arXiv:2607.01819v2 Announce Type: replace-cross Abstract: The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Data-driven techniques, like extended dynamic mode decomposition (EDMD), kernel EDMD, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.
arXiv:2606.25170v2 Announce Type: replace-cross Abstract: We introduce a PAC framework in which the learner can access sampling oracles both before and at decision time. Sample complexity is measured by a pair $(n,m)$, where $n$ is the learning budget spent before a query is known and $m$ is the additional sampling budget per query. We demonstrate its relevance in discounted Markov decision processes with exogenous i.i.d.\ contexts revealed before acting. Contexts may affect both rewards and transitions but remain uncontrolled by the agent. The learner can sample the unknown context distribution and the transition kernel. We study policy evaluation (PE), best-value estimation (BVE), and best-policy extraction (BPE). When rewards and transitions are known, a variance-reduced algorithm solves all three tasks with sample complexity $\bigl(\widetilde O((1-\gamma)^{-3}\varepsilon^{-2}),0\bigr)$, which is minimax optimal up to logarithmic factors. Let $\mathcal{X}$ be the controlled state space. When transitions are also unknown, we give a PE algorithm with complexity $\bigl(\widetilde O(|\mathcal X|(1-\gamma)^{-3}\varepsilon^{-2}), \widetilde O((1-\gamma)^{-2}\varepsilon^{-2})\bigr)$ and matching lower bounds at this budget pair. For BVE and BPE, we give an algorithm with a common offline budget $\widetilde O(|\mathcal X|^2|\mathcal A|(1-\gamma)^{-4}\varepsilon^{-2})$ and respective query costs $\widetilde O(|\mathcal A|(1-\gamma)^{-2}\varepsilon^{-2})$ and $\widetilde O(|\mathcal A|(1-\gamma)^{-3}\varepsilon^{-2})$. Importantly, all bounds are independent of the context-space cardinality.
arXiv:2605.09125v2 Announce Type: replace-cross Abstract: Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully defined, requiring new solutions to be generated at a high cadence across varying parameter values. When combined with the indirect approach to optimal control, diffusion models can accelerate this search by learning distributions that represent high-quality initial costates. However, generating training data remains expensive, and opportunities exist to better exploit past data. We propose a transfer-learning framework that combines homotopy in a mission parameter with Markov chain Monte Carlo (MCMC) to generate training data more efficiently. The approach reformulates a multiobjective optimization problem as sampling from an unnormalized target distribution in costate space. We compare three MCMC algorithms on a planar multi-revolution transfer in the circular restricted three-body problem, with homotopy in the system mass parameter. The results show that gradient-based MCMC variants achieve the best trade-off between sample quality and computational cost. For the test transfer, the proposed framework generates 40 % more feasible solutions and achieves a higher-quality Pareto front than a state-of-the-art indirect approach based on adjoint control transformations and gradient-based optimization. Finally, the MCMC-generated samples are used to fine-tune a diffusion model conditioned on the mass parameter, enabling it to learn a global representation of the underlying solution distribution and efficiently generate new solutions. These findings establish the transfer-learning framework as a practical method for efficiently solving indirect trajectory optimization problems with varying parameters.
arXiv:2604.04328v4 Announce Type: replace-cross Abstract: Soft Tournament Equilibrium (STE) is a differentiable layer for Top-Cycle (TC) and Uncovered-Set (UC) inference from reciprocal pair probabilities. Normalized log-sum-exp reachability and covering give smooth scores with approximation, perturbation, and margin-recovery bounds. We distinguish structural supervision, posterior uncertainty, and the final set decision through controlled synthetic studies and reconstruction of recorded ordinal profiles. Matched-epoch training improves F1 under a common structural readout, but a separate equal-budget soft-UC comparison does not demonstrate an advantage. A prospective equal-budget hard-UC study improves selective F1 at 24 alternatives from 0.6327/0.6292 for ordinary/relational native heads to 0.6676, while exact recovery remains only 1.16%. On 36 human profiles held out by source, a separate exploratory comparison favors Jeffreys posterior inference over learned independent-edge and mixture distributions in native expected-F1 decoding (0.8742 versus 0.8704/0.8366). Only three references are non-singleton selective cores. Completion certificates and full-depth TC diagnostics clarify additional identification, smoothing, and computational limits. The evidence supports conditional synthetic overlap gains, while preserving the soft-set null and the absence of a demonstrated learning advantage over strong count-based human-profile controls.
arXiv:2604.04246v2 Announce Type: replace-cross Abstract: This paper extends the Transmission Neural Network model proposed by Gao and Caines in [1]-[3] to incorporate inhibitory connections and neurotransmitter populations. The extended network model contains binary neuronal states, transmission dynamics, and inhibitory and excitatory connections. Under technical assumptions, we establish the characterization of the firing probabilities of neurons, and show that such a characterization considering inhibitions can be equivalently represented by a neural network where each neuron has a continuous state of dimension 2. Moreover, we incorporated neurotransmitter populations into the modeling and establish the limit network model when the number of neurotransmitters at all synaptic connections go to infinity. Finally, sufficient conditions for stability and contraction properties of the limit network model are established.
arXiv:2602.03762v5 Announce Type: replace-cross Abstract: Visually-guided acoustic highlighting seeks to rebalance audio in alignment with the accompanying video, creating a coherent audio-visual experience. While visual saliency and enhancement have been widely studied, acoustic highlighting remains underexplored, often leading to misalignment between visual and auditory focus. Existing approaches use discriminative models, which struggle with the inherent ambiguity in audio remixing, where no natural one-to-one mapping exists between poorly-balanced and well-balanced audio mixes. To address this limitation, we reframe this task as a generative problem and introduce a Conditional Flow Matching (CFM) framework. A key challenge in iterative flow-based generation is that early prediction errors -- in selecting the correct source to enhance -- compound over steps and push trajectories off-manifold. To address this, we introduce a rollout loss that penalizes drift at the final step, encouraging self-correcting trajectories and stabilizing long-range flow integration. We further propose a conditioning module that fuses audio and visual cues before vector field regression, enabling explicit cross-modal source selection. Extensive quantitative and qualitative evaluations show that our method consistently surpasses the previous state-of-the-art discriminative approach, establishing that visually-guided audio remixing is best addressed through generative modeling.
arXiv:2512.16545v3 Announce Type: replace-cross Abstract: Cu NPs have a broad applicability, yet their synthesis is sensitive to subtle changes in reaction parameters. This sensitivity, combined with the time- and resource-intensive nature of experimental optimization, poses a major challenge in achieving reproducible and size-controlled synthesis. While ML shows promise in materials research, its application is often limited by scarcity of large high-quality experimental data sets. This study explores ML to predict the DLS-derived hydrodynamic diameter of Cu NPs using a small data set of 25 syntheses. Latin Hypercube Sampling is used to efficiently cover the parameter space while creating the experimental data set. Ensemble regression models successfully predict hydrodynamic diameters with good predictive performance given the limited dataset. Since quantitative regression requires a unique DLS-derived hydrodynamic diameter, the regression model is restricted to mono-modal DLS distributions, while a complementary classification model identifies synthesis conditions for which quantitative prediction is applicable. Using equivalent out-of-sample validation, the ML and DoE models showed comparable generalization. The final ensemble model achieved an R2=0.74 compared to 0.60 for the DoE model, while retaining the complete synthesis parameter space, making it better suited for synthesis guidance. Additionally, classification models using both random forests and LLMs are evaluated to distinguish between large and small particles. These classification models exhibited only modest predictive performance, indicating that this small dataset is insufficient to fully exploit the capabilities of complex LLMs. Overall, this study demonstrates that carefully curated small data sets, paired with robust classical ML, can effectively support the synthesis of Cu NPs and highlights that for lab-scale studies, complex models like LLMs may offer limited benefits.
arXiv:2508.08833v4 Announce Type: replace-cross Abstract: Frontier large language models (LLMs) now reach near-ceiling accuracy on standard mathematical-reasoning benchmarks and gold-medal-level performance at the International Mathematical Olympiad. As these benchmarks saturate and their items leak into training data, a high score no longer shows whether a model reasons robustly or which component of its reasoning fails. To evaluate reasoning while keeping results informative and failures diagnosable, we propose GAP (Generalisation-and-Perturbation), a methodology that automatically generates mathematically equivalent variants of existing mathematics problems at scale using two disjoint, interpretable transformations: (1) surface renames, probing the binding between identifiers and latent variable roles, and (2) kernel rewrites, probing whether a high-level proof plan survives a change of mathematical setting. Compared with existing benchmarks, GAP has two key benefits: (1) novel, likely unseen variants mitigate data leakage, and (2) performance across transformation families enables failure diagnosis, each transformation testing a hypothesis about the cause of failure. We instantiate GAP on all 1,051 William Lowell Putnam Competition problems from 1938 to 2024, adding 5,255 unseen variants to form PutnamGAP, a 6,306-item competition-level mathematics corpus and the first public machine-readable dataset from the full Putnam archive. Using PutnamGAP, we evaluated 18 commercial and open-source models spanning sizes and providers. Accuracy drops across all models and variant families, most severely under kernel rewrites. This gap does not close with model strength, suggesting that even the strongest models' dominant weakness is transferring a proof plan to a changed mathematical setting, rather than handling surface changes. Further analysis provides finer failure diagnoses and potentially useful insights for improving LLM reasoning.
arXiv:2506.15971v2 公告类型:替换交叉版本 摘要:无监督域适应(UDA)能够有效弥合有标注源域与无标注目标域之间的域差异,但其前提是假设两个域具有相同的模态。异构域适应(HDA)则处理跨域的不同特征空间,但要求目标域样本带有标注,或存在连接源域与目标域的配对数据。当有标注源域和完全无标注目标域分别具有完全不同的模态(例如二维图像和三维点云)时,上述两种方法均不适用。为解决这一局限,我们提出了一种新的设置,称为异构模态无监督域适应(HMUDA)。该设置通过一个无标注桥接域跨模态迁移知识,其中包含来自两种模态的配对观测,且其分布可能偏离源域和目标域的分布。为在HMUDA设置下进行学习,我们提出了Latent Space Bridging(LSB),这是一种双分支框架:通过对桥接域配对样本施加特征一致性损失来缩小模态差异,并通过类别质心对齐损失来减小源域与目标域之间的差异。在涵盖二维到三维和三维到二维迁移的八种基准设置上进行的大量实验表明,LSB达到了最先进的性能。
arXiv:2505.24311v3 Announce Type: replace-cross Abstract: We study the large-sample variational problem for t-distributed stochastic neighbor embedding with a class of input and output kernels. The input law has compact support and a density continuous on that support. An entropy equation determines the scale parameter in the input kernel, and we prove that this parameter exists and is unique at interior points of positive density. We then give sufficient conditions for solutions to exist and be uniformly bounded on the entire support. Under these conditions and a decay assumption on the output kernel, the discrete optimal values converge to a continuum minimum. Empirical measures of approximate minimizers are tight after translation; every subsequential limit is a compactly supported minimizer satisfying the equilibrium equation. The admissible output kernels include Gaussian kernels and, in output dimension two, the Cauchy kernel. Numerical examples compare the two-dimensional representations obtained with different kernels.
arXiv:2504.12392v3 Announce Type: replace-cross Abstract: Archetypal analysis (AA) was originally proposed in 1994 by Adele Cutler and Leo Breiman as a computational procedure for extracting distinct aspects, so-called archetypes, from observations, with each observational record approximated as a mixture (i.e., convex combination) of these archetypes. AA thereby provides straightforward, interpretable, and explainable representations for feature extraction and dimensionality reduction, facilitating the understanding of the structure of high-dimensional data and enabling wide applications across the sciences. However, AA also faces challenges, particularly as the associated optimization problem is nonconvex. This is the first survey that provides researchers and data mining practitioners with an overview of the methodologies and opportunities that AA offers, surveying the many applications of AA across disparate fields of science, as well as best practices for modeling data with AA and its limitations. The survey concludes by explaining crucial future research directions concerning AA.
arXiv:2502.02679v3 Announce Type: replace-cross Abstract: Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of networks on approximation capabilities is compared with its influence on consistency in learning from samples of data. It is shown that, whereas finite VC dimension is desirable for uniform convergence of empirical errors, it may not be desirable for approximation of functions drawn from a probability distribution modeling the likelihood that they occur in a given type of application. Based on the concentration-of-measure properties of high dimensional geometry, it is proven that both errors in approximation and empirical errors behave almost deterministically for networks implementing sets of input-output functions with finite VC dimensions in processing large data sets. Practical limitations of the universal approximation property, the trade-offs between the accuracy of approximation and consistency in learning from data, and the influence of depth of networks with ReLU units on their accuracy and consistency are discussed.
arXiv:2501.09223v4 Announce Type: replace-cross Abstract: This is a book about large language models. As indicated by the title, it primarily focuses on foundational concepts rather than comprehensive coverage of all cutting-edge technologies. The book is structured into six main chapters, each exploring a key area: pre-training, generative models, prompting, alignment, inference, and reasoning. It is intended for college students, professionals, and practitioners in natural language processing and related fields, and can serve as a reference for anyone interested in large language models.
arXiv:2610.05196v2 Announce Type: replace Abstract: Risk regulation imposes directional constraints on scores; we adopt their strict per-input form -- the score monotone non-decreasing in every exposure input -- as a normative commitment. Deployed pipelines -- monotone hand-crafted aggregates feeding sign-constrained gradient boosting -- already satisfy it by composition, so constrained-versus-unconstrained comparisons price a guarantee the incumbent has for free. We instead hold admissibility fixed on both sides and measure what learning the aggregation is worth. Our instrument is a recurrent network whose state is classical risk statistics (an exponentially weighted moving average and a high-water mark with learned transforms), monotone by construction in every input and per MC-dropout sample. The central finding, by functional regression, is a subsumption boundary: a learned monotone channel reproduces the geometrically weighted separable family of hand-crafted statistics, one channel per member, to Spearman $\rho \ge 0.996$, approximates window statistics with measurable ceilings, and fails at consecutivity ($\rho = 0.924$) and time localization (0.628), both structural, and at the exposure floor (0.829), a learnability boundary. One explicit admissible basis repairs each failure (rank correlation 1.000). In or near the separable family, learned and engineered aggregation are substitutes, and the learned channel is never statistically behind at full sample size and specified capacity. Its advantages are incumbent-specific: a committed grid pays up to 0.019 AUC in decay regions it leaves uncovered (the learned channel stays within 0.004 of the strongest engineered consumer at every swept point); the highest-dimensional comparator degrades fastest with scarce data; and beyond the training support, grid-fed tree-ensemble scores go flat while a strictly increasing head keeps ranking. No single incumbent is dominated on all three axes.
arXiv:2610.04988v2 Announce Type: replace Abstract: Latent world models plan by rolling a frozen predictor forward under candidate action sequences and ranking the candidates by the latent distance between their imagined end state and the goal. However, this ranking breaks down when the goal lies several plans away, because the latent distance measures how closely an end state resembles the goal rather than how far it remains from reaching it. To address this, we propose TEMPO, a temporal-distance planning objective that leaves the world model untouched, learns only from the recorded trajectories already used to train it, and adds negligible cost to the planner's search. TEMPO learns a small map of the frozen latent in which the distance between two states of an episode reflects the number of environment steps between them, and blends this distance into the planner's cost. It requires no rewards, policies or success labels and, being a cost rather than a model, applies to frozen world models with one latent vector per state that plan by a latent distance. We evaluate TEMPO on eleven simulated environments (e.g., maze navigation, tabletop pushing, robotic arm control and three-dimensional manipulation) with the LeWM and PLDM planners. With a small MLP that adds at most 0.3% to a plan's arithmetic, TEMPO improves both planners at every goal distance, including the one-plan setting of their evaluations, raises LeWM from 36% to 99% on TwoRoom three plans from the goal, and remains competitive on a broad range of 2D and 3D navigation, reaching and manipulation tasks.
arXiv:2609.33563v2 Announce Type: replace Abstract: World models improve sample efficiency by training policies on imagined trajectories, but their usefulness depends on learning representations that capture the information needed for future control. We study whether self-supervised joint-embedding prediction (JEPA) can provide this learning signal for multi-agent reinforcement learning. We introduce MA-JEPA, a stochastic world model that replaces observation reconstruction with prediction of target representations, enabling model-based multi-agent reinforcement learning with centralized training and decentralized execution. A categorical latent state and a causal Transformer are trained with posterior and action-conditioned dynamics prediction objectives and are then used for actor-critic learning from latent imagination. A training-only joint predictor conditions on all agents' local states and actions to predict each agent's next local observation embedding. These predictions are passed through the same local posterior used during real interaction with a centralized critic that is used only for value learning, with execution remaining decentralized. Our experiments show that this architecture performs strongly on SMAC, matching or exceeding the strongest reported comparator mean win rate on four of eight evaluated maps.