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01.
arXiv (CS.CV) 2026-06-12

Skill-3D: Evolving Scene-Aware Skills for Agentic 3D Spatial Reasoning

This paper explores agentic 3D spatial understanding, i.e., MLLM agents performing 3D reasoning through tool use. Existing methods often misuse tools and exhibit biased tool preferences under 3D scenarios, leaving the agentic paradigm with only marginal gains over non-agentic strategies. We reveal that 3D spatial reasoning tasks are heterogeneous across scenes, while these agents apply a uniform tool-use strategy to all scenes rather than selecting tools according to the specific scene and task. To address this, we propose Skill-3D, a framework that learns self-evolving scene-aware skills. Specifically, Skill-3D identifies the task scene and records the agent's tool-use trajectory into a Scene Memory, where successful trajectories from similar scenes are aggregated and distilled into a reusable scene-aware skill, with failed ones attached to the skill as lessons. During training, once a similar scene recurs, the corresponding skill is injected to guide the agent, producing new trajectories whose successes and failures further refine the skill, forming a loop in which the memory and the skill library co-evolve. Experiments show that Skill-3D substantially improves tool utilization in 3D spatial reasoning (from 39% to 78% on VSI-Bench), driving the agent toward correct and sufficient tool use. For instance, it improves Gemini-3-Flash by 67% on MMSI-Bench. Furthermore, we conduct agentic post-training over skill-guided trajectories, which boosts Qwen3-VL-8B by 60% on VSI-Bench.

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

Tying the Loop – Tied Expert Layers in Mixture-of-Experts Language Models

Authors:

Mixture-of-Experts (MoE) architectures efficiently scale Large Language Models (LLMs) by activating only a small fraction of their experts per token, yet the full parameter count - dominated by the expert parameters - must be held in training and inference memory. To address this, we introduce Expert Tying, an architectural modification that shares expert parameters across consecutive transformer layers while preserving independent, layer-wise routing and attention. We evaluate this approach across common, state-of-the-art architectures, including OLMoE, Qwen3, and DeepSeek-style MoEs. Our pretraining experiments demonstrate that tying experts can reduce memory footprint by almost 2x at virtually no degradation in perplexity or downstream quality. By exploiting the parameter redundancy inherent in MoE pathways, our method provides a highly favorable compute-to-memory trade-off, advancing efficient training and scaling of next-generation LLMs.

04.
arXiv (CS.LG) 2026-06-19

Doeblin Curves

arXiv:2606.19859v1 Announce Type: cross Abstract: Recent research on Doeblin coefficients has shed light on their usefulness as a multi-way generalization of the Dobrushin contraction coefficient for TV distance, in a separate vein from their classic role in the theory of Markov chain ergodicity. However, strong conditions, such as being bounded away from 0, are typically necessary for Doeblin coefficients to establish the existence of information contraction. Building on recently formulated concepts of nonlinear information contraction, we aim to propose a finer-grained Doeblin-based characterization of multi-way contraction behavior which yields non-vacuous contraction guarantees even for channels whose Doeblin coefficient is 0. To this end, we introduce the notion of a Doeblin curve – a nonlinear function which quantifies the contraction behavior of a Markov kernel on collections of input distributions at specific levels of divergence and power. Through the course of our analysis, we develop a new variational characterization of Doeblin coefficients, present several properties of Doeblin curves, define several versions of power-constrained Doeblin curves, and derive upper and lower bounds using our aforementioned variational characterization. We then utilize these results in diverse areas, including generalization bounds for noisy iterative optimization, error bounds for reliable computation with noisy circuits, and differential privacy guarantees for online iterative algorithms. In particular, we extend results in these areas to broader domains or group settings, leveraging Doeblin curves to reveal finer-grained contraction phenomena than Doeblin coefficients.

05.
arXiv (CS.CV) 2026-06-19

Holo-World: Unified Camera, Object and Weather Control for Video World Model

Video world models are moving toward preserving an observed world under controllable camera and object motion while allowing its environmental state to change. Yet these controls remain isolated, and weather generation typically relies on a source video or reconstructed scene that already specifies future structure. We study a first-frame-anchored source-to-state setting, where the model starts from a single image and follows explicit camera and object controls and an optional weather instruction, then generates a video that either preserves the source world or transfers it to a target weather state. To address these challenges, we first build HoloStateData, a state video dataset that turns diverse videos into unified control samples for camera, object, and weather supervision. Second, we introduce Holo-World, a unified controllable video world model that jointly controls scene from a single image. Its Unified Scene Adapter factorizes world preservation and weather transfer into distinct parameter subspaces, using rendered background, geometry buffers, and object controls to maintain controlled scene structure while modeling weather-dependent appearance and particle effects. Additionally, Scene-Weather Decomposed CFG guides scene and weather residuals separately, strengthening target weather effects without over-amplifying the full condition. Quantitative and qualitative experiments demonstrate that Holo-World maintains precise camera and object control with consistent scene structure while transferring scenes into diverse target weather state, outperforming video-to-video weather editing baselines on weather-state generation. Our project page is available at \url{https://xiangchenyin.github.io/Holo-World/}.

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

Creativity Reconsidered: Generative AI and the Problem of Intentional Agency

arXiv:2601.15797v2 Announce Type: replace Abstract: Many theorists maintain that conscious intentional agency is a necessary condition of creativity. We argue that this requirement, which we call the Intentional Agency Condition (IAC), should be abandoned. We motivate this by highlighting the problems this criterion encounters in the face of recent advances in generative AI, which is ostensibly creative despite being incapable of intentional agency. We present two corpus analyses to illustrate the rapidly increasing tendency of people to predicate creativity to generative AI. In response to this predicament, theorists of creativity have proposed a range of conflicting solutions, which we critically evaluate. We find that none of these satisfyingly resolves the initial predicament, and we therefore propose a novel approach. Our claim is that ascriptions of creativity are dependent on what we call creative ability. This solution explains why intentional agency is important for judgements of creativity, without being a necessary condition. Our approach thereby accommodates AI creativity without dismissing the intuition that perceived intentions are of key importance for ascriptions of creativity.

07.
arXiv (CS.AI) 2026-06-15

Learning Coordinated Preference for Multi-Objective Multi-Agent Reinforcement Learning

arXiv:2606.14693v1 Announce Type: cross Abstract: Cooperative multi-objective multi-agent reinforcement learning (MOMARL) models team decision making under multiple, potentially conflicting objectives. In this setting, conflicts arise not only across objectives but also across agents with different observations, roles, and contributions. We propose Preference Coordinated Multi-agent Policy Optimization (PCMA), which learns coordinated agent-specific preferences to enable complementary trade-offs among agents. Theoretically, we formulate cooperative MOMARL as a team-optimal game and show that, under suitable conditions, preference diversity can induce team improvement through a first-order improvement decomposition. Experiments on multiple cooperative MOMA environments and a practical traffic-control scenario show that PCMA improves both performance and trade-off coordination.

08.
arXiv (CS.AI) 2026-06-16

Task-guided cross-subject latent alignment: a multi-encoder-decoder VAE

arXiv:2606.15989v1 Announce Type: cross Abstract: Aligning neural activity across subjects offers the promise of discovering shared computational principles and generalizable decoders. However, traditional alignment methods require shared stimuli across subjects, a constraint that limits applicability to naturalistic paradigms with limited or non-overlapping data. We introduce a Multi-Encoder-Decoder Variational Autoencoder (MED-VAE) that achieves cross-subject alignment without shared stimuli by anchoring representations to a common scaffold provided by a pretrained ANN. Using the Natural Scenes Dataset, we show that MED-VAE creates common latent spaces with superior semantic organisation, achieving higher cross-subject alignment than common methods while maintaining robust generalisation to held-out stimuli where traditional methods degrade. Reconstructing from these common spaces back to each subject's original neural space, MED-VAE preserves equal stimulus-driven signal in its cross-subject latent space. Finally, we show that this superior alignment directly enables cross-subject neural prediction, as demonstrated via cross-subject image decoding. In summary, we introduce a framework to identify generalisable common subspaces for cross-subject predictions and downstream tasks, demonstrated here for visual cortex responses to static images.

09.
arXiv (quant-ph) 2026-06-16

Connecting entanglement growth with local integrals of motion in the disordered Fermi-Hubbard model

arXiv:2606.15481v1 Announce Type: new Abstract: Generically a quantum system initialized in an unentangled state will, under unitary dynamics, rapidly become entangled, a process closely related to information transport and to thermalization. Disorder can suppress the growth of entanglement and result in memory of initial conditions. In non-interacting systems this arises from localization of single-particle states, the occupancy of which is fixed by the initial condition. In interacting systems similar localized conserved quantities persist, but with the added feature that they are coupled, resulting in entanglement growth which is distinct from both non-interacting localized systems and from generic ergodic systems. The Fermi-Hubbard model has two degrees of freedom per site – charge and spin – and disorder may be present in both of these. We study the growth of entanglement in two scenarios – disorder in charge equal and unequal to that in spin, and determine the distinct contributions of charge and spin degrees of freedom by expanding the Hamiltonian in terms of a set of optimally localized conserved quantities with separate charge and spin character. We find that coupling between charge and spin is significantly weaker than charge-charge and spin-spin coupling. While this decoupling is present in all our results, it is only apparent when the strength of the disorder in the two sectors is different such that there is a separation between the characteristic timescales of the contributions to entanglement made by charge and by spin.

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

From Tokens to Regions: CUDA-Sensitive Instruction Tuning for GPU Kernel Generation

arXiv:2606.16231v1 Announce Type: cross Abstract: High-performance CUDA kernels are essential for scalable AI systems, while Large Language Models (LLMs) still struggle to generate correct kernels due to strict and implicit execution constraints. Existing LLM-based approaches either rely on costly agentic or reinforcement-learning (RL) pipelines, or adopt supervised fine-tuning (SFT) objectives that fail to explicitly model CUDA sensitivity, namely code tokens or regions tightly coupled with execution constraints. In this work, we investigate CUDA sensitivity from the perspective of token confidence patterns, showing that CUDA sensitivity appears at both token and region levels, where most CUDA-sensitive tokens are predicted with high confidence, while a smaller low-confidence subset forms regions corresponding to execution-critical structures. These findings suggest that effective CUDA kernel generation should both leverage high-confidence CUDA-sensitive tokens and preserve low-confidence CUDA-sensitive regions. Building on these insights, we propose \underline{CUDA-\underline{Se}nsitive Instruction \underline{T}uning (CuSeT)}, a low-cost post-training method within a simple SFT framework. CuSeT follows the principle of ``from tokens to regions'' by combining adaptive token-level masking with region-aware sample reweighting. Experiments show that CuSeT consistently improves functional correctness across multiple model families and scales, outperforming standard SFT and advanced SFT variants, while achieving competitive performance against frontier CUDA kernel generation models with substantially lower inference cost.

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

Mach's principle in atomic transitions

arXiv:2606.11608v1 Announce Type: new Abstract: We investigate the atomic transition probabilities in atom-mirror set-ups that are in circular motion. In one scenario, the atom is in circular motion inside a static cylindrical mirror. In the other scenario, the cylindrical mirror rotates around its central axis while the atom remains static. We report structural similarity in the atomic transition probabilities between these two cases – these probabilities are equivalent upon interchanging the field frequencies between the two scenarios. We interpret such an observation as a semi-classical phenomenon analogous to the classical Mach's principle.

12.
arXiv (CS.LG) 2026-06-19

Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions

arXiv:2512.17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$, NMD seeks matrices $W \in \mathbb{R}^{m \times r}$ and $H \in \mathbb{R}^{r \times n}$ such that $X \approx f(WH)$, where $f$ is an element-wise nonlinear function. We evaluate our method on several representative nonlinear models: the rectified linear unit activation $f(x) = \max(0, x)$, suitable for nonnegative sparse data approximation, the component-wise square $f(x) = x^2$, applicable to probabilistic circuit representation, and the MinMax transform $f(x) = \min(b, \max(a, x))$, relevant for recommender systems. The proposed framework flexibly supports diverse loss functions, including least squares, $\ell_1$ norm, and the Kullback-Leibler divergence, and can be readily extended to other nonlinearities and metrics. We illustrate the applicability, efficiency, and adaptability of the approach on real-world datasets, highlighting its potential for a broad range of applications.

13.
arXiv (CS.CL) 2026-06-19

GEMS: Geometric Constraints Enable Multi-Semantic Superposition in LLMs

Authors:

Activation steering controls model behavior by modifying intermediate hidden states at inference time without retraining. Existing methods handle only single-direction injection; when multiple semantic directions are superposed without constraints, the model collapses. We show that this collapse decomposes into two independently acting sources: distributional deviation, where additive perturbations accumulate in norm across layers and drive activations outside the training distribution, and directional interference, where non-orthogonal semantic vectors mutually dampen when superposed. These two sources define the design constraints that any training-free multi-directional intervention must address. As one instantiation of these principles, we propose GEMS, a training-free method that maps each source to a corresponding geometric constraint: norm-preserving weighted superposition and targeted attention-pathway injection for distributional deviation, and real-time orthogonalization for directional interference. On GSM8K, injecting three concurrent non-mathematical directions preserves accuracy at 98% (baseline 92%), while unconstrained addition collapses to 4%; on Wikitext-2, the same injection incurs only 2.2% PPL increase. Component ablation isolates the causal role of each constraint, and layer-level probes confirm that orthogonalized signals survive the FFN pathway and reach the output distribution with semantic specificity. Qualitative steering effects transfer across architectures from 3B to 31B.

14.
arXiv (CS.AI) 2026-06-15

ChronoID: Infusing Explicit Temporal Signals into Semantic IDs for Generative Recommendation

arXiv:2606.14260v1 Announce Type: cross Abstract: Semantic IDs are crucial in generative recommendation, but with a fundamental limitation: temporal information is not well incorporated into semantic IDs. Instead, time influences recommendation only implicitly (e.g., through session construction heuristics, preference alignment, or sequence order), while existing semantic ID learning remains entirely time-agnostic. This design conflates interactions occurring under distinct temporal contexts into identical semantic representations, implicitly assuming that item semantics and user intent are temporally stationary. Such an assumption is misaligned with real-world recommendation scenarios, where evolving interaction rhythms play a central role. In this work, we investigate where and how the explicit time should be incorporated into semantic ID for generative recommendation. First, we systematically characterize the design space along three orthogonal dimensions of temporal signals and present a unified framework, ChronoID, for time-aware semantic ID learning. Then, by contributing a new time-explicit generation recommendation benchmark, ChronoID answers the questions: what is the effective way of infusing time, how to design the architecture, and where does the gain come from.

15.
arXiv (CS.LG) 2026-06-18

PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling

arXiv:2602.11467v2 Announce Type: replace Abstract: Understanding how anatomical shapes evolve in response to developmental covariates - and quantifying their spatially varying uncertainties - is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce PRISM, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. PRISM models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate PRISM's strong performance across diverse tasks - from modeling shape evolution to personalized shape prediction and anomaly detection - within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.

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

Optical Creation of Synthetic Microgravity for Quantum Degenerate Gases

arXiv:2606.14985v1 Announce Type: cross Abstract: Microgravity environments provide unique opportunities for ultracold-atom experiments by enabling long interrogation times and reduced acceleration-induced dynamics. However, their realization has largely been restricted to specialized facilities such as drop towers, sounding rockets, and space-based laboratories. Here we realize synthetic microgravity for quantum degenerate gases using optically engineered force landscapes that compensate Earth's gravity to the milli-g level while maintaining continuous confinement of the atomic ensemble. These force landscapes are generated by dynamically painted optical dipole potentials and calibrated in situ through Bloch oscillations in a vertical optical lattice, enabling precise control of the residual acceleration. We use this capability to demonstrate matter-wave beam splitting with arm separations of several hundred microns. We further implement a Bloch-band atom interferometer in which interaction-induced dephasing is strongly suppressed through controlled three-dimensional expansion in the synthetic microgravity potential. This reduction of mean-field effects restores near-$\sqrt{N}$ scaling of interferometric sensitivity for large quantum degenerate ensembles. Our results establish a versatile platform for realizing synthetic microgravity with trapped quantum gases in terrestrial laboratories, bringing the advantages of microgravity experiments to continuously operating systems and opening new opportunities for quantum sensing, matter-wave interferometry, and precision measurements.

17.
arXiv (CS.AI) 2026-06-18

Maturing Markov Decision Processes: Decision Making under Increasing Information and Shrinking Action Sets

arXiv:2606.18820v1 Announce Type: cross Abstract: Sequential decision problems often exhibit an asymmetric evolution of information and decision flexibility: as a decision cycle unfolds, the agent receives richer information while feasible actions expire due to operational cutoffs, commitments, or resource constraints. Standard MDP formulations typically flatten this structure into stage-dependent state descriptions and action masks, thereby obscuring the nested information–action asymmetry that determines which decisions are urgent and which can be deferred. We introduce Maturing Markov Decision Processes (MMDPs), a formulation built around this information–action asymmetry. We characterize one of its key consequences through an expiring-action priority principle, which identifies the actions that must be resolved before the next stage. Motivated by this structure, we develop a structure-aware reinforcement learning framework with stage-aware policy design, expiring-action abstraction, and search-augmented learning with distillation. Experiments on a controlled multi-supplier replenishment problem, simplified cash-management environments of increasing complexity, and a production-scale simulator show that explicitly modeling this asymmetry improves learning efficiency and becomes increasingly valuable as decision problems scale.

18.
arXiv (CS.AI) 2026-06-12

Meta-Learning Transformers to Improve In-Context Generalization

arXiv:2507.05019v2 Announce Type: replace-cross Abstract: In-context learning enables transformer models to generalize to new tasks based solely on input prompts, without any need for weight updates. However, existing training paradigms typically rely on large, unstructured datasets that are costly to store, difficult to evaluate for quality and balance, and pose privacy and ethical concerns due to the inclusion of sensitive information. Motivated by these limitations and risks, we propose an alternative training strategy where we leverage a collection of multiple, small-scale, and domain-specific datasets. We empirically demonstrate that the increased quality and diversity of such data improve the generalization abilities of in-context learners beyond their training domain, while achieving comparable performance with models trained on a single large-scale dataset. We investigate this paradigm by leveraging meta-learning to train an in-context learner on the Meta-Album collection under several settings. Firstly, we show the performance in a controlled environment, where the test domain is completely excluded from the training knowledge. Secondly, we explore the robustness of these models to forgetting in a continual scenario where the information is accessible for a limited time. Finally, we explore the more challenging unsupervised scenario. Our findings demonstrate that transformers still generalize for in-context prediction when trained on a curated dataset collection while offering advantages in modularity and replaceability.

19.
bioRxiv (Bioinfo) 2026-06-22

Drug-Prot: A query system for statistical inference of drug effects and interactions in dynamic proteomic networks

Understanding drug effects and drug-drug interactions is essential for developing combination therapies. We present Drug-Prot, a computational framework that leverages large-scale perturbation proteomics to quantify causal drug effects, drug-drug interactions, and dynamic protein relationships. Using data from 63 single drugs and 59 drug combinations applied to 18 breast cancer cell lines at 6, 24, and 48 hours, Drug-Prot estimates drug effects on protein expression and reconstructs directed temporal protein dependency networks. The publicly available software enables targeted analyses of user-defined protein sets, substantially reducing the multiple-testing burden. Through an interactive web application, users obtain corrected p-values for single-drug and combination effects, directed temporal dependency networks, and downloadable results without requiring access to the underlying proteomic dataset. As a use case, we apply invariance-regularized Random Forests to triple-negative breast cancer cell lines to identify proteins associated with drug response. Querying these proteins in Drug-Prot reveals drug-specific and interaction effects at the protein-network level, illustrating how the framework links candidate causal protein features to actionable drug combinations.

20.
arXiv (CS.CL) 2026-06-11

ALIGNBEAM : Inference-Time Alignment Transfer via Cross-Vocabulary Logit Mixing

Domain fine-tuning degrades the safety of large language models: fine-tuned specialists readily comply with harmful prompts framed in domain language. Existing inference-time defenses that mix logits from a safe anchor model require both models to share a vocabulary, which rules them out for the cross-family specialists where safety is most degraded. We present ALIGNBEAM, a training-free method that lifts this restriction by translating anchor logits into the target model's vocabulary token-by-token at each decoding step; a small LLM judge then selects the safest among K candidate continuations. No weights are changed, and the safety-utility trade-off can be tuned at deployment without retraining. Across both cross-vocabulary and same-vocabulary evaluation pairs, ALIGNBEAM substantially raises refusal on adversarial benchmarks while keeping task accuracy and inference overhead within practical bounds. The results show that safety alignment can be transferred between model families at inference time, without touching either model's weights.

21.
arXiv (CS.AI) 2026-06-16

Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling

arXiv:2606.15959v1 Announce Type: cross Abstract: Neural networks are used as generative surrogate models for scientific discovery, which are trainable approximations of scientific simulations. These models enable users to replace time-consuming numerical simulations with learned alternatives, providing quick solutions. However, high-fidelity generative surrogate models require massive training datasets, which can create storage and I/O challenges. Lossy compression is a promising way to reduce this burden, but compression errors may affect the model quality in subtle ways, making it challenging to quantify their impact. In this work, we examine how lossy compression of training data impacts the quality of generative surrogate models. We begin by characterizing the uncertainty inherent in training neural networks, showing that identical training configurations can produce different models. By exploiting this variability, we propose a method to estimate how much compression-induced error a surrogate model can tolerate without affecting its accuracy. Evaluation of two application simulations demonstrates that our approach significantly reduces memory/storage requirements and speeds up training while producing high-quality surrogate models. These results show that lossy compression saves data storage up to 23.7x and 39x with negligible impact on the quality of the surrogate model. Meanwhile, reducing the size of the training data set also enhances the data loading speed and reduces the training time by up to 3x.

22.
arXiv (CS.LG) 2026-06-19

DF-ExpEnse: Diffusion Filtered Exploration for Sample Efficient Finetuning

arXiv:2606.19656v1 Announce Type: cross Abstract: A natural recipe for intelligent robotic decision-making is initializing from pretrained generative control policies, which have summarized offline experience, and adapting them to self-collected online experience. We present DF-ExpEnse, an exploration technique that improves the quality of online experience collection, thus increasing finetuning sample-efficiency. DF-ExpEnse leverages the multimodal modeling capabilities of the generative control policy to create an expressive and tractably evaluatable candidate set. It then utilizes an ensemble of critics to identify the action that best balances quality with high exploration interest. In fleet settings, DF-ExpEnse further enables cross-agent communication to facilitate collaborative exploration as a group. DF-ExpEnse can be seamlessly integrated with existing strategies that finetune pretrained generative control policies via reinforcement learning. We experimentally validate consistent sample-efficiency benefits through DF-ExpEnse across a variety of manipulation and locomotion tasks, compared to default finetuning and alternative action selection schemes. Project can be found at https://df-expense.github.io.

23.
arXiv (math.PR) 2026-06-12

Characterizing metric-space-valued processes: separating classes and weak invariance principles for measure-theoretic inference

arXiv:2606.13084v1 Announce Type: cross Abstract: This article investigates stochastic processes taking values in metric spaces that lack a topological vector space structure, a regime characterized by intricate interplay between topological, geometric, and temporal dependence structures. It is formally established that spaces admitting an isometric Hilbertian embedding constitute a strict subclass within the much broader class of metric spaces possessing the ball property. While traditional kernel methods are susceptible to geometric distortion when the underlying space cannot be isometrically embedded into a Hilbert space, we bypass such limitations by exploiting a fundamental structural property inherent to this broader class; namely, that Borel probability measures are uniquely determined by their values on balls. These separating classes provide the foundation for the subsequently introduced measure-theoretic inference methodology. We derive uniform convergence of a family of time-dependent random measures, alongside weak invariance principles for the corresponding nonstationary random fields. This framework explicitly exposes how dependence and geometric complexity influence sample path regularity. Furthermore, because the rapid decay of small-ball probabilities can prohibit the existence of limiting distributions for supremum-based discrepancy measures, we develop $L^p$-based alternatives. By directly leveraging the introduced convergence results, this approach circumvents the need for higher-order $U$-process formulations. Finally, for spaces that do admit an isometric Hilbertian embedding, and where $U$-processes naturally arise, we establish limit theory for both degenerate and nondegenerate multi-parameter $U$-processes, and demonstrate that local discrepancy tests maintain asymptotic stability under dynamic parameter regimes.

24.
arXiv (quant-ph) 2026-06-16

QALM: Escaping Local Minima via Interleaved Exploration and Exploitation in Quantum Circuit Optimization

arXiv:2606.16221v1 Announce Type: new Abstract: Quantum circuit optimizers face a fundamental limitation in how they tolerate temporary cost increases. At one extreme, greedy rule-based optimizers immediately apply any cost-reducing transformation, achieving high efficiency but quickly becoming trapped in local minima. At the other extreme, search-based optimizers accept cost-increasing moves to explore the circuit space and escape such minima. However, because search-based optimizers cannot determine within a reasonable time budget whether a given point is promising, that is, whether its neighborhood contains a deeper local minimum, they must blindly explore higher-cost regions. As a result, escaping the current basin to reach a promising point takes exponentially many steps. In this work, we show that this limitation can be overcome with a hybrid framework that interleaves the exhaustive exploration capabilities of search algorithms with the efficiency of rule-based optimization. We implement this framework as QALM, a novel optimizer designed to escape local minima without incurring the runtime penalties of pure search. Crucially, our results demonstrate that QALM does not merely strike a balance; it outperforms existing rule-based and search-based optimizers in circuit reduction rates while operating with the computational efficiency of rule-based systems. In a comprehensive evaluation across 248 circuits, QALM matches or exceeds the fidelity of the strongest baseline on 83.9% of these circuits, given the same time budget.