arXiv:2604.26075v2 Announce Type: replace
Abstract: Governments increasingly deploy AI in public services, making transparency essential for accountability and public trust. Australia's Standard for AI Transparency Statements (AITS) requires government bodies to disclose how AI is used in practice, yet little empirical evidence exists on how these requirements are realised in documents. This paper presents a government AITS dataset, dubbed AITS-101, and provides one of the first systematic analysis of their content. Using stylometric, quantitative, and qualitative document analyses, we examine disclosure coverage, structure, and recurring patterns. Our findings reveal substantial variation in AI-related practice disclosure, highlight gaps between policy intent and implementation, and inform the design of more effective public-sector AI transparency standards.
Science Journals
arXiv:2604.24222v3 Announce Type: replace
Abstract: Large Language Models (LLMs) have achieved strong performance on general code generation, but their effectiveness drops sharply in enterprise settings where software development relies on internal private libraries absent from public pre-training corpora. Existing Retrieval-Augmented Generation (RAG) methods provide a training-free solution by retrieving static API documentation, but our analysis shows that documentation mainly helps models identify what APIs to use and remains insufficient for teaching how to use them correctly. Even with oracle API-document retrieval, LLMs still make recurring errors at the API, cross-API, and task levels, including API misuse or hallucination, flawed API composition, and incorrect solution strategies. To address this limitation, we propose MEMCoder, a training-free self-evolving memory framework for private-library code generation. MEMCoder augments existing RAG pipelines with a Multi-level Evolving Memory that continuously accumulates and reuses execution-derived Usage Guidelines at the API, cross-API, and task levels. During generation, MEMCoder retrieves both static API documentation and relevant historical memories to guide code generation; after execution, it analyzes feedback to refine memory through a closed loop of generation, execution, reflection, and update. Extensive experiments on NdonnxEval and NumbaEval show that MEMCoder consistently enhances different RAG backbones across LLMs of different scales, yielding an average absolute pass@1 improvement of 18.41 percentage points. Moreover, MEMCoder outperforms existing self-evolving memory methods and validates the effectiveness of organizing execution feedback into multi-level usage memories.
arXiv:2607.06616v1 Announce Type: new
Abstract: Label skew in federated learning (FL) causes client drift and degrades global accuracy. Synthetic data augmentation can reduce this imbalance; however, full class balancing requires substantial computation cost. We propose FedEAS, a policy that assigns each client an entropy-adaptive per-class generation budget computed from its local label distribution. The budget jointly decides \emph{how much} each client generates and \emph{WHERE} the samples go. Accordingly, the total generation budget follows from the per-client budgets rather than being fixed in advance. FedEAS recovers most of the accuracy gain of full class balancing while reducing the generation budget by 94.1\%. At the same total generation budget, it outperforms Uniform allocation by up to 18.82\% across CIFAR-10 and CIFAR-100.
arXiv:2607.07244v1 Announce Type: cross
Abstract: This paper investigates the backward problem in time for photoacoustic tomography (PAT) in attenuating media. It is well-established that photoacoustic imaging in attenuating media can be accurately modeled by spatial fractional-order damping. This inverse problem is ill-posed in the sense of Hadamard. In this work, we construct a novel class of Carleman estimates independent of spatial variables, and by virtue of these estimates, we establish conditional stability estimates for this problem for the first time. Building upon this, we propose a Tikhonov-type regularization functional and derive its associated adjoint system. Furthermore, leveraging the established conditional stability results, we derive the convergence rate of the proposed regularization approach. Finally, we validate the effectiveness of our theoretical findings through extensive numerical experiments.
arXiv:2607.06786v1 Announce Type: new
Abstract: Standards bodies, including TM Forum, 3GPP, and ETSI, are converging on Agentic AI as the foundation for next-generation network management, where Large AI Model (LAM)-based agents autonomously interpret intent, coordinate resources, and adapt operational behaviors at runtime. However, achieving this vision at the scale and complexity of 6G networks requires management systems that can generate and evolve their own automation software during operation. We introduce Autogenic network management, a reference architecture that extends agentic capabilities with self-programming, self reflection, self-orienting, and self-architecting capabilities. The architecture supports practical staged deployment beginning with human-supervised LAM-based agents and progressing toward autonomous operation as confidence builds. We demonstrate the approach through high-priority operator scenarios drawn from TM Forum's autonomous network use cases, showing how autogenic management addresses real operational challenges. We conclude with a research roadmap outlining the technical advances needed to make autogenic network management realistic in future 6G networks.
arXiv:2607.07669v1 Announce Type: new
Abstract: Large language models increasingly \emph{understand} dialectal English, yet still \emph{produce} only standard, US-leaning English, leaving dialectal generation, the harder half of the problem, largely unaddressed. We introduce \textbf{DiaLLM}, which continually pretrains three open-weight language model families on the International Corpus of English and applies implicit and explicit post-training paradigms, each combined with three model alignment strategies, giving the first controlled comparison of these components across Australian, Indian, and Northern British English. Our results reveal that dialectal robustness and generation are \emph{dissociated}: benchmarks are shaped by continual pretraining and SFT, while alignment visibly reshapes generation in ways benchmarks do not capture. Explicit variety-targeted adaptation produces output reliably recognised as dialectal and preferred over broad alignment, yet the method that most aggressively optimises the dialectal reward is not preferred by human evaluators. Independent linguistic analysis corroborates this reward-quality gap, most clearly on two of the three families. No single alignment method dominates, and closing the gap will require richer reward designs and continued investment in dialectal resources. We release all code, checkpoints, and preference datasets.
arXiv:2607.07657v1 Announce Type: new
Abstract: Surface plasmon polaritons (SPPs) and magnetic polaritons (MPs) are fundamental resonance modes that are widely used to tailor the thermal radiation properties of micro/nanostructured metamaterials. Lumped circuit models (LCMs) are usually constructed empirically to describe the MP resonance conditions, and different LCMs have to be constructed for different orders of MPs, but these are difficult to be built for high-order MP modes due to the complex electromagnetic field distribution. This work proposes a new type of circuit model, distributed circuit model (DCM), to describe and predict multi-order MP resonances inside the structure based on the minimum total impedance condition. This allows both fundamental and high-order MP resonances to be predicted with a unified circuit, significantly simplifying the analysis of high-order MPs. More importantly, the DCM shares a similar and clear physical picture as the LCM for describing MPs. The MP resonance conditions for four typical structures are derived. Theoretical predictions based on DCMs are compared with and validated by rigorous numerical simulations. This study deepens the understanding and facilitates the design of MP-based thermal radiation metamaterials.
arXiv:2607.07658v1 Announce Type: new
Abstract: Hadronic vacuum polarization (hVP) enters simple atomic systems at a level that is small yet decisive for the precision spectroscopy now underway. We evaluate the hVP contributions to the Lamb shift and the hyperfine splitting (HFS) in ordinary and muonic hydrogen (H and $\mu$H) and hydrogen-like helium-3 ions ($^3$He$^+$ and $\mu^3$He$^+$), using the dispersive data-driven approach and state-of-the-art empirical parametrizations of the $R$ ratio. At the centre of the analysis is the interplay of recoil and finite-size effects: the recoil corrections that dominate the HFS in muonium (Mu), where both constituents are pointlike, are shown to be suppressed by the nuclear elastic form factors (FFs). Our results for the leading hVP contribution to the Lamb shift agree with the literature within uncertainties. Furthermore, we present a first evaluation of the subleading $O(Z^5\alpha^6)$ hVP-finite-size correction, which is by no means negligible in $\mu^3$He$^+$. Our results for the hVP contribution to the HFS deviate significantly from all previous evaluations. For the ground-state HFS, we obtain $2.153(11)~\mu$eV in $\mu$H and $-15.19(57)~\mu$eV in $\mu^3$He$^+$, as well as $0.0860(4)~$kHz and $-0.476(17)~$kHz in ordinary H and $^3$He$^+$, respectively. Notably, our result for $\mu$H differs from previous evaluations by roughly ten times the experimental precision anticipated by the upcoming CREMA and FAMU measurements.
arXiv:2605.08630v3 Announce Type: replace
Abstract: Evaluating visualization systems in niche domains such as genomics is challenging due to scarcity of domain experts and difficulty recruiting a representative user base. While LLM-based synthetic personas are increasingly used to ease evaluation bottlenecks, they face well-founded skepticism. Rather than weighing synthetic personas as substitutes for real users, we ask a fundamental open question: when synthetic personas evaluate a real visualization system, what do they actually produce, and how does that output change when grounded in documented human contexts? We present Sycamore, an exploratory three-condition probe design using Geranium, a search engine for multimodal genomics visualization, as a case study. Sycamore evaluates Geranium using: (1) ungrounded synthetic personas from generic LLM priors; (2) grounded synthetic personas constrained by voice-of-customer artifacts from a prior interview study; and (3) a published baseline study of real domain experts. We observe that grounding shifts synthetic feedback toward the language and concerns of documented users, while ungrounded evaluators drift toward operational specifics that real participants did not raise; both synthetic conditions, however, converge on a find-and-adapt frame and miss the image-modality preference observed in the expert study. We discuss what these observations imply for where synthetic personas might fit alongside expert studies in domain-specific visualization evaluation. All supplemental materials are available at https://osf.io/kdfr3/.
arXiv:2605.08843v2 Announce Type: replace
Abstract: Neural surrogate models for physical simulations are trained on discretized samples of continuous domains, where the induced empirical measure leads to uneven supervision, biasing optimization and causing spatial inconsistencies in physical fidelity. To mitigate this measure-induced bias, we propose M$^3$ (Multi-scale Morton Measure), a scalable framework that balances training measures by partitioning space according to physical variation and allocating supervision across multiple scales. Applied to three industrial-scale datasets with diverse discretizations, M$^3$ consistently improves predictions in the continuous physical domain, achieving up to 4.7$\times$ lower error in large-scale volumetric cases. These gains persist under aggressive subsampling (160M $\rightarrow$ 16M $\rightarrow$ 1.6M points), where M$^3$-trained models outperform those trained on higher-resolution data, reducing physics-weighted relative $L_2$ error by 3--4$\times$ and the corresponding MSE by up to 13$\times$. These results highlight data distribution as a key factor in operator learning and position M$^3$ as a scalable, data-efficient approach for physically consistent modeling. Code is available at https://github.com/PhysDataRefine/M3.
arXiv:2605.11325v3 Announce Type: replace
Abstract: Current LLM memory benchmarks evaluate answer quality rather than retrieval accuracy. Consequently, a system that dumps its entire belief store can achieve perfect recall and mask severe precision failures. We show this evaluation gap persists across multiple embedding models where similarity-based retrieval over domain-specific corpora inherently struggles to isolate target beliefs from semantically proximate ones. Furthermore, multi-turn topic drift compounds this retrieval noise while driving up latency and operational costs.
To decouple retrieval quality from generative performance, we introduce PrecisionMemBench, an 89-case benchmark measuring precision, noise isolation, session latency, and belief mutability. We also present Tenure, a structured belief-store proxy that resolves scope and retrieval before inference and injects typed belief state as ambient instruction before the model sees the prompt, removing model-side discretion over whether memory is consulted. Evaluated across 13 providers, Tenure achieves perfect retrieval passes across all active, non-session, and session test cases. In contrast, the baseline configurations fail to reach even half of the active passes, with precision scores clustering at 0.22 and below. Our results demonstrate that while current memory systems successfully store information, they fail to retrieve it cleanly; a structural vulnerability that traditional answer-quality benchmarks conceal.
arXiv:2605.19723v3 Announce Type: replace
Abstract: Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning capabilities, understanding how well they perform mathematical reasoning has become increasingly important. This survey synthesizes recent advancements in mathematical reasoning with LLMs through a structured analysis of datasets, architectures, training strategies, and evaluation protocols. Our systematic review encompasses approximately 120 peer-reviewed studies and preprints, examining the evolution of this research area and providing a unified analytical framework to understand current progress and limitations. Our study particularly introduces a unified taxonomy of mathematical datasets, distinguishing between pretraining corpora, supervised fine-tuning resources, and evaluation benchmarks across varying levels of reasoning complexity. A systematic analysis of reasoning architectures and training strategies, including tool integration, verifier-guided reasoning, and parameter-efficient adaptation, is presented to assess their effects on reasoning robustness and generalization. Moreover, a comparative evaluation of existing metrics highlights the gap between final-answer accuracy and process-level reasoning verification. By synthesizing insights across these areas, our analysis identifies recurring failure modes, such as reasoning faithfulness issues, benchmark biases, and generalization limitations, and outlines key research directions toward improving symbolic grounding, evaluation reliability, and the development of more robust and trustworthy LLM-based reasoning systems.
arXiv:2607.06896v1 Announce Type: new
Abstract: Robust dynamic object detection and tracking are essential for enabling robots to operate safely and effectively alongside humans in complex environments such as construction sites. While LiDAR-based SLAM and occupancy grid methods offer viable solutions for detecting and tracking motion, many state-of-the-art 3D vision approaches rely heavily on pre-trained neural networks and require additional post-processing to identify moving objects. Sensor fusion techniques, combining the precision of LiDAR with the semantic richness of RGB imagery, offer a promising alternative. In this work, we present a novel framework that enhances a quadruped robot equipped with a LiDAR sensor and an upward-facing fisheye camera for real-time dynamic object detection and tracking. After identifying moving objects within a registered point cloud, our method assigns semantic labels by projecting 3D coordinates onto a 2D cylindrical panorama, aligning with real-time image-based detections for observation update of the Kalman filter. The proposed system demonstrates high precision, simplicity, and robustness, particularly in handling objects transitioning between dynamic and static states, thus it is well-suited for deployment in real-world construction environments.
arXiv:2607.07693v1 Announce Type: new
Abstract: Reinforcement learning from human feedback (RLHF) has emerged as a powerful paradigm for aligning generative models with human preferences. However, applying RLHF to diffusion models remains highly feedback inefficient, as existing approaches typically require large amounts of human or reward model evaluations. This limitation reduces the practicality of diffusion RLHF in realworld settings where feedback is the primary bottleneck. In this paper, we propose two complementary strategies that substantially improve the feedback efficiency of diffusion RLHF while preserving generalization to unseen prompts. Our key observation is that reward information in diffusion trajectories is unevenly distributed: not all denoising timesteps or trajectories contribute equally to learning from a reward signal. By emphasizing informative timesteps and trajectories during optimization, we obtain more effective gradient updates. First, we introduce a per-timestep weighting scheme that reweights denoising steps during policy optimization. We theoretically connect this weighting to the optimal convergence properties of proximal policy optimization (PPO) and approximate the resulting weighting trend empirically. Second, we introduce a replay mechanism that prioritizes informative trajectories, enabling the model to reuse past samples instead of repeatedly querying new rewards. Together, these strategies significantly improve the feedback efficiency of diffusion RLHF. Under identical hyperparameter settings, our approach achieves up to a 6$\times$ improvement in sample efficiency compared to widely used diffusion RLHF baselines.
arXiv:2605.21133v2 Announce Type: replace
Abstract: In this paper, we explore spatial-aware humanoid whole-body manipulation task. Compared with tabletop settings, this task poses two key challenges: 1) Spatial understanding is challenging in complex 3D environments with diverse spatial relations. 2) Action generation is difficult to generalize, as limited and costly real-robot data restricts data-driven models generalization. To address these challenges, we propose a generalizable humanoid loco-manipulation framework that leverages the spatial perception and action generation capabilities of multi-agent large models. Specifically, our framework includes two components: Active Spatial Brain for active spatial perception and decision-making, and Generalizable Action Cerebellum for executable robot action generation. The first component actively perceives the spatial scene and makes decisions on task planning and subtask decomposition. The second component generate executable robot actions based on the decisions made by the first module without needs of task-specific real robot data. To benchmark our framework, we design a set of spatial manipulation tasks from two perspectives: evaluating spatial perception and understanding, and assessing real-robot task performance. The results demonstrate strong performance on both aspects across diverse tasks and environments.
arXiv:2605.22140v2 Announce Type: replace
Abstract: In recent years, large language models have shown substantial potential in psychological support tasks. However, existing psychological counseling data mostly rely on single-turn question answering or short multi-turn dialogues, making it difficult to characterize how college students' psychological distress accumulates, interacts, and gradually evolves over long periods within campus life events. To address this issue, this paper proposes Psy-Chronicle, a structured data-generation framework for synthesizing long-horizon campus psychological counseling dialogues. We generate a semester-spanning temporal stress event graph to model the chronological order and evolutionary dependencies among campus stress events. Through interactive simulation between a student agent and a counselor agent, together with a structured memory integration mechanism, Psy-Chronicle generates long-horizon dialogues with continuity across counseling sessions. Based on Psy-Chronicle, we construct and open-source CPCD, a Chinese long-horizon dialogue dataset for college psychological counseling, containing 100 student profiles, 90,000 counseling dialogues. We further build CPCD-Bench to evaluate models' long-horizon campus counseling capabilities from three dimensions: session-level response, long-horizon memory recall, and temporal-causal reasoning. Experimental results show that CPCD effectively improves session-level response generation and long-horizon memory recall for models with the same base architecture. Meanwhile, improvements in temporal-causal reasoning remain limited, indicating that event-chain organization and causal explanation are key challenges in long-horizon psychological counseling modeling. The related code and data are available at: https://github.com/EdwinUSTB/Psy-Chronicle
arXiv:2605.22305v4 Announce Type: replace
Abstract: We analytically solve the Mountain Car problem, a canonical benchmark in RL, and derive an optimal control solution, closing a gap after 36 years. This enables us to reveal two surprising insights: The optimal control is quite simple, yet modern RL agents display a large gap to optimality. Motivated by the analysis of the optimal control, we introduce Chebyshev policies as a universal (i.e. dense) class of RL policies from first principles. They can be trained as drop-in replacements of neural nets, reducing the regret by a factor of 6.18, while requiring 277 times fewer parameters, fostering sample efficiency, explainability and realtime capability. Chebyshev policies are evaluated on further RL tasks, including a real-world nonlinear motion control testbed. They consistently improve performance over neural nets with PPO, ARS and REINFORCE. Our results demonstrate how Chebyshev policies offer a compelling and lightweight alternative or addition to neural nets for low-dimensional control tasks.
arXiv:2605.24892v4 Announce Type: replace
Abstract: Physical world knowledge resides mainly in videos. Equipping Vision-Language-Action (VLA) models with such knowledge is fundamental for safe and generalizable planning. Predictive world modeling enables VLA to internalize physical dynamics and long-term causality by predicting future video from past observations. However, naive next-frame prediction faces two challenges: 1) unlike semantically distinct text tokens, video tokens are low-entropy and redundant, causing prediction to degenerate into trivial extrapolation. 2) world modeling poses a temporal dilemma: dense prediction captures instantaneous dynamics, but cannot efficiently model long-horizon causality.
To learn world knowledge effectively, we introduce X-Foresight, a predictive world model integrated directly into the VLA architecture to jointly learn world modeling and real-time action control. At its core lies a long-horizon chunk-wise auto-regressive strategy that addresses both challenges: by predicting semantically distant chunks rather than adjacent frames, it escapes trivial extrapolation, while preserving dense intra-chunk frames for instantaneous dynamics and sparse inter-chunk transitions for long-term causality. A curriculum learning schedule progressively extends prediction horizons and stabilizes long-horizon training. To capture long-term causality effectively, we present temporal importance sampling, which concentrates supervision on safety-critical chunks identified by ego-motion and behavioral signals. We further delegate photorealistic synthesis to a diffusion-based multi-view renderer, improving photorealistic appearance.
Comprehensive experiments demonstrate that X-Foresight significantly outperforms VLA baselines in planning performance while maintaining strong generative fidelity, establishing a robust paradigm for world-knowledge-driven autonomous systems.
arXiv:2605.27147v2 Announce Type: replace
Abstract: We give a more space-efficient implementation of adaptive mergesort: Virtual-Memory Powersort. Using internal buffering techniques, we significantly reduce the memory consumption of the algorithm; specifically, for sorting $n$ objects the required buffer area is reduced from space for $n/2$ objects to $O(\sqrt{n \log n})$ objects. While this space-efficiency can be achieved (indeed reduced to $O(1)$) conceptually very easily with known inplace merging algorithms, using these as a drop-in replacement for the standard merge algorithm incurs a substantial slow-down. Virtual-Memory Powersort, by contrast, uses the same number of moves and comparisons as previous Powersort implementations up to an additive $O(n)$ term. We report on an empirical running-time study comparing our implementation against other Powersort variants and state-of-the-art stable sorting methods, demonstrating that almost in-place stable sorting can be achieved with negligible overhead in many scenarios.
arXiv:2605.27395v2 Announce Type: replace
Abstract: As the rapid proliferation of AI systems and harms spurs efforts in AI governance around the world, prioritizing among competing policy options has become increasingly challenging for policymakers and researchers. We introduce a methodology for identifying viable policy options to mitigate specified AI harms, helping policymakers and researchers target areas that warrant greater time and resource investment. This method combines participatory evaluation of policies, expert assessment of implementation costs, and an LLM-based assessment of perceived harm mitigation under each policy option. We leverage a genetic algorithm-based simulation study to explore a vast solution space of potential policy combinations, and examine how outcomes change under different weightings of cost, participatory input, and harm mitigation. We find that this method enables exploration of different balances between participatory and expert components, allowing policymakers and researchers to assess how much weight to assign to each. We argue that the diversity of viable policy combinations found by the genetic algorithm could be a useful starting point for deliberation. This method operationalizes existing work on participatory AI by integrating it directly into practical policy development pipelines.
arXiv:2605.30170v2 Announce Type: replace
Abstract: While Large Vision-Language Models (VLMs) excel at interpolation, they suffer catastrophic failures in systematic generalization, most notably in visual counting. In this work, we investigate this extrapolation bottleneck by deconstructing visual counting into three cognitive stages: visual individuation, magnitude awareness, and symbolic mapping. Using synthetic Go boards and linear probes, we demonstrate that visual backbones maintain robust, linearly separable representations of quantity well into the extrapolation regime, ruling out perceptual failure. Furthermore, models retain latent magnitude awareness, successfully performing comparative reasoning on quantities they fail to enumerate. We pinpoint the collapse to the symbolic mapping stage, where the model fails to project valid visual magnitudes onto symbolic tokens. Our findings support a frac tured magnitude hypothesis: VLMs fail to acquire a universal number space, instead learning disjoint, modality-specific statistical manifolds that prevent cross-modal grounding for unseen quantities. Validated on the state-of-the-art foundation model, our results suggest that bridging this gap requires inductive priors enforcing unified representations, as data scaling alone is insufficient.
arXiv:2606.00893v2 Announce Type: replace
Abstract: Hypergraphs provide a natural framework for describing complex networked systems with higher-order, non-dyadic interactions. Due to their high dimensionality and often redundant structure, a key challenge is to develop methods that simplify hypergraph representations while preserving the essential structure of interactions. Here we present a principled, efficient, and non-parametric information-theoretic method for pruning nested and/or redundant structures in hypergraphs, enabling a minimal representation of higher-order interactions in the presence of local heterogeneity. Our approach naturally extends to weighted hypergraphs, where higher-order topology and hyperedge weights combine to identify the system's structural backbone. We validate the method on controlled synthetic hypergraphs and apply it to empirical datasets from diverse domains, demonstrating substantial sparsification without loss of core structural information.
arXiv:2607.07325v1 Announce Type: cross
Abstract: We study a bulk-driven nonlinear variant of the Kipnis-Marchioro-Presutti model of stochastic energy diffusion in which local collisions are biased to induce a net energy flow, resembling the effect of an external field. Starting from the microscopic master equation, we derive the hydrodynamic description of the driven system via a local equilibrium approximation, obtaining explicit expressions for the energy current and the associated diffusivity and mobility transport coefficients, which are nonlinear functions of the local energy density. We test our findings in kinetic Monte Carlo simulations of the model and, as a proof of concept, we demonstrate the versatility of this driving mechanism to control nonlinear energy transport by inducing time-crystalline phases. In particular, we show that appropriately designed packing fields induce the spontaneous formation of traveling energy condensates, exhibiting robust long-range temporal order reminiscent of continuous time crystals. Our results provide a simple yet powerful framework to study bulk-driven nonlinear energy diffusion in stochastic many-body systems, offering a bridge between microscopic dynamics, macroscopic transport, and controlled spatiotemporal order.
arXiv:2606.02263v3 Announce Type: replace
Abstract: We study exact uniform sampling of permutations of length $n$ whose longest increasing subsequence (LIS) has prescribed length $k$. Our main result is, to the best of our knowledge, the first polynomial-time exact sampler for this problem, valid for every $1\le k\le n$. Via the Robinson--Schensted correspondence the problem reduces to sampling a Young diagram with first row of length $k$ from the hook-length-squared (conditioned Plancherel) law. We sample this shape one coordinate at a time, where each conditional weight, a sum over exponentially many completions, collapses, through the Cauchy--Binet formula, to a single coefficient of the determinant of a small polynomial matrix. A direct implementation runs in expected $\tilde O(n^4k^5)$ time in the word-RAM model. Aggregating the scores and exploiting the Hankel structure of the evaluated matrices reduces this to $\tilde O(n^2k^4)$. In the linear regime $k\in\Theta(n)$ we give a direct rejection sampler running in expected $O(n\log\log n)$ time, matching, up to constants, the cost of computing the LIS of one permutation. For the relaxed constraint $LIS(\pi)\le k$, plain rejection sampling gives expected $O(n\log\log n)$ time for every $k\ge4\sqrt n$, and so the worst case over all $k$ improves to $\tilde O(n^4)$.
arXiv:2606.03834v2 Announce Type: replace
Abstract: Flow matching has recently emerged as a powerful approach for imitation learning, enabling scalable, expressive, and multimodal motion policies. However, when modeling these policies as dynamical systems, incorporating formal stability guarantees into these generative models is a prerequisite to ensure safe and generalizable robot behaviors, which remains a significant challenge. This paper introduces Stable Flow Matching Dynamical Systems (SFMDS), a novel framework that bridges the gap between highly expressive generative modeling and formal stability guarantees. SFMDS parametrizes dynamical systems via flow matching while constraining the model to satisfy positive invariance and/or Lyapunov stability conditions. We propose two variants: a soft constraint based on a penalty term, and a hard structural constraint embedded directly into the model architecture. We further extend both formulations to Lie groups to robustly handle orientation trajectories. Experiments on benchmark datasets, in simulation, and on a humanoid robot show that SFMDS learns stable, scalable, and multimodal dynamical systems in low- and high-dimensional state spaces, enabling safe and expressive robot motion generation. SFMDS matches or outperforms state-of-the-art methods on unimodal datasets, while substantially improving performance on multimodal datasets, where competing approaches fail to capture multi-modal behaviors. Accompanying source code and video are available at: https://let-the-dynamics-flow.github.io/SFMDS/.