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1,325 records · Page 3Linked to original sources
arXiv2026

Algorithmic threshold for high-dimensional projection pursuit I: general theory

We study a null model of high-dimensional projection pursuit: we are given $M$ points sampled i.i.d. from a standard gaussian in $N$ dimensions, where $M,N\to\infty$ with $M/N\toα\in(0,\infty)$. Our goal is to characterize the possible empirical distributions of these points' projections along a data-dependent direction $x$, which ranges over either the sphere $S_N=\sqrt{N}\mathbb{S}^{N-1}$ or cube $Σ_N=\{-1,+1\}^N$. We consider this problem in an algorithmic setting, where $x$ must be the output of an algorithm with dimension-free Lipschitz dependence on the input; this class of algorithms includes general gradient-based methods such as Langevin dynamics and approximate message passing (AMP). Our main result exactly characterizes the set of empirical distributions attainable by this class in terms of a one-dimensional stochastic control problem. As a consequence of our main result, we obtain exact algorithmic thresholds for optimizing the Hamiltonian of a spherical or Ising perceptron model with general bounded continuous activation. For the spherical problem, independent work of Montanari and Zhou (2024) characterized the empirical distributions attainable by a related two-stage AMP algorithm, also in terms of stochastic control. Our proof of hardness builds on the branching overlap gap property introduced in earlier work by the first two authors. Our main innovation is to develop stochastic control theory within the branching OGP framework, significantly expanding the settings in which it locates an exact algorithmic threshold. Notably, our methods apply even though the non-algorithmic problem of characterizing all feasible projections remains a major outstanding challenge. For the matching algorithmic result, we construct a new incremental AMP algorithm that acts on a Brownian-bridge revelation of the gaussian disorder and simulates the same family of controlled SDEs.

math.PR↗
arXiv2026

ODMA-based MIMO Massive Unsourced Random Access with Soft-Output Polar Codes

This paper investigates the design of the on-off division multiple access (ODMA) transmission scheme for multiple-input multiple-output (MIMO) massive unsourced random access (URA) systems with soft-output (SO) polar codes. First, a three-segment pilot-uncoupled coding scheme is introduced under the ODMA framework, which reduces the coding rate of the data segment without increasing the transmission overhead, improving the overall system performance. Building upon this architecture, a hierarchical pattern detection framework is developed. Specifically, a coarse-grained candidate set of transmission patterns is first identified through correlation operations. Based on this, a message-passing (MP)-based pattern detection algorithm is developed to iteratively estimate the posterior probabilities of transmission patterns, followed by the \textit{maximum a posteriori} (MAP) estimation to obtain the precise pattern detection result. Furthermore, a joint pattern detection and data decoding algorithm based on the bit-wise SO information of polar decoder is investigated, where the posterior probability information provided by the polar decoder is exploited to refine the pattern detection and contribute to an improved accuracy. In addition, by leveraging bit-wise SO information of the successive cancellation list polar decoder, an MP-based iterative decoding algorithm is developed to significantly enhance the decoding performance. The proposed scheme simultaneously exploits the transmission gain of uncoupled-ODMA framework, the coding gain of polar codes in the short-blocklength regime, and the iterative decoding gain enabled by SO information, while the computational complexity is significantly reduced through the hierarchical detection framework. Simulation results demonstrate that the proposed scheme achieves strong robustness ...

cs.IT↗
arXiv2026

Quantum Circuit and Tensor Network Implementation of the 2D Acoustic Wave Equation

We present a cohesive framework for simulating seismic wave propagation utilizing quantum computing paradigms and their classical tensor network equivalents. We detail a quantum circuit-based formulation for the explicit finite-difference time-domain (FDTD) solution of the two-dimensional acoustic wave equation and map this quantum architecture onto a tensor train representation, namely for Matrix Product State (MPS). The MPS solver enables deterministic simulation of large-scale wavefield dynamics on classical high-performance computing systems. We demonstrate the MPS representation by computing 2D seismic wavefields on the Marmousi model. Our results indicate that the MPS representation is a viable direction for computing and scaling wavefield propagation.

quant-ph↗
arXiv2026

An End-to-End Hybrid Quantum--Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study

Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($τ\approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7\text{M}$ ESS/s versus $488\text{K}$ ESS/s for the quantum sampler ($36\times$ mean rate, $153\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \in \{8,10,12\}$. An MPS scaling study ($n \le 40$) shows bond dimension $χ=32$ achieves $F=0.721\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \in \{8,10,12\}$ shows VQC fidelities fall far below MPS: $(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\times$, $34.1\times$, and $113.8\times$.

quant-ph↗
arXiv2026

Multi-bounce Drum Roll with Optimized Active Tricks to Leverage Soft Embodiment

This paper presents a soft robotic drummer for accurate and efficient drum rolls. High-frequency drum rolls require the "multi-bounce technique," where a drumstick bounces multiple times with a single stroke. In robotic reproduction of this technique, the body's elasticity is key, while the fine motion during the stroke is also crucial for maximizing the potential of that elasticity. Therefore, we design two tricks: i) Tap-Pull (TP) trick to increase the number of rebounds by adding a pulling motion after impact; and ii) Micro-Pulse (MP) trick to keep the drumming volume by injecting small oscillations during the stroke. Due to the nonlinear complexity of soft embodiment, both tricks are efficiently tuned using Bayesian optimization in a data-driven manner for accomplishing the respective objectives quantified. We evaluated the optimized behaviors with soft and rigid end-effectors. As a result, the soft TP achieved the highest bounce count (12.25 per stroke) with uniform intervals. The soft MP suppressed the volume decay, yielding 6.8-times higher acoustic efficiency compared to the rigid MP. These results indicate that the proposed tricks with the combination of elasticity and optimization can make robots play excellent drum rolls.

cs.RO↗
arXiv2026

Reasoning-supported Robustness Validation of Automotive E/E Components

This article presents an ontology-supported approach to tackle the complexity of the Robustness Validation (RV) process of automotive electrical/electronic (E/E) components. The approach uses formalized knowledge from the RV process and stress, operating, and load profiles, so-called Mission Profiles (MPs). In contrast to the error-prone industrially established manual procedure, we show how component characteristics are formalized in OWL in order to form the foundation of an efficient automated analysis selection and decision support during the RV process. Additionally, a rule-based transformation of component characteristics upon propagation via SWRL is described. The proposed approach is based on the idea of mapping MPs to an OWL representation in order to allow to execute semantic queries against MP data to improve their integration into the RV process. The resulting ontology-supported application framework has been applied to an industrial use-case from automotive power electronics. A generalization of the approach is described and demonstrated by applying it to stress test selection within the AEC Q100 standard. We present experimental results showing that the RV process can be significantly improved in terms of reduced design time and increased exhaustiveness by automating the analyses selection step and the provisioning of all the relevant data to be used.

cs.AI↗
arXiv2026

Two Centuries of Sexism in British Parliament: A Computational Analysis of Women's Representation in the Hansard Corpus

The language a legislature uses to debate women's rights, even in favour of them, encodes systematic patterns of sexism that persist across two centuries. In this work, we analyse 6,531 speeches over 200 years of UK parliamentary debate (Hansard, 1803-2005) by using large language models to classify a speaker's perspective towards women's suffrage and political representation, as well as analyse sexist speech in parliament from the lens of the Ambivalent Sexism Inventory. We also release this parliamentary dataset, an organized and metadata-enriched version of the publicly available Hansard Corpus optimized for computational social science research, with 6.7 million speeches across 1.2 million debates, with 89% gender-matching for speeches by MPs from the House of Commons. We find that 54% of speeches opposing women's representation contain sexist content, compared to 21% of speeches that are for the cause, and that the two sides use fundamentally different types of sexism: anti-suffrage rhetoric combines hostile and benevolent framing, while pro-suffrage sexism is overwhelmingly benevolent. Female MPs support women's political rights at 93% compared to 70% for male MPs, a gap that closes only after enfranchisement. Our findings are evidence that benevolent and hostile sexism are used in different rhetorical contexts in a manner consistent with the theory of Ambivalent Sexism.

cs.CL↗
arXiv2026

Enhancing Interpretability of Stochastic Programming Solutions: A Multiparametric Approach

Stochastic programming (SP) is a powerful framework for decision-making under uncertainty, but its practical adoption in industry is often hindered by the difficulty in understanding the causal relationships that drive optimal solutions. In the two-stage SP, strategic first-stage decisions are coupled with operational second-stage recourse decisions. When the number of scenarios under consideration is large, understanding the direct link between the uncertainty realization and optimal recourse strategy becomes computationally and cognitively demanding. Common approaches to improve interpretability include trained classification trees or scenario reduction, replacing the large scenario set with a representative subset. This is often achieved through post-hoc clustering (e.g., k-means) based on uncertainty realizations or optimal recourse decisions. While useful, these methods only provide a statistical approximation of the solution space and may fail to reveal the underlying structural properties of the recourse problem that drive optimal first-stage decisions. This work introduces a novel, deterministic approach to explainability using multiparametric programming (mp) within a Benders decomposition framework. We reformulate the recourse subproblem as a multiparametric linear program, generating an explicit map of Critical Regions (CRs), which are polyhedral partitions of the uncertainty space. This allows us to cluster scenarios analytically rather than statistically. We demonstrate this methodology on a supply chain planning under demand uncertainty. Our results show that 100 stochastic scenarios map to exactly six critical region clusters. This mapping allows us to explain optimal capacity planning decisions as a precise trade-off between specific operational modes, providing a fully transparent interpretation of the stochastic solution.

math.OC↗
arXiv2026

Text-guided flow matching enables sample-efficient crystal structure generation

Crystal generators can now propose periodic structures, but their control interfaces remain poorly matched to the mixed descriptors used in materials design. Text provides a compact way to combine composition, symmetry, prototype and property cues, yet it has not been clear whether such information can steer flow-based crystal generation. Here we introduce TFMat, a text-conditioned flow-matching framework that uses structured materials language as a semantic prior for a CrystalFlow generator. Across Perov-5, Carbon-24 and MP-20 crystal structure prediction benchmarks, TFMat improves one-candidate match rates over CrystalFlow and reaches a 92.04% MP-20 match rate with 20 candidates; in de novo generation, it improves element-count and density distribution alignment while retaining coarse property consistency in composition-selected outputs. These results position structured text as an inspectable control layer for translating human-readable materials intent into candidate crystals for downstream simulation and validation.

cond-mat.mtrl-sci↗
arXiv2026

Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography

Parameterised graph theory studies how the complexity of graph-theoretic problems depends on structural parameters of the input graph. This perspective has proved useful in analysing tensor-network simulation (Markov and Shi, 2008). Its implications for tensor-network representations and tomography are less well understood. In particular, which graph parameters determine whether a tensor-network state (TNS) admits a tractable matrix product state (MPS) or tree tensor network (TTN) representation, and which control the complexity of learning the state? We address these questions using parameterised graph theory. First, we show that cutwidth and tree-cutwidth bound the bond dimension overhead required to represent a TNS as an MPS or TTN. In the TTN case, tree-cutwidth also bounds the local dimension of the grouped subsystems. The proofs are based on entanglement rerouting, a tensor-network analogue of rerouting information in a classical network. Second, we derive graph-dependent upper bounds on the sample and computational complexity of realisable TNS tomography, with exponents that depend on cutwidth, tree-cutwidth, and a new graph parameter, learning complexity, which we bound in terms of degree and treewidth. We obtain these results by extending the disentangling MPS learner of (Cramer et al., 2010), as analysed further in (Bakshi et al., 2025; Lin et al., 2025), to TTNs and to tensor networks on arbitrary known graphs. Finally, we extend the framework beyond the realisable setting. For an arbitrary input state, our agnostic learner outputs a pure state whose fidelity is within additive error $ε$ of the optimum over tensor-network states on the given graph with a given bond dimension, with explicit graph-dependent bounds on sample and computational complexity.

quant-ph↗
arXiv2026

A priori Assessment of Tensor-Network Encoding for Isotropic Turbulent Flows

Tensor networks (TNs), originally developed for simulating many-body quantum systems, provide a systematic framework for approximating high-dimensional fields. This is achieved by factorizing the field into interconnected tensors with small bond dimensions, thereby restricting the correlations captured across field bipartitions. Belonging to the family of TNs, the matrix product state (MPS) ansatz is utilized here as a reduced-order modeling framework to construct truncated representations of isotropic turbulent flow data. Two direct numerical simulation (DNS) datasets are considered: the hydrodynamic field of an incompressible three-dimensional flow, and a conserved Fickian scalar in a similar flow. Each field is encoded as an MPS through a sequence of singular value decompositions (SVDs) in which small singular values are discarded. The truncated representation is contracted back to the full grid, and the resulting reconstructed field is compared against DNS. An interleaved ordering of the spatial tensor indices of the transport variables is applied prior to decomposition in order to localize the dominant inter-tensor correlations. Velocity reconstructions achieve $99.8\%$ fidelity using only $5\%$ of the original DNS memory, while the scalar field reaches the same fidelity at $15\%$ memory usage. A wide range of lower- and higher-order statistics, including velocity gradients, dissipation, and structure functions, are systematically examined. At these compression levels, the total kinetic energy and the scalar energy are both recovered within $0.2\%$ relative error, while the mean dissipation and mean scalar dissipation remain within approximately $10\%$ of the DNS generated values. These findings support the suitability of MPS for scalable reduced-order analysis of complex turbulent datasets and motivate further exploration of TN-based methods in computational turbulence.

physics.flu-dyn↗
arXiv2026

Benchmarking Zero-Setup Quantum Circuit Simulators

Practitioners increasingly rely on hosted simulation environments, but their performance characteristics remain poorly documented. We present a systematic benchmarking study of GPU-accelerated approximate quantum simulation across two widely used methods: matrix product states (MPS) and Pauli path simulation (PPS), comparing BlueQubit (a hosted tool that handles hardware provisioning, simulator configuration, and job orchestration) against AWS Braket, Quantum Rings, Qiskit pauli-prop, and PauliPropagation (written in Julia). For MPS, we find that GPU runtime yields sub-quadratic scaling with bond dimension, with a growing advantage over CPU at increasing scale. For Pauli path simulation on IBM's 127-qubit kicked Ising benchmark, GPUs deliver up to ${\sim}1{,}700\times$ speedup at fine truncation thresholds ($δ= 2.5 \times 10^{-5}$, 27.6M Pauli terms), and are the only backends that reach accuracy regimes below $δ= 10^{-5}$, which remained inaccessible to the commodity CPU-based implementations and self-contained SDKs evaluated here. We also provide a reproducible characterization of these simulators across regimes, including tradeoffs that isolated evaluations do not show. All benchmarking code and configurations are in a public GitHub repository.

quant-ph↗
arXiv2026

CrystalGRPO: Target-Aligned and Coverage-Preserving Reinforcement Learning for Flow-Based Crystal Structure Prediction

Flow-based generative models can efficiently produce candidate structures for crystal structure prediction (CSP), but their pretrained objectives do not directly optimize downstream target recovery. Reinforcement-learning post-training offers a flexible solution, yet existing approaches rely primarily on energy rewards and coordinate-only stochastic policies. Predicted energy does not identify the reference polymorph, while reward-driven concentration can reduce the candidate coverage required for Top-N recovery. We introduce CrystalGRPO, a CSP-aligned post-training framework that extends existing ODE-to-SDE policy constructions to the joint coordinate--lattice state. CrystalGRPO combines MACE-predicted energy with a StructureMatcher-based recovery score and provides two operating modes: CrystalGRPO-Q, which prioritizes single-draw recovery, and CrystalGRPO-C, which combines full-trajectory reference regularization with a coverage-aware group advantage to preserve finite-budget target recovery. Across MP-20 and MPTS-52 with PXRDGen and OMatG backbones, both variants reduce one- and twenty-sample RMSE relative to coordinate-only reinforcement in all four backbone--dataset settings. CrystalGRPO-Q consistently improves Top-1, whereas CrystalGRPO-C achieves a higher Top-20 across all settings.

cs.LG↗
arXiv2026

Tracing Mathematical Proficiency Through Problem-Solving Processes

Knowledge Tracing (KT) aims to model student's knowledge state and predict future performance to enable personalized learning in Intelligent Tutoring Systems. However, traditional KT methods face fundamental limitations in explainability, as they rely solely on the response correctness, neglecting the rich information embedded in students' problem-solving processes. To address this gap, we propose Knowledge Tracing Leveraging Problem-Solving Process (KT-PSP), which incorporates students' problem-solving processes to capture the multidimensional aspects of mathematical proficiency. We also introduce KT-PSP-25, a new dataset specifically designed for KT-PSP. Building on this, we present StatusKT, a KT framework that employs a teacher-student-teacher three-stage LLM pipeline to extract students' Mathematical Proficiency (MP) as intermediate representation. In this pipeline, the teacher LLM first extracts problem-specific proficiency indicators, then a student LLM generates responses based on the student's solution process, and a teacher LLM evaluates these responses to determine mastery of each indicator. The experimental results on KT-PSP-25 demonstrate that StatusKT improves the prediction performance of existing KT methods. Moreover, StatusKT provides interpretable explanations for its predictions by explicitly modeling students' mathematical proficiency. Code is available \href{https://github.com/jungyangpark/KT-PSP-25}{here}.

cs.LG↗
arXiv2026

When Seeing Overrides Knowing: Visual Dominance and Deferral-Based Method for Personalized Safety in VLMs

Vision-language models (VLMs) are increasingly deployed in high-stakes settings, where a response that is reasonable in general may still be unsafe for a particular user whose medical, emotional, or situational context is unknown to the model. We study this problem of personalized safety in multimodal systems and introduce MPS-Bench, a benchmark of 5,181 scenarios from 584 real-world images across 12 high-risk domains, each paired with a hidden user profile. Evaluating eight frontier VLMs, we find that they almost always respond directly (86-99%) rather than seek missing context, and none exceeds 2.6/5 on personalized safety. To understand why these failures arise, we analyze multimodal interactions and identify visual dominance: visual information enters text representations early and suppresses textual risk signals during multimodal fusion. Causal interventions reveal a two-stage mechanism in which visual affect is first transferred into the text stream in early layers and then shapes the final decision through this altered text representation, making late-stage internal remediation unreliable. Motivated by this mechanism, we propose PRISM, a lightweight input monitor that uses bidirectional cross-modal modulation to predict when a query is likely to require deferral. PRISM achieves 0.978 AUC and strictly dominates the safety-utility Pareto frontier across all tested models.

cs.CV↗
arXiv2026

AtomCite: Verification and Correction of Supplied Page-Level Citations in Multi-Page Documents

Large language models answering questions over multi-page documents are expected to cite the supporting pages, yet supplied citations are sometimes inaccurate, and current evaluations score citations at generation time or against text passages: no existing benchmark evaluates whether a system can verify and correct a page-level citation already attached to an answer. We propose AtomCite, an agentic framework that parses an answer into claims, checks each claim against the image of its cited page, and applies a deterministic repair policy. To evaluate it, we introduce DocCite, to our knowledge the first benchmark for systems that verify and correct page-level citations in document images. Built on MP-DocVQA and DUDE, it combines 928 validated injected instances with 2,468 candidate natural errors harvested from frontier- and efficiency-tier models, of which a two-annotator audit confirms 1,909 as genuine errors. Primary labels are assigned deterministically, not by LLM judges, with the human audit as a separate validation layer. Across three model families (Gemini, Claude, and GPT), AtomCite reaches around 93% binary verification accuracy on the injected benchmark, significantly outperforming every OCR-only condition, including a compute-matched control, and exceeding every prior text-based baseline given the same OCR text. Its repair policy lifts citation precision on the injected mix from a constructed 34% to 87-90% while retaining over 90% of correct claims. AtomCite also transfers: with frozen prompts and zero training, it raises the hallucination-detection scores of two open 7-8B models on five public benchmarks above the same models prompted as direct judges. Finally, the audit shows that noise in automatic labels biases measured verifier accuracy and can reverse system rankings, so evaluations relying only on synthetic or automatic labels risk mismeasuring verification capability.

cs.CL↗
arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗