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Characterizing the complete wall-pressure spectrum in turbulent wall-bounded flows requires simultaneous access to the viscous-scale high-wavenumber content and the outer-layer low-wavenumber content -- a requirement that neither short-domain direct numerical simulation (DNS) nor sparse experimental measurements alone can satisfy. We propose Patched Flow Matching (Patched FM), a generative framework that fuses these two complementary sources by learning a patch-local prior over inner-scaled wall-pressure statistics from short-domain DNS and assimilating sparse sensor measurements at inference time through training-free posterior sampling. The patch-additive decomposition of the flow matching vector field decouples the generative prior from the global domain size, enabling reconstruction on domains arbitrarily larger than the training configuration. By expressing the patch prior in inner-scaled coordinates, where high-wavenumber wall-pressure statistics are approximately Reynolds-number invariant, the framework extends to higher Reynolds numbers through hierarchical transfer learning with as few as \(500\) short-domain snapshots (\(2.5\%\) of the base training data) at a fraction of the scratch-training cost. Applied to compressible channel-flow DNS at \(Re_τ= 180\), \(500\), and \(1000\), Patched FM reconstructs full-resolution wall-pressure fields on a domain four times larger than the training configuration (\(L_x^L = 16πδ\) versus \(L_x^S = 4πδ\)) from sensor coverage as low as \(0.25\%\), recovering the low-wavenumber spectral content inaccessible to short-domain DNS with high fidelity in both streamwise and spanwise directions. Zero-shot generalization to unseen Reynolds numbers and ablation studies further confirm the role of inner scaling as a physical prerequisite for data-efficient Reynolds-number transfer.

Diffusion models excel at capturing multi-modal action distributions in robot imitation learning. However, in multi-task and long-horizon scenarios, monolithic architectures lack structural generalization capabilities, suffering from gradient conflicts between distinct semantic sub-stages. While pure data-driven Mixture-of-Experts (MoE) methods introduce labor division, they frequently trigger routing collapse, and instantiating full-scale experts causes parameter explosion and high expansion costs. To address these issues, we propose Concept-prior Routed Diffusion Experts (CoRDE), a structure-guided variational distillation framework. CoRDE extracts semantic distributions from a frozen concept encoder to guide the variational posterior responsibility via a learnable soft mapping matrix. This mechanism introduces an entropy-controlled responsibility inference process that encourages confident routing under reliable semantic predictions while preserving the stochastic diffusion term for behavioral diversity. To overcome parameter inflation, CoRDE employs a parameter-efficient expert pool using Low-Rank Adaptation (LoRA) on a shared frozen backbone. Theoretical analysis shows that the mixture score discrepancy is bounded by responsibility-weighted local expert errors, supporting high-fidelity generation under low-rank expert adaptation. Empirical evaluations confirm that, compared to existing baselines, CoRDE systematically reduces routing collapse, forming robust, semantically aligned expert allocations while achieving superior action quality and incremental learning efficiency.

Standard continuous-depth models, such as Neural Ordinary Differential Equations (NODEs), offer significant advantages in modeling physical systems by learning continuous vector fields rather than discrete temporal steps. However, when applied to complex dynamical systems, standard NODEs frequently struggle with highly nonlinear dynamics. This paper investigates the Frequency-domain Neural ODE (FNODE), an architecture that projects continuous temporal dynamics into the frequency domain using the Fast Fourier Transform (FFT). By operating in the frequency domain, the model provides better generalization to the dynamical system. The architecture is empirically evaluated against discrete models, specifically Gated Recurrent Units (GRUs) and Long Short-Term Memory (LSTMs), and other continuous-depth variants, including Augmented Neural ODE (ANODE), across four distinct dynamical systems: the Lotka-Volterra model, the forced Duffing oscillator, the Van der Pol oscillator, and the Lorenz system. To rigorously assess generalization and robustness, curriculum and ensemble learning are used to evaluate the model's convergence by estimating confidence intervals across different ensemble models. The empirical results demonstrate that the FNODE architecture achieves better generalization while exhibiting remarkable convergence stability.

Solving high-dimensional and high-order PDEs is challenged by the coupled growth of spatial dimensionality and derivative order. Recent stochastic derivative estimators reduce this cost by replacing full derivative tensors with randomized dimension or Taylor estimators, but they are mostly designed for fixed physical parameters and require retraining for each new parameter. We show that direct conditional parameterization of such solvers entangles physical parameters with the high-order automatic differentiation graph, causing extra memory growth and parameter-induced variance amplification. We propose Parameterized Representations via Implicit Stochastic Modulation (PRISM), a plug-and-play framework for parameterized high-dimensional and high-order stochastic neural PDE solvers. PRISM uses a hyper-generator to map physical parameters to affine modulators that scale and shift a purely spatial latent manifold, while keeping parameter branches value-connected but spatial-tangent-disconnected. This design preserves unbiased stochastic dimension and Taylor estimators, removes the parameter encoder from high-order spatial AD, and provides a variance-aware Lipschitz envelope over the parameter space. We prove parameterized unbiasedness, estimation-error bounds, and convergence under bounded stochastic variance. Experiments with PRISM-STDE and PRISM-SDGD on nonlinear parameterized PDEs show stable zero-shot generalization, reduced memory usage, and scalability up to 100,000 dimensions on a single GPU, with efficient low-rank SVD adaptation for unseen parameters.

In recent years, weight quantization that encodes the learnable parameters of large language models in an \(n\)-bit format has garnered significant attention due to its potential for model compression and inference acceleration. Many practical techniques have been developed; however, the theoretical understanding of many aspects, especially the approximation and degradation of expressive power as the number of quantization bits decreases, remains unclear. In this paper, we provide a theoretical investigation into the expressive capability of large language models relative to the number of quantization bits. We argue that 1.58-bit is the limiting precision for weight quantization by establishing the universal approximation and expressive collapse properties of weight-quantized models with respect to the number of quantization bits. Additionally, we confirm that weight quantization leads to expressive degradation, in which the expressive capacity of weight-quantized models degrades polynomially as the number of quantization bits decreases. These theoretical findings provide a solid foundation for advancing weight quantization in the context of scaling laws and shed insights for future research in model compression and inference acceleration.

We present AdaPrivate-TS, a differentially private contextual bandit algorithm that combines Thompson Sampling with batched zCDP composition. Our key insight is that differential privacy noise inflates the posterior covariance in a structured way: adding Gaussian noise \(N(0,σ^2 I)\) to \(b\) yields sampling covariance \(v^2 A^{-1} + σ^2 A^{-2}\), which Thompson Sampling interprets as increased uncertainty rather than pure corruption. Under event-level privacy (protecting individual interactions) with stochastic contexts, we prove that the privacy cost is only \(O(\sqrt{d}\,\log T/\sqrtρ)\), logarithmic in \(T\), because parallel composition amortizes noise across batches. Additionally, we explore privacy amplification via Poisson subsampling, which can reduce effective noise at stringent privacy budgets. Experiments on synthetic and real-world datasets demonstrate: (1) AdaPrivate-TS achieves 93-99% of non-private performance at \(\varepsilon \in [0.5, 5]\), outperforming UCB by 0.5-3.7% and up to 18% with tuned adaptive exploration at extreme \(\varepsilon\); (2) privacy amplification provides additional 2-5% gains at low \(\varepsilon\); (3) on MovieLens and Jester, AdaPrivate-TS achieves the best overall performance among event-level baselines, dominating at \(\varepsilon \geq 2\); (4) under DP-SVD private features, TS's advantage over UCB grows to +11%, confirming noise-as-uncertainty is not limited to reward privacy. We provide rigorous proofs for privacy guarantees under interactive zCDP composition and comprehensive evaluation including convergence curves, 12-seed CIs, and DP-SVD feature ablation.

We present Reflow-regularized Flow Matching Policy Gradients (ReFPO), a simple online RL method that adds explicit Reflow regularization to FPO for efficient flow-based control. We uncover a key structural property: the gradient updates in Flow Matching Policy Gradients (FPO) can be interpreted as an implicit advantage-weighted Reflow process, providing a new geometric perspective on flow-based policy gradients. Building on this insight, ReFPO introduces an explicit geometric regularizer that can be implemented with a single line of code change without incurring additional computational overhead or auxiliary distillation stages. By synergizing advantage-guided updates with path rectification, our method reduces CFM proxy-ratio spikes, stabilizes PPO-style training, and enables high-fidelity one-step inference that often matches or exceeds multi-step performance. We experimentally demonstrate that ReFPO improves average performance and discretization robustness across GridWorld, MuJoCo Playground, and high-dimensional Humanoid Control tasks, providing a scalable and stable approach for generative policies in complex physical simulations.

Vision Language Models (VLMs) have demonstrated impressive performance in tasks requiring joint understanding of images and text, such as image captioning and Visual Question Answering (VQA), but our understanding of their internal processes remains limited. Recently, Sparse Autoencoders (SAEs) have emerged as a promising tool to support the interpretation of concepts encoded in VLMs. However, most SAE-based approaches focus only on textual or visual concepts separately, ignoring multimodal concepts. This limitation hinders a comprehensive understanding of VLMs, since concepts that integrate both modalities can be misclassified. Moreover, previous visual approaches often produce low-quality visual concept descriptions that are vague or incomplete, limiting their usefulness for understanding model reasoning. We propose a framework based on SAEs to extract and analyze visual, textual, and multimodal concepts from VLMs. For each neuron, we propose a candidate human-interpretable concept and compute the alignment between the concept and the dataset samples using cosine similarity scores. Experiments on a VQA dataset (LLaVA-NeXT) demonstrate that our framework improves visual concept quality by up to 45\% compared to existing SAE-based methods, while maintaining high textual concept quality and enabling systematic identification of multimodal concepts. This work contributes new insights into the conceptual space of VLMs, providing a structured approach to distinguish between visual, textual, and multimodal concepts. The code is available at https://github.com/PHDLanza/Multidata_SAE

In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.

Deep reinforcement learning is pivotal for closed-loop autonomous driving yet remains constrained by severe bottlenecks in sampling efficiency. Standard parallel sampling mitigates this but suffers from the straggler effect, where the premature termination of a single environment necessitates a synchronized batch re-initialization, leading to suboptimal sample utilization and prohibitive re-initialization latency. To address this, we propose FAST, a synchronous parallel framework tailored for closed-loop simulation. Specifically, FAST employs Dynamic Parallel Sampling Alignment (DPSA) to maintain vectorization synchronization by extending terminated episodes via virtual continuation, thereby decoupling the sampling loop from individual terminations. By dynamically triggering global truncation based on the termination rate of parallel clips, FAST effectively eliminates the bottleneck of premature resets without sacrificing data diversity. Furthermore, to strictly preserve theoretical consistency, we incorporate a Scaled Mask-Padding Optimization (SMPO) that leverages validity masking and adaptive loss normalization to nullify the bias from auxiliary padding data. Empirical evaluations demonstrate that FAST achieves at least a 1.78 times wall-clock speedup over the single-clip baseline while preserving statistical unbiasedness.

Robots must generate trajectories that remain faithful to learned expert behavior while satisfying safety constraints and task-specific objectives specified only at inference time. We formulate constrained trajectory generation for pretrained diffusion and flow-matching policies as Bayesian posterior sampling, with the learned demonstration distribution as a prior and an inference-time, cost-derived likelihood tilting it toward feasible, optimal trajectories. To sample from this posterior without any retraining of the base policy, we leverage the Feynman--Kac corrector framework, originally formulated for diffusion models, and extend it to deterministic flow-matching policies. The result is a unified, inference-time, retraining-free sampler for diffusion and flow policies. We validate the approach on pretrained Diffusion Policy, GR00T-N1.6, and \(π_{0.5}\) checkpoints across simulated and real-world manipulation tasks, including planning around non-convex obstacles introduced at inference time, and show improvements over the base \(π_{0.5}\) on zero-shot tasks.

To generate natural and accurate sentence-level sign language, synthesizing the "gloss", the fundamental semantic unit, is essential. However, most current sign-language production (SLP) methods generate entire sequences at once. While this end-to-end approach is often efficient, it is prone to temporal drift and hand motion blur as sentences get longer, and fails to accurately control individual glosses. In this paper, we propose the Context-aware Gloss-wise AutoRegressive Diffusion model (GARD), a gloss-wise diffusion framework that models coarticulation by conditioning on both semantic (linguistic) and kinematic (motion) contexts. To ensure natural continuity between gloss motions, GARD introduces two additional strategies: i) Inter-Gloss Transition Guidance, which applies gradient-based guidance to kinematically align inter-gloss boundaries and ensure seamless pose consistency. ii) Global Motion Harmonizer, refining the entire gloss motion sequence based on the boundary poses adjusted by Inter-Gloss Transition Guidance. Extensive experiments on Phoenix-T and CSL-Daily datasets demonstrate that GARD achieves superior performance over existing SLP methods in terms of both linguistic accuracy and motion similarity.

Quantum pure-state ensembles live on complex projective space, making flat Euclidean generative modeling geometrically mismatched. We introduce Intrinsic Flow Matching (IFM), a deterministic transport framework on \(\mathbb{CP}^{d-1}\) that learns tangent velocity fields using Pancharatnam phase-aligned conditional paths. IFM replaces local score teachers and reverse-time stochastic sampling with manifold probability flow, while horizontal parameterization removes redundant ambient directions. We show that the IFM objective recovers the induced marginal transport field, represents deterministic projective ensemble flows, and yields endpoint and stability guarantees. Empirically, IFM often improves over ambient Euclidean flow matching across higher-qubit, multimodal, spin-coherent, physics-inspired, and amplitude-encoded MNIST image-vector benchmarks, with strongest gains on high-dimensional and coherence-sensitive tasks but not uniformly across every metric.

Unsupervised domain adaptation (UDA) aims to learn a target-domain classifier from labeled source data and unlabeled target data under distribution shift. Recent diffusion-based UDA methods approach this problem by synthesizing labeled target-style images and training on the resulting synthetic data. However, their performance depends heavily on the conditioning design: class prompts provide only coarse guidance, while domain adaptation modules mainly control appearance, which may leave target-style synthesis insufficiently specified. We propose VT-DUDA, a visual-token conditioning framework for diffusion-guided UDA. Instead of relying only on text prompts, VT-DUDA uses source images to provide additional instance-level visual context for target-style synthesis. Specifically, VT-DUDA maps each source image to a compact sequence of visual tokens and forms a hybrid conditioning context by concatenating these tokens with the corresponding text embeddings along the cross-attention context dimension of a latent diffusion model. This provides instance-dependent conditioning beyond text alone, while synthesis is performed with the target-domain adapter branch. Because guidance is represented explicitly as a token sequence, the same interface also permits inference-time manipulation of the conditioning signal through token selection and token-strength adjustment. The proposed method preserves the standard diffusion objective and can be integrated into existing adapter-based diffusion frameworks without modifying the backbone. Across Office-31, Office-Home, and VisDA-2017, VT-DUDA improves average target-domain accuracy over strong discriminative and diffusion-based UDA baselines. The results suggest that, in generation-based UDA, a stronger conditioning interface can improve the downstream usefulness of synthetic target-style data.

Autoregressive text-to-image (T2I) generation has recently advanced rapidly, yet aligning generated images with human preferences remains challenging. GRPO-style online reinforcement learning provides an effective framework; however, existing methods typically treat reference-policy divergence as fixed, despite its direct impact on policy optimization. We study this overlooked factor within a unified f-divergence framework, encompassing forward KL, reverse KL, and JS divergence, for GRPO-style autoregressive T2I alignment. Our systematic theoretical analysis reveals that different divergences reshape token-level updates in distinct ways. In particular, under the sampled-token shaping form used, JS regularization achieves a favorable trade-off by mitigating uniform bias relative to the reference policy while still discouraging large deviations. Extensive experiments on LlamaGen and Janus-7B show that JS divergence achieves the strongest or highly competitive optimization performance on most evaluation metrics while maintaining favorable generation diversity. The code is available at https://github.com/tuoyou-hao/BPD-GRPO.

Single domain generalization (SDG) aims to learn a robust model, which could perform well on many unseen domains while there is only one single domain available for training. One of the promising directions for achieving single-domain generalization is to generate out-of-domain (OOD) training data through data augmentation or image generation. Given the rapid advancements in AI-generated content (AIGC), this paper is the first to propose leveraging powerful pre-trained text-to-image (T2I) foundation models to create the training data. However, manually designing textual prompts to generate images for all possible domains is often impractical, and some domain characteristics may be too abstract to describe with words. To address these challenges, we propose a novel Progressive Adversarial Prompt Tuning (PAPT) framework for pre-trained diffusion models. Instead of relying on static textual domains, our approach learns two sets of abstract prompts as conditions for the diffusion model: one that captures domain-invariant category information and another that models domain-specific styles. This adversarial learning mechanism enables the T2I model to generate images in various domain styles while preserving key categorical features. Extensive experiments demonstrate the effectiveness of the proposed method, achieving superior performances to state-of-the-art single-domain generalization approaches.

Decentralized bilevel optimization (DBO) provides a powerful framework for multi-agent systems to solve local bilevel tasks in a decentralized fashion without the need for a central server. However, most existing DBO methods rely on lower-level strong convexity (LLSC) to guarantee unique solutions and a well-defined hypergradient for stationarity measure, hindering their applicability in many practical scenarios not satisfying LLSC. To overcome this limitation, we introduce a new single-loop DBO algorithm called diminishing quadratically-regularized bilevel decentralized optimization (DUET), which eliminates the need for LLSC by introducing a diminishing quadratic regularization to the lower-level (LL) objective. We show that DUET achieves an iteration complexity of \(O(1/T^{1-5p-\frac{11}{4}τ})\) for approximate KKT-stationary point convergence under relaxed assumptions, where \(p\) and \(τ\) are control parameters for LL learning rate and averaging, respectively. In addition, our DUET algorithm incorporates gradient tracking to address data heterogeneity, a key challenge in DBO settings. To the best of our knowledge, this is the first work to tackle DBO without LLSC under decentralized settings with data heterogeneity. Numerical experiments validate the theoretical findings and demonstrate the practical effectiveness of our proposed algorithms.

Understanding the generalization capabilities of visuomotor policies is essential in the development of capable robotic agents. Generalizable models learn structures that transfer across domains. However, in practice, visuomotor policies test performance by interpolation on known distributions using unstructured domain shifts (e.g. lighting, clutter, diverse objects). We argue that to measure generalization capabilities we must instead test the inductive capacity of policies on progressively harder, out-of-distribution task variants. We call this inductive generalization, drawing directly on how axis-based evaluation has revealed inherent generalization limitations in language models (e.g. sequence length, counting) arXiv:2502.00197 . We provide a reusable and formal evaluation protocol for measuring inductive generalization in any manipulation policy, and establish baselines showing that existing paradigms fail this test; e.g. SoTA Vision-Language-Action models and find that policies that appear to generalize to prior domain shifts (distractors, etc) fail inductive generalization tests. These results expose a class of learning challenges orthogonal to those addressed by data and model scaling in robot learning, yet are imperative to solve in order to realize general purpose robots.

Causal discovery is critical for understanding complex data-generating mechanisms, yet traditional algorithms often struggle with highly non-linear and noisy systems, or suffer from severe computational bottlenecks. Recent tabular foundation models based on Prior-Data Fitted Networks (PFNs) have demonstrated remarkable zero-shot inference capabilities, but their potential for explicit structural causal discovery remains underexplored. To bridge this gap, we propose DCD-PFN, a decoupling-aware foundation model for causal discovery. Instead of directly amortizing global graph reconstruction, DCD-PFN focuses on local causal discovery through a decoupling-based paradigm. Through pre-training on diverse synthetic Structural Causal Models (SCMs), the model learns sample-wise decoupling weights that enable Markov boundary (MB) identification. Furthermore, by leveraging parallelized local discovery, DCD-PFN efficiently reconstructs global causal graphs while remaining grounded in the theoretical foundations of decoupling-based causal discovery. Experiments demonstrate that our foundation model achieves robust zero-shot generalization.

We consider the parameter estimation problem in logistic regression with Gaussian design: the estimation of a fixed unknown parameter \(θ^*\in \mathbb{R}^d\) (\(\|θ^*\|_2\ge 1\)) from \(n\) i.i.d. samples \(\{(x_i,y_i)\}_{i=1}^n\), where \(x_i\sim N(0,I_d)\) and \(y_i|x_i \sim {\rm Bernoulli}(1/(1+\exp(-x_i^\top θ^*)))\). Our main aim is to characterize the finite-sample estimation performance and convergence behavior of gradient descent (GD) on the maximum likelihood objective (i.e., the logistic loss). Under small \(O(1)\) stepsize and \(0\) initialization, we show that GD linearly converges to a small neighborhood of \(θ^*\) achieving an \(\ell_2\) error of order \(O(\sqrt{\|θ^*\|_2^5d/n})\). This substantially goes beyond existing theoretical results that lack non-asymptotic estimation error rate and exhibit much slower parameter convergence. We also establish a faster local linear convergence to the same statistical error under a large \(Θ(\|θ^*\|_2)\) stepsize. The main technical component is to show that the gradient of the logistic loss satisfies a certain approximate invertibility condition (AIC). To that end, we uniformly control the deviation of the gradient from its population counterpart by covering and peeling arguments, and then show that the population GD is a contraction by a delicate analysis based on the eigenvalues of population Hessian matrices. Finally, we build upon the recent work Matsumoto and Mazumdar (2025) and devise a novel efficient estimator that attains a sharper rate in high dimensions. This indicates that the existing non-asymptotic guarantees exhibit sub-optimal dependence on \(\|θ^*\|_2\), and that in many regimes \(Θ(\sqrt{\|θ^*\|_2d/n})\) is the tight estimation error rate. Numerical examples are provided to corroborate our theoretical results.