arXiv:2609.38561v2 Announce Type: replace-cross Abstract: Zeroth-order optimization methods are essential for solving black-box problems where gradient information is unavailable or expensive to compute. This paper presents POEM-ES, a novel parameter-free stochastic zeroth-order algorithm that extends the recent POEM method by integrating subspace preconditioning with ellipsoidal randomized sampling. In contrast to traditional zeroth-order approaches that rely on isotropic random directions, POEM-ES performs anisotropic sampling guided by a fixed structural symmetric positive semi-definite (SPSD) preconditioner $\hat{\Sigma}$ that encodes the underlying low-dimensional geometry. Under a standard structural spectral normalization where $\lambda_{\max}(\hat{\Sigma}) = 1$, we introduce the use of the empirical effective dimension $d^* = \operatorname{tr}(\hat{\Sigma})$, which reflects the intrinsic dimensionality of the problem and guides both the sampling and randomized smoothing parameter schedules. In practice, such a preconditioner can be effectively obtained via pilot sampling, historical trajectories, or domain-specific expert knowledge. We prove that POEM-ES achieves a dimension-reduced convergence rate under low-rank structural assumptions, requiring only $\tilde{\mathcal{O}}\left( \frac{\left( r^2 \kappa(\hat{\Sigma}) + d^* \right) L^2 D_{\mathcal{X}}^2}{\varepsilon^2} \right)$ stochastic zeroth-order oracle queries. The method remains fully parameter-free and demonstrates significant improvements over the original POEM in problems with low-rank structure where $d^* \ll d$. Numerical experiments on hinge-loss binary classification tasks using LibSVM datasets confirm the practical superiority of the proposed approach.
arXiv:2609.38472v2 Announce Type: replace-cross Abstract: Behavior cloning provides an offline route to autonomous-driving policy learning, but mean-squared-error regression is poorly matched to demonstrations in which one observation admits several valid actions. Diffusion policies can represent conditional multimodal action distributions, yet their closed-loop performance may be unstable when visual features and control are learned from limited data. This paper presents Diffusion-2BC, which combines a diffusion denoising objective with an auxiliary deterministic behavior-cloning loss over a shared visual encoder. The auxiliary branch is used only during training; inference remains diffusion-based. The proposed method is evaluated in the controlled Claw environment and in bird's-eye-view CARLA navigation, including route-conditioned driving, route-free navigation through multiple intersections, and cross-map evaluation from Town01 to Town02. In the Claw task, Diffusion-2BC reduced the mean mask-distance error by approximately 10% relative to a diffusion-based behavior-cloning baseline and by 85% relative to standard deterministic behavior cloning. In route-free CARLA, Diffusion-2BC traveled substantially farther before termination under the evaluation protocol than both baselines in Town01 and Town02. Additional qualitative rollouts revealed distinct route choices, showing the multimodal behavior of the proposed diffusion-based agent. The results indicate that an auxiliary regression signal can improve the closed-loop reliability of diffusion behavior cloning while preserving multimodal prediction in the controlled benchmark.
arXiv:2609.20821v2 Announce Type: replace-cross Abstract: Embedding spaces define notions of semantic similarity and distance. We study whether those embeddings reflect physical measurements of mass, distance, time and volume, which admit a unique, objective notion of semantic equivalence and distance. We find that physical measurement is only weakly modeled in the embedding space, and that instead quite peculiar measurement patterns can be observed. Further analysis indicates that embedding representations of physical measurements are strongly influenced by superficial string similarity, and recalibration of similarity does not substantially improve the alignment.
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:2603.25414v5 Announce Type: replace-cross Abstract: Concurrency, parallelism and distributed execution become truly fearless when the compiler tracks wait-for edges, proves multi-threaded work is sound and preserves distributed boundary contracts. In this design, our Composer compiler preserves proofs while lowering Clef directly to native CPU, GPU, NPU and FPGA code, without translation through C or vendor APIs. Our Program Semantic Graph retains the values, relationships and premises that justify BAREWire's unboxed boundary contracts. And C & C++ interfacing is an explicit marshaling boundary, with proofs tied to actual arguments, conversions and returned values. Four verification tiers connect an account of our design. Tier 1 supplies structural inference, founded on principal dimensional types. Tier 2 generates and checks local arithmetic, representation, and computational integrity at the node level. Tier 3 instantiates reusable domain and system lemmas, including distributed proofs supported by Iris, Actris and Aneris. Tiers 1-3 require no developer annotations, with a quotation based lemma library design to extend coverage as use cases expand. Tier 4 admits computational and probabilistic relational proofs, with project annotations identifying the required relations. We extend the same library direction toward recognizing relational constructions from hypergraph structure. A formal composition rule connects arithmetic, ownership, protocol and realization evidence. Our worked distributed reduction preserves one specified result across concurrent workers, reordered arrivals and boundary mappings. Its probabilistic extension carries worker and conversion error with an explicit failure budget. With recent work by Urschel, we show bounds supply a relevant source of reusable proof terms. These constructions make verification a core engineering discipline for truly fearless programs and systems across a variety of hardware targets.
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:2601.21243v5 Announce Type: replace-cross Abstract: We consider max-min and min-max problems with objective functions that are possibly non-smooth, submodular with respect to the minimiser and concave with respect to the maximiser. We investigate the performance of a zeroth-order method applied to this problem. The method is based on the subgradient of the Lov\'asz extension of the objective function with respect to the minimiser and based on Gaussian smoothing to estimate the smoothed function gradient with respect to the maximiser. In expectation sense, we prove the convergence of the algorithm to an $\epsilon$-saddle point in the offline case. Moreover, we show that, in the expectation sense, in the online setting, the algorithm achieves $O(\sqrt{N(1+\bar{P}_N)})$ online duality gap, where $N$ is the number of iterations and $\bar{P}_N$ is the path length of the sequence of optimal decisions. The complexity analysis and hyperparameter selection are presented for all the cases. The theoretical results are illustrated via numerical examples.
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.