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01.
medRxiv (Medicine) 2026-06-15

Epileptogenicity alters intrahippocampal ripple propagation

Objective: Tracing the propagation of high-frequency oscillations (HFOs) aids in localizing epileptogenic regions and improving surgical outcomes. We examined how hippocampal epileptogenicity influences the propagation properties of the HFOs it generates. Methods: We analyzed non-REM sleep stereo-EEG from 49 patients (68 hemispheres) with verified hippocampal contacts. Hippocampi were stratified by excitability: 28 seizure onset zone (SOZ), 22 more-irritative non-SOZ (>6 interictal epileptiform discharges [IED]/min), and 18 less-irritative non-SOZ (

02.
arXiv (CS.CL) 2026-06-18

Rethinking Cross-lingual Gaps from a Statistical Viewpoint

Any piece of knowledge is usually expressed in one or a handful of natural languages on the web or in any large corpus. Large Language Models (LLMs) act as a bridge by acquiring knowledge from a source language and making it accessible when queried using target languages. A cross-lingual gap is a drop in accuracy incurred when querying knowledge in a target language rather than the source language. Existing research focused on modeling or training failures leading to cross-lingual gaps. In this work, we take an alternative view to characterize the nature of cross-lingual error, and hypothesize that the variance of responses in the target language is a key cause of this gap. For the first time, we formalize the cross-lingual gap in terms of biased and unbiased errors. We empirically validate our hypothesis through multiple inference-time interventions that control variance and reduce the cross-lingual gap. We demonstrate a few test-time ensemble methods that reduce response variance, and thereby improve source-target transfer scores by up to 12 absolute points yielding relative gains of 8% to over 50% across various LLMs.

03.
arXiv (CS.CV) 2026-06-16

Differentiable Packing of Irregular 3D Objects with Adaptive Container Estimation

Most existing approaches either fix the container in advance or optimize only a single container dimension through an outer search loop, leaving the remaining dimensions as a manual tuning problem. We present a differentiable packing framework that jointly optimizes all 6N object pose parameters and all three container side lengths inside a single gradient-based loop. The formulation combines six physics-inspired, differentiable loss terms computed directly on triangle meshes through axis-aligned bounding-box proxies. An adaptive squeezing mechanism periodically tightens the container whenever the overlap loss falls below a pair-count-scaled threshold, producing a large initial drop in container volume, followed by small refinements. All pairwise computations are written in tensor-broadcasting form, giving a 3.4 to 54 times speedup over a reference loop-based implementation. The pipeline is implemented in Python and PyTorch, with no physics engine, FFT library, or convex decomposition. On multiple object categories, the method produces containers that are 11 to 32 percent smaller than time-matched DBLF and simulated-annealing baselines at N =100, while running in under 4 minutes per instance on a single consumer GPU.

04.
arXiv (CS.CL) 2026-06-16

VibeThinker-3B: Exploring the Frontier of Verifiable Reasoning in Small Language Models

This technical report introduces VibeThinker-3B, a compact dense model with 3B parameters developed to investigate how far verifiable reasoning can be pushed within a strictly small-model regime. Building upon the Spectrum-to-Signal post-training paradigm, we systematically enhance the model through an optimized pipeline that includes curriculum-based supervised fine-tuning, multi-domain reinforcement learning, and offline self-distillation. Experimental evaluations demonstrate that VibeThinker-3B achieves frontier-level performance on highly demanding verifiable tasks. Specifically, it attains a score of 94.3 on AIME26 (improving to 97.1 with claim-level test-time scaling), an 80.2 Pass@1 on LiveCodeBench v6, and exhibits strong out-of-distribution generalization with a 96.1\% acceptance rate on recent unseen LeetCode contests. This effectively places it in the performance band of first-tier reasoning systems, matching or exceeding flagship models that are orders of magnitude larger, such as DeepSeek V3.2, GLM-5, and Gemini 3 Pro. Furthermore, a score of 93.4 on IFEval confirms that this extreme reasoning enhancement does not compromise strict instruction controllability. Extending our previous 1.5B work, these findings motivate the Parametric Compression-Coverage Hypothesis, which views verifiable reasoning as compressible into compact reasoning cores, while open-domain knowledge and general-purpose competence require broad parameter coverage over facts, concepts, and long-tail scenarios. This perspective suggests that compact models are not merely deployment-efficient substitutes, but a complementary path toward frontier-level performance in parameter-dense capability regimes.

05.
arXiv (CS.AI) 2026-06-12

Prefill Awareness in Large Language Models

arXiv:2606.12747v1 Announce Type: new Abstract: Safety-relevant studies of language models, including alignment and jailbreaking evaluations and AI control protocols, often rely on prefilling model outputs. If AI models can recognize and act on the fact their prior assistant messages have been inserted or edited, the effectiveness and validity of these methods could be compromised. We investigate whether frontier language models can distinguish between tampered and untampered assistant-side context, a capability we call prefill awareness. To do so, we construct a binary preference benchmark across three prefill mechanisms, filtering for cases where models show consistent stances. We find that frontier models show substantial prefill awareness: Claude Opus 4.5 detects prefills opposing its preferences in 9-35% of cases with a 0% false positive rate when prompted; additionally, models often revert towards baseline behavior without explicitly reporting that the prefill was foreign. Controlled ablations later also show that detection and resistance rely on different cues, where stylistic mismatch mainly affects whether models flag a prefill as foreign, while preference mismatch mainly affects whether they revert toward their baseline answer. We also examine more realistic agentic settings such as misalignment-continuation evaluations and SWE-bench trajectories, where frontier models sometimes disavow prefilled assistant turns in ways that depend strongly on dataset, task success, and hidden formatting artifacts. Our results indicate that prefill awareness is already a substantial confound for some prefill-based methods. We recommend that model developers track this capability in frontier systems.

06.
arXiv (quant-ph) 2026-06-17

Quantum Computing Algebra (QCA), the theory and implementation

arXiv:2606.17621v1 Announce Type: new Abstract: We present a real geometric algebra framework designed for the direct translation of the Dirac formalism into geometric algebra representations. Unlike previous approaches based on positive-definite signatures, QCA employs a split-signature construction that enables a natural realization of quantum states and operators while simplifying computational implementation. We further present an implementation of QCA using the GAALOP software and show how quantum gates and multi-qubit systems can be efficiently represented and generated computationally. As an application, we demonstrate the use of QCA in quantum game theory, where the real-algebraic formulation provides computational advantages for modeling entangled strategies and quantum interactions. The proposed framework establishes a practical bridge between the abstract formalism of quantum computation and efficient geometric algebra implementations.

07.
arXiv (CS.CV) 2026-06-17

Adversarial Attacks Leverage Interference Between Features in Superposition

Why do adversarial examples exist, and why do they transfer between models? Existing explanations appeal to high-dimensional geometry, non-robust patterns in the input, and decision boundary structure, but none provides a representation-level mechanism that explains why specific perturbations succeed and why attacks transfer between models. In this paper, we show that adversarial vulnerability can stem from efficient information encoding in neural networks. Specifically, vulnerability can arise from superposition - the phenomenon where networks represent more concepts than they have dimensions, forcing non-orthogonal representation and thus interference. This interference causes perturbations targeting one representation to affect others, creating vulnerabilities determined by interference patterns. In synthetic settings with precisely controlled superposition, we establish that superposition suffices to create adversarial vulnerability. The resulting attacks are predictable: PGD-discovered perturbations align with theoretically optimal perturbations derived from the interference geometry. Models trained on similar data develop similar interference patterns, explaining attack transferability. We then show that successful attacks on image classifiers exhibit the structure predicted by our proposed mechanism. These findings reveal that adversarial vulnerability can be a byproduct of networks' representational compression, complementing existing explanations based on data properties or architectural factors.

08.
arXiv (CS.LG) 2026-06-17

Instrumental and Proximal Causal Inference with Gaussian Processes

arXiv:2603.02159v2 Announce Type: replace-cross Abstract: Instrumental variable (IV) and proximal causal learning (Proxy) methods are central frameworks for causal inference in the presence of unobserved confounding. Despite substantial methodological advances, existing approaches rarely provide reliable epistemic uncertainty (EU) quantification. We address this gap through a Deconditional Gaussian Process (DGP) framework for uncertainty-aware causal learning. Our formulation recovers popular kernel estimators as the posterior mean, ensuring predictive precision, while the posterior variance yields principled and well-calibrated EU. Moreover, the probabilistic structure enables systematic model selection via marginal log-likelihood optimization. Empirical results demonstrate strong predictive performance alongside informative EU quantification, evaluated via empirical coverage frequencies and decision-aware accuracy rejection curves. Together, our approach provides a unified, practical solution for causal inference under unobserved confounding with reliable uncertainty.

09.
arXiv (CS.CL) 2026-06-17

Scaling Enterprise Agent Routing: Degradation, Diagnosis, and Recovery

Production LLM assistants route user requests to growing libraries of specialized tools, but how does routing accuracy degrade as the catalog scales? We study single-step routing on a 110-agent, 584-tool catalog from a deployed enterprise productivity assistant, evaluating three frontier models from 10 to 110 agents. Routing F1 on under-specified requests drops 16–23 percentage points across models. An oracle analysis decomposes the degradation into a retrieval gap (the model cannot surface the right tool) and a confusion gap (even with perfect retrieval, the oracle ceiling drops 10pp). Embedding-based shortlisting recovers +10–11pp F1 at full scale across all three models and two providers. A production annotation study (1,435 human-labeled utterances, three annotators) confirms the recovery on real traffic at +10–17pp despite 10–15pp lower absolute performance.

10.
arXiv (CS.CL) 2026-06-16

XAI-Grounded Explanation Generation for Speech Deepfake Detection with Training-Free Multimodal Large Language Models

Speech deepfake detection (SDD) systems require trustworthy explanations for reliable decision-making. Existing explanation ways mainly fall into two categories. Traditional explainable AI (XAI), such as gradient-based attribution, produces low-level attribution signals tightly coupled with model decisions, and harder to be understood by human than natural language explanations. Meanwhile, large language model (LLM)-based explanation generation often produces generic and ungrounded descriptions due to the lack of heuristic evidence and task-specific supervision, stemming from limited grounded explanation datasets for SDD. We therefore propose a training-free explanation framework that integrates XAI evidence with multimodal LLMs to generate grounded and specific explanations. Using the PartialSpoof dataset, we construct a grounded explanation dataset and show that methods with XAI increase inside accuracy by over 45\%, verified through human evaluation and faithfulness checks.

11.
arXiv (CS.AI) 2026-06-16

Haiku to Opus in Just 10 bits: LLMs Unlock Large Compression Gains

arXiv:2604.02343v2 Announce Type: replace-cross Abstract: We study the compression of LLM-generated text across lossless and lossy regimes, characterizing a compression-compute frontier where more compression is possible at the cost of more compute. For lossless compression, domain-adapted LoRA adapters can improve LLM-based arithmetic coding by 2x over compression with the base LLM alone. For lossy compression, prompting a model for a succinct rewrite then applying arithmetic coding can achieve compression ratios of approximately 0.03, a 2x improvement over compressing the original response. We further introduce Question-Asking compression (QA), an interactive lossy protocol inspired by the game 'Twenty Questions'. A small model iteratively refines its response by asking yes/no questions to a stronger model, transferring exactly one bit per answer. On 8 benchmarks spanning math, science, and code, 10 binary questions recover 23% to 72% of the capability gap between a small and large model on standard benchmarks and 7% to 38% on harder benchmarks, achieving compression ratios of 0.0006 to 0.004. This is over 100x smaller than prior LLM-based compression (Deletang et al., 2024), suggesting that interactive protocols can transfer knowledge far more efficiently than transmitting full responses.

12.
arXiv (quant-ph) 2026-06-11

Enhancing Many-Body Chaos via Entropy Injection from Environment

arXiv:2606.11784v1 Announce Type: new Abstract: In closed quantum systems, local information spreads throughout the entire system and becomes highly complex under unitary evolution. In contrast, when the system is embedded in an environment, system-environment coupling can transfer information from the system into the environment, thereby reducing the rate of complexity growth within the system. This leads to the environment-induced scrambling transition established in previous works. In this work, we identify entropy injection from the environment as a different physical process that instead enhances many-body chaos. Our setup consists of coupling a system that is already in equilibrium with one environment to another environment, which serves as an entropy reservoir and drives the system into a non-equilibrium state. When entropy flows into the system through either heat transfer or particle transfer, the effective Hilbert space explored by the system enlarges, a mechanism that can enhance many-body chaos. We explicitly demonstrate this idea by constructing a solvable complex Brownian SYK model, in which both the relaxation toward the steady state and the steady-state quantum Lyapunov exponent can be computed analytically. Our results provide a controllable mechanism for tuning quantum scrambling through entropy flow in quantum many-body systems coupled to environments.

13.
arXiv (CS.LG) 2026-06-17

Expanding SPHERE-JEPA: A Family of Statistical Regularizers for the Hypersphere

arXiv:2606.17603v1 Announce Type: new Abstract: In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective. However, current frameworks typically rely on sliced statistical regularizers such as SIGReg (used in LeJEPA) and SUSReg (used in SPHERE-JEPA), which approximate this continuous objective via Monte Carlo sampling along random 1D directions. This stochasticity injects projection variance into the training gradients, destabilizing optimization, and hindering convergence. In this work, we first show that analytically integrating out these random projections natively yields a deterministic Maximum Mean Discrepancy (MMD), bypassing the variance of sliced methods. Motivated by this equivalence, we formulate full-dimensional objectives for MMD, Kernel Stein Discrepancy (KSD), and Kullback-Leibler (KL) divergence directly on the sphere to enforce a uniform distribution. To prevent spatial bias, we equip these tests with rotationally invariant kernels constructed via spectral theory, systematically evaluating two canonical families: smooth exponential decay (Heat) and strict frequency cutoff (Bandlimited) filters. Empirically, removing projection-induced noise results in more stable optimization, faster convergence, and consistent improvements over stochastic sliced regularizers on ImageNet and Galaxy10. Furthermore, we reveal that the choice of the statistical test shapes the geometry of the learned latent space: MMD and KSD favor locally clustered organization suitable for object-centric domains, whereas the continuous KDE-based KL divergence promotes fine-grained instance separation, yielding the strongest results on unclustered procedural texture retrieval.

14.
arXiv (quant-ph) 2026-06-16

The Quantum Transition State

arXiv:2606.10266v2 Announce Type: replace Abstract: The transition state – the critical configuration separating reactants from products – is the central organizing concept of chemical reaction rate theory, yet for nearly a century it has been thought to have no exact quantum counterpart: the recrossing-free, one-way flux through a transition state appears to demand simultaneous knowledge of position and momentum, in conflict with the uncertainty principle. We show this obstruction is illusory and construct the quantum transition state directly from the exact quantum flow. Its stable and unstable invariant manifolds intersect in a unique bounded trajectory – the quantum transition-state trajectory – anchoring a moving dividing surface that each reactive characteristic crosses exactly once, yielding a one-way flux of the standard quantum probability current. The geometric framework underlying classical transition-state theory thus survives intact in exact quantum mechanics, in a fundamentally quantum form.

15.
arXiv (CS.LG) 2026-06-15

MOSIC: Model-Agnostic Optimal Subgroup Identification with Multi-Constraint for Improved Reliability

arXiv:2504.20908v3 Announce Type: replace Abstract: Current subgroup identification methods typically follow a two-step approach: first estimate conditional average treatment effects and then apply thresholding or rule-based procedures to define subgroups. While intuitive, this decoupled approach fails to incorporate key constraints essential for real-world clinical decision-making, such as subgroup size and propensity overlap. These constraints operate on fundamentally different axes than CATE estimation and are not naturally accommodated within existing frameworks, thereby limiting the practical applicability of these methods. We propose a unified optimization framework that directly solves the primal constrained optimization problem to identify optimal subgroups. Our key innovation is a reformulation of the constrained primal problem as an unconstrained differentiable min-max objective, solved via a gradient descent-ascent algorithm. We theoretically establish that our solution converges to a feasible and locally optimal solution. Unlike threshold-based CATE methods that apply constraints as post-hoc filters, our approach enforces them directly during optimization. The framework is model-agnostic, compatible with a wide range of CATE estimators, and extensible to additional constraints like cost limits or fairness criteria. Extensive experiments on synthetic and real-world datasets demonstrate its effectiveness in identifying high-benefit subgroups while maintaining better satisfaction of constraints.

16.
arXiv (CS.AI) 2026-06-12

On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators

arXiv:2301.12538v2 Announce Type: replace-cross Abstract: This paper develops an Operator Learning framework for approximating the dynamic response of synchronous generators. The framework can be used to (i) build a neural network-based generator model that interacts with a power grid simulator or (ii) shadow the true generator's transient response. First, we develop a data-driven Deep Operator Network (DeepONet) to approximate the infinite-dimensional solution operator of the generators. Then, we design a numerical scheme based on DeepONet that simulates the generator's response over a given time horizon. The proposed scheme recursively employs the trained DeepONet to simulate the response for a given multi-dimensional input that describes the interaction between the generator and the power grid. In addition, we design a residual DeepONet numerical scheme that can incorporate information from existing mathematical models. We accompany this residual DeepONet scheme with an estimate for the prediction's cumulative error. Finally, we build a data aggregation (DAgger) strategy that allows fine-tuning of DeepONets using aggregated training data that the DeepONets will likely encounter during interactive simulations with other grid components. As a proof of concept, we demonstrate that the proposed frameworks can effectively approximate the transient model of a synchronous generator.

17.
arXiv (CS.LG) 2026-06-16

Understanding Latent Diffusability via Fisher Geometry

arXiv:2604.02751v2 Announce Type: replace Abstract: Diffusion models often degrade in latent spaces, yet the formal causes remain poorly understood. We quantify latent-space diffusability via the rate of change of the Minimum Mean Squared Error (MMSE) along the diffusion trajectory. Our framework decomposes this MMSE rate into contributions from Fisher Information (FI) and Fisher Information Rate (FIR). We demonstrate that while global isometry ensures FI alignment, FIR is governed by the interplay between encoder and data geometries. Our analysis decouples diffusion degradation into four penalties: dimensional compression, tangential distortion, high-frequency encoder curvature, and intrinsic data curvature. We derive theoretical conditions for FIR preservation to ensure stable diffusability. Experiments across diverse autoencoding architectures demonstrate the implications of our theoretical bounds. We establish FI and FIR as a comprehensive analytical framework for understanding latent diffusability.

18.
arXiv (CS.AI) 2026-06-18

R2D-RL: A RoboCup 2D Soccer Environment for Multi-Agent Reinforcement Learning

arXiv:2606.18786v1 Announce Type: new Abstract: Robot soccer is a challenging testbed for multi-agent reinforcement learning because it combines partial observability, cooperative and adversarial interaction, sparse rewards, and long-horizon tactical behavior. RoboCup 2D Soccer Simulation (RCSS2D) provides a mature robot-soccer platform, but its competition-oriented server-client architecture is difficult to use directly with modern Python-based MARL workflows. We introduce R2D-RL, a reinforcement learning environment that connects RCSS2D and HELIOS-based player clients to a Python MARL interface through shared-memory communication and cycle-level synchronization. R2D-RL supports full-field and scenario-based training with configurable opponents, Base discrete and Hybrid parameterized action spaces, action masks, expected possession value (EPV)-based reward shaping, and parallel execution. We provide front-goal scenarios and an 11-vs-11 full-field benchmark, together with baseline results.

19.
arXiv (CS.CV) 2026-06-11

TopoCap: Learning Topology-Agnostic Motion Priors for Monocular Video-to-Animation

The explosion of generative 3D assets has created a massive demand for animation, yet current motion capture methods remain brittle, restricted to species-specific templates (e.g., SMPL) or requiring labor-intensive manual rigging. We introduce TopoCap, the first unified framework capable of extracting motion from monocular video and retargeting it onto characters with arbitrary, unseen skeletal topologies, i.e., from bipeds to hexapods and inanimate objects, without test-time optimization. Our key insight is that while skeletal structures are combinatorial and discrete, the underlying physics of motion occupy a continuous, low-dimensional manifold. We materialize this insight via a two-stage generative pipeline. First, we learn a Universal Motion Manifold using a Graph CVAE that compresses heterogeneous kinematic chains into a shared, fixed-length latent code. By explicitly conditioning the decoder on a structural embedding of the target rig, we disentangle motion dynamics from skeletal topology. Second, we treat video-to-animation as a conditional flow matching problem, predicting these topology-agnostic codes from visual features. To learn this generalized prior, we introduce Mobjaverse, a massive-scale dataset curated from Objaverse-XL. Comprising over 5,000 unique skeletal topologies and 2 million frames, it exceeds the structural diversity of existing datasets by two orders of magnitude. Extensive experiments demonstrate that \MethodMotion outperforms specialist models on human and quadruped benchmarks while enabling zero-shot retargeting for the long tail of 3D creatures. Dataset is publicly available at https://huggingface.co/datasets/duckduckplz/Mobjaverse.

20.
arXiv (CS.LG) 2026-06-12

An Empirical Study on Predictive Maintenance for Component X in Heavy-Duty Scania Trucks

arXiv:2606.12486v1 Announce Type: new Abstract: Condition-based Predictive Maintenance (PdM) for truck fleets has gained momentum in recent years. This maintenance strategy aims to minimize unplanned downtimes and reduce costs by monitoring the health status of vehicles and taking proactive action based on their condition. However, the implementation of condition-based PdM systems is challenging due to the large volume of data generated by the trucks, the inherent complexity of detecting failures through sensor data and the difficulties in finding cost-effective trade-offs in the solution's implementation. In this paper, we define and validate a condition-based PdM methodology built on the assumption that the wear-and-tear state of the monitored component can be represented as a monotonically non-decreasing time series. It involves selecting only the most recent observations from the time series and transforming them into a tabular format for classification using machine learning (ML) models designed for tabular data. Our results indicate that the proposed methodology reduces costs on the Scania Component X dataset compared to current state-of-the-art (SOTA) approaches, while also simplifying the modeling process through AutoML.

21.
arXiv (quant-ph) 2026-06-11

Experimental straintronics in nanotube quantum dots

arXiv:2606.12180v1 Announce Type: cross Abstract: Single-wall carbon nanotubes (SWCNTs) are narrow ribbons of graphene with atomically precise edges and a single quantum transport channel, at experimentally-relevant dopings. This makes them ideal systems to harness quantum transport straintronics (QTS), i.e. using mechanical strain to control accurately quantum transport. We present QTS data from three single-wall carbon nanotube quantum dot (SWCNT-QD) transistors over a broad range of in-situ tunable and reversible uniaxial strain ($\Delta\varepsilon_mech\approx$ 0 to 3 %). We first present the nanofabrication of the suspended SWCNT transistors whose channel lengths are $\approx$ 30 nm. The channels are strained by moving gold clamps holding firmly the nanotubes. We present detailed charge transport data, $dI/dV_{B} - V_{B} - V_{G}$ and $dI/dV_{B} - V_{B} - \Delta\varepsilon_mech$, showing a large mechanical-gating effect of the SWCNT-QDs. The precise reversibility of the data, and their agreement with QTS theory, confirms that the tubes are strained elastically. We demonstrate that the mechanical control of the QD doping is not due to capacitive-gating effects, but to quantitatively predictable bandstructure changes including a strain-tunable bandgap. This precise mechanical control of the doping and bandgap of SWCNT-QDs could find applications in qubits, condensed matter physics, and homojunction molecular transistors.

23.
arXiv (CS.AI) 2026-06-15

ANSR-DT: A Neuro-Symbolic Framework for Adaptive and Explainable Digital Twins

arXiv:2501.08561v4 Announce Type: replace Abstract: Digital twins are increasingly used to monitor and optimize industrial systems, yet many existing frameworks remain difficult to interpret, slow to adapt, and limited in their ability to incorporate explicit domain knowledge. This paper presents ANSR-DT, an adaptive neuro-symbolic framework that unifies temporal anomaly detection, symbolic reasoning, and reinforcement-learning-based decision support within a single digital twin pipeline. ANSR-DT combines a CNN-LSTM model for multivariate pattern recognition with Prolog-based reasoning that converts learned signals into explicit rules, enabling transparent diagnoses and traceable decision paths. A PPO-based adaptation layer further refines operational responses under changing conditions while preserving interpretability. Experiments against 8 baselines show that ANSR-DT delivers competitive predictive performance together with stable rule extraction, scalable symbolic reasoning, and actionable explanations. Additional validation on the Skoltech Anomaly Benchmark (SKAB) further indicates that the framework transfers beyond synthetic settings. These findings position ANSR-DT as a practical foundation for trustworthy, adaptive, and explainable industrial digital twins.

24.
arXiv (CS.LG) 2026-06-18

Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space

arXiv:2605.17232v2 Announce Type: replace Abstract: Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge under singular priors such as the masked distribution, while bounds in total variation (TV) depend on the state space size $S$ and become vacuous for modern language tasks, where vocabularies contain hundreds of thousands of tokens. We develop a unified adjoint-equation-based framework that establishes dimension-free convergence guarantees in any integral probability metric (IPM). To the best of our knowledge, our bounds are the first to be entirely free of $S$ and applicable to both masked and uniform priors. Importantly, our theory relies only on a single standard rate-matrix regularity assumption and applies to general priors. Five novel techniques drive our improvements: working in the space of observables via adjoint equations rather than directly with probability measures, a regularity analysis that yields bounds on any IPM, a coupling argument that removes $S$-dependence under uniform transitions, and score-marginal cancellation and exit-routing techniques that remove $S$-dependence under masked transitions. Our framework thus sharply departs from prior analyses and avoids the shortcomings of pathspace-KL and existing TV-based approaches. Beyond convergence bounds, our framework provides a versatile toolkit for further theoretical study of discrete diffusion models, including principled choices of loss functions and dimension-free step complexity.

25.
arXiv (quant-ph) 2026-06-19

GPU-accelerated semidefinite programming for causal games

arXiv:2606.20519v1 Announce Type: new Abstract: The process matrix formalism describes quantum correlations in scenarios without a fixed causal order between local laboratories. Operational signatures of such correlations can be investigated through causal games. A paradigmatic example is the Guess-Your-Neighbour's-Input game, in which two parties attempt to guess each other's inputs. Correlations compatible with any definite, or probabilistically mixed, causal order cannot achieve a winning probability exceeding $1/2$. The best process-matrix strategy currently known attains a value of approximately $0.6218$ using local dimension $d=5$, while the strongest known dimension-independent upper bound is $0.7592$. In this work, we investigate whether increasing the local dimension beyond $d = 5$ can narrow this gap. To this end, we employ a see-saw optimization scheme in which each step is formulated as a semidefinite program. For scalability, we develop a custom implementation of the SCS solver in which the dominant computational cost, the projection onto the positive-semidefinite cone, is offloaded to a GPU, yielding a six-fold speedup. Using this implementation, we explore local dimensions up to $d = 8$, and we do not find significant improvements over the value at $d=5$. Our results suggest that either qualitatively different strategies are required to approach the known upper bound, or that the bound itself is not tight.