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01.
arXiv (CS.CL) 2026-06-16

A Mechanistic Understanding of Pronoun Fidelity in LLMs

Faithful and robust pronoun use is important for fair and coherent generations, yet large language models largely fail when multiple referents use different pronouns. To study the interplay of reasoning, repetition, and bias in this task, prior work relies exclusively on behavioural approaches, which may not reflect a model's internal workings. Therefore, we provide a mechanistic, model-internal perspective on pronoun fidelity, testing whether three mechanisms – group entity binding (G), recency bias (R), and stereotypical bias (S) – are causally implemented across several SOTA language models. Using Boundless Distributed Alignment Search, we find all three coexist as causal subspaces distributed across network depth. No single mechanism fully explains model behaviour, but a combination of the three consistently accounts for 91-99.5%. An attention head analysis further reveals two competing copying routes; group binding and stereotype share a localized concept-level route that retrieves a bound occupation-pronoun unit, while recency uses a distributed token-level route that repeats surface forms. In sum, pronoun fidelity arises from competition between simultaneously active causal subspaces.

02.
arXiv (CS.CL) 2026-06-16

Data Augmentations for Data-Constrained Language Model Pretraining

As AI labs approach a data ceiling where compute capacity outpaces the rate of new high-quality text generation, language model pretraining is shifting toward a data-constrained, compute-abundant regime that demands productive multi-epoch training on fixed corpora. Standard autoregressive (AR) pretraining overfits severely in this setting, reaching its optimum early and then continuously deteriorating. We investigate data augmentation as a regularizer to mitigate this overfitting and enable productive training for hundreds of epochs on the same data. We introduce three orthogonal categories of augmentation for AR pretraining: token-level noise (masking, random replacement), sequence permutations (right-to-left prediction, Fill-in-the-Middle), and target offset prediction ($x_{t+i}$ for $i > 1$). Through systematic ablations, we find that individual augmentations delay overfitting and lower validation loss relative to the baseline, with random token replacement achieving the best minimum loss among individual methods. Combining augmentation categories further lowers the minimum validation loss. Our experiments demonstrate that data augmentations mitigate AR pretraining's data inefficiency and offer a promising solution to the data-constrained regime. All code and data are available at https://github.com/michaelchen-lab/data-augmentations-for-pretraining

03.
arXiv (CS.AI) 2026-06-19

ROSE: Benchmarking the Perception-to-Action Gap in Multimodal Models

arXiv:2606.19965v1 Announce Type: cross Abstract: Multimodal large language models (MLLMs) are increasingly expected to act on visual information, yet the same scene may require different actions under different task contexts. How reliably can a model turn the same visual evidence into the action required by the current context? To answer this question, we introduce \textsc{ROSE} (Reference-conditioned Oddity and Symbolic Execution), a controlled benchmark that holds the visual scene fixed while varying region constraints and required symbolic outputs. Through coupled counting and coordinate-action tasks, \textsc{ROSE} tests whether models can infer an implicit majority reference and act on the resulting fine-grained visual evidence under changing contexts. Across nine recent MLLMs, performance drops by as much as 44.5 percentage points from counting-oriented tasks to region-conditioned action, despite 98.8\% human performance. The gap persists on paired scenes and regions for which the same model returns the correct count, while global-click and matched local controls show that coordinate grounding explains only part of the loss, revealing a distinct, model-dependent bottleneck in turning shared visual evidence into context-specific actions.

04.
arXiv (CS.CV) 2026-06-11

Weakly Supervised Segmentation as Semantic-Based Regularization

Weakly supervised semantic segmentation (WSSS) trains dense pixel-level segmentation models from partial or coarse annotations such as bounding boxes, scribbles, or image-level tags. While recent work leverages foundation models such as the Segment Anything Model (SAM) to generate pseudo-labels, these approaches typically depend on heuristic prompt choices and offer limited ways to incorporate prior knowledge or heterogeneous labels. We address this gap by taking a neurosymbolic perspective: integrating differentiable fuzzy logic with deep segmentation models. Weak annotations and domain-specific priors are unified as continuous logical constraints that fine-tune SAM under weak supervision. The refined foundation model then produces improved pseudo-labels, from which we train a second-stage prompt-free segmentation model. Experiments on Pascal VOC 2012 and the REFUGE2 optic disc/cup segmentation dataset show that our logic-guided fine-tuning yields higher-quality pseudo-labels, leading to state-of-the-art segmentation accuracy that often exceeds densely supervised baselines.

05.
arXiv (CS.CL) 2026-06-11

Claw-SWE-Bench: A Benchmark for Evaluating OpenClaw-style Agent Harnesses on Coding Tasks

General-purpose agents such as OpenClaw are increasingly used as autonomous tool users, but their coding ability is difficult to measure under SWE-bench: a generic agent does not by itself satisfy the clean Docker workspace, patch, and prediction contract required for scoring. We introduce Claw-SWE-Bench, a multilingual SWE-bench-style benchmark and adapter protocol that makes heterogeneous agent harnesses, or claws, comparable under fair settings including a fixed prompt, runtime budget, workspace contract, patch extraction procedure, and evaluator. The full benchmark contains 350 GitHub issue-resolution instances across 8 languages and 43 repositories, drawn from SWE-bench-Multilingual and SWE-bench-Verified-Mini after future-commit cleanup. We also release Claw-SWE-Bench Lite for faster validation, which is an 80-instance subset selected by a cost-aware, rank-aware procedure over 17 calibration columns. On the full benchmark, OpenClaw with a minimal direct-diff adapter scores only $19.1\%$ Pass@1, whereas the full adapter reaches $73.4\%$ with the same GLM 5.1 backbone, showing that adapter design is essential for enabling OpenClaw-style harnesses to perform coding tasks effectively. Across an OpenClaw $\times$ nine-model sweep and a five-claw $\times$ two-model sweep, model choice changes Pass@1 by $29.4$ pp and harness choice by $27.4$ pp under fixed models; systems with similar accuracy can differ substantially in total API cost. Claw-SWE-Bench therefore treats harness and cost accounting as first-class axes of SWE-style coding-agent evaluation, providing both a full benchmark and a low-cost reference set for reproducible comparison. The data is available at https://github.com/opensquilla/claw-swe-bench and https://huggingface.co/datasets/TokenRhythm/Claw-SWE-Bench.

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

Sub-Poissonian Statistics and Quantum Non-Gaussianity from High-Harmonic Generation

arXiv:2602.10882v4 Announce Type: replace Abstract: Quantum technologies are powered by platforms to generate complex non-classical states of matter or light to realize applications. We investigate the non-classical properties of high-harmonic generation in semiconductors, an emerging photonic platform. Measuring the click statistics of three double-digit orders, we evaluate witness operators to certify the non-classicality of the generated states. We show that higher-order harmonics driven by a coherent laser are squeezed and entangled. The properties of the emission are well retrieved with an entangled Gaussian state model, obtained by numerical state optimization to multiple observables. Additionally, we perform inter-order heralded measurements to engineer the quantum state of the emission. The heralded states have distinct properties, showing sub-Poissonian photon statistics. Further, we witness the generation of a quantum non-Gaussian state, a resource highly relevant for quantum information. With this, we establish high-harmonic generation as a platform for generating quantum optical resources.

07.
arXiv (CS.AI) 2026-06-16

EMS: Multi-Agent Voting via Efficient Majority-then-Stopping

arXiv:2604.02863v2 Announce Type: replace Abstract: Majority voting is the standard for aggregating multi-agent responses into a final decision. However, traditional methods typically require all agents to complete their reasoning before aggregation begins, leading to significant computational overhead, as many responses become redundant once a majority consensus is achieved. In this work, we formulate efficient multi-agent voting as a reliability-aware agent scheduling problem and propose Efficient Majority-then-Stopping (EMS) to improve reasoning efficiency. EMS first estimates a Task-Conditioned Reliability Ordering (TCRO) for each agent by retrieving its historical consensus evidence on semantically similar queries, and then invoking agents in descending reliability order. Next, Adaptive Incremental Voting (AIV) terminates the process once the current leading answer cannot be overturned by any possible votes from the remaining agents, and returns this answer. Finally, Reliability History Updating (RHU) updates only the invoked agents according to their consensus with the final decision. Extensive evaluations across five benchmarks show that EMS preserves the accuracy of Majority Voting while reducing the average number of invoked agents by 35% and token consumption by 44%, respectively. The code is available at https://github.com/fuyu66/EMS.

08.
arXiv (CS.LG) 2026-06-11

The ASE-LSE Disagreement Landscape: An End-to-End Characterisation of Extremes and Structural Drivers

arXiv:2605.22346v3 Announce Type: replace-cross Abstract: Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same graph. Yet the structural reasons behind this disagreement remain incompletely understood. This paper provides an end-to-end account of ASE-LSE latent subspace disagreement. We first prove that the two methods produce identical latent subspaces for every embedding dimension whenever the Laplacian is a scalar multiple of the adjacency matrix, and show that this scalar relationship holds if and only if the graph is either regular or bipartite biregular. This anchor result identifies a sufficient condition for perfect agreement that pins down the floor of the disagreement spectrum and supplies the baseline for the perturbation analysis. We then prove that no maximal-disagreement graph or family of graphs exists: the disagreement is always strictly below its theoretical ceiling, and we exhibit a witness family demonstrating that no finite maximum is attainable, so the disagreement landscape has no maximiser. With both endpoints established, we derive a Regularity Departure Bound whose two terms isolate degree heterogeneity and eigengap as the primary structural factors influencing disagreement in the middle regime. Empirical validation across thousands of simulated graphs confirms the mechanisms predicted by the bound: heterogeneity pushes disagreement up, eigengap suppresses it, and their joint ratio emerges as a unified predictor of ASE-LSE disagreement, suggesting when the two embeddings can be treated as interchangeable and when they cannot.

09.
arXiv (CS.AI) 2026-06-11

FreeBridge: Variational Schrödinger Bridges for Cellular Transition Dynamics

arXiv:2606.11286v1 Announce Type: cross Abstract: High-content imaging assays quantify cellular responses to chemical and genetic perturbations, yet continuous trajectories of individual cells are unobservable because cells are chemically fixed at acquisition. Perturbation modeling therefore reduces to inferring stochastic transport between control and treated populations observed only as separate marginals. While recent generative models achieve strong end-point alignment, boundary consistency does not determine intermediate evolution: multiple stochastic processes may connect identical marginals while traversing regions unsupported by observed single-cell morphologies. We introduce FreeBridge, a Schrödinger Bridge formulation for single-cell transition modeling under endpoint-only supervision. FreeBridge defines atomic states as instance-segmented single-cell representations, establishing a fixed cellular manifold, and learns stochastic transport constrained within this geometry via empirical latent support regularization. Across BBBC021, RxRx1, and JUMP, FreeBridge maintains competitive or improved endpoint fidelity and mechanism-of-action retention under a unified evaluation protocol; on BBBC021, it further reduces intermediate support violations. These findings highlight the importance of geometric grounding for biologically interpretable perturbation dynamics. Project page: https://y-research-sbu.github.io/FreeBridge/.

10.
arXiv (CS.AI) 2026-06-17

Confusion-Aware Transfer Teacher Curriculum Learning Framework: Disentangling Scoring and Pacing Effects

arXiv:2606.17706v1 Announce Type: cross Abstract: Curriculum learning couples two design choices, how samples are scored by difficulty and how harder samples are paced into training, making it difficult to attribute observed gains to either component. We disentangle these factors with two evaluation protocols: stage-wise test subsets that validate scoring functions independently of curriculum training, and a baseline that applies the same pacing schedule to randomly ordered data. Within the Transfer Teacher framework (TTF), we use these protocols to evaluate a confusion-aware difficulty score that considers both correct-class confidence and the probability distribution over incorrect classes. On CIFAR-10 with ResNet-18 and VGG-16, the proposed score produces model-interpretable difficulty rankings that align with human intuition. However, at full data, neither curriculum nor anti-curriculum ordering improves accuracy over standard training, indicating that improving the scoring function alone is insufficient to overcome the known failure modes of curriculum learning in TTF. In contrast, We find that confusion-aware curriculum ordering result in consistent data-efficiency benefits, outperforming random ordering by up to 8.7% points at the 20% data regime, suggesting the potential of TTF as a data-efficient training method.

11.
arXiv (quant-ph) 2026-06-19

Topological Codes Based on Space Groups

arXiv:2606.20548v1 Announce Type: new Abstract: Topological codes form one of the most important classes of stabilizer codes. Most existing algebraic constructions and analyses of topological codes assume translation invariance. Here we show that topological codes can arise in more general settings by incorporating point group operations. The central construction is a class of Calderbank-Shor-Steane (CSS) codes called space-group codes, whose check operators are built from group-algebra templates over space groups that combine translations with point-group operations. We develop methods for analyzing topological properties of space-group codes using ring-modules and their invariant theory. At first glance, space-group codes might appear to complicate practical implementation; however, we find that they can exhibit greater locality than previous codes based purely on translations. Our framework thus extends the landscape of topological codes and opens up a broader design space for the co-design of topological codes with quantum computing platforms.

12.
arXiv (quant-ph) 2026-06-19

Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid

arXiv:2606.19482v1 Announce Type: new Abstract: High-performance quantum low-density parity-check codes promise substantial reductions in the overhead of fault-tolerant quantum computation, but most constructions require long-range connectivity or qubit shuttling, both of which are difficult to realise in superconducting architectures. Here we introduce a family of quantum low-density parity-check codes that, for the first time, combines planar open-boundary layouts, finite-size advantages over surface codes, and syndrome extraction using only nearest-neighbour gates on a square grid of qubits. The key idea is to generate check-data connectivity dynamically: nearest-neighbour iSWAP walks both define the stabiliser supports and implement their measurement, avoiding the need for a long-range hardware graph. The resulting circuits achieve optimal constant-depth stabiliser measurement, independent of code size, and naturally remove leakage from the system by exchanging the role of check and data qubits at each syndrome extraction round. We find finite-size instances such as a [[323,14,15]] code, whose code-efficiency ratio is nearly an order of magnitude larger than that of rotated surface-code patches. At around 30 circuit qubits per logical qubit, the best directional tile-code layouts reduce the per-logical per-round logical error rate by up to a factor of 1000 relative to rotated surface-code memories. These results show that the advantages of quantum low-density parity-check codes can survive compilation into strictly planar nearest-neighbour circuits, bringing low-overhead fault-tolerant memories closer to near-term hardware.

13.
arXiv (CS.CL) 2026-06-15

SIMMER: Benchmarking Latent Failures in LLM Executable Planning with a World Model

Large language models (LLMs) are increasingly deployed as planners for autonomous agents in household environments. While existing benchmarks evaluate whether LLM-generated plans execute successfully, they overlook a critical type of failure: latent failures. Unlike immediate failures that trigger instant feedback at execution time and enable timely correction, latent failures do not immediately halt plan execution but silently compromise goal achievement. In severe cases, they cause irreversible harm. To address this gap, we introduce SIMMER, a benchmark for evaluating latent failures in LLM planning through a human-curated symbolic world model grounded in the kitchen domain. SIMMER defines a world model comprising 77 actions, 262 unique objects, and approximately 46,800 possible interactions that are semantically realistic, derived from real-world cooking scripts. It then leverages a state machine executor that validates plans against the world model and detects immediate precondition violations, latent hazards, and irreversible failures. Experiments across six LLMs show that even frontier models achieve at most 17% error-free plans. Moreover, up to 56% of plans contain latent failures, the majority of which lead to irreversible consequences. We further demonstrate that explicit state reasoning via counterfactual foresight simulation can reduce latent failures by up to 72% and irreversible cases by up to 75%, suggesting a promising direction for more robust LLM planners.

14.
arXiv (CS.LG) 2026-06-16

DiRecT: Safe Diffusion-Based Planning via Receding-Horizon Denoising

arXiv:2606.15359v1 Announce Type: new Abstract: Diffusion models have emerged as powerful tools for planning and control by learning multimodal distributions over actions and trajectories. Yet reliable inference-time safety enforcement remains a key barrier to their deployment in safety-critical tasks. Existing approaches typically project each denoising iterate onto the feasible set, even though constraints are defined only on the final clean trajectory. Enforcing feasibility on noisy intermediate samples can therefore overconstrain the sampling dynamics, substantially degrading sample quality. To address this limitation, we introduce DiRecT (Diffusion-based planning via Receding-horizon denoising with Terminal constraints), a training-free algorithm for constrained sampling from diffusion models via stochastic optimal control (SOC). DiRecT enforces constraints only on the final clean sample, avoiding unnecessary restrictions on the intermediate denoising dynamics. Inspired by model predictive control, we derive a principled receding-horizon surrogate for the otherwise intractable constrained SOC formulation, yielding an efficient algorithm that cleanly separates stochastic denoising from constraint satisfaction, progressively steering samples toward feasible final trajectories without distorting the learned diffusion dynamics. Furthermore, DiRecT is highly flexible: it can leverage off-the-shelf or domain-specific optimizers, incorporate priors over environment dynamics, and optimize additional soft rewards. Extensive experiments on safe planning benchmarks demonstrate that DiRecT substantially improves deployment safety and task performance over existing diffusion-based planning baselines.

15.
arXiv (CS.CV) 2026-06-12

Ex-Omni: Enabling 3D Facial Animation Generation for Omni-modal Large Language Models

Omni-modal large language models (OLLMs) aim to unify multimodal understanding and generation, yet extending them to jointly produce speech and 3D facial animation remains largely unexplored despite its importance for natural human-computer interaction. A key challenge is the mismatch between the discrete semantic reasoning of LLMs and the dense temporal dynamics required for 3D facial motion. We propose Expressive Omni (Ex-Omni), an open-source model that augments OLLMs with native speech-accompanied 3D facial animation. Ex-Omni decouples semantic reasoning from temporal generation through a blendshape-aware speech unit generator and a blendshape decoder, where speech units provide temporal scaffolding and hidden speech representations carry facially relevant cues. We further introduce a unified token-as-query gated fusion (TQGF) mechanism for controlled semantic injection, as well as InstructS2SF-1200K, a dataset consisting of 1200K samples for pre-training. Extensive experiments show that Ex-Omni maintains competitive speech understanding and generation ability while achieving better audio-visual synchronization and lower face-generation latency than cascaded pipelines.

17.
arXiv (CS.LG) 2026-06-11

Energy Use of AI Inference, Efficiency Pathways, and Test-Time Scaling

arXiv:2509.20241v2 Announce Type: replace Abstract: As AI inference scales to billions of queries, estimates of per-query energy use are increasingly important for capacity planning, efficiency interventions, and policy. Yet many public estimates assume non-production settings, leading to systematic overestimation. We introduce a bottom-up framework estimating inference energy from token throughput, node power, and overhead under large-scale deployment assumptions. For frontier-scale models (>200B parameters) on H100 nodes, we estimate a median energy of 0.31 Wh/query (IQR 0.16-0.60), indicating widely cited estimates are overstated by 4-20x. In test-time scaling scenarios 15x longer than typical queries, the median energy rises 13x to 3.91 Wh (IQR 2.15-7.05). Across models, serving systems, and hardware, we estimate 8-20x line-of-sight energy reductions. At datacenter scale, serving 1 billion queries/day requires 0.7 GWh; if 10% are long queries, demand rises to 1.7 GWh/day. With efficiency interventions, it falls to 0.8 GWh/day, mitigating the energy impact of test-time scaling.

18.
arXiv (CS.CV) 2026-06-16

MVOFormer: Flow-Semantic Transformer for Robust Monocular Visual Odometry

Monocular visual odometry (MVO) is foundational to autonomous navigation and robotic localization. However, existing learning-based MVO approaches often struggle with either a lack of interpretable, complementary features or overly complex multi-stage architectures. These limitations inherently restrict their robustness and cross-domain generalization. In this work, we propose MVOFormer, a novel transformer framework for robust monocular visual odometry. Our architecture features a Flow-Semantic Dual Branch Encoder that synergizes dense geometric motion cues with object-centric semantic priors, explicitly distinguishing static structures from dynamic distractors. These representations are then fused by an Iterative Multimodal Decoder, enabling coarse-to-fine pose refinement while dynamically suppressing attention on unreliable regions. Extensive evaluations demonstrate that, without any target-domain fine-tuning, MVOFormer achieves superior zero-shot generalization and robustness, significantly outperforming prior learning-based frame-to-frame methods across diverse benchmarks including TartanAir, KITTI, TUM-RGBD, and ETH3D-SLAM.

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

Sparsified Kolmogorov-Arnold Networks for Interpretable Quantum State Tomography

arXiv:2606.11814v1 Announce Type: cross Abstract: Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance $z$, the real off-diagonal component $c$, and the imaginary off-diagonal component $s$. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.

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

MPMWorlds: Material-Point-Method Simulations for Inferring and Extrapolating Physical Dynamics

To study the ability to infer physical dynamics from videos and extrapolate them forward in time, we assemble a dataset of 2D Material Point Method (MPM) physical simulations covering rich physical phenomena such as deformable objects, fluids, kinetic objects, and emitters. We study code generation and video diffusion approaches on this dataset, identifying their strengths and weaknesses by varying the amount of physically relevant side information. The code generation model, beyond giving a working demonstration of automatic synthesis of MPM simulations, reveals that such an approach struggles with inferring physical parameters from visual input, but relative to video diffusion, produces physically and temporally stable extrapolations forward in time, while the video diffusion model more strongly identifies geometric properties from visual input but produces physically implausible extrapolations.

21.
arXiv (CS.AI) 2026-06-15

Q-Net: Queue Length Estimation via Kalman-based Neural Networks

arXiv:2509.24725v4 Announce Type: replace-cross Abstract: Estimating queue lengths at signalized intersections is a long-standing challenge in traffic management. Partial observability of vehicle flows complicates this task despite the availability of two privacy-preserving data sources: (i) aggregated vehicle counts from loop detectors near stop lines, and (ii) aggregated floating car data (aFCD) that provide segment-wise average speed measurements. However, how to integrate these sources with differing spatial and temporal resolutions for queue length estimation is rather unclear. Addressing this question, we present Q-Net: a queue estimation framework built upon a state-space formulation. This design addresses key challenges in queue modeling, such as violations of traffic conservation assumptions. Q-Net follows the Kalman predict-update structure and maintains physical interpretability in both the state evolution and measurement models. Q-Net uses an AI-augmented Kalman filter to learn time-varying gain dynamics from data. The framework supports real-time implementation and improves spatial transferability by grouping aFCD measurements into fixed-size local groups, making the number of learnable parameters independent of section length. Evaluations on urban main roads in Rotterdam, the Netherlands, show that Q-Net outperforms baseline methods, tracks queue formation and dissipation accurately, and mitigates aFCD-induced delays. By combining data efficiency, interpretability, real-time applicability, and spatial transferability, Q-Net makes accurate queue length estimation possible without costly sensing infrastructure like cameras or radar.

22.
arXiv (math.PR) 2026-06-16

Transposition Approach to Optimal Control of McKean-Vlasov SPDEs

arXiv:2603.06245v2 Announce Type: replace Abstract: In this paper, we investigate an optimal control problem for McKean-Vlasov stochastic partial differential equations, in which the coefficients depend on the law of the state process. For systems with nonconvex control sets, we establish a Pontryagin-type stochastic maximum principle that provides necessary optimality conditions for admissible controls. The analysis is based on the classical spike variation method together with the introduction of an adjoint backward stochastic partial differential equation involving Lions derivatives with respect to probability measures. Our results extend the stochastic maximum principle for McKean-Vlasov controlled stochastic differential equations to the infinite-dimensional SPDE setting.

23.
arXiv (CS.LG) 2026-06-11

Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

arXiv:2606.12050v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) combine machine learning with physical laws to solve differential equations. While existing results provide rigorous a posteriori upper bounds for PINN prediction errors, complete certification also requires complementary lower information in order to obtain computable two-sided error enclosures. In this paper, we derive computable a posteriori lower bounds for PINN errors in ordinary differential equations on suitable certified state-space domains under a localized strong monotonicity condition. We combine these estimates with complementary localized upper bounds under a one-sided Lipschitz condition, which is weaker than the global Lipschitz assumption used in previous work and can yield sharper upper error bands. The resulting bounds depend only on the neural-network approximation, the ODE residual, and local monotonicity and growth constants, and therefore do not require access to the exact solution. For linear time-invariant and time-varying systems, we further derive explicit formulas in terms of the minimal and maximal eigenvalues of the symmetric part of the system matrix. We also discuss the distinction between soft and hard enforcement of initial conditions in PINNs and explain why exact enforcement can make the scalar lower certificate uninformative. To recover nontrivial lower information in the linear setting, we use a signed-residual finite-probe certificate based on coordinate unit vectors. We also formulate a certificate-informed training strategy in which the propagated upper certificate is used as an auxiliary regularizer, while lower certificates remain post-training diagnostics. Altogether, the proposed framework provides rigorous and practically computable error certificates for PINN approximations of ODEs, while making explicit the domains and model classes for which the assumptions can be verified.

24.
arXiv (CS.CL) 2026-06-12

SkMTEB: Slovak Massive Text Embedding Benchmark and Model Adaptation

We introduce SkMTEB, the first comprehensive MTEB-style text embedding benchmark for Slovak, a low-resource West Slavic language, comprising 31 datasets across 7 task types – nearly 4$\times$ the depth of existing multilingual benchmark coverage for Slovak. Our evaluation of 31 embedding models reveals that large instruction-tuned multilingual models achieve the strongest performance, while existing Slovak-specific models trained for NLU tasks transfer poorly to embedding tasks. To address the need for efficient, locally-deployable Slovak embeddings, we develop \texttt{e5-sk-small} (45M parameters) and \texttt{e5-sk-large} (365M) by applying vocabulary trimming and fine-tuning to Multilingual E5 models. Despite size reductions of up to 62\%, our open-source models achieve competitive performance with proprietary APIs while remaining locally deployable for semantic search and retrieval-augmented generation (RAG). We release the benchmark, models, datasets, and code openly, hoping our approach offers a replicable path for other under-resourced languages.

25.
arXiv (CS.AI) 2026-06-16

Quantum Machine Learning for Industrial Applications

arXiv:2606.14822v1 Announce Type: cross Abstract: Recent advances in Machine Learning have transformed numerous industrial sectors, yet classical paradigms face fundamental limitations: rapidly growing data volumes, rising computational costs, significant energy consumption, and the physical scaling limits of conventional hardware architectures. Quantum computing has emerged as a promising computational paradigm to address these challenges, giving rise to the field of Quantum Machine Learning (QML). In this thesis, the theoretical foundations of QML are investigated, with a focus on near-term and future practical applications. Three central challenges are addressed: the trainability of variational quantum circuits, their expressivity, and their resistance to efficient classical simulation. The trainability of Hamming-weight preserving variational quantum circuits is first studied, and theoretical guarantees are established that resolve an open conjecture on the absence of barren plateaus for this circuit family. Subspace-preserving QML algorithms are then introduced, including photonic circuits and quantum convolutional neural networks, and are designed to mimic classical ML subroutines while offering polynomial quantum advantage. Finally, variational quantum circuits are analyzed as quantum Fourier models, and a framework is derived to jointly characterize expressivity and trainability, from which conditions are obtained under which quantum models provably separate from their classical counterparts. These contributions are intended to advance the theoretical roadmap for harnessing near-term and future quantum technologies in real-world applications.