark (TGB), a collection of challenging and diverse benchmark datasets for realistic, reproducible, and robust evaluation of machine learning models on temporal graphs. TGB datasets are of large scale,…
This study addresses the Min-Max Multiple Traveling Salesmen Problem ($m^3$-TSP), which aims to coordinate tours for multiple salesmen such that the length of the longest tour is minimized. Due to its NP-hard nature, exact solvers become…
We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is…
We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing…
Accurate Traffic Prediction is a challenging task in intelligent transportation due to the spatial-temporal aspects of road networks. The traffic of a road network can be affected by long-distance or long-term dependencies where existing…
Test-Time Scaling (TTS) improves large language models (LLMs) by allocating additional computation during inference, typically through parallel, sequential, or hybrid scaling. However, prior studies often assume fixed collaboration…
Two-trust-region subproblem (TTRS), which is the minimization of a general quadratic function over the intersection of two full-dimensional ellipsoids, has been the subject of several recent research. In this paper, to solve TTRS, a hybrid…