arXiv:2605.15620v1 Announce Type: cross Abstract: We study risk-aware offline policy learning, aiming to learn a decision rule from logged data that is optimal under general risk criteria. This problem is crucial in high-stakes domains where online interaction is infeasible and adverse outcomes must be carefully controlled. However, existing literature on offline contextual bandits either centers on expected-reward criteria or restricts risk considerations to policy evaluation instead of optimization. In this work, we propose a unified distributional framework for optimizing Lipschitz-continuous risk functionals, a broad class of risk measures encompassing mean-variance, entropic risk, and conditional value-at-risk, among others. By developing novel empirical concentration inequalities for importance sampling-based distributional estimators, our analysis derives data-dependent suboptimality bounds with an $\tilde{\mathcal{O}}(1/\sqrt{n})$ rate, without relying on restrictive uniform overlap assumptions. This rate is minimax optimal and matches that of risk-neutral offline policy optimization, indicating that optimizing general Lipschitz risk criteria incurs no additional statistical cost relative to the expected-reward.
Science Journals
arXiv:2509.05030v2 Announce Type: replace Abstract: To enable large-scale reuse of real-world 3D assets, where garments and characters rarely share skeletons, templates, or dense correspondences, we present a fully automated virtual try-on system that dresses complex, multi-layer garments onto diverse, arbitrarily posed humanoids. Our key idea is to use SMPL as an intermediate proxy and decompose clothing-to-body transfer into two correspondence tasks with distinct challenges: (1) clothing-to-SMPL (partial-to-complete alignment) and (2) body-to-SMPL (large pose/shape variation and stylization). We address clothing-to-SMPL using a geometry-driven correspondence model, and introduce a diffusion-based body-to-SMPL correspondence approach that leverages multi-view consistent appearance features together with a pretrained 2D foundation model. Using these correspondences, we register SMPL/SMPL+D (Displacement) to the garment and target body and then perform simulator-driven fitting by transferring the garment along a smooth SMPL-to-SMPL+D transition, producing physically plausible draping on the target. Our system handles complex garment topology (including non-manifold meshes) and generalizes to a wide range of humanoid characters (e.g., humans, robots, cartoons, and creatures) while remaining computationally practical. Upon draping, our system also supports fast customization of clothing size. We show that our system can produce high-quality 3D clothing fittings without any human labor, even when 2D clothing sewing patterns are not available. Our project page is: https://cao-cong0.github.io/LUIVITON-Learned-Universal-Interoperable-VIrtual-Try-ON/.
arXiv:2509.10825v5 Announce Type: replace Abstract: Explaining a trained model requires a clear account of how explanatory evidence is generated. We propose CUBE, a post-hoc explanation framework that brings factorial experimental design to black-box model analysis. CUBE evaluates a trained predictor on balanced low--high probe combinations and summarizes the responses as factorial effects. Main effects and pairwise interactions are interpreted as controlled contrasts on a specified explanation region. Complete factorial probes identify these effects exactly on the selected design space, while fractional probes reduce query cost and expose aliasing and resolution constraints. Experiments on synthetic and real tabular tasks show that CUBE recovers dominant learned effect structure and clarifies the identifiability limits of query-efficient explanations.
arXiv:2509.17189v3 Announce Type: replace Abstract: Turbulence remains one of the last unresolved problems of classical physics and a major bottleneck to accurate flow prediction in climate, aerospace, and energy systems. Industrial simulations therefore rely on averaged representations of turbulence, which often struggle to predict flows governed by multiple interacting mechanisms. We present a unified, data-driven turbulence modeling framework designed to learn robustly from sparse, indirect observations across diverse flow regimes. The framework embeds physical consistency into a flexible, frame-invariant closure, automatically selects representative training cases based on similarity of flow-feature distributions, and learns a single, unified model through a multi-objective ensemble strategy that balances competing objectives across flows and quantities of interest. The resulting unified foundation model adapts seamlessly across regimes without manual intervention. It outperforms existing turbulence models across a broad spectrum of canonical flows and maintains improved performance in complex three-dimensional configurations of industrial relevance, including a gas turbine diffuser, a generic car, and a generic aircraft. When application-specific accuracy is required, the framework further enables specialist models through additive fine-tuning on targeted flow datasets. The results demonstrate the feasibility of a deployable and generalized turbulence modeling approach that unifies multiple flow mechanisms within a single architecture for a broad range of natural and industrial flows.
arXiv:2509.20349v3 Announce Type: replace Abstract: Accurate time-series forecasting for complex physical systems is the backbone of modern industrial monitoring and control, yet deep learning models often lack the physical consistency required in regulated environments.To bridge this gap, we introduce Process-Informed Forecasting (PIF) models for temperature in pharmaceutical lyophilization, embedding deterministic production recipes as macro-structural priors. We investigate classical methods (e.g., Autoregressive Integrated Moving Average (ARIMA) model) and modern deep learning architectures, including Kolmogorov-Arnold Networks (KANs). We compare three different loss function formulations that integrate a process-informed trajectory prior: a fixed-weight loss, a dynamic uncertainty-based loss, and a Residual-Based Attention (RBA) mechanism. We evaluate all models not only for accuracy and physical consistency but also for robustness to sensor noise. Furthermore, we test the practical generalizability of the best model in a transfer-learning scenario to a new process. Our results show that PIF models outperform their data-driven counterparts in terms of accuracy, physical plausibility and noise resilience, offering a scalable framework for reliable and generalizable forecasting solutions in critical manufacturing.
arXiv:2605.15472v1 Announce Type: new Abstract: We introduce the Estimated Dynamic Equilibrium Model (EDEM), an agent-based framework that treats supply and demand as a coupled stochastic process driven by heterogeneous, noisy agent valuations. The model's primary technical contribution is the identification of a generative mechanism for persistent disequilibrium: when market-clearing prices are sequentially sampled from the upper tail of noisy bid distributions and recycled as inputs for future valuations, expected prices drift upward despite strictly zero-mean estimation errors. We derive this order-statistic bias in closed form for i.i.d. uniform bids and use simulations to show that compounding this bias across epochs yields exponential price growth without requiring assumptions of investor optimism or irrationality. This framework extends Miller's divergence-of-opinion theory to a dynamic setting, recovering Walrasian equilibrium and Miller's static premium as limiting cases. Through controlled experiments and sensitivity analysis on a simulated real-estate neighborhood, we identify six distinct regimes-ranging from band-stability to runaway bubbles-emerging from a single agent ruleset. These results offer a potential explanation for the contradictory findings in the empirical divergence-of-opinion literature and suggest that machine-learning valuation algorithms may inadvertently amplify this inherent statistical bias.
arXiv:2605.15844v1 Announce Type: new Abstract: In this study, we develop an interface-contact simulation framework based on physical criteria and machine-learning-assisted classification to describe coalescence and bouncing within a unified formulation. The framework realizes interfacial coalescence and bouncing through the fusion and generation of multiple volume-of-fluid fields. When adjacent interfaces are predicted to coalesce, multiple VOF fields are collapsed into a single VoF field. When approaching interfaces are predicted to bounce, a single VOF field is regenerated into multiple VOF fields, allowing the interfaces to continue evolving independently. With this treatment, the difficulties associated with topological transition, regime-map identification, increasing computational demand, and stochastic behavior during interfacial approach are separated from the interface-tracking procedure. These decisions are instead assigned to a physics-guided machine-learning model with strong adaptability. This strategy avoids the direct resolution of an ultrathin gas film and reduces the dependence on empirical molecular-force parameters. Simulations of droplet--droplet collisions show that the proposed framework can reproduce both coalescence and bouncing over different impact conditions. By further introducing a drainage-time criterion, the framework is extended to the simulation of droplet impact on a liquid surface. For this problem, the numerical results agree well with both previous experimental observations and the present experiments. Moreover, the framework captures the complete sequence of bouncing followed by subsequent coalescence within a single simulation, These results demonstrate that the proposed framework has strong adaptability for interfacial contact problems and provides a unified modeling route for droplet coalescence, bouncing.
arXiv:2511.18127v2 Announce Type: replace Abstract: Real-time 3D hand forecasting is a critical component for fluid human-computer interaction in applications like AR and assistive robotics. However, existing methods are ill-suited for these scenarios, as they typically require offline access to accumulated video sequences and cannot incorporate language guidance that conveys task intent. To overcome these limitations, we introduce SFHand, the first streaming framework for language-guided 3D hand forecasting. SFHand autoregressively predicts a comprehensive set of future 3D hand states, including hand type, 2D bounding box, 3D pose, and trajectory, from a continuous stream of video and language instructions. Our framework combines a streaming autoregressive architecture with an ROI-enhanced memory layer, capturing temporal context while focusing on salient hand-centric regions. To enable this research, we also introduce EgoHaFL, the first large-scale dataset featuring synchronized 3D hand poses and language instructions. We demonstrate that SFHand achieves new state-of-the-art results in 3D hand forecasting, outperforming prior work by a significant margin of up to 35.8%. Furthermore, we show the practical utility of our learned representations by transferring them to downstream embodied manipulation tasks, improving task success rates by up to 13.4% on multiple benchmarks. Dataset page: https://huggingface.co/datasets/ut-vision/EgoHaFL, project page: https://github.com/ut-vision/SFHand.
arXiv:2511.18225v2 Announce Type: replace Abstract: Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need for reliable and trustworthy predictions. Recent work has introduced quantum conformal prediction, a framework that produces prediction sets that are guaranteed to contain the true outcome with a user-specified probability. In this work, we formalise how the time-varying noise inherent in quantum processors can undermine conformal guarantees, even when calibration and test data are exchangeable. To address this challenge, we draw on Adaptive Conformal Inference, a method which maintains validity over time via repeated recalibration. We introduce Adaptive Quantum Conformal Prediction (AQCP), an algorithm which provides asymptotic average coverage guarantees under arbitrary hardware noise conditions. Empirical studies on an IBM quantum processor demonstrate that AQCP achieves the target coverage level and exhibits greater stability than quantum conformal prediction.
arXiv:2511.19399v3 Announce Type: replace Abstract: Deep research agents perform multi-step research to produce long-form, well-attributed answers. However, most open deep research agents are trained on easily verifiable short-form QA tasks via reinforcement learning with verifiable rewards, which does not extend to realistic long-form tasks. We address this with Reinforcement Learning with Evolving Rubrics (RLER), where rubrics are constructed and maintained to co-evolve with the policy model during training. This allows the rubrics to incorporate newly explored information from search and contrasting model responses, enabling better fact checking and more discriminative on-policy feedback. Using RLER, we develop Deep Research Tulu (DR Tulu-8B), the first fully open model that is directly trained for open-ended, long-form deep research. Across four long-form deep research benchmarks in science, healthcare, and general domains, DR Tulu substantially outperforms existing open deep research agents (by 15.6% over Tongyi DR on average) and matches or exceeds proprietary deep research agents (by 0.7% over OpenAI DR on average), while being significantly smaller and cheaper per query (1000x cheaper than OpenAI DR per query).
arXiv:2511.21277v3 Announce Type: replace Abstract: This paper presents LatencyScope, a mathematical framework for computing one-way uplink and downlink latency in fifth-generation radio access networks across diverse system configurations. LatencyScope models latency sources across the protocol stack, including radio interfaces, scheduling decisions, processing delays, frame structures, and hardware and software constraints, while capturing dependencies among configuration parameters and stochastic sources of delay. The framework also includes a configuration analyzer that uses these models to search billions of candidate settings and identify those that satisfy latency-reliability targets under user-specified constraints. We validate LatencyScope on two open-source fifth-generation radio access network testbeds, as well as on measurements from a public commercial fifth-generation network. The results show that LatencyScope closely matches empirical latency distributions, captures observed lower and upper latency bounds, and substantially outperforms prior analytical models and widely used fifth-generation network simulators. LatencyScope can determine whether ultra-reliable low-latency communication targets are feasible for a given deployment and, when they are feasible, efficiently find satisfying configurations, helping network operators reason about latency modeling, configuration analysis, and system-level bottlenecks.
arXiv:2605.15227v1 Announce Type: new Abstract: Self-driving laboratories (SDLs) have attracted increasing attention as a means of accelerating scientific discovery; however, developing SDL software remains technically demanding. To improve accessibility, orchestration software frameworks have been proposed to coordinate SDL components. Nevertheless, existing frameworks are primarily designed for human interaction and do not provide standardized interfaces suitable for AI agents. In this work, we propose an SDL software architecture based on the Model Context Protocol (MCP), in which all SDL functionalities are exposed through MCP servers. Following this design principle, we introduce an MCP-based SDL orchestrator, named NIMO Controller. It provides a visual programming interface automatically generated through MCP-based tool discovery, allowing human users to design experimental workflows without writing code. The same MCP backend can also be accessed by AI agents, providing a unified interface for both human users and AI agents. We demonstrate the proposed system through a case study on a color-matching SDL. The results validate the usability of the proposed MCP-based SDL architecture.
arXiv:2605.15228v1 Announce Type: new Abstract: Modern cloud and enterprise systems rely on identity-centric authorization, assuming that callers possessing valid credentials are safe to execute commands. The emergence of autonomous AI agents invalidates this assumption: agents can generate syntactically valid but semantically unsafe actions, making standing privileges a significant operational risk. This risk becomes especially acute in sovereign AI systems, where autonomous agents may interact with cloud infrastructure, regulated data, financial workflows, and national-scale digital services. Governed mutation substrates reduce this risk by interposing on agent actions: agents submit intents, infrastructure evaluates context and policy, and execution is mediated. However, this shifts the trust boundary: how can the decision to authorize an intent be made verifiable, distributed, and replayable? We introduce a Distributed Trust Framework (DTF), a verification framework for governed mutation systems that computes execution authority from structured, verifiable artifacts. DTF introduces a Justification Proof to encode the admissibility basis of an action, a consensus model for independent evaluation, an ephemeral Execution Identity derived from the approved proof, and an append-only Evidence Chain that preserves the authorization lifecycle. Under stated substrate assumptions, this architecture enforces a compact authorization invariant: no high-stakes execution without a proof object, no derived authority without consensus, and no valid mutation detached from evidence. We define the model, instantiate it over an OpenKedge-based governed mutation substrate, and show how it maps onto cloud-native environments. By shifting authorization from standing identity to proof-derived authority, DTF provides an infrastructure foundation for making agentic execution governable, auditable, and bounded in sovereign AI deployments.
arXiv:2603.01290v3 Announce Type: replace Abstract: The 2026 Formula 1 technical regulations introduce a fundamental change to energy strategy: under a 50/50 internal combustion engine / battery power split with unlimited regeneration and a driver-controlled Override Mode, the optimal energy deployment policy depends not only on a driver's own state but on the hidden state of rival cars. This creates a Partially Observable Stochastic Game that cannot be solved by single-agent optimisation methods. We present a tractable two-layer inference and decision framework. The first layer is a 40-state Hidden Markov Model (HMM) that infers a probability distribution over each rival's ERS charge level (four modes: H, M, L_harvest, L_derate), Override Mode status, and tyre degradation state from six publicly observable telemetry signals. The second layer is a Deep Q-Network (DQN) policy that takes the HMM belief state as input and selects between energy deployment strategies. We formally characterise the counter-harvest trap, a deceptive strategy in which a car deliberately suppresses observable deployment signals to induce a rival into a failed attack, and show that detecting it requires belief-state inference over both ERS level and the harvest/derate sub-mode. On synthetic races, the HMM achieves 96.8% ERS-level accuracy (random baseline 25%), classifies L_harvest vs. L_derate with 89.4% accuracy, and detects counter-harvest trap conditions with 96.3% recall. Pre-season analysis indicates circuit-dependent recharge availability (1.0x to 2.2x per lap) as the primary confound; Melbourne is the hardest-case validation environment. Baum-Welch calibration on 2026 race telemetry begins with the Australian Grand Prix (8 March 2026).
arXiv:2605.15232v1 Announce Type: new Abstract: Test Suite Minimization (TSM) reduces the size of test suites while preserving their fault detection capability. In black-box TSM, reduction is performed without analyzing production code. While several black-box TSM approaches have explored metrics like test logs or test similarity, those often suffer from scalability and efficiency issues. On the other hand, change-proneness (CP), recently emerged as an efficient and scalable alternative metric, has only been applied at class level. To accurately identify fault-revealing test cases, we propose CP at finer-grained method-level and implement Method-level Change-proneness based Test-suite Minimization (MCTM). MCTM first calculates CP for each method from version control metadata, then determines the dependency between test cases and methods by analyzing the test-code call-graph. Next, it scores the association between test cases and their invoked methods using statistical measures such as Average, Geometric Mean etc. Finally, test cases with the highest scores are selected to form the reduced suite. Evaluation on 15 open-source Java projects with 635 buggy versions shows MCTM achieves 0.93 accuracy and 0.94 fault detection rate on average, significantly outperforming class-level CP and similarity-based approaches while maintaining superior efficiency.
arXiv:2605.15234v1 Announce Type: new Abstract: Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to do this include Dynamical Mode Decomposition and variants, subspace identification and eigenvalue realisation algorithms. Typical outputs of these algorithms include a range of isolated, peripheral eigenvalues capturing persistent emergent patterns in the system. However, there is no objective way to assess which of these discrete eigenvalues are artefacts of finite data error, and which are reflections of a fully sampled operator. n this paper, we present a sampling pseudospectrum $P(\lambda)$, that provides probabilistic information on the behaviour of finite-data eigenvalues in the complex plane, and an estimator $\hat P(\lambda)$, which can be obtained by reprocessing our finite data sample. The estimator, which is computationally efficient to implement, allows us to test statistically for the location of the true eigenvalues. This gives us a rigorous and very general way to assess whether the patterns we extract from finite data are likely to be signal or noise.
arXiv:2512.08052v3 Announce Type: replace Abstract: Embodied agents, such as robots and virtual characters, must continuously select actions to execute tasks effectively, solving complex sequential decision-making problems. Given the difficulty of designing such controllers manually, learning-based approaches have emerged as promising alternatives, most notably Deep Reinforcement Learning (DRL) and Deep Imitation Learning (DIL). DRL leverages reward signals to optimize behavior, while DIL uses expert demonstrations to guide learning. This document introduces DRL and DIL in the context of embodied agents, adopting a concise, depth-first approach to the literature. It is self-contained, presenting all necessary mathematical and machine learning concepts as they are needed. It is not intended as a survey of the field; rather, it focuses on a small set of foundational algorithms and techniques, prioritizing in-depth understanding over broad coverage. The material ranges from Markov Decision Processes to REINFORCE and Proximal Policy Optimization (PPO) for DRL, and from Behavioral Cloning to Dataset Aggregation (DAgger) and Generative Adversarial Imitation Learning (GAIL) for DIL.
arXiv:2605.15235v1 Announce Type: new Abstract: Multimodal physiological data powers clinical AI systems from intensive care units to wearable devices, but sensors routinely fail in practice. Two failure modes are common: modality missing, where an entire channel is absent, and within-modality missing, where a contiguous time segment is lost. No existing benchmark evaluates multiple fusion architectures under both failure modes at controlled severity levels across diverse clinical datasets. We present MuteBench, a benchmark covering 9 datasets from 7 clinical domains, 6 fusion architectures, and 2 missing-data modes over 125,000 samples. Through this benchmark, we find that architecture family is the strongest predictor of robustness, outweighing parameter count. Channel-independent models tolerate modality missing well but can be sensitive to within-modality missing, especially on short sequences. Curriculum modality dropout protects reliably only up to the maximum dropout rate used in training. We also find that channel count, sequence length, and modality alignment jointly determine which failure mode poses the greater threat. Finally, a PTB-XL case study suggests that diffusion-based imputation can improve downstream classification under within-modality missing, with the largest gains for models whose expert routing is most sensitive to corrupted inputs, though broader validation across datasets remains an open direction. MuteBench provides practitioners with concrete guidance for both selecting existing architectures and informing the design of future robust multimodal fusion methods.
arXiv:2512.24366v2 Announce Type: replace Abstract: Text-based explainable recommendation aims to generate natural-language explanations that justify item recommendations, to improve user trust and system transparency. Although recent advances leverage LLMs to produce fluent outputs, a critical question remains underexplored: are these explanations factually consistent with the available evidence? We introduce a comprehensive framework for evaluating the factual consistency of text-based explainable recommenders. We design a prompting-based pipeline that uses LLMs to extract atomic explanatory statements from reviews, thereby constructing a ground truth that isolates and focuses on their factual content. Applying this pipeline to five categories from the Amazon Reviews dataset, we create augmented benchmarks for fine-grained evaluation of explanation quality. We further propose statement-level alignment metrics that combine LLM- and NLI-based approaches to assess both factual consistency and relevance of generated explanations. Across extensive experiments on six state-of-the-art explainable recommendation models, we uncover a critical gap: while models achieve high semantic similarity scores (BERTScore F1: 0.81-0.90), all our factuality metrics reveal alarmingly low performance (LLM-based statement-level precision: 4.38%-32.88%). These findings underscore the need for factuality-aware evaluation in explainable recommendation and provide a foundation for developing more trustworthy explanation systems.
arXiv:2605.15253v1 Announce Type: new Abstract: Machine learning research increasingly bifurcates into two disconnected modes: benchmark-driven engineering that prioritizes metrics over understanding, and idealized theory that often fails to transfer to modern systems. In this position paper, we argue that the field focuses too heavily on these endpoints, neglecting the central scientific object: the idea. We propose an Ideas First framework in which ideas are valued for the behavioral signatures they predict in modern models, and these signatures are tested through tailored experiments designed to detect the relevant patterns rather than to win leaderboards. This shift not only bridges the gap between theory and practice but also promotes equity by removing the "complexity premium," enabling rigorous scientific contributions from researchers with modest computational, financial, and human resources. Ultimately, we advocate for a research culture centered on ideas, treating benchmarks and theorems as instruments for testing mechanistic hypotheses rather than as ends in themselves.
arXiv:2605.15254v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN training still suffers from high-dimensional non-convex loss landscapes, imbalanced multiobjective constraints, and ineffective information propagation. Existing curriculum learning and causality-guided strategies improve training stability, but mainly focus on temporal or parametric progression, lacking explicit treatment of spatial information propagation and inter-region consistency. Moreover, they are not directly applicable to boundary value problems (BVPs) with strong spatial coupling. To address this issue, we propose a spatially correlated curriculum learning framework for PINNs. To the best of our knowledge, this is the first work to address PINN training difficulties from the perspective of spatial coupling among subregions. First, spatial causal weights guide information from near-boundary regions inward, reducing optimization failures and spurious convergence. Second, a low-frequency information bridge enforces pseudo-label-based consistency across spatially separated regions, suppressing global low-frequency drift. Third, a region-adaptive reweighting strategy adjusts subregion losses to reduce local residuals and recover high-frequency details. Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy. The code is available at https://github.com/pigofmomo/CurriculumLearningPINN.
arXiv:2601.00361v3 Announce Type: replace Abstract: We introduce the first iterative algorithm for constructing a $\varepsilon$-coreset that guarantees deterministic $\ell_p$ subspace embedding for any $p \in [1,\infty)$ and any $\varepsilon > 0$. For a given full rank matrix $\mathbf{X} \in \mathbb{R}^{n \times d}$ where $n \gg d$, $\mathbf{X}' \in \mathbb{R}^{m \times d}$ is an $(\varepsilon,\ell_p)$-subspace embedding of $\mathbf{X}$, if for every $\mathbf{q} \in \mathbb{R}^d$, $(1-\varepsilon)\|\mathbf{Xq}\|_{p}^{p} \leq \|\mathbf{X'q}\|_{p}^{p} \leq (1+\varepsilon)\|\mathbf{Xq}\|_{p}^{p}$. Specifically, in this paper, $\mathbf{X}'$ is a weighted subset of rows of $\mathbf{X}$ which is commonly known in the literature as a coreset. In every iteration, the algorithm ensures that the loss on the maintained set is upper and lower bounded by the loss on the original dataset with appropriate scalings. So, unlike typical coreset guarantees, due to bounded loss, our coreset gives a deterministic guarantee for the $\ell_p$ subspace embedding. For an error parameter $\varepsilon$, our algorithm takes $O(\mathrm{poly}(n,d,\varepsilon^{-1}))$ time and returns a deterministic $\varepsilon$-coreset, for $\ell_p$ subspace embedding whose size is $O\left(\frac{d^{\max\{1,p/2\}}}{\varepsilon^{2}}\right)$. Here, we remove the $\log$ factors in the coreset size, which had been a long-standing open problem. Our coresets are optimal as they are tight with the lower bound. As an application, our coreset can also be used for approximately solving the $\ell_p$ regression problem in a deterministic manner.
arXiv:2601.06304v2 Announce Type: replace Abstract: We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which relates multiple measurements to external sources through a linear duality relation, we first introduce a linear positional embedding that identifies the source location by aligning the measurement vector with the embedding. To capture weakly nonlinear effects that arise when the source intensity is finite, we then incorporate a quadratic correction represented as a symmetric bilinear operator and approximated via a truncated eigen-expansion obtained with Krylov subspace iterations. This yields quadratic positional embeddings that augment the linear adjoint field, enabling measurement data to be projected onto a higher-dimensional hyperplane, spanned by the linear and quadratic embeddings. A source search algorithm is formulated based on principal angle minimization between this hyperplane and the observation vector, providing a natural probabilistic interpretation of source location. The method operates in a one-shot fashion without iterative updates of candidate source positions, and it can be readily extended to scenarios involving multiple sources. Demonstrations on benchmark inverse problems include perturbation-source identification in the viscous Burgers equation and heat-source detection in a two-dimensional laminar stratified channel. The results with quadratic embeddings show significant improvements in localization accuracy compared with linear adjoint-based sensitivity methods, especially in the region where linear adjoint sensitivity vanishes.
arXiv:2601.09512v2 Announce Type: replace Abstract: To teach robots complex manipulation tasks, a common approach is to fine-tune a pre-trained vision-language-action model (VLA) on task-specific data. However, since this recipe updates existing representations, it is unsuitable for long-term operation in the real world, where robots must continually adapt to new tasks and environments while retaining the knowledge they have already acquired. Existing continual learning methods for robotics commonly require storing previous data (exemplars), struggle with long task sequences, or rely on task identifiers for deployment. To address these limitations, we propose CLARE, a general, parameter-efficient framework for exemplar-free continual learning with VLAs. CLARE introduces lightweight modular adapters into selected VLA modules and autonomously expands the model only where necessary when learning a new task, guided by layer-wise feature similarity. During deployment, an autoencoder-based routing mechanism dynamically activates the most relevant adapters without requiring task labels. Through extensive experiments on the LIBERO benchmark and five real-world tasks, we show that CLARE achieves high performance on new tasks without catastrophic forgetting of earlier tasks, significantly outperforming even exemplar-based methods. Code, data, and videos are available at our website: https://tum-lsy.github.io/clare.
arXiv:2510.15714v3 Announce Type: replace-cross Abstract: Second-order optimization methods offer superior convergence rates but are often bottlenecked by the wall-clock cost of Hessian computation and factorization. In the moderate-dimensional regime where the full Hessian fits in memory, factorization $\mathcal{O}(d^3)$ typically dominates gradient evaluation $\mathcal{O}(nd)$, creating a synchronization barrier that negates the per-iteration progress of classical second-order methods. We propose the \emph{Split-Client} framework, which decouples optimization into parallel gradient and curvature processes. Unlike Lazy Hessian approaches, whose arithmetic-complexity analysis does not charge factorization time and whose optimal reuse frequency requires tuning, our method is fully \textbf{delay-adaptive}: its wall-clock complexity scales with the \emph{average} delay $\Bar{\tau}$, and it matches the optimally-tuned Lazy rate of $\mathcal{O}(\eps^{-3/2}\sqrt{\Bar{\tau}})$ without any tuning. For persistent curvature error, we provide a noise-adaptive schedule with $\widetilde{\mathcal{O}}(T^{-3/4})$ rate (on $E[\|\nabla f\|]^{3/2}$), recovering the rate that uniform-error analyses such as Kamzolov et al (2023) achieve via inflated regularization. Under a verifiable subspace-alignment condition, an additional \emph{structured} analysis based on the secant condition of L-BFGS gives a faster $\mathcal{O}(T^{-1})$ rate, with a hybrid theorem interpolating smoothly between the two regimes. We extend the framework to Subsampled Cubic Newton with adaptive batch sizes and an aggregate sampling budget linear in $T$. Experiments on two non-convex problems show wall-clock speedups of up to $800\times$ over Vanilla and $30\times$ over Lazy in the strongly factorization-dominated regime.