arXiv:2605.15314v1 Announce Type: new
Abstract: We study nonconvex stochastic optimization under the Blum-Gladyshev ($\mathsf{BG}$-0) noise model, where the stochastic gradient variance grows quadratically with the distance from the initialization. We consider this problem under both standard smoothness and the symmetric generalized-smoothness framework, which captures objectives whose local curvature can scale with the gradient norm. We prove that normalized stochastic gradient descent with momentum, using only one stochastic gradient per iteration, converges under $\mathsf{BG}$-0 noise with oracle complexity $O(\varepsilon^{-6})$. This rate holds both for standard smoothness and for $\alpha$-symmetric generalized smoothness, showing that generalized smoothness is rate-neutral for normalized momentum in this setting. We then study a variance-reduced normalized STORM method. Under mean-square smoothness and sharp initialization, the method achieves the minimax optimal $O(\varepsilon^{-4})$ complexity, matching the lower bound. Under expected $\alpha$-symmetric generalized smoothness, the STORM recursion couples gradient-dependent smoothness with distance-dependent noise, leading to complexity $O(\varepsilon^{-(4+\alpha)})$ for $\alpha\in(0,1)$ and $O(\varepsilon^{-5})$ for $\alpha=1$. When the distance-growth parameter in the noise model vanishes, our guarantees recover the standard bounded-variance rates: $O(\varepsilon^{-4})$ for momentum, $O(\varepsilon^{-3})$ for variance reduction, and $O(\varepsilon^{-2})$ in the deterministic case. To our knowledge, these are the first convergence guarantees for normalized methods in non-convex stochastic optimization under $\mathsf{BG}$-0 noise without bounded domains, increasing batch sizes, or explicit anchoring, covering both standard and generalized smoothness regimes.
Science Journals
arXiv:2605.15528v1 Announce Type: new
Abstract: Autonomous underwater vehicle (AUV) swarms are emerging as intelligent underwater networks, where each node must sense, communicate, process local data, and make decisions under severe acoustic constraints. Persistent underwater target tracking is a typical task with moving targets, changing communication topology, intermittent acoustic links, and limited observation for each AUV. Multi-agent reinforcement learning (MARL) is a natural candidate for distributed tracking, yet existing studies still lack a unified open-source platform for evaluating different MARL algorithms under six-degree-of-freedom AUV dynamics. In addition, policies trained with raw geometric states and low-level force actions often struggle to represent task phases, observation reliability, link quality, and local cooperation roles. This paper addresses these issues by developing an open-source MARL-AUV platform that integrates DI-engine with a six-degree-of-freedom underwater AUV target-tracking simulator. To the best of our knowledge, it is the first open platform that connects a public MARL training framework with physically modeled AUV swarm-based tasks, and provides a unified experimental protocol for fair training, testing, and comparison of representative RL and MARL algorithms. Based on this platform, we propose STG-MAPPO, a Semantic Task Graph-enhanced variant of Multi-Agent Proximal Policy Optimization. STG-MAPPO builds semantic policy inputs from tracking diagnostics, task phases, observation confidence, link availability, neighbor tracking quality, and local role advantage. A compact semantic task graph links communication-constrained network states to decentralized actor decisions, and a velocity-level action abstraction maps high-level cooperative decisions to executable six-degree-offreedom AUV control inputs.The code is available at https://github.com/dasjsaj/MARL-AUV.
arXiv:2605.15559v1 Announce Type: new
Abstract: Recent years have witnessed significant progress in autonomous navigation using reinforcement learning. However, existing approaches largely emphasize reinforcement learning framework design, such as input representations, action spaces, and reward functions, while providing limited analysis of sim-to-real transfer and insufficient insight into how training strategies affect real-world deployment performance. To bridge this gap, we not only introduce an effective RL framework but also present a complete training and deployment pipeline, along with a systematic empirical study that disentangles the key factors affecting sim-to-real transfer in reinforcement learning-based navigation, including sensor noise, perception failures, system latency, and control response. Building on insights from this analysis, we introduce perturbation-aware fine-tuning, a post-training adaptation strategy that improves transfer robustness by explicitly accounting for empirically identified domain discrepancies. To further mitigate perception degradation and enhance control smoothness in real-world deployment, we propose a Transformer-based temporal reasoning policy that leverages short-horizon observation for navigation control. We quantitatively evaluate how individual sim-to-real perturbations and training design choices impact navigation performance across environments. Experimental results demonstrate that the proposed training strategy and policy architecture outperform learning-based baselines in both static and dynamic environments, while achieving performance comparable to optimization-based planners in static settings. We validate our approach through real-world deployment on multiple robotic platforms, including aerial and legged robots, across navigation-centric tasks such as exploration and inspection, demonstrating zero-shot sim-to-real transfer.
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:2605.07557v4 Announce Type: replace
Abstract: Semi-supervised learning faces significant challenges in realistic scenarios where labeled data is scarce and unlabeled data follows unknown, arbitrary distributions. We formalize this critical yet under-explored paradigm as Universal Semi-supervised Learning (UniSSL). Existing methods typically leverage unlabeled data via pseudo-labeling. However, they often rely on the idealized assumption of a uniform unlabeled data distribution or require sufficient labeled data to estimate it. In the UniSSL setting, such dependencies lead to numerous erroneous pseudo-labels, thereby triggering representation confusion. Fortunately, we observe that inter-sample relations captured by representations are more reliable than pseudo-labels. Leveraging this insight, we shift our focus to representation-level structural inference to bypass distribution estimation. Accordingly, we propose Simplex Anchored Graph-state Equipartition (SAGE), which captures high-order inter-sample dependencies to establish structural consensus for guiding representation learning. Meanwhile, to mitigate representation confusion, we employ vectors that satisfy a simplex equiangular tight frame to serve as a coordinate frame for guiding inter-class representation separation. Finally, we introduce a weighting strategy based on distribution-agnostic metrics to prioritize reliable pseudo-labels and an auxiliary branch to isolate potentially erroneous pseudo-labels. Evaluations on five standard benchmarks show that SAGE consistently outperforms state-of-the-art methods, with an average accuracy gain of $\textbf{8.52%}$.
arXiv:2601.12894v2 Announce Type: replace
Abstract: Diffusion Policy has dominated action generation due to its strong capabilities for modeling multi-modal action distributions, but its multi-step denoising processes make it impractical for real-time visuomotor control. Existing caching-based acceleration methods typically rely on $\textit{static}$ schedules that fail to adapt to the $\textit{dynamics}$ of robot-environment interactions, thereby leading to suboptimal performance. In this paper, we propose $\underline{\textbf{S}}$parse $\underline{\textbf{A}}$ction$\underline{\textbf{G}}$en ($\textbf{SAG}$) for extremely sparse action generation. To accommodate the iterative interactions, SAG customizes a rollout-adaptive prune-then-reuse mechanism that first identifies prunable computations globally and then reuses cached activations to substitute them during action diffusion. To capture the rollout dynamics, SAG parameterizes an observation-conditioned diffusion pruner for environment-aware adaptation and instantiates it with a highly parameter- and inference-efficient design for real-time prediction. Furthermore, SAG introduces a one-for-all reusing strategy that reuses activations across both timesteps and blocks in a zig-zag manner, minimizing the global redundancy. Extensive experiments on multiple robotic benchmarks demonstrate that SAG achieves up to 4$\times$ generation speedup without sacrificing performance. Project Page: https://sparse-actiongen.github.io.
arXiv:2605.15481v1 Announce Type: new
Abstract: InGaP-on-insulator, with its intrinsically high $\chi^{(2)}$ optical nonlinearity, has emerged as an efficient and bright integrated photonic platform for frequency conversion and on-chip entanglement generation, but high waveguide propagation loss in the visible wavelength range has limited its overall performance. Here, we identify the dominant loss mechanism through mode-profile analysis and effectively mitigate the loss using a surface treatment method. Statistical analysis of the resonator quality factor and propagation loss reveals the optimal ring radius that maintains a strong nonlinear interaction while suppressing significant bending related loss, resulting in loss as low as 0.49 dB/cm (4.31 dB/cm) at 1560 nm (780 nm). The method provides a 3.5--4$\times$ linear performance enhancement, enabling a second-harmonic generation efficiency of $3.01\times10^{5}$ %/W and a photon-pair generation rate of $11.7,\mathrm{MHz}/\mu\mathrm{W}$ and coincidence-to-accidental ratio as high as 10,000. The quasi-phase matching condition is experimentally verified, and nonlinear conversion is systematically characterized across the entire parameter space. This work establishes a scalable pathway for classical and quantum photonics in a low-loss, highly nonlinear, and wafer-scale integration platform.
arXiv:2505.03307v3 Announce Type: replace-cross
Abstract: Simulating Clifford and near-Clifford circuits using the extended stabilizer formalism has become increasingly popular, particularly in quantum error correction. Compared to the state-vector approach, the extended stabilizer formalism can solve the same problems with fewer computational resources, as it operates on stabilizers rather than full state vectors. Most existing studies on near-Clifford circuits focus on balancing the trade-off between the number of ancilla qubits and simulation accuracy, often overlooking performance considerations. Furthermore, in the presence of high-rank stabilizers, performance is limited by the sequential property of the stabilizer formalism. In this work, we introduce a parallelized version of the extended stabilizer formalism, enabling efficient execution on multi-core devices such as GPU. Experimental results demonstrate that, in certain scenarios, our Python-based implementation outperforms state-of-the-art simulators such as Qiskit and Pennylane.
arXiv:2605.15312v1 Announce Type: new
Abstract: Large-scale facial datasets like CelebA are widely used in computer vision, yet the cultural biases embedded in their labels remain underexplored. Fairness research has distinguished representational from allocational harms, but audits of computer vision datasets have mostly examined categorical labels, leaving open how such harms appear in learned features and model attention. This paper examines CelebA at three levels: dataset structure, learned feature weights, and spatial attention, focusing on how gendered double standards of ageing and beauty are encoded in the data and reproduced in model behaviour. First, hierarchical clustering of 202,599 images shows that the 39 attributes organise into latent trait bundles aligned with cultural archetypes: performative femininity (youth, makeup, adornment) and professional masculinity (ageing, facial hair, formal attire). Female faces, though more often rated attractive overall, incur steep penalties when assigned to ageing or masculine-coded clusters. Second, XGBoost with SHAP analysis reveal gender-specific effects, such as adiposity reducing attractiveness only for females. Third, Grad-CAM finds that predictions for female and younger male subgroups concentrate on mid-face cues, whereas predictions for older males drift toward peripheral cues such as hair and clothing. Older males attain the highest accuracy but the lowest average precision, indicating categorical exclusion of groups outside the dataset's evaluative templates. Cultural double standards thus pass from media representation into dataset labels, feature weights, and model attention, producing two representational harms: hyper-scrutiny of women under a narrow evaluative template, and exclusion of older men from the scheme entirely. Fairness metrics focused on performance disparities mask both, underscoring the need to address representational harm in fairness research.
arXiv:2605.15311v1 Announce Type: new
Abstract: The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks in which the neurons' states are governed by time-varying dynamics. The proposed model provides the learnable time-varying dynamics through a dictionary of basis functions, where each basis function evolves differently over time. We evaluate the proposed approach on both synthetic data from switching systems and a speech denoising task where real audio is corrupted with switching dynamics noise. The results show that the proposed time-varying model consistently outperforms its time-invariant counterparts while maintaining comparable computational complexity. Our investigations also reveal which aspects of the time-varying dynamics of the data most need to be captured by the proposed time-invariant models, how the additional freedom provided by time-varying basis functions should be allocated across model components, and to what extent larger models can compensate for time-invariant limitations.
arXiv:2506.00182v3 Announce Type: replace-cross
Abstract: Will further scaling up of machine learning models continue to bring success? A significant challenge in answering this question lies in understanding generalization gap, which is the impact of overfitting. Understanding generalization gap behavior of increasingly large-scale machine learning models remains a significant area of investigation, as conventional analyses often link error bounds to model complexity, failing to fully explain the success of extremely large architectures. This research introduces a novel perspective by establishing a model-independent upper bound for generalization gap applicable to algorithms whose outputs are determined solely by the data's histogram, such as empirical risk minimization or gradient-based methods. Crucially, this bound is shown to depend only on the R\'enyi entropy of the data-generating distribution, suggesting that a small generalization gap can be maintained even with arbitrarily large models, provided the data quantity is sufficient relative to this entropy. This framework offers a direct explanation for the phenomenon where generalization performance degrades significantly upon injecting random noise into data, where the performance degrade is attributed to the consequent increase in the data distribution's R\'enyi entropy. Furthermore, we adapt the no-free-lunch theorem to be data-distribution-dependent, demonstrating that an amount of data corresponding to the R\'enyi entropy is indeed essential for successful learning, thereby highlighting the tightness of our proposed generalization bound.
arXiv:2605.07074v2 Announce Type: replace
Abstract: Detecting AI-generated images across unseen architectures remains challenging, as existing models often overfit to generator-specific fingerprints and semantic content rather than learning universal forgery traces. We attribute this failure to feature entanglement: detectors learn these factors as a single entangled representation, where universal forgery traces are inextricably confounded with both generator-specific fingerprints and semantic content. Crucially, our spectral analysis reveals that this entanglement is avoidable: distinct generator-specific fingerprints (e.g., GAN stripes vs. Diffusion Model spots) occupy disjoint frequency subspaces and coexist as independent superpositions. Leveraging this physical orthogonality, we propose the Orthogonal Decomposition and Purification Network (ODP-Net) to structurally disentangle these factors. Specifically, ODP-Net employs (1) Instance-aware Orthogonal Decomposition to project features into mutually exclusive subspaces: universal forgery traces, generator-specific fingerprints, and semantic content; (2) Perturbation-based Purification to enforce semantic invariance via cross-sample feature injection; and (3) Manifold Alignment to bridge domain gaps. By explicitly decoupling universal forgery traces from generator-specific fingerprints and semantic content, ODP-Net achieves state-of-the-art performance on unseen architectures (e.g., Stable Diffusion 3), validating that structural disentanglement is key to generalization.
arXiv:2605.03548v2 Announce Type: replace
Abstract: Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.
arXiv:2605.15557v1 Announce Type: new
Abstract: Continuous diffusion and flow models are attractive for non-autoregressive text generation because they can update all positions in parallel. A major difficulty is the interface between continuous latent states and discrete tokens. This report studies a draft-conditioned latent refinement model built from a frozen BERT encoder, a parallel decoder, a denoising DraftPrior, a local FlowNet, and a learned diagonal MetricNet. Early Gaussian-start experiments showed that good latent-space metrics, such as scale matching or cosine similarity, do not guarantee good decoding. Generated latents can be close to real encoder latents but still produce high-entropy, biased, or repetitive token distributions. We therefore frame the task as controlled local refinement rather than full generation from noise. On ROCStories, using the first two sentences as prompt and the last three as target, full 768-dimensional BERT latents recover tokens much better than compressed 256-dimensional latents. With 768-dimensional latents, DraftPrior target-token probability is 0.938 for clean drafts, 0.613 for 3% token dropout, 0.483 for 5% dropout, and 0.272 for 10% dropout. Local flow refinement and fused decoder-aware readout give modest additional gains, while metric learning and OT-style alignment improve geometry but do not close the decoder gap. The main result is a diagnostic one: latent geometry alone is not enough. Continuous latent text generation should be evaluated by decoder recoverability, the quality of the start distribution, and whether refinement preserves decoder-readable structure.
arXiv:2511.09378v2 Announce Type: replace
Abstract: A series of influential studies established that large language models cannot reliably solve even simple planning tasks. We show that the latest generation of frontier models overturns this conclusion. We evaluate three families of frontier LLMs on a challenging set of planning tasks based on the most recent International Planning Competition following rigorous evaluation guidelines: solutions are verified with a validation tool, tasks are freshly created to avoid data contamination, and performance is compared against state-of-the-art classical planners. On standard task descriptions, Gemini 3.1 Pro outperforms the strongest planner baseline (245 vs. 234 solved tasks out of 360), while GPT-5 achieves comparable performance to the baselines. When all semantic information is obfuscated from the descriptions to test for pure symbolic planning, performance degrades but Gemini 3.1 Pro remains competitive with the strongest baselines. A longitudinal comparison across model generations -- from GPT-3.5, which solves zero tasks, to GPT-5 -- reveals a striking upward trajectory. Frontier LLMs might finally be able to plan; the question now is how far this capability will extend.
arXiv:2605.03964v2 Announce Type: replace
Abstract: Training machine learning interatomic potentials (MLIPs) for reactive chemistry is often bottlenecked by the high cost of quantum chemical labels and the scarcity of transition state configurations in candidate pools. Active learning (AL) can mitigate these costs, but its effectiveness hinges on the acquisition rule. We investigate whether the latent space of a pretrained MLIP already contains the information necessary for effective acquisition, eliminating the need for auxiliary uncertainty heads, Bayesian training and fine-tuning, or committee ensembles. We introduce two acquisition signals derived directly from a pretrained MACE potential: a finite-width neural tangent kernel (NTK) and an activation kernel built from hidden latent space features. On reactive-chemistry benchmarks, both kernels consistently outperform fixed-descriptor baselines, committee disagreement, and random acquisition, reducing the data required to reach performance targets by an average of 38% for energy error and 28% for force error. We further show that the pretrained model induces similarity spaces that preserve chemically meaningful structure and provide more reliable residual uncertainty estimates than randomly initialised or fixed-descriptor-based kernels. Our results suggest that pretraining aligns latent-space geometry with model error, yielding a practical and sufficient acquisition signal for reactive MLIP fine-tuning.
arXiv:2605.15468v1 Announce Type: new
Abstract: Digital systems have become simultaneously more powerful and more wasteful. Features accumulate that nobody uses. Data is collected that nobody analyzes. AI is deployed at significant energy and water costs for gains that a simpler approach could have achieved. And through all of it, the people who depend on these systems quietly absorb the consequences in cognitive load, lost time, and eroded trust. This paper introduces GreenZ, a three-layer Sustainable UX Framework for complex digital systems. Its three layers are a Philosophy Layer built around ten published principles, an Operational Frameworks Layer comprising five applied systems, and a Tools and Canvases Layer of practical audit instruments and decision models. Two contributions sit at the framework's core: a Digital Waste Taxonomy classifying eight distinct waste types, and an AI Sufficiency Decision Model that asks whether AI should exist in a given flow before any question of how to implement it. GreenZ v1 is theoretically grounded but empirically unvalidated. A practitioner expert review study is underway at the time of submission. The paper presents the framework's architecture, its conceptual foundations, its position relative to existing literature, and an honest account of what remains to be established.
arXiv:2605.15309v1 Announce Type: new
Abstract: Despite remarkable progress, image generation is far from solved. The dominant metric, FID, conflates sample fidelity with mode coverage and is close to being saturated. Yet a model can still exhibit mode collapse while achieving a low FID, since a handful of sharp, near-duplicate images can outscore a model that faithfully covers the full data distribution. We argue that precision and recall are essential complements to FID, and that because FID is already saturated, the more meaningful goal is to improve diversity and coverage. Achieving high recall requires a model that explicitly prioritizes mode coverage, unlike most generative models, which optimize sample fidelity. We introduce RTM, which replaces the single-pass latent mapping in style-based generators with an iterative refinement process, and show that this consistently improves both quality and diversity. Integrated with Implicit Maximum Likelihood Estimation (IMLE), which optimizes mode coverage by design, RTM achieves the highest precision and recall among current state-of-the-art approaches while maintaining competitive FID, with improvements across CIFAR-10, CelebA-HQ at 256x256, and nine few-shot benchmarks. RTM also improves StyleGAN2 and StyleGAN2-ADA on CIFAR-10 and AFHQ-v1 at 512x512, demonstrating that the benefit is not specific to IMLE. Unlike flow-matching baselines that achieve competitive FID at the expense of coverage, recursive refinement improves both quality and diversity simultaneously.
arXiv:2507.02032v2 Announce Type: replace-cross
Abstract: One of the forthcoming major challenges in particle physics is the experimental determination of the Higgs trilinear self-coupling. While efforts have largely focused on on-shell double- and single-Higgs production in proton-proton collisions, off-shell Higgs production has also been proposed as a valuable complementary probe. In this article, we design a hybrid neural simulation-based inference (NSBI) approach to construct a likelihood of the Higgs signal incorporating modifications from the Standard Model effective field theory (SMEFT), relevant background processes, and quantum interference effects. It leverages the training efficiency of matrix-element-enhanced techniques, which are vital for robust SMEFT applications, while also incorporating the practical advantages of classification-based methods for effective background estimates. We demonstrate that our NSBI approach achieves sensitivity close to the theoretical optimum and provide expected constraints for the high-luminosity upgrade of the Large Hadron Collider. While we primarily concentrate on the Higgs trilinear self-coupling, we also consider constraints on other SMEFT operators that affect off-shell Higgs production.
arXiv:2507.05961v2 Announce Type: replace-cross
Abstract: Low-temperature spin dynamics can become trapped in long-lived patterns shaped by the geometry of the interaction network. Here we introduce Chladni states: spin configurations obtained by binarizing the eigenmodes of the interaction Laplacian. These graph-spectral patterns organize the metastable configurations reached by Ising systems under non-ergodic relaxation. The resulting Topological Mode Decomposition provides a compact way to monitor and reconstruct frozen spin configurations in ferromagnets, frustrated antiferromagnets, and spin glasses.
arXiv:2601.13039v2 Announce Type: replace
Abstract: In this work, we study projection-based model order reduction (MOR) for switched linear systems (SLS) in control form, where the projection matrices are obtained from the solutions of generalized Lyapunov equations (GLEs). We investigate how numerical inaccuracies in solving the GLEs propagate through the MOR process and impact the accuracy and reliability of the resulting reduced-order model. This highlights the importance of accounting for such inaccuracies, motivating the introduction of a novel error bound to quantify and control the error in the approximation of the GLE solution.
Moreover, classical balanced truncation error estimates for SLS are neither theoretically sound nor practically applicable, as they rely on restrictive assumptions requiring several linear matrix inequalities (LMIs) to be satisfied exactly by numerically computed GLE solutions. To address these limitations, we propose a new MOR framework for SLS, termed piecewise balanced reduction (PBR). The approach is based on solving multiple GLEs and constructing projection matrices that are piecewise constant in time. By extending the standard balanced truncation error bound for SLS, we show that the PBR framework effectively controls errors arising from inexact LMI satisfaction. In addition, the proposed error bound captures the influence of the piecewise constant in time projection matrices. Altogether, this makes the PBR approach applicable to a broad and flexible class of switched linear systems. Numerical experiments are presented to support the theoretical results.
arXiv:2605.15603v1 Announce Type: new
Abstract: Model-based reinforcement learning (RL) offers a compelling approach to offline RL by enabling value learning on imagined on-policy trajectories. However, it often suffers from compounding errors due to repeated model inference on self-generated states. While geometric horizon models (GHM) alleviate this issue through direct prediction over a discounted infinite-horizon future, they remain challenged in accurately modeling distant future states. To this end, we introduce universal horizon models (UHM), a generalization of GHM that directly predicts future states under arbitrary horizons. Leveraging this flexibility, we propose a scalable value learning method that employs a winsorized horizon distribution to stabilize training by capping excessively large horizons. Experimental results on 100 challenging OGBench tasks demonstrate that the proposed method outperforms competitive baselines, particularly on tasks with highly suboptimal datasets and those requiring long-horizon reasoning. Project page: https://rllab-snu.github.io/projects/UHM/
arXiv:2504.21850v3 Announce Type: replace
Abstract: Visual instruction tuning (VIT) datasets have grown rapidly in scale, yet the informativeness of individual training samples has largely been overlooked. Recent dataset selection methods have shown that a small fraction of such datasets enriched with informative samples can lead to efficient finetuning of Multimodal Large Language Models. In this work, we explore the impact of sample complexity on informative data curation and introduce COMPACT (COMPositional Atomic-to-complex Visual Compositional Tuning), a compositional VIT data recipe that scales training sample complexity by combining multiple atomic visual capabilities in a single training example. Concretely, we synthesize rich and informative text questions for each image, allowing us to significantly reduce the number of training examples required for effective VIT. COMPACT demonstrates superior data efficiency compared to existing data reduction methods. When applied to the LLaVA-665K VIT dataset, COMPACT reduces the data budget by 90% while still achieving 100.2% of the full VIT performance (compared to only 97.5% by the state-of-the-art method) across eight multimodal benchmarks. Furthermore, training on the COMPACT data outperforms training on the full-scale VIT data on particularly complex benchmarks such as MM-Vet (+8.6%) and MMStar (+2.9%). COMPACT offers a scalable and efficient synthetic data generation recipe to improve on vision-language tasks.
arXiv:2605.15604v1 Announce Type: new
Abstract: Modern language models often need to optimize a primary accuracy objective while also accommodating secondary behavioral preferences, such as verbosity, agreeableness, or the level of technical expertise in its response. In practice, a base model may exhibit a desired behavior very rarely or not at all. Thus, endowing the model with a target behavior creates a sparse behavioral reward bottleneck. To address such multi-objective problems, we introduce Vector-Steered Policy Optimization (VSPO) which employs a steering vector associated with the target behavior to control the behavior intensity of the generated rollouts. VSPO is obtained by modifying GRPO to sample rollouts with varying steering intensities. This process can be interpreted as an on-policy latent self-distillation procedure where the model internalizes its steering vector. By varying steering intensities, VSPO upsamples rare behaviors and enriches rollout diversity, which alleviates the sparse reward issue and provably accelerates the policy optimization. Through comprehensive theory and experiments, we establish that VSPO has favorable properties compared to vanilla reward shaping and other alternative approaches. Specifically, under a bandit abstraction, VSPO provably achieves better iteration complexity than reward-shaped GRPO when the steering-induced distributions are sufficiently aligned with the target behavior. We evaluate VSPO across multiple reasoning benchmarks, including MATH and MMLU-Pro, for four target behaviors: explanation expertise, confidence expression, robustness to misleading context, and response verbosity. Our results show that VSPO consistently improves the control along target behavior while maintaining or improving task accuracy compared with reward shaping, teacher-trace distillation, and guidance-based baselines.
arXiv:2508.03810v4 Announce Type: replace-cross
Abstract: Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number $N$ using scalar $\phi^4$ theory in $d$ Euclidean dimensions as an example. We find that the renormalized $O(1/N)$ corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.