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arXiv:2606.00179v1 Announce Type: cross Abstract: In this paper, we investigate contraction analysis for nonlinear time-delay systems described by functional differential equations. We first extend the concept of Lyapunov-Krasovskii functionals within the differential framework. We then show that its existence is equivalent to that of an incremental Lyapunov-Krasovskii functional and guarantees uniform incremental exponential stability. Ne..
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Agentic Transformers Provably Learn to Search via Reinforcement Learning
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arxiv.org
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2 days ago
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eng
arXiv:2606.00183v1 Announce Type: cross Abstract: Tree search is a central abstraction behind many language-agent reasoning and decision-making tasks: agents must explore actions, remember failures, and backtrack toward promising alternatives. Yet, we lack a theoretical understanding of how transformer-based policies acquire such search capabilities from the training dynamics of reinforcement learning (RL). We study this question in a stoc....
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arXiv:2606.00245v1 Announce Type: cross Abstract: We develop a new algorithm for computing the second discrete homology group of a graph which is much faster when compared to existing algorithms. To do so, we identify five basic shapes, which are quotient graphs of the 3-cube with the property that the injective maps from them detect all possible 2-boundaries in the singular chain complex computing discrete homology.
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High-Dimensional Expanders, the Sparsest Cut Problem, and Steurer's Conjecture
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arxiv.org
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2 days ago
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eng
arXiv:2606.00292v1 Announce Type: cross Abstract: In 2010, Steurer conjectured that any family of $n$ unit-norm vectors $v_1,\dots,v_n$ with polynomially small average correlation $\mathbb{E}_{i,j}|\langle v_i,v_j\rangle|\leq n^{-\epsilon}$ contains linear-sized constant-separated sets. We refute this conjecture in a strong sense using the machinery of sparse high-dimensional expanders: such vector families do not even have linear-sized $\..
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arXiv:2606.00296v1 Announce Type: cross Abstract: Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining. Despite strong empirical evidence, the theoretical foundations of this phenomenon remain unclear. In this work, we provide a systematic theoretical study of zero-shot super-resolut..
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arXiv:2606.00311v1 Announce Type: cross Abstract: The causal propagator (or Pauli-Jordan function), which multiplied by $i$ is the spacetime commutator of the field $[\phi(x),\phi(x')]$, plays an essential role in scalar quantum field theory. We discuss the role of the causal propagator and its spectrum in recent developments in defining quantum field theory in a more explicitly covariant manner, as well as in causal set theory. We then pr..
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Generalized Model Predictive Path Integral Control as Expectation--Maximization
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arxiv.org
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2 days ago
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eng
arXiv:2606.00317v1 Announce Type: cross Abstract: Model Predictive Path Integral (MPPI) control is a powerful sampling-based method for solving stochastic optimal control problems and has enabled real-time control in complex robotic systems. Despite its empirical success, its theoretical understanding remains limited. In this work, we show that MPPI can be interpreted as a special case of the Expectation-Maximization (EM) algorithm applied....
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Data-Driven Spectral Prediction for Accelerating Large-Scale Electronic Structure Calculations
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arxiv.org
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2 days ago
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eng
arXiv:2606.00401v1 Announce Type: cross Abstract: Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies. While modern Density Functional Theory (DFT) codes exhibit linear scaling, solving the associated large, sparse generalized eigenproblems remains a critical computational bottleneck on exascale architectures. In the context of the LimitX project, we propose a data-driven framework to acc....
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Verifying global identifiability of parametric linear ODE models is NP-hard
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arxiv.org
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2 days ago
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eng
arXiv:2606.00412v1 Announce Type: cross Abstract: Global parameter identifiability is a property of a parametric ODE model to recover the parameter values uniquely from the input-output data. Not all parametric ODE models have this property, and checking for parameter identifiability is a prerequisite to perform numerical parameter estimation. There are many algorithms and software packages for global parameter identifiability, and frequen..
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arXiv:2606.00436v1 Announce Type: cross Abstract: Clustering is a central tool for discovering latent structure in unlabeled data; yet modern clustering pipelines often end with a hard assignment of each observation to a cluster without rigorous measures of assignment uncertainty. We propose a novel weighted conformal approach for constructing valid confidence sets for cluster labels. The key difficulty is that the labels available for cal....
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arXiv:2606.00442v1 Announce Type: cross Abstract: Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks. Surprisingly, no previous work has exploited the curvature constraints that arise from well known weight-space symmetries in loss landscapes. By analytically averaging over group actions that leave the loss invariant, we construct struc....
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Solving 2D Black Scholes Equation via Hermitian Block Embedding and Generalised Quantum Signal Processing
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arxiv.org
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2 days ago
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eng
arXiv:2606.00458v1 Announce Type: cross Abstract: The Black Scholes equation provides a fundamental model for the no arbitrage pricing of financial derivatives. After finite difference discretisation, the pricing problem can be formulated as a finite dimensional linear algebra problem involving the inverse of a non Hermitian time step matrix. Recent advances in quantum linear algebra algorithms, particularly the generalised quantum signal ....
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Stochastic Analysis of Cybersecurity Defense Strategies Under Single Attack Scenario
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arxiv.org
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2 days ago
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eng
arXiv:2606.00481v1 Announce Type: cross Abstract: This research presents a novel stochastic framework for proactive cybersecurity defense timing under a single attack scenario. The approach models the defense process as a continuous observation mechanism in which the defense instant and the subsequent observation slot follow independent exponential distributions. Laplace-Carson transforms combined with first-excess theory yield the joint d....
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arXiv:2606.00500v1 Announce Type: cross Abstract: We present a simple and efficient algorithm for robust approximate message passing (AMP) in the spiked matrix setting. In particular, let $\varepsilon$ be a sufficiently small constant, and suppose that $X \in \mathbb R^{n \times n}$ is a Gaussian matrix with a planted rank-$1$ spike, and $E \in \mathbb R^{n \times n}$ is an adversarially chosen matrix supported on an $\varepsilon n \times ....
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Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression
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arxiv.org
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2 days ago
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eng
arXiv:2606.00512v1 Announce Type: cross Abstract: In many modern machine learning pipelines, abundant pretrained representations serve as noisy proxy covariates, while task-specific labels remain scarce. We study semi-supervised regression in this setting, and propose a simple two stage estimator that learns kernel eigenfeatures from all proxy covariates and fits a ridge predictor on labeled data. We derive finite sample bounds showing tha..
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GNMR: Runtime Stability Control for Low-Precision Large Language Model Training
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arxiv.org
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2 days ago
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eng
arXiv:2606.00539v1 Announce Type: cross Abstract: Training stability is a key bottleneck in low-precision language model training: efficient low-cost paths can still produce short-lived numerical risks at a small set of operators. We formulate this as runtime stability control and present Gradient Norm-to-Mean Ratio (GNMR), a lightweight controller that compares each recoverable unit's current gradient norm with its historical mean. Togeth..
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arXiv:2606.00632v1 Announce Type: cross Abstract: Control science is a core representative of the third industrial revolution and is so important to modern civilization. Control systems are the main subject of control science and may involve many aspects of consideration, such as hardware consideration, software consideration, operation consideration, maintenance consideration, economy consideration, society consideration. However, besides....
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Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds
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arxiv.org
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2 days ago
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eng
arXiv:2606.00643v1 Announce Type: cross Abstract: Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise data-fidelity term, added at a few points in the domain to the standard residual and boundary....
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LLM-Driven Co-Evolutionary Automated Heuristic Design for Bi-Component Coupled Combinatorial Optimization
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arxiv.org
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2 days ago
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eng
arXiv:2606.00718v1 Announce Type: cross Abstract: While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing methods typically generate and evolve heuristics as a single operator or search strategy, limiting their ability to model strong coupling among multiple decision substructures in problems such as the Traveling Thief Problem (TTP) and the Traveling Purchaser Problem (TPP). In this wor....
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Eulerian-spanning set and coboundary operator: An investigation of maxcut beyond planar graphs
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arxiv.org
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2 days ago
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eng
arXiv:2606.00725v1 Announce Type: cross Abstract: Using the concepts of Eulerian-spanning set and coboundary operator, we generalize Hadlock's conversion of the maxcut problem on planar graphs to one on general graphs with non-negative weights. Using our conversion, we can explore algorithms for maxcut beyond the class of planar graphs. We obtain a Fixed-Parameter Tractable algorithm for $k$-contraction apex graphs. Specifically, our algor..
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Beyond Pure Sampling: Hybrid Optimization Mechanisms for Non-Convex Model Predictive Control
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arxiv.org
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2 days ago
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eng
arXiv:2606.00737v1 Announce Type: cross Abstract: This paper investigates the optimization mechanisms of non-convex Model Predictive Control (MPC) using the Maximum Entropy Differential Dynamic Programming (ME-DDP) framework. Navigating non-convex cost landscapes induced by nonlinear dynamics, multiple obstacles, etc. remains a fundamental challenge in robotics, where gradient-based methods frequently converge to suboptimal local minima. W....
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arXiv:2606.00749v1 Announce Type: cross Abstract: We combine Reimann's spectral typicality theorem -- a modern formulation of quantum ergodicity -- with the framework of Interval Quantum Mechanics (IQM). In IQM, quantum states are represented not by points but by \emph{quantum parcels}: weak open convex sets of density matrices defined by finitely many expectation intervals. Such parcels are the exact mathematical representation of the epi....
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Bayesian Inference of Nonlinear Malaria Dynamics in Ghana via an Ensemble Markov Chain Monte Carlo Sampler
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arxiv.org
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2 days ago
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eng
arXiv:2606.00783v1 Announce Type: cross Abstract: Reliable quantification of malaria dynamics in sub-Saharan Africa is hindered by short, noisy, and spatially heterogeneous surveillance records. In Ghana, health-facility data from 2014 to 2023 reveal non-linear and age-specific fluctuations in hospital admissions, yet existing approaches struggle to capture stochastic variability or provide credible uncertainty bounds. This study develops ....
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Hybrid Probabilistic Forecasting of Under-Five Malaria Admissions in Ghana: A Gaussian Process Regression with Holt-Winters Smoothing
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arxiv.org
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2 days ago
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eng
arXiv:2606.00834v1 Announce Type: cross Abstract: Accurate malaria forecasting remains a major challenge in sub-Saharan Africa, where strong seasonality, reporting uncertainty, and non-stationary transmission dynamics reduce the reliability of conventional models. In Ghana, district-level malaria surveillance requires forecasting frameworks that are probabilistically rigorous and robust under limited data. This study proposes a hybrid fram....
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arXiv:2606.00858v1 Announce Type: cross Abstract: This article is concerned with change point detection for object-valued data that reside in a metric space, which has attracted some recent interests in statistics and econometrics literature. The existing methods either focus on independent data or can only detect change in the Fr\'echet mean or variance. In this paper, we propose a self-normalization (SN, hereafter) based statistic for de....
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Another Look at Bandwidth-free Inference: a Sample Splitting Approach
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arxiv.org
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2 days ago
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eng
arXiv:2606.00864v1 Announce Type: cross Abstract: The bandwidth-free tests/inferences for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional HAC-based approaches, where consistent long run variance estimation was involved. However, whe....
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arXiv:2606.00887v1 Announce Type: cross Abstract: Testing simple or composite hypothesis on a functional parameter has attracted considerable attention in time series analysis. To accommodate for the unknown temporal dependence, classical nonparametric approaches such as block bootstrapping and subsampling all involve a bandwidth parameter, the choice of which can substantially affect the finite sample performance. The self normalization (....
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Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
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arxiv.org
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2 days ago
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eng
arXiv:2606.00937v1 Announce Type: cross Abstract: Neural operators provide fast surrogate models for PDE simulations, but standard architectures often treat geometry and discretization as secondary to field data. Physical states are usually represented as grid-channel stacks, even when different quantities naturally belong on vertices, edges, faces, cells, boundaries, or interfaces and must satisfy compatibility constraints. We propose Cel....
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arXiv:2606.01002v1 Announce Type: cross Abstract: Engression is a recently proposed and effective framework for conditional distribution learning. Its multi-step Reverse Markov extension further improves generative flexibility by decomposing complex conditional sampling into sequential reverse transitions. Despite their strong empirical performance, rigorous finite-sample statistical guarantees for these methods remain unavailable. In this..
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Wilson Holonomy and Spectral Monodromy in Spin-Orbit Rings: Effective Gauge Connections and Loop Observables
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arxiv.org
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2 days ago
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eng
arXiv:2606.01029v1 Announce Type: cross Abstract: A spin-orbit Hamiltonian with an effective gauge structure carries two distinct loop objects that are routinely conflated: an energy-independent Wilson holonomy, which organizes interference and internal spin transport, and an energy-dependent monodromy, which quantizes the spectrum. We show that cleanly separating these objects supplies a precise, computable bridge between the loop/holonom....
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How (and when) can you fit examples to logic-based hypothesis classes over infinite structures?
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arxiv.org
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2 days ago
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eng
arXiv:2606.01107v1 Announce Type: cross Abstract: We study fitting problems, sometimes called ``training problems'', where we have a finite sample consisting of inputs and outputs, and we want to know whether there is a function in a certain class that could produce these outputs, exactly or approximately, on the given inputs. We focus on the computational and descriptive complexity of fitting for logically-defined classes in common decida..
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The Heuristic Approach to General Relativity in the Laplace-Beltrami Formalism
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arxiv.org
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2 days ago
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eng
arXiv:2606.01129v1 Announce Type: cross Abstract: The Laplace-Beltrami formalism, in which the Ricci tensor in the Einstein field equations (EFEs) is formulated at leading-order in terms of the partial-differential Laplace-Beltrami operator, was previously applied to coalescing compact binaries (CCBs) generating gravitational waves (GWs). Supposing that the CCB is an effective singular body -- a hollow mass-shell -- that follows a Kerr met....
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arXiv:2606.01216v1 Announce Type: cross Abstract: The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors. In order to leverage the geometry of the space, we formulate the learning of such matrices as optimization on a Riemannian..
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Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces
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arxiv.org
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2 days ago
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eng
arXiv:2606.01244v1 Announce Type: cross Abstract: We study operator learning using encoder--decoder neural networks. Inspired by the function-space theory of neural networks, we introduce a variation space as an infinite-dimensional structural class for nonlinear operators. This space is defined through vector-valued measures directly on the input and output spaces. For operators in this space, we establish approximation bounds for encoder....
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arXiv:2606.01354v1 Announce Type: cross Abstract: We consider integrable hierarchies such as KP, modified KP, 2D Toda lattice, BKP (small and large), DKP, Pfaff-Toda and their multi-component generalizations. We work in the framework of the bilinear formalism in which the universal dependent variable is a tau-function satisfying bilinear equations of the Hirota-Miwa type. Our principal interest in this paper is the dispersionless versions ....
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GPTQ-intrinsic LoRA: A Near-optimal Algorithm for Low-precision Quantization with Low-rank Adaptation
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arxiv.org
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2 days ago
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eng
arXiv:2606.01412v1 Announce Type: cross Abstract: Post-training quantization is widely used for compressing large neural networks, but aggressive low-bit quantization can significantly degrade model quality. A common remedy is to augment the quantized weights with a low-rank correction, leading to approximations of the form $W\approx Q+LR$. In this paper, we study this low-precision plus low-rank representation through the layer-wise recon....
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Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence
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arxiv.org
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2 days ago
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eng
arXiv:2606.01444v1 Announce Type: cross Abstract: Scientific discovery is not only answer generation but revision of the representational regime in which evidence, artifacts, operations, and verifiers are typed. We develop a category-theoretic account of agentic discovery for materials science. In a fixed regime b with schema category S_b, the system state is a copresheaf I_t: S_b -> Set, and provenance is the category of elements \int_{S_....
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Estimating Mutual Information between Time Series and Temporal Event Sequences Across Diverse Analysis Tasks
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arxiv.org
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2 days ago
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eng
arXiv:2606.01602v1 Announce Type: cross Abstract: Pairwise dependence measures such as correlation and causality are fundamental to temporal data mining, yet there is still no principled and robust way to quantify dependence between heterogeneous data types, especially between continuous time series and discrete temporal event sequences. Existing approaches rely on ad hoc transformations or mutual-information estimators that are highly sen....
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arXiv:2606.01713v1 Announce Type: cross Abstract: We propose FlipItRight, a framework for stable planar pose-targeted throw-flip with a high-DoF manipulator. The task is decomposed into an object-level planner, which generates candidate release states satisfying the desired landing pose, and a robot-level planner, which evaluates executability and constructs a feasible swing motion. Treating the release state as an explicit intermediate re....
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arXiv:2606.01733v1 Announce Type: cross Abstract: Preconditioning is a fundamental technique for accelerating classical linear system solvers, and understanding when its benefits persist in quantum linear system (QLS) solvers is important for assessing the practical resource requirements of quantum linear algebra. In QLS algorithms, however, the potential advantage of preconditioning may be offset by the normalization overhead incurred by ....
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Stochastic convergence of parallel asynchronous adaptive first-order methods
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arxiv.org
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2 days ago
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eng
arXiv:2606.01787v1 Announce Type: cross Abstract: A new class of asynchronous adaptive first-order optimization methods is introduced, comprising asynchronous variants of several popular algorithms. Versions of these methods using momentum and/or inexact normalization are also considered. The convergence of methods in the class on non-convex functions is analyzed in a fully stochastic setting, and is shown to be (up to logarithmic factors)..
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arXiv:2606.01863v1 Announce Type: cross Abstract: Continual learning struggles to balance retaining past knowledge with absorbing new tasks. Stefan-CL elegantly resolves this stability-plasticity dilemma through the physics of melting. It frames consolidated knowledge as a protected "solid" and unused capacity as an adaptable "liquid." As the network learns, this boundary expands, governed by a "latent heat" tuning dial. By mathematically ..
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Quasi-bound States of Scalar field inside the Dyonic Kerr-Sen Black Hole
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arxiv.org
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2 days ago
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eng
arXiv:2606.01877v1 Announce Type: cross Abstract: We found sets of exact analytic quasi-stationary states of a massive scalar field in a dyonic Kerr-Sen black hole~(DKSBH) background in the maximally extended spacetime region. A central novelty is the use of horizon-regular ingoing Eddington-Finkelstein coordinates, which enables a direct and unambiguous imposition of the ingoing boundary condition at the horizon. The exact radial solution....
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An Explicit Scott-Type Bound for Absolutely Maximally Entangled States with Arbitrary Defect
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arxiv.org
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2 days ago
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eng
arXiv:2606.01943v1 Announce Type: cross Abstract: Absolutely maximally entangled (AME) states and, more generally, $k$-uniform states in $(\C^q)^{\otimes n}$ are central objects in multipartite entanglement theory, with applications to quantum secret sharing, quantum masking, and quantum error correction. In the extremal case $k=\lfloor n/2\rfloor$, Scott (2004) proved a sharp nonexistence bound showing that AME states cannot exist once th....
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