arXiv:2605.17739v1 Announce Type: new Abstract: We study hyperinterpolation and its spectral multiplier variants on the sphere under weak cubature assumptions formulated through Sobolev discrepancy estimates. In contrast with classical hyperinterpolation theory, our framework does not require exact polynomial cubature formulas or Marcinkiewicz--Zygmund inequalities. The main idea is to interpret the discretization error as the action of a spectral multiplier operator on the cubature discrepancy measure. This viewpoint separates approximation properties of the underlying spectral operator from geometric properties of the sampling measure, leading to stable Sobolev approximation estimates under weak cubature assumptions. The resulting theory applies to a broad class of spectral approximation operators, including sharp spectral projections, compactly supported smooth filters, Bessel potential operators, and heat kernel operators. For sufficiently localized spectral multipliers, we additionally obtain uniform $L^\infty$-stability of the corresponding discrete approximation operators. The results establish a direct connection between hyperinterpolation, Sobolev discrepancy, and quasi-Monte Carlo (QMC) designs, showing that stable approximation from scattered data can be achieved without exact polynomial reproduction.
Science Journals
arXiv:2605.18632v1 Announce Type: new Abstract: Neural network checkpoints have quietly become a large-scale data resource: millions of trained weight vectors now exist, each encoding task-, domain-, and architecture-specific knowledge. This position paper argues that model checkpoints should be treated as a first-class data modality, and that generative modeling in weight space should be standardized as a core machine learning primitive. Recent advances demonstrate that neural weights can be synthesized on demand, often matching fine-tuning performance while reducing adaptation cost by orders of magnitude. We contend that these results reflect an underlying structural fact: high-performing models occupy low-dimensional, highly structured regions of weight space shaped by symmetry, flatness, modularity, and shared subspaces. Building on this view, we organize existing methods into a five-stage pipeline, survey applications where the approach is already practical, and clarify current limits: adapter-scale and conditional generation are advancing rapidly, while unrestricted frontier-scale checkpoint synthesis remains open. Our goal is to shift the community's default mindset from optimizing models per task to sampling models from learned weight distributions, accelerating toward an era in which AI systems routinely improve or create other AI systems.
arXiv:2405.19189v3 Announce Type: replace Abstract: With the great success of diffusion models (DMs) in generating realistic synthetic vision data, many researchers have investigated their potential in decision-making and control. Most of these works utilized DMs to sample directly from the trajectory space, where DMs can be viewed as a combination of dynamics models and policies. In this work, we explore how to decouple DMs' ability as dynamics models in fully offline settings, allowing the learning policy to roll out trajectories. As DMs learn the data distribution from the dataset, their intrinsic policy is actually the behavior policy induced from the dataset, which results in a mismatch between the behavior policy and the learning policy. We propose Dynamics Diffusion, short as DyDiff, which can inject information from the learning policy to DMs iteratively. DyDiff ensures long-horizon rollout accuracy while maintaining policy consistency and can be easily deployed on model-free algorithms. We provide theoretical analysis to show the advantage of DMs on long-horizon rollout over models and demonstrate the effectiveness of DyDiff in the context of offline reinforcement learning, where the rollout dataset is provided but no online environment for interaction.
arXiv:2605.17363v1 Announce Type: cross Abstract: Single-layer molybdenum disulfide ($MoS_2$) possesses significant potential for nanoscale optoelectronics, but achieving high-intensity, long-term-stable photoluminescence (PL) emission remains a challenge. In this work, we demonstrate a remarkably robust, more than 8-fold maximum enhancement in the PL intensity of exfoliated and CVD-grown single-layer $MoS_2$ via a non-destructive ultraviolet (UV) laser treatment method. This substantial increase in radiative efficiency is accompanied by a trion-to-neutral exciton transition in the PL signal and a corresponding blue shift of the Raman $E_{2g}^1$ and $A_{1g}$ vibrational modes, signaling successful electron depletion (p-doping) and formation of Mo-O bonds, respectively. Furthermore, we demonstrate precise spatial control over PL properties by confining PL treatment exclusively to the UV laser-treated area. Crucially, the enhanced PL performance shows exceptional longevity; the CVD sample and the exfoliated sample remained stable for the entire monitoring period (72 and 32 days, respectively) under ambient conditions. We further investigated UV laser treatment in a controlled-environment chamber under argon, nitrogen, and oxygen atmospheres, distinguishing the influence of oxygen as the PL treatment agent. These findings establish a reliable pathway for the permanent treatment of single-layer $MoS_2$ PL properties, an essential step toward practical, high-performance nanophotonic devices.
arXiv:2605.18263v1 Announce Type: new Abstract: 3D Gaussian Splatting (3DGS) enables real-time novel view synthesis with high visual quality. However, existing methods struggle with semi-transparent specular surfaces that exhibit both complex reflections and clear transmission, often producing blurry reflections or overly occluded transmission. To address this, we present RT-Splatting, a framework that disentangles each Gaussian's geometric occupancy from its optical opacity. This factorization yields a unified surface-volume scene representation with a single set of Gaussian primitives. Our hybrid renderer interprets this representation both as a surface to capture high-frequency reflections and as a volume to preserve clear transmission. To mitigate the ambiguity in jointly optimizing reflection and transmission, we introduce Specular-Aware Gradient Gating, which suppresses misleading gradients from highly specular regions into the transmission branch, effectively reducing distracting floaters. Experiments on challenging semi-transparent scenes show that RT-Splatting achieves state-of-the-art performance, delivering high-fidelity reflections and clear transmission with real-time rendering. Moreover, our factorization naturally enables flexible scene editing. The project page is available at https://sjj118.github.io/RT-Splatting.
arXiv:2605.18702v1 Announce Type: new Abstract: Tabular foundation models (TFMs) achieve strong performance on health datasets, but their inference cost and infrastructure requirements limit practical use. We study whether their predictive behavior can be transferred to lightweight tabular models through knowledge distillation. Since in-context TFMs condition on the training set at inference time, naive distillation can introduce context leakage; we address this with stratified out-of-fold teacher labeling. Across $19$ healthcare datasets, $6$ TFM teachers, $4$ student families, and several multi-teacher ensembles, we find that distilled students retain at least $90\%$ of teacher AUC, outperforming teachers in some cases, while running at least $26\times$ faster on CPU and preserving calibration and fairness critical for health applications. Moreover, multi-teacher averaging does not consistently improve over the best single teacher. Leakage-aware distillation is thus a viable route for bringing TFM-quality predictions into inference-constrained health settings.
arXiv:2605.16693v1 Announce Type: cross Abstract: Many biological processes, from cell division to viral lysis, are triggered when an internal stochastic variable reaches a threshold. Here we introduce Branching under First-Passage Resetting, a general framework in which replication events arise endogenously from first-passage dynamics rather than from externally imposed lifetime clocks. We show that the resulting population dynamics obey an exact renewal equation linking single-trajectory first-passage statistics to the population growth rate. This mapping shows that, for fixed offspring number and fixed mean replication time, stochastic timing fluctuations necessarily enhance growth relative to a deterministic clock. When offspring yield depends on the first-passage time, however, fluctuations have non-trivial effects and expose a fundamental yield-delay trade-off: waiting longer can increase the number of descendants, but delays all future lineages. Our framework allows us to address this optimization problem analytically, and upon application to bacteriophage lysis, gives an optimal lysis time and growth rate consistent with empirical data.
arXiv:2507.09148v2 Announce Type: replace-cross Abstract: Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our algorithm takes an (approximate) SDP solution, constructs one deterministic sparse solution and several randomized solutions, and outputs the best among them. Our algorithm has an approximation ratio of at most the sparsity constant with high probability, if called enough times. Under a technical assumption, which is consistently satisfied in our numerical tests, the average approximation ratio is also bounded by $\mathcal{O}(\log{d})$, where $d$ is the number of features. We show that this technical assumption is satisfied if the SDP solution is low-rank, or has exponentially decaying eigenvalues. We then present two classes of instances for which this technical assumption holds. We also demonstrate that in a covariance model, which generalizes the spiked Wishart model, the deterministic solution in our algorithm achieves a near-optimal approximation ratio. We demonstrate the efficacy of our algorithm through numerical tests on real-world datasets.
arXiv:2605.18246v1 Announce Type: new Abstract: We study reinforcement learning (RL) in multi-dimensional continuous state and action spaces with one-sided feedback, where the agent receives partial observations of the state and obtains reward information for only a subset of the state-action space at each time step. This setting introduces substantial challenges in both learning efficiency and privacy preservation. To address these challenges, we propose POOL, a novel privacy-preserving RL algorithm. We conduct a comprehensive theoretical analysis of POOL, deriving a sample complexity bound that matches the known lower bounds for non-private RL. Here, E_rho denotes the privacy parameter, H is the time horizon, and alpha is the optimality-gap parameter. Our findings show that it is possible to enforce strong privacy guarantees while maintaining high learning efficiency, marking a significant step toward practical, privacy-aware RL in multi-dimensional environments with one-sided feedback.
arXiv:2605.18080v1 Announce Type: cross Abstract: We present a novel parameterized 4-qubit Eisert-Wilkens-Lewenstein (EWL) quantum game circuit for recommender systems in quadruple helix innovation ecosystems (academia, industry, government, and civil society). The local strategy operators $U_{i} = R_y(\theta_{i})$ for each helix actor are directly tuned by normalized dominance weights extracted from real participant funding data (\texit{ecContribution}) in the European Commission CORDIS Horizon Europe database (project COVend, ID 101045956). The circuit employs a multi-qubit EWL entangler followed by parameterized local rotations, inverse entangler, and full measurement, achieving only 22 gates and circuit depth 11 while scaling as $O(n)$ for $n$-round helix communications. Measurement probabilities after the quantum game serve as recommender scores for disruptive versus sustaining innovation trends. These scores are subsequently mapped into the diagonal Dirac potential of a Dirac-Solow-Swan Hamiltonian, enabling time-evolution simulation of capital accumulation and bifurcation dynamics under disruptive innovation. Numerical experiments on real CORDIS quadruple-helix collaboration networks demonstrate the circuit's NISQ compatibility and its ability to forecast disruptive capital trajectories with high fidelity. The proposed framework bridges quantum game theory, parameterized quantum circuits, and relativistic economic growth models, offering a computationally efficient tool for innovation policy and strategic decision-making in complex socio-economic ecosystems. Complexity analysis and reproducibility are provided through open Qiskit implementations.
arXiv:2605.10236v3 Announce Type: replace Abstract: Modern off-policy reinforcement learning algorithms often rely on simple uniform replay sampling and it remains unclear when and why non-uniform replay improves over this strong baseline. Across diverse RL settings, we show that the effectiveness of non-uniform replay is governed by three factors: replay volume, the number of replayed transitions per environment step; expected recency, how recent sampled transitions are; and the entropy of the replay sampling distribution. Our main contribution is clarifying when non-uniform replay is beneficial and providing practical guidance for replay design in modern off-policy RL. Namely, we find that non-uniform replay is most beneficial when replay volume is low, and that high-entropy sampling is important even at comparable expected recency. Motivated by these findings, we adopt a simple Truncated Geometric replay that biases sampling toward recent experience while preserving high entropy and incurring negligible computational overhead. Across large-scale parallel simulation, single-task, and multi-task settings, including three modern algorithms evaluated on five RL benchmark suites, this replay sampling strategy improves sample efficiency in low-volume regimes while remaining competitive when replay volume is high.
arXiv:2605.10759v2 Announce Type: replace Abstract: Diffusion and flow-matching models scale because pretraining is supervised regression: a clean sample is noised analytically, and a model regresses against a closed-form target. RL post-training aligns the model with a reward. In image generation, this makes samples compose objects correctly, render text legibly, and match human preferences. Existing methods rely on costly SDE rollouts, reward gradients, or surrogate losses, sacrificing pretraining's regression structure. We show that the structure extends to RL post-training. Under KL-regularized reward maximization, the optimal generative process tilts the clean-endpoint distribution towards samples with higher reward and leaves the noising law unchanged. Combining this with the adjoint-matching optimality condition and a REINFORCE identity, we derive Reinforce Adjoint Matching (RAM): a consistency loss that corrects the pretraining target with the reward. At each step, we draw a clean endpoint from the current model, evaluate its reward, noise it as in pretraining, and regress. No SDE rollouts, backward adjoint sweeps, or reward gradients are required. Like the pretraining objective, RAM is simple and scales. On Stable Diffusion 3.5M, RAM achieves the highest reward on composability, text rendering, and human preference, reaching Flow-GRPO's peak reward in up to $50\times$ fewer training steps.
arXiv:2605.18715v1 Announce Type: new Abstract: Globally trained scientific labor is a substantial component of U.S. universities, yet the organizational mechanisms linking foreign degree training to elite scientific output remain poorly understood. We link comprehensive U.S. faculty rosters to more than 12 million OpenAlex-indexed faculty-publication observations from 2011 to 2020. Faculty with non-U.S. degrees constitute one-tenth of the U.S. professoriate but account for larger shares of total publications and top-1% cited papers. This overrepresentation is concentrated in high-output disciplinary domains and research-intensive institutions. Within institution - domain - rank - year strata, however, differences in top-1% output, FWCI, and corresponding-author share attenuate sharply, indicating that much of the aggregate pattern reflects organizational placement rather than large within-context citation advantages. Collaboration structure further differentiates foreign- and domestically trained faculty: mixed domestic-foreign faculty teams exhibit substantially elevated elite-output rates, and the association attenuates strongly after accounting for team size, suggesting that collaboration scale is central to the pattern. Topic-distinctiveness analyses show little evidence that foreign-degree faculty occupy unusually rare research niches. Overall, foreign-degree training is best understood less as an individual productivity attribute than as a structural feature of elite U.S. science, operating through institutional concentration and collaborative integration.
arXiv:2605.18407v1 Announce Type: cross Abstract: While modern Large Language Models (LLMs) and agentic artificial intelligence (AI) have demonstrated transformative capabilities in digital domains, the realization of embodied AI capable of real-world scientific discovery remains a difficult frontier. The advancements are hindered by the inherent complexity of integrating high-level reasoning, multimodal information processing and real-time physical execution. Here we introduce Qumus, the first AI quantum materials experimentalist. Physically embodied within a robotic mini-laboratory, Qumus is an intelligent, multimodal, and multi-agent system designed for the creation and nano-processing of atomically thin two-dimensional (2D) materials and stacked van der Waals (vdW) structures. Qumus autonomously navigates the full scientific cycle, from hypothesis generation and protocol planning to multi-step experimental execution, result analysis and reporting, acting as an experimentalist. Markedly, the system has achieved, for the first time, the AI-creation of graphene, as well as the first AI-fabrication of complex nanodevices including atomically thin field-effect transistors via vdW stacking. Qumus excels at these tasks by demonstrating autonomous error correction and closed-loop experimentation. Our results establish a generalizable framework for self-improving embodied AI systems that learn directly from the quantum world, opening a pathway toward accelerated discovery in quantum materials, electronics and beyond.
arXiv:2605.18727v1 Announce Type: new Abstract: Evaluating embodied systems on real dexterous hardware requires more than isolated primitive skills: an agent must perceive a changing tabletop scene, choose a context-appropriate action, execute it with a dexterous hand, and leave the scene usable for later decisions. We introduce DexHoldem, a real-world system-level benchmark built around Texas Hold'em dexterous manipulation with a ShadowHand. DexHoldem provides 1,470 teleoperated demonstrations across 14 Texas Hold'em manipulation primitives, a standardized physical policy benchmark, and an agentic perception benchmark that tests whether agents can recover the structured game state needed for embodied decision making. On primitive execution, $\pi_{0.5}$ obtains the highest task completion rate ($61.2\%$), while $\pi_{0.5}$ and $\pi_0$ tie on scene-preserving success rate ($47.5\%$). On agentic perception, Opus 4.7 obtains the best strict problem-level accuracy ($34.3\%$), while GPT 5.5 obtains the best average field-wise accuracy ($66.8\%$), exposing a gap between isolated visual sub-capabilities and complete routing-relevant state recovery. Finally, we instantiate the full embodied-agent loop in three case studies, where waiting, recovery dispatches, human-help requests, and repeated primitive execution reveal how perception and policy errors accumulate during closed-loop deployment. DexHoldem therefore evaluates dexterous tabletop execution, agentic perception, and embodied decision routing in a shared physical setting. Project page: https://dexholdem.github.io/Dexholdem/.
arXiv:2305.10721v2 Announce Type: replace Abstract: Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer can achieve competitive performance. This paper investigates the intrinsic effectiveness of recent LTSF approaches and reveals the critical role of affine mapping. Materials and methods: We conduct comprehensive experiments on both simulated and real-world datasets to analyze the components of state-of-the-art models. A theoretical analysis is provided to explain the working mechanisms of affine mapping in periodic signal forecasting. We evaluate the impact of reversible normalization and input horizon extension on model robustness. Results: We find that (1) affine mapping dominates forecasting performance across commonly utilized benchmarks, with models learning similar transition matrices from input to output; (2) affine mapping effectively captures periodic patterns but struggles with non-periodic signals or time series with varying periods across channels; (3) reversible normalization significantly enhances trend forecasting by transforming non-periodic trends into periodic-like patterns; (4) increasing input horizon improves performance on multi-channel data with different periods. Code is available at: \url{https://github.com/plumprc/RTSF}. Conclusions: Our findings provide theoretical and experimental insights into the working mechanisms of LTSF models, highlighting both the strengths and limitations of linear approaches. The results suggest that future model development should focus on handling cross-channel period variations and non-periodic components.
arXiv:2605.18509v1 Announce Type: new Abstract: Automated decision-making algorithms drive applications such as recommendation systems and search engines. These algorithms often rely on off-policy contextual bandits or off-policy learning (OPL). Conventionally, OPL selects actions that maximize the expected reward from an existing action set. However, in many real-world scenarios, actions, such as news articles or video content, change continuously, and the action space evolves over time after data collection. We define actions introduced after deploying the logging policy as new actions and focus on OPL with new actions. Existing OPL methods identify optimal actions from the existing set effectively but cannot learn and select new actions because no relevant data are logged. To address this limitation, we propose a new OPL method that leverages action features. We first introduce the Local Combination PseudoInverse (LCPI) estimator for the policy gradient, generalizing the PseudoInverse estimator initially proposed for off-policy evaluation of slate bandits. LCPI controls the trade-off between reward-modeling condition and the condition for data collection regarding the action features, capturing the interaction effects among different dimensions of action features. Furthermore, we propose a generalized algorithm called Policy Optimization for Effective New Actions (PONA), which integrates LCPI, a component specialized for new action selection, with Doubly Robust (DR), which excels at learning within existing actions. We define PONA as a weighted sum of the LCPI and DR estimators, optimizing both the selection of existing and new actions, and allowing the proportion of new action selections to be adjusted by the weight parameter. Through extensive experiments, we demonstrate that PONA efficiently selects new actions while maintaining the overall policy performance as opposed to most existing methods that cannot select new actions.
arXiv:2510.23641v2 Announce Type: replace Abstract: Transformers are very effective in capturing both global and local correlations within high-energy particle collisions, but they present deployment challenges in high-data-throughput environments, such as the CERN LHC. The quadratic complexity of transformer models demands substantial resources and increases latency during inference. In order to address these issues, we introduce the Spatially Aware Linear Transformer (SAL-T), a physics-inspired enhancement of the linformer architecture that maintains linear attention. Our method incorporates spatially aware partitioning of particles based on kinematic features, thereby computing attention between regions of physical significance. Additionally, we employ convolutional layers to capture local correlations, informed by insights from jet physics. In addition to outperforming the standard linformer in jet classification tasks, SAL-T also achieves classification results comparable to full-attention transformers, while using considerably fewer resources with lower latency during inference. Experiments on a generic point cloud classification dataset (ModelNet10) further confirm this trend. Our code is available at https://github.com/aaronw5/SAL-T4HEP.
arXiv:2510.08702v2 Announce Type: replace Abstract: Code Large Language Models (LLMs) are revolutionizing software engineering. However, scaling laws that guide the efficient training are predominantly analyzed on Natural Language (NL). Given the fundamental differences like strict syntax between code and NL, it is unclear whether these laws are directly applicable to code. To address this gap, we conduct the first large-scale empirical study of scaling laws for code, comprising 117 experimental runs with model sizes from 0.2B to 3.8B and training tokens from 2B to 128B. We fit the Chinchilla law and the Farsser law. First, the results show that the more expressive Farseer law offers greater accuracy. Second, the analysis reveals that Code LLMs scale effectively with model size. Crucially, code represents a more data-hungry regime, requiring a substantially higher data-to-parameter ratio than NL. Finally, two additional sets of experiments on code-NL mixtures show that NL benefits resource-constrained scenarios, but becomes a detriment at higher compute budgets.
arXiv:2510.14466v3 Announce Type: replace Abstract: Large language models (LLMs) continue to struggle with low-resource languages, primarily due to limited training data, translation noise, and unstable cross-lingual alignment. To address these challenges, we propose LiRA (Linguistic Robust Anchoring for LLMs)-a plug-and-play framework that requires only lightweight fine-tuning on top of existing pretrained backbones. LiRA jointly optimizes representation stability and cross-lingual semantic consistency by combining two key components: Arca (Anchored Representation Composition Architecture), which aligns low-resource inputs to a shared English semantic space through anchor-based alignment and collaborative encoding; and LaSR (Language-coupled Semantic Reasoner), a lightweight, language-aware head that enforces consistency regularization for unified cross-lingual understanding, retrieval, and reasoning. We theoretically show that under controlled anchoring error and translation-induced bias, LiRA guarantees bounded representation deviation and stable downstream performance under local Lipschitz continuity. To facilitate research, we release a new multilingual product retrieval dataset covering five Southeast Asian and two South Asian languages. Extensive experiments across diverse low-resource benchmarks demonstrate consistent improvements in retrieval, ranking, question answering, and reasoning tasks. Code will be publicly available on GitHub, and the dataset will be hosted on Hugging Face.
arXiv:2511.12493v3 Announce Type: replace Abstract: l flows and flat-plate boundary layers. However, it predicts too low a turbulent kinetic energy. This is a feature it shares with most other two-equation turbulence models. When comparing the terms in the k equations with DNS data it is found that the production and dissipation terms are well predicted but the turbulent diffusion is not. In the present work the poor modeling of the turbulent diffusion is improved using Physics Informed Neural Network (PINN) and Neural Network (NN).The k equation is turned into an ordinary differential equation for the turbulent viscosity in the k equation, nu_{t,PINN}, which is solved using PINN. A new turbulent Prandtl number is then computed as sigma_{k} = nu_{t}/nu_{t,PINN} where nu_t = k/omega.To compensate for the new, larger turbulent kinetic energy, three coefficients in the new k-omega model are computed using three NN models. The new turbulence model, called the k-omega-PINN-NN model, is shown to produce excellent velocity, skin friction and turbulent kinetic profiles in channel flow at Re_tau = 2 000, 5 200 and Re_tau = 10 000 as well as in flat-plate boundary layer flow (slightly too large a k for the latter case). The k-omega-PINN-NN model is also used for predicting the flow over a periodic hill and the agreement with DNS is very good. At the end of the Conclusions, we give an example on how a NN model can be replaced with a Python symbolic regression (pySR); the latter may conveniently be imported in commercial CFD codes. All Python PINN, NN and pySR scripts as well as the Python CFD code can be downloaded (Davidson, 2025a).
arXiv:2605.18750v1 Announce Type: new Abstract: Pipeline parallelism is a key technique for scaling large-model training, but modern workloads exhibit runtime variability in computation and communication. Existing pipeline systems typically consume static, profiled, or adaptively generated schedules as pre-committed execution orders. When realized task readiness diverges from the pre-committed order, stages may wait for not-yet-ready work even though other executable work is available, creating stage misalignment, idle bubbles, and reduced utilization. We present Runtime-Readiness-First Pipeline (RRFP), a readiness-driven runtime for pipeline-parallel training. RRFP changes how schedules are consumed at runtime: instead of treating a schedule as a sequence that stages must wait to follow, it treats the schedule as a non-binding hint order for ranking currently ready work. To support this model, RRFP combines message-driven asynchronous communication, lightweight tensor-parallel coordination for collective consistency, and ready-set arbitration for low-overhead dispatch. We implement RRFP in a Megatron-based training framework and evaluate it on language-only and multimodal workloads at up to 128 GPUs. RRFP improves over fixed-order pipeline baselines across all settings. Using the BFW hint, RRFP achieves up to 1.77$\times$ speedup on language-only workloads and up to 2.77$\times$ on multimodal workloads. In cross-framework comparisons, RRFP with the default BF hint outperforms the faster available external system by up to 1.84$\times$ while preserving training correctness.
arXiv:2509.05383v2 Announce Type: replace-cross Abstract: Models that describe Newtonian liquid films evolving due to the competing effects of surface tension and attractive intermolecular or van der Waals forces are known to rupture in finite time in a self-similar manner. We extend the computation of similarity solutions to non-Newtonian power-law liquid films. The resulting bifurcation diagram, indexed by power law exponent $n$, has a highly nontrivial structure with branches merging via a snaking bifurcation around $n=1$. A countably infinite number of solutions are also found in the extreme shear-thinning ($n\to 0$) limit, in which similarity solutions possess an exponentially small inner region. Numerical simulations of the time-dependent model are shown to be attracted to the single primary branch of similarity solutions. The asymptotic structure of solutions in the small $n$ limit is also determined.
arXiv:2605.18500v1 Announce Type: new Abstract: Large language models (LLMs) have increasingly leveraged tool invocation to enhance their reasoning capabilities. However, existing approaches typically tightly couple tool invocation with immediate execution. Such immediate tool interaction may disrupt the reasoning coherence of LLMs and constrain their expressivity, ultimately degrading reasoning performance. To this end, for the first time, we propose and formalize the problem of decoupling tool invocation from execution during reasoning, and introduce delayed execution with explicit control to enhance tool-integrated reasoning (TIR). Furthermore, we propose a hierarchical control framework and theoretically derive a surrogate loss that enables an implicitly hierarchical policy to learn behavior equivalent to that of an explicit hierarchical policy, leading to the proposed IH-GRPO algorithm. Extensive experiments on IH-GRPO achieve absolute improvements of 1.87\%, 2.16\%, and 2.53\% on Qwen3-1.7B, Qwen3-4B, and Qwen3-8B across six out-of-domain mathematical reasoning benchmarks over the strongest baseline method, while also yielding consistent performance gains in other domains. Our code is available at https://github.com/Lumina04/IH-GRPO-01.
arXiv:2505.03205v3 Announce Type: replace Abstract: Transformers serve as the foundational architecture for large language and video generation models, such as GPT, BERT, SORA and their successors. Empirical studies have demonstrated that real-world data and learning tasks exhibit low-dimensional structures, along with some noise or measurement error. The performance of transformers tends to depend on the intrinsic dimension of the data/tasks, though theoretical understandings remain largely unexplored for transformers. This work establishes a theoretical foundation by analyzing the performance of transformers for regression tasks involving noisy input data near a manifold. Specifically, the input data are in a tubular neighborhood of a manifold, while the ground truth function depends on the projection of the noisy data onto this manifold, referred to as the task-level manifold. We prove approximation and generalization errors which crucially depend on the intrinsic dimension of the task-level manifold. Our results demonstrate that transformers can leverage low-complexity structures in learning task even when the input data are perturbed by high-dimensional noise. Our novel proof technique constructs representations of basic arithmetic operations by transformers, which may hold independent interest.