生成模型理论与方法

Generalizable robot manipulation requires policies that can anticipate how visual scenes evolve while executing language instructions. While recent Vision-Language-Action models benefit from large-scale pretraining, their predominantly static pretraining objectives provide limited supervision for physical dynamics and temporal causality, leaving control-relevant knowledge to be learned from downstream robot demonstrations. Video generative models offer a promising foundation by encoding rich spatiotemporal priors through future predictions. However, existing Video-Action Models either couple video and action prediction in a shared backbone, making policy adaptation harder to optimize, or under-utilize video information when guiding the action branch. In this work, we introduce DeVA, a Decoupled Video-Action model with specialized video and action experts, multi-level feature transfer, and physically salient guidance. DeVA transfers representations from multiple video layers to the action expert, enabling rich information exchange while making policy learning more tractable. It further supervises intermediate video features and the action stream with physically salient guidance (affordance/depth). Experiments on both simulation benchmarks and real-world deployment demonstrate strong performance with limited data, faster convergence than a unified architecture, and clear performance gains from physical guidance.

Existing methods mainly adapt pretrained autoregressive (AR) language models to masked diffusion, whereas we directly adapt them to uniform-noise diffusion, where every token remains editable during sampling. However, adapting AR checkpoints across corruption kernels remains challenging because existing DLMs use different objectives and prediction parameterizations. We establish connections among SEDD, MDLM/GIDD, M2S, and Neural CTMC by expressing their conditional losses as a single generalized Kullback--Leibler objective over model reverse rates. We further derive conversions from clean-token predictions to concrete-score, posterior-mean, and exit-rate/jump parameterizations, yielding a shared \(x_0\) interface that supports switching between mask and uniform kernels. Building on these connections, we propose \ours{}, a simple continual pre-training approach for directly adapting pretrained GPT2 checkpoints to uniform-noise diffusion. Through systematic evaluation of 124M- and 355M-parameter models, we show that \ours{} steadily improves the trade-off between generative perplexity (GenPPL) and unigram entropy as the sampling budget increases from 16 to 256 steps. At 256 steps, \ours{}-S and \ours{}-M achieve GenPPL/entropy pairs of \(97.783/5.2626\) and \(71.516/5.6669\), respectively; no evaluated model at the same scale simultaneously outperforms \ours{} on both metrics. At both scales, \ours{} also achieves the highest WinoGrande, SIQA, and BBH accuracy among the compared diffusion models.

The vast chemical design space and complex, interdependent design variables make catalyst discovery for targeted properties highly labor- and resource-intensive. Although generative models have emerged as a promising solution, existing approaches are generally limited to single-property conditioning or narrow chemical spaces. Here, we present Catalyst Diffusion Transformer (CatDiT), a unified framework for inverse catalyst design that generates valid and novel structures ranging from intermetallic alloys to oxide surfaces. By learning compressed latent representations, CatDiT enables efficient training and rapid sampling while supporting simultaneous conditioning on adsorbate type, binding energy, and catalyst class. The model provides reliable control of discrete properties and directional control of continuous properties, enriching candidate pools for reaction-specific catalyst discovery. As a representative application, multi-conditional generation for the nitrogen reduction reaction (NRR) yields 28 density functional theory (DFT)-relaxed alloy candidates that satisfy the target activity window and lie above the pure-metal *N-*H scaling line, corresponding to a ~1.5-fold enrichment over the source distribution. These results establish CatDiT as a practical and scalable approach for property-directed catalyst inverse design and targeted catalyst generation.

Generative models of temporal graphs are trained on one stretch of an evolving network and deployed on the next, and they degrade badly in the gap. We show this degradation is derivable, general, and not fixable from observations. The masked flow-matching loss decomposes exactly, with no independence assumption, into an irreducible entropy plus a divergence whose derivative along the training path is positive precisely for structures rare during training and common at deployment, diverging as their training probability goes to zero. Empirically the trade-off is a power law with exponent $-0.605$ ($R^2=0.9977$), and drift raises the sampler's error floor without changing how many steps reach it: across seven well-powered conditions the drift-period marginal error varies by at most $6%$ over a $50\times$ range of sampling budgets, while the floor sits $2.2\times$ to $34.3\times$ above the in-period floor. Because the deployment period is observed, correction looks like a matter of measurement. It is not. We prove that any corrector measurable with respect to past observations leaves at least the conditional variance of the statistic it tracks, and that trend extrapolation beats trusting the last observation only when $μ^2>v(1-2ρ)$. Both premises are measurable and both go the wrong way: the drift is trendless and mean-reverting, with a one-step innovation as large as the drift itself. An oracle removes $60%$ of the error, the best observation-based corrector recovers $5.7%$ of that, and extrapolation is strictly worse than doing nothing clever.

Few-step distilled diffusion models generate high-quality images quickly, but often lose per-prompt diversity, producing near-identical samples across random seeds. Optimizing the initial noise at inference time offers an appealing way to recover this diversity, yet existing methods directly update the initial noise in an unconstrained Euclidean space, ignoring both the geometry of the Gaussian prior and the model's sensitivity to noise frequencies. They therefore introduce auxiliary quality-control objectives to maintain generation fidelity, adding compute and weighting hyperparameters while still requiring conservative updates to prevent degradation. In this work, we propose MoNO, a training-free method that performs Manifold-constrained Noise Optimization on a low-dimensional, quality-stabilizing noise manifold. MoNO sequentially optimizes each new initial noise so that its predicted visual feature complements previous generations, while Riemannian updates on an affine low-frequency sphere preserve prior likelihood and fix unstable high-frequency components by construction. This enables large geodesic steps, removes the need for auxiliary quality-control objectives, and converges in far fewer iterations than prior noise-optimization methods. Experiments with multiple distilled text-to-image diffusion models show that MoNO consistently improves per-prompt diversity while maintaining image quality.

Feed-forward 3D Gaussian Splatting (3DGS) enables scalable scene reconstruction without per-scene optimization, yet produces dense Gaussians that are costly to store and transmit. Existing feed-forward Gaussian compression methods formulate decoding as deterministic representation recovery, which becomes inadequate at low bitrates when high-frequency textures and view-dependent appearance are discarded. Although generative models offer a promising alternative, using them as standalone post-processing decouples generation from the transmitted scene structure, thereby compromising cross-view consistency. To address these limitations, we propose GenSplatCodec, a unified feed-forward Gaussian codec that reformulates low-bitrate Gaussian compression as geometry-guided generative decoding. We present a detail-aware feed-forward Gaussian coding scheme within a dual-stream formulation, where the resulting compact Gaussian structural stream is complemented by a lightweight reference appearance stream. We further introduce a geometry-guided one-step generative decoding approach that jointly exploits decoded structural and appearance cues through hierarchical geometry control to reconstruct high-fidelity and view-consistent novel views. Finally, we develop a three-stage optimization strategy that stabilizes the learning of the unified codec and adapts the generative decoder to codec-derived structural and appearance cues. Extensive experiments across multiple datasets demonstrate that GenSplatCodec consistently achieves superior rate-distortion (RD) performance over existing methods.

Modern large language models scale successfully by pairing capacity growth with efficiency, keeping per-token and deployment costs under control as capacity grows. AIGC Foundation Models (AFMs), especially diffusion-transformer backbones, have begun to adopt sparse experts, but recent efforts mostly enlarge total parameter counts and sparsity ratios without importing the efficiency mechanisms that made LLM scaling practical, so generation quality is seldom balanced against training and deployment cost. This raises a natural question: can the architectural principles behind efficient LLM scaling be adapted to AFMs in a more balanced way? We introduce ModernMOE (MMOE), a modernization of SiT-style diffusion transformers that systematically adapts routed experts, shared and lightweight experts, gate-residual routing, and attention-residual information reuse to AIGC generation. Rather than treating MoE as a single plug-in replacement, MMOE studies how different modern expert components affect convergence, efficiency, and generation quality when composed inside a diffusion transformer. Every experiment in this paper is trained on a single eight-GPU H100 node with batch size 256 for 400k steps, an accessible single-machine budget. Under matched training and sampling protocols and at this budget, MMOE reaches lower FID at every recorded checkpoint, that is, it converges faster per training step, than dense and intermediate sparse-expert baselines, and among the sparse variants it attains the best quality-cost balance. Routing analysis further shows stable expert specialization across depth, substantial use of lightweight routes, and modest step-to-step routing changes during denoising. These results suggest that AFMs can follow the balanced scaling path of LLMs by importing proven efficiency designs, rather than by simply increasing total parameters and sparsity ratios.

We study empirical risk minimization for learning non-linear dynamical systems whose transition dynamics may switch over time. Under stability assumptions, and i.i.d switching over a set of $K$ modes, we derive non-asymptotic bounds on the prediction risk expressed in terms of the metric entropy of the underlying function class. We instantiate our general result for Hölder and linear function classes, obtaining explicit convergence rates that depend on the effective sample size $Tp_i$, where $T$ is the trajectory length and $p_i$ is the probability of observing mode $i$. Numerical simulations support our theoretical findings. To the best of our knowledge, these results are the first non-asymptotic guarantees for learning switched nonlinear dynamical systems from a single trajectory.

Ad creative optimization is increasingly constrained by evaluation rather than generation. Generative models can produce many plausible creatives, but reliable evaluation requires online experiments, in which only a limited slate can be tested. We study how to use data from historical A/B tests to generate and select the candidates in that slate. We developed and deployed a performance-driven offline-to-online workflow that guides creative generation with a predictive model as an inference-time critic. In the offline phase, we use a predictive model trained on historical experiments to rank and refine variants created by a generative model. A final test slate is then deployed in an online adaptive experiment. In a 50-arm field experiment, we found that the best creative generated with this method yielded 45.1% higher engagement than the best human-authored creative. Two additional experiments showed the same upper-tail pattern, with lifts of 46.7% and 36.2%. We found that despite the predictive model being too noisy to directly identify the best creative offline, it effectively guides the generative model toward creating strong candidates that can be efficiently evaluated in an adaptive experiment. The results suggest a design principle for creative optimization with generative models: use predictive models to guide generation of a slate to test, judge the slate by whether it contains high-performing candidates at a feasible test size, and use adaptive experiments to select among candidates while limiting traffic lost to weak arms.

Conventional recommenders capture users' preferences by optimizing observed user-item relations, whereas continuous generative recommendation additionally learns the trajectory of synthesizing a target item. Flow matching drives this process by gradually shaping initial noise into a definitive next-item representation through intermediate states in a continuous embedding space. However, item catalogs are discrete and sparsely supported, meaning even a straight Euclidean path can cross continuous regions that contain little evidence of valid item semantics. Formalizing this failure as the Euclidean void, we propose MIRAGE, a Manifold-Informed Rectification framework for Accelerated Generation of Embeddings in sequential recommendation, which rectifies the learned embedding geometry around an unchanged straight probability path. By leveraging an item co-occurrence graph as a proxy for the underlying semantic manifold, MIRAGE aligns interpolated path states with local anchors, reorganizing the embedding space to ground the trajectory in valid item support. MIRAGE retains the original probability path and uses the graph only during training, thereby enabling accurate and efficient one-step inference. Extensive experiments on four real-world datasets reveal that MIRAGE consistently outperforms state-of-the-art baselines, effectively boosting performance on sparsely observed targets while achieving robust overall accuracy. Our code will be made publicly available upon publication.

Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm. We develop contact Hamiltonian systems as a setting where the transfer can be made precise. A contact Hamiltonian $H$ on $J^1(\mathbb{R}^n)$ obeys the intrinsic decay identity $\dot H = -H\,\partial_s H$, so an augmented energy $\mathcal{E}$ built from $H$, together with the conformal rate $\partial_s H$, is a continuous-time rate certificate whenever $\mathcal{E}$ controls the objective gap. Our main theorem states, under three named and independently checkable hypotheses, that an order-$r$ contact splitting with step $h$ transfers this certificate over the finite horizon set by backward error analysis. The discrete decay envelope is governed by the modified conformal factor up to $O(h^r)$ perturbations plus a backward-error shadowing defect, and the mechanism is inherited exactly because the modified Hamiltonian is itself a contact Hamiltonian. Quadratic heavy ball is a fully solvable example: its projected dissipative-leapfrog spectrum agrees with established conformal-symplectic optimization theory, while the augmented contact Hamiltonian yields a sharp objective-to-certificate comparison that verifies the transfer hypotheses. For strongly convex objectives with state-dependent damping, an explicit Bregman-type Lyapunov certificate instead transfers by an auxiliary-shadowing corollary. The decomposition $H=K+V+D$ into kinetic, objective-encoding potential, and dissipation terms serves as a design template, with a catalogue of closed-form sub-flows including contact-specific damping families. Numerical experiments confirm the predicted conformal-factor tracking orders and show competitive performance on ill-conditioned benchmarks and deep-learning tasks.

High-resolution image and video diffusion models, including SD3, FLUX, and recent video diffusion transformers, have substantially improved generative quality but remain expensive at inference time because they repeatedly evaluate attention-heavy denoisers over many sampling steps. We address this inefficiency by exploiting redundancy in intermediate diffusion features rather than changing model weights or retraining. We identify four complementary redundancy sources in image and video generation: intra-frame, inter-frame, motion, and denoising-step redundancy. Based on this analysis, we propose OmniCache, a unified hierarchical caching framework that performs multidimensional feature reuse through Token Cache, Frame Cache, Block Cache, and Layered Cache. Unlike token-merging baselines that average matched features, OmniCache uses similarity matching to select cacheable features, skips redundant computation, and restores positionally consistent cached activations, preserving feature order and spatial-temporal structure. The resulting framework reuses spatial features in temporal layers and temporal features in spatial layers, while Layered Cache captures cross-step redundancy at the model-layer level. Across SD3, SVD-XT, and Latte, OmniCache reduces inference latency by up to 35%, 25%, and 28%, respectively, while maintaining visual fidelity and motion coherence in a training-free setting.

Mixed continuous--categorical data pose a representation problem for continuous generative models. Flow Matching and Gaussian diffusion operate in Euclidean spaces, whereas categorical laws lie on probability simplices and may be highly imbalanced. We study a logit-coordinate framework that encodes categorical variables as smoothed natural parameters and combines them with transformed numerical variables. This yields common formulations of Logit Flow Matching and Logit Diffusion. We introduce a mixed-distribution discrepancy separating categorical marginal error from conditional continuous Wasserstein error, and derive stability bounds and imbalance-aware nonparametric rates linking vector-field or drift error to decoded mixed-distribution error. Controlled simulations show that scaled-logit coordinates improve or match one-hot coordinates, especially under severe rare-cell imbalance. Across four real-data benchmarks and ten splits per dataset, Logit FM improves the primary distributional metrics on three datasets and is comparable on Churn2; Block-Conditional Logit FM consistently improves the flat model; and Logit Diffusion generally improves over or matches One-Hot Diffusion.

AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations. Learning a direct mapping from load conditions to OPF solutions can accelerate this computation, yet with deepening renewable penetration, a single optimal dispatch is no longer sufficient. Operators require a characterization of the distribution of feasible near-optimal solutions for risk quantification, sensitivity analysis, and multi-objective trade-off assessment. Supervised neural networks provide fast point predictions but cannot capture this conditional distribution. Diffusion-based generative models can sample diverse solutions in principle, yet existing methods operating in the raw state space exhibit degraded solution quality and fail to scale beyond medium-sized systems. We identify the root cause as the conflation of two distinct tasks within a single model. Compressing the high-dimensional OPF solution manifold is one task, and learning the conditional mapping from loads to that manifold is another. This paper presents FMOPF, a framework that resolves this conflation by decoupling compression from generation through latent flow matching and by explicitly modeling load-state coupling through a Constraint-Aware Interaction Prior Network. Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts, achieves the lowest tail risk among generative methods, and is the first such method to scale to systems with several hundred buses while preserving full feasibility. Ablation studies confirm that the latent generation pipeline is a necessary condition for physical feasibility and that the interaction prior functions as a late-stage tail-risk controller.

Given a strongly convex function $u$, equip $R^d$ with a Riemannian metric given by the Hessian $\nabla^2 u$. This is a so-called Hessian manifold. Given a probability density $μ$ one may run a Langevin diffusion intrinsic to the manifold with stationary distribution $μ$. Such (Hessian) manifold-valued Langevin diffusions are called Mirror Langevin diffusions (MLD) which have recently become popular. One of the questions we explore is whether, given $μ$, one can choose $u$ to get an exponential convergence to equilibrium for the MLD, especially if $μ$ is not strongly log-concave. Our results are based on Lyapunov function methods and give sufficient conditions for a Poincaré or a log-Sobolev inequality to hold for the MLD. These, in turn, imply exponential convergence. We also introduce a Markov chain approximation to the MLD given by a two step Gibbs sampler with stationary distribution $μ$. This Markov chain is a variant of the Sinkhorn Markov chain introduced in arXiv:2307.16421 that is conjectured to converge to a time-inhomogeneous generalization of the MLD. Under suitable assumptions, we prove that the Markov chain has a guaranteed convergence rate in $χ^2$ that is consistent with the diffusion time scale. Our proofs are based on ideas from entropic optimal transport and strong data processing inequalities.

Explainable AI (XAI) in creative practice can be less about technocentric explanation and more about enabling artists to inspect modify and debug models as part of making Yet largescale texttoimage diffusion systems are typically presented as opaque endtoend tools limiting this kind of material engagement We argue that even large models can function as creative materials when their internal structure is made visible and manipulable To support this we propose a handson approach to explainability centred on experimentation and intervention We instantiate this approach with a model bending and an interactive (inspection) interface integrated into ComfyUIs nodebased workflow including interactive layer selection and intervention controls Through qualitative and quantitative analysis of bending interventions in Stable Diffusion 15 we show how manipulating specific components of a diffusion pipeline produces relatively consistent families of visual effects allowing artists to build practical layerlevel intuition about how different parts of the model shape generated images

Molecular glue degraders have emerged as a promising strategy for targeted protein degradation by inducing ternary complex formation between an E3 ubiquitin ligase and a target protein. Despite their therapeutic potential, computational design of molecular glues remains largely unexplored. Unlike conventional structure-based drug design, molecular glue design is governed by the unknown protein-protein interface and requires the simultaneous modeling of ligand generation, protein-protein docking, and ternary complex assembly. In this work, we formulate molecular glue design as a ternary complex generation problem and propose a biology-inspired generative framework, TriGlue. Motivated by the mechanism of molecular glue action, we decompose ternary complex generation into two coupled stages: interface estimation and interface-conditioned complex generation. First, we develop an SE(3)-equivariant interface estimation module that predicts a geometrically constrained protein-protein interface from unbound monomer structures. Second, we introduce an interface-conditioned ternary flow matching network that jointly generates the molecular glue and predicts the rigid-body transformation required to assemble the ternary complex. Extensive experiments demonstrate that TriGlue generates chemically valid molecules and produces plausible ternary complexes, which highlight the potential of biology-inspired generative modeling for accelerating molecular glue discovery. Our code is available at https://anonymous.4open.science/r/molecular-glue-design-806B.

For decades, the bootstrap has been a default tool for statistical inference because of its broad applicability and minimal analytic requirements. Although its validity is well understood for smooth parametric estimators, its theoretical properties for many modern semiparametric and machine-learning estimators remain largely unstudied. Nevertheless, bootstrap procedures are often used routinely in such settings, even when their validity is unknown and their computational cost is substantial. We develop the $V$-fold jackknife as a computationally efficient and theoretically justified alternative for semiparametric inference. It requires only $V$ leave-fold-out refits and uses the empirical dispersion of jackknife pseudo-values to quantify uncertainty, without deriving or evaluating an influence function. For regular asymptotically linear estimators of pathwise differentiable parameters, we show that, for fixed $V$, the Studentized $V$-fold jackknife statistic converges to a $t$-distribution with $V-1$ degrees of freedom, giving valid confidence intervals even though the jackknife variance estimator does not converge in probability. When $V\to\infty$, we establish consistency of the variance estimator at rate $V^{-1/2}$, allowing $V$ to diverge slowly, for example at rate $\log n$. We also develop simultaneous confidence bands based on the correct componentwise-Studentized limiting distribution. Finally, we extend the theory to generalized asymptotically linear estimators with diverging influence-function variance and slower-than-$\sqrt n$ convergence; scale invariance of Studentization eliminates the need to know the effective convergence rate. Simulations on the average treatment effect, Kaplan--Meier survival curve, and highly adaptive lasso dose-response curves confirm reliable inference, including where influence-function-based standard errors are anti-conservative or unstable.

Diffusion models typically suffer from error accumulation during iterative sampling, commonly referred to as exposure bias. We reveal systematic frequency-dependent discrepancies between training and inference, which can be interpreted as frequency-dependent SNR error. Crucially, the direction of this mismatch varies across models and timesteps, indicating that fixed correction rules do not generalize. We propose Spectral Alignment (SPA), a lightweight, guidance-based method that calibrates the power spectrum of intermediate predictions to a pre-computed prior. Our approach consists of two stages: (1) offline fitting of a parametric spectrum model from training data, and (2) inference-time guidance via efficient FFT-based gradient computation. SPA introduces minimal computational overhead (3-4%) and is complementary to Classifier-Free Guidance (CFG). We demonstrate consistent improvements across diverse architectures, from pixel-space models (DDPM, ADM) to latent diffusion models (SD2.0, SDXL) and flow-matching models (SD3.5, FLUX). Our implementation is available at https://github.com/SonyResearch/SPA.

Zermelo's algorithm is a classical method for computing the maximum likelihood estimator in the Bradley--Terry (BT) model, but its convergence can be slow in practice. To accelerate computation, Newman introduced a family of Zermelo-type fixed-point iterations parameterized by $α$, with Zermelo's algorithm recovered at $α=1$. Empirical evidence suggests that the choice $α=0$ often converges substantially faster, making it a promising alternative, yet the mechanism underlying this acceleration remains elusive. This paper provides theoretical insight into this phenomenon through a systematic local convergence analysis. We derive closed-form expressions for local convergence factors under synchronous and asynchronous updates and analyze their dependence on $α$ via spectral analysis of the associated Jacobian matrices. For synchronous updates, we show that the algorithm may fail to converge when $α<1$, and its local convergence factor is quasi-convex in $α$ under the population BT model. In contrast, asynchronous updates are always locally convergent, and their local convergence factor is provably monotonically increasing in $α$ under the population BT model of consistently ordered bipartite comparison graphs, establishing the optimality of $α=0$ in this setting. We further establish asymptotic approximation results for the population convergence factors under the BT model, justifying their practical relevance. Numerical experiments on synthetic and real-world datasets confirm the theory. Our analysis complements existing convergence results and shows that the acceleration of $α=0$ arises not only from the parameter choice but, more importantly, from the use of asynchronous updates.

Score-based diffusion models have achieved remarkable empirical success in generative modeling, yet their approximation-theoretic foundations remain incomplete. In particular, although classical universal approximation theorems guarantee that neural networks can approximate score functions, it remains unclear whether such approximation guarantees translate into approximation of the probability distributions generated by reverse diffusion processes. In this paper, we establish a rigorous quantitative connection between these two notions. Specifically, we prove that if a neural network approximates the true score function sufficiently accurately, then the probability distribution generated by the corresponding reverse diffusion model is close to the target data distribution in Kullback-Leibler (KL) divergence, up to an irreducible mismatch between the terminal distribution of the forward diffusion process and the prior used to initialize the reverse process. More precisely, we derive an explicit upper bound on the distribution approximation error in terms of the score approximation error, the diffusion noise schedule, and the terminal prior mismatch. Our analysis combines Hornik's universal approximation theorem, Girsanov's theorem on path space, and the data processing inequality for relative entropy. Complementary to recent work that studies score approximation under finite-sample statistical settings and structural assumptions on the data distribution, our work develops an approximation-theoretic analysis based on classical neural network approximation theory. The resulting theorem provides a simple and explicit guarantee linking neural network approximation of score functions to approximation of the probability distributions generated by reverse diffusion models.

We study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. We demonstrate that natural invariant measures - a fundamental concept from ergodic theory - provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, we prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, we show that this framework extends beyond simple strategy frequencies to general observables, enabling the precise calculation of long-term time averages for broad classes of economic metrics - including payoffs, social cost, and regret - despite chaos. Our results reveal that this simple learning algorithm captures the full spectrum of behaviors found in one-dimensional dynamical systems, from unique or multiple absolutely continuous invariant measures to complex periodic attractors as well as coexisting chaotic and stable (periodic) behaviors. By bridging game theory and dynamical systems, we show that statistical predictability is attainable even in the absence of pointwise convergence.

Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data. This makes data preparation and model training expensive. We propose Graph Wavelet Compressed Sensing (GWCS), a learning-based framework for offline compression of graph signals by representing them as sparse, interpretable wavelet-domain representations using the spectral graph wavelet transform. The framework combines a nonparametric multilevel importance sampler, which retains high-energy wavelet coefficients within each scale for a given compression ratio, with a scale-aware graph neural network that reconstructs the signal from the sparse coefficients. We evaluate the proposed framework on synthetic approximately band-limited graph signals over random graphs and four PDE simulation datasets over meshes, which include Turbulent Radiative Layer, Viscoelastic Instability, Kolmogorov Flow, and Dynamic Stall. We compare against graph signal sampling methods and graph autoencoder baselines. Results demonstrate that the framework achieves high reconstruction fidelity and substantial data compression compared to existing benchmarks.

Fine-tuning Vision Transformers (ViTs) with low-rank adapters (LoRA) promises better communication efficiency under federated setup, yet existing aggregation strategies face fundamental limitations. Independently averaging these LoRA factors is mathematically inconsistent, introducing cross-term aggregation error. In contrast, approaches that preserve heterogeneous client ranks by concatenating local adapters on the server substantially increase download cost and often require merging global LoRA updates into pretrained weights on the clients, causing reinitialization lag and unstable convergence. Other approaches further increase server-side overhead by reconstructing dense weight updates or training auxiliary models to refine aggregation error. In this work, we propose SpecTraL, spectral transformation for layer-wise global rank discovery, that resolves these challenges within a unified design. SpecTraL stacks local LoRA modules from clients and performs orthonormal Householder Transformation of the stacked adapters directly in the low-rank latent space, eliminating dense reconstruction of the global update and any auxiliary refinement on the server. By leveraging the Spiked Covariance Model from Random Matrix Theory, SpecTraL analytically separates the global consensus signal from non-IID noise, discovering optimal layer-wise global ranks without manual hyperparameter tuning. To match local ranks in subsequent rounds, we introduce a padding-aware initialization framework that lets clients incorporate residual LoRA dimensions without re-merging them into the pre-trained base model. Experiments on federated fine-tuning of ViT-B/16 and ViT-L/16 over DomainNet and NICO++ demonstrate improved accuracy-communication trade-offs, reduced server computation, and elimination of hyperparameter search for rank selection. Our code is available at https://github.com/DASS-Lab-Group/SpecTraL

Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. Here, we introduce Expanding Generative Flows (EFlows), which define flows between distributions of increasing dimensionality along an expanding interpolant that grows the state by augmenting it with conditional noise. Building on this construction, we propose Expanding Flow Maps (EFMs), a new class of flow maps that distill the expanding interpolant into efficient few-step generative models. Each EFM factors the map between any two timesteps into two learnable operations: an expand operator, which augments the state space with new coordinates or tokens conditioned on the current state, and a transport map, which pushes the expanded state forward along the interpolant. Composing these operators yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as the special case in which the expand operator is the identity. We further extend the framework to the discrete simplex, enabling variable-size graph generation and variable-length sequence generation. Across both continuous and discrete modalities, we establish EFlows and EFMs as a principled framework for settings in which output size is itself a learned, controllable degree of freedom.

Fine-tuning large diffusion models for new domains or styles involves a trade-off: improving target-specific generation often degrades the pretrained model's broad generative capability. Existing full and parameter-efficient fine-tuning methods typically handle this trade-off only implicitly. In this work, we propose a novel source-prior-driven selective adaptation method to efficiently fine-tune diffusion models, achieving a favorable trade-off. Our method relies on two key observations: (1) the loss of general generative capability is highly inconsistent across pretrained parameters, and (2) parameters that have a relatively small impact on the model's general generative capability remain structurally inconsistent across layers and parameter types. Motivated by these observations, we first learn a static mask to explicitly identify parameters better suited for downstream adaptation, and then construct structured update strategies for the selected subset. Experiments show that our method achieves a better adaptation-retention trade-off than existing strong baselines.

The modeling of hydrometeorological time series with limited observations is a key challenge in the monitoring of hydro-systems and water resources, as well as for flood or drought risk assessment. Due to the high variability of the underlying processes and the sparsity of available measurements, traditional statistical approaches often struggle to accurately represent their dynamics. In this context, recent advances in deep learning offer a promising direction for improving the representation and generation of complex temporal processes sampled at several observation sites. This study investigates the application of transformer-based diffusion models to the simulation and reconstruction of hydrological time series. The proposed framework is applied to the joint modeling of water quantity and quality at six sites spread across three adjacent headwater catchments located in North-East France on a limestone plateau covered by forests and field crops. The model is calibrated and validated using available observational data, which has been quality controlled and corrected for sensor drift and malfunction through collaborative efforts by LNE metrology expertise and Andra monthly quality control over more than 15 years. Its performance is compared with several established baseline approaches commonly used for time series modeling. Quantitative evaluation metrics are employed to assess the ability of the proposed method to reproduce key temporal characteristics of the observed signals in two settings: the imputation of incomplete time series and the forecasting of upcoming hydrological conditions. Results support the effectiveness of the transformer-based approach and highlight its capacity to capture and simulate the complex patterns present in hydrological data. In particular, the results indicate that diffusion models can efficiently sample realistic time series distributions under observation settings with variable missing data for both forecasting and imputation.

Generative models can support decision-making under uncertainty by producing ensembles of plausible future system trajectories, but statistical plausibility does not ensure structural feasibility. This study investigates whether post-sampling symbolic constraints can improve the reliability of generative trajectory modeling in dynamic graph-structured systems. A conditional diffusion model generates future graph-state trajectories from partial observations, while an external symbolic layer applies hard filtering, soft weighting, or projection-based repair. The framework is evaluated on two controlled synthetic regimes: a compact graph and a medium-complexity dependency graph, using metrics for structural validity, sample efficiency, diversity, robustness, and calibration. In the compact regime, the model produces an invalid probability mass of 0.002996, indicating an almost entirely admissible trajectory manifold. Under the same architecture and training protocol, invalid mass increases to 0.155929 in the medium-complexity regime. Hard filtering removes all invalid retained trajectories while preserving 84.4% of generated samples, whereas soft weighting preserves effective sample size but yields only limited validity gains. Family-level analysis shows that dependency constraints account for nearly all observed inadmissibility. These results indicate that statistical plausibility and structural admissibility are distinct reliability properties and that symbolic constraint handling becomes more valuable as graph-structural complexity increases.

Radio map (RM) estimation aims to reconstruct the spatial distribution of wireless signal characteristics, such as received signal strength (RSS), from sparse measurements, a task that is critical for spectrum management, interference mitigation, and localization in modern wireless networks. Traditional approaches, including interpolation and deep learning, either struggle to capture complex propagation effects or require large-scale retraining for each new sampling pattern, which limits their generalization. More recently, prior-based methods have combined pre-trained generative models with measurements to reduce the need for deployment-time model fine-tuning, but they typically treat the prior as a simple regularizer and lack explicit transmitter-aware integration. In this paper, we propose RadioTrace, a novel RM estimation framework without deployment-time fine-tuning that tightly integrates sparse RSS measurements with a frozen pre-trained diffusion prior. RadioTrace incorporates transmitter (Tx) location estimation directly into the denoising loop, iteratively refining Tx coordinates based on reconstruction quality to guide the generative process. To further enhance robustness, we introduce a propagation-guided K-means initialization that mitigates poor local minima in the Tx update and provides a geometry-consistent starting point. Moreover, we provide a stochastic stability analysis for the Tx-coordinate refinement component, showing that the Tx update remains stable under perturbations induced by diffusion sampling and Tx-map relaxation. Extensive experiments demonstrate that RadioTrace achieves competitive performance with state-of-the-art learning-based methods under random sampling, and maintains strong reconstruction quality under restricted-area sampling, highlighting its adaptability, robustness, and practical relevance.

Score Entropy Discrete Diffusion (SEDD) parameterizes discrete reverse processes with unconstrained positive score ratios. While positivity guarantees nonnegative reverse jump rates, it does not ensure Bayes realizability: ratios at a noisy state need not be jointly induced by any clean-token posterior under the forward kernel. The score-entropy loss has the correct population optimum but does not enforce this constraint away from it. In a trained pure-uniform SEDD checkpoint, roughly one quarter of complete score vectors violate the coordinate box, while more than half lie inside it yet remain materially incompatible with any valid posterior. Such violations can produce negative pre-normalization weights in finite-step sampling. Projecting raw scores onto the bridge polytope removes all observed negative weights and improves external generative PPL from $203.6$ to $175.1$ without changing the sampler. We introduce mean-to-score (M2S), which predicts a clean-token posterior mean and converts it to the score through an exact kernel-dependent linear map. The construction applies to any known coordinate-wise continuous-time Markov chain (CTMC) satisfying a mild support condition. For uniform corruption, it maps the probability simplex onto the bridge polytope; for absorbing-mask corruption, the resulting objective recovers MD4 exactly. In a controlled 28.4M-parameter CIFAR-10 comparison, M2S lowers test BPD from $3.173$ to $3.129$ and FID-50k from $\CifarSEDDFID$ to $\CifarMtwoSFID$. A 170M-parameter M2S model trained on about 262B OpenWebText token slots outperforms the evaluated pure-uniform SEDD, GIDD, and Neural CTMC checkpoints at every tested sampling budget, reaching generative PPL $143.3$ at 128 steps versus $183.6$ for the strongest pure-uniform baseline.