arXiv:2610.36633v1 Announce Type: cross Abstract: System identification, namely the inference of mathematical representations of dynamical systems from measured data, is fundamental to engineering diagnostics, prognostics, and decision-making. Bayesian filtering offers a principled framework for probabilistic state estimation but traditionally relies on prescribed transition and observation models. Recent advances in deep Bayesian filtering address this limitation by embedding learnable representations within probabilistic state-space formulations, enabling data-driven identification of unknown dynamics while retaining physical structure and uncertainty-aware inference. This tutorial provides a systematic introduction to deep Bayesian filtering for nonlinear structural system identification, focusing on the interplay between learned dynamics, physical inductive biases, and posterior inference. The Deep Markov Model serves as a data-driven reference, while the Physics-guided Deep Markov Model (PgDMM) and Neural Extended Kalman Filter (Neural EKF) illustrate complementary approaches based on amortized variational inference and differentiable Kalman filtering, respectively. Their capabilities are examined through dynamic state estimation and joint dynamic state and parameter estimation on a three-dimensional shear-frame benchmark with hysteretic Bouc-Wen connections and sparse acceleration measurements. The results highlight important distinctions between measurement-conditioned reconstruction and open-loop forecasting, demonstrate how physical structure can improve latent-state interpretability without necessarily ensuring predictive fidelity, and reveal differences in the robustness of response and parameter estimation. Practical guidelines for model construction, training, evaluation, and deployment are provided, together with an outlook on remaining challenges in uncertainty calibration, identifiability, and real-world validation.

arXiv:2610.36581v1 Announce Type: cross Abstract: Dimension-reduction methods such as PCA identify a subspace capturing most of the variation in the data, but not a distinguished basis within it. Selecting a basis in which the samples are sparsely represented is a recurring task in unsupervised learning, addressed by methods in factor analysis, dictionary learning, and subspace clustering. We pose this task as Wasserstein approximation of the data distribution by measures supported on the axes of an orthogonal frame, which, in turn, reduces to a nonsmooth optimization problem over the orthogonal group $\mathrm{O}(d)$. We show that, under mild assumptions, both empirical risk minimizers and a locally initialized stochastic gradient method recover the population-optimal frame at the near-parametric rate $\widetilde{O}_d(n^{-1/2})$, where $n$ is the sample size. The main difficulty is that, although the population objective is smooth, the empirical objective is not-this mismatch precludes standard covering arguments. We overcome this issue by replacing Lipschitz continuity of the empirical gradient with a coarsely Lipschitz bound, a tool that may be of independent interest. Numerical experiments support our theoretical findings.

arXiv:2610.36311v1 Announce Type: cross Abstract: Typed decision models return a probability distribution over options supplied by the caller, and software tends to act on that number as if it were a guarantee. We measure what it licenses, comparing the open-weight Laya, in five checkpoints, with Jev 1.13, available only through an API. A probability licenses a statement about groups of decisions, not about one decision, and a gate that promises an accuracy among the cases it decides alone keeps that promise only with a lower bound checked on data like its traffic. Across 190 exchangeable evaluations, a threshold chosen by point estimate breaks the promise in 147, Learn then Test keeps it in all of them, and a Beta lower-bound rule decides more items on average than Learn then Test in 128 and fewer in none, without its guarantee. Calibrated in English, Jev keeps a promise of 95% in 8 of 51 locales. Ordinary typing noise breaks a promise calibrated on clean text, and, in exploratory runs, training with noise raises the noisy accuracy with no loss on clean text. In four further domains, a fine-tuned Laya needs from 250 to 8,000 labels to be non-inferior to Jev, and does not get there on LIAR2. Under drift, the preregistered claim for a Bayesian retraining loop is not supported: the loop avoids needless retraining where the change does not degrade the model, at a cost equivalent to recalibration alone, and re-qualifying the threshold in every window keeps the promise more often where it does. On the monthly series of M3, neither decider predicts the direction of the next value better than a constant answer. Confidence separates right from wrong answers with an AUROC from 0.80 to 0.96, but it does not select faithful explanations, and exact coalition games of single decisions show what an explanation can still say through an API that rounds to two decimals. We release the frozen answers with a datasheet, a promise check and the code.

arXiv:2610.36097v1 Announce Type: cross Abstract: We study full-information online linear optimisation on the unit $\ell_p$ ball in $\mathbb{R}^d$, for fixed $2\le p<\infty$ and losses of dual norm at most one. Let $\Delta_T$ denote the cumulative loss of the best fixed action above each round's minimum. A follow-the-regularised-leader (FTRL) algorithm attains, on every loss sequence and without knowing $T$ or $\Delta_T$, regret $O_p(1+\min\{\Delta_T^{1-1/p},\, d^{1/2-1/p}\sqrt{\Delta_T}\})$. Matching lower bounds show that this rate is minimax for each fixed $p$, and its constant $(2+o(1))p/\log p$ is optimal as $p\to\infty$ among guarantees uniform in $d$ and $T$. The algorithm uses a bounded radial regulariser and switches at most once to its quadratic augmentation. On some paths where follow-the-leader (FTL) has regret one, its regret grows with $T$. A switching extension keeps the sharp constant and also guarantees $\mathrm{Reg}_T\le 2\,\mathrm{Reg}_T^{\mathrm{FTL}}$. For i.i.d. losses whose mean has no zero coordinates, we compute the exact $\log T$ coefficient of the expected regret, which separates FTL's variance term from the bias of the regulariser.

arXiv:2610.35975v1 Announce Type: cross Abstract: Wind farm layout optimization becomes increasingly difficult as turbine count grows, especially when high-fidelity aerodynamic models are used. Conventional Kriging-based Bayesian optimization often suffers from low sample efficiency in high-dimensional layout spaces because sparse training data provide limited domain coverage. We develop a Graph-informed Kriging framework that embeds reusable aerodynamic interaction information into the surrogate mean function. The wind farm is represented as a directed aerodynamic graph, where pairwise turbine interactions defined in a low-dimensional relative-coordinate space are assembled into a farm-scale mean. This structured mean captures the dominant variation in annual energy production (AEP), allowing the Gaussian process to model only the residual structure and uncertainty. Numerical experiments show that Graph-informed Kriging consistently improves AEP prediction accuracy over ordinary and generic-trend Kriging under sparse-data conditions, with increasing benefits as layout dimension and wake-interaction strength grow. Embedded in Bayesian optimization, it substantially improves sample efficiency and achieves competitive solutions for the IEA Wind Task 37 benchmark with about 280 AEP evaluations. In a controlled 16-turbine case, it also outperforms ordinary and multi-fidelity Kriging under the same high-fidelity evaluation budget. The framework is further extended to a 48-turbine wind farm, demonstrating applicability to large-scale CFD-based layout optimization. These results show that Graph-informed surrogate modeling can enable more efficient use of high-fidelity aerodynamic models for reliable large-scale wind farm layout design.

arXiv:2610.35967v1 Announce Type: cross Abstract: We present LatentLieODE, a novel neural ODE method to discover linear Lie symmetries and first integrals of the learned dynamics from timeseries observations such as video inputs. It starts with an autoencoder, which learns a low dimensional representation of the observed system and then maps trajectories to decorrelated latent coordinates $z \in \mathbb{R}^d$. A bank of linear infinitesimal generators $\mathbf{A}_k \in \mathbb{R}^{d \times d}$ is fitted jointly against a differentiable Lie-bracket residual $\mathbf{J}_f(z)\mathbf{A}z - \mathbf{A} f(z)$, while an MLP optimises the latent ODE $f(z) = \mathrm{d}z/\mathrm{d}t$ to reconstruct the observation-space timeseries. After suitable generators and $f$ are found, we fit a third network $H_\phi$ to generate the first integral of the system. Across six benchmark systems (harmonic oscillator, simple and twin pendulums, Lotka-Volterra, pixel pendulum, sphere geodesics) we find each system's relevant symmetries, and the discovered invariants match ground-truth conserved quantities at $|\rho| \geq 0.978$. On the sphere, the pipeline recovers a non-abelian $\mathfrak{so}(3)$, certified by the negative-definite Killing form of its recovered structure constants. This work presents significant advances in data-driven discovery of symmetries and provides a new pathway for neural surrogates of dynamical systems.

arXiv:2610.35877v1 Announce Type: cross Abstract: Changing a deployment policy can invalidate a world model's uncertainty while leaving the physical transition mechanism and predictor unchanged. For one-step prediction, if source and target laws share the conditional mechanism $P(Y|X)=Q(Y|X)$, then the intervention is identified by the pre-outcome change of measure $w(X)=dQ_X/dP_X$. For policy-controlled dynamics this ratio factors into state-occupancy and action-propensity terms. Weighted conformal calibration transports marginal coverage to the target law; with an estimated ratio $\hat w$, $P_Q\{Y \in C_{\hat w}(X)\} \ge 1-\alpha-TV(Q,\hat Q) \ge 1-\alpha-E_P|w-\hat w|$. Population log-loss regret for a source-versus-target domain classifier bounds the same ratio error. If $h$ is its clipped target posterior, $\rho$ is the target-domain prior, and $\Delta(h)$ is population log-loss regret, then $E_P|w-\hat w_h| \le (1/(\rho\gamma))\sqrt{\Delta(h)/2}$. An exact cancellation improves the dependence from a generic odds-map bound of order $\gamma^{-2}$ to $(\rho\gamma)^{-1}$. Our experiments use a released DINO-feature world model and physical Franka trajectories. Under the strongest controlled state-action shift, ordinary 90% conformal sets cover 55.0%, whereas oracle and learned-ratio calibration cover 91.0% and 90.9%. The learned surrogate remains within 0.9% total variation of the target law. Calibration is relative to the deployment law: the model can remain fixed while calibration follows the intervention. We machine-check in Lean 4 the finite-support algebraic and causal identities used in the classifier-regret argument, including its coverage-composition step.

arXiv:2610.34801v1 Announce Type: cross Abstract: Per-point data-valuation scores -- Data Shapley, influence, leverage -- are routinely used to select training data: keep the points with the top $k$ scores. We argue that top-$k$ by a fixed, mode-blind per-point score is the wrong selection rule precisely in the regime where data selection matters. The reason is that a point's value is not a fixed number but depends on what else has been selected -- a near-duplicate of an already-chosen point adds almost nothing, however high its score -- and a per-point scalar cannot express this interaction. The theory quantifies this failure exactly: in an equal latent-mode model, fixed top-$k$ selection incurs a closed-form excess risk over adaptive coverage because it repeatedly spends budget on already-covered modes. The gap is largest when the budget is tight, the learner representation is redundant, and missing a mode is costly. The practical rule is simple: use balance when the labels available at selection identify the learner's modes, and use explicit coverage when they do not. On standard classification tasks with strong pretrained features, class-balancing the same per-point scores recovers the missing coverage and matches or outperforms generic set coverage across our datasets. Without labels, label-free coverage improves accuracy by up to +0.20 while raw top-$k$ can fall below random; when labels are coarser than the modes, coverage within coarse strata performs best. We turn this distinction into a pre-specified diagnostic and validate it across both favorable and stress-test settings. The limits are part of the claim: the advantage is representation-relative. Coverage fails when the relevant modes are not expressed in the learner geometry, as with spurious subgroups, or when data quality varies independently of coverage -- exactly as the theory predicts.

arXiv:2610.37473v1 Announce Type: new Abstract: Quickest detection problems (QDPs) arise in a wide range of applications. However, the complementarity structure of the associated variational inequalities poses substantial challenges for traditional numerical methods, particularly in high-dimensional settings. We propose a PINN-based framework for estimating the optimal stopping boundary in QDPs with high-dimensional diffusion processes and spatial dependence, while overcoming the curse of dimensionality. Theoretically, we establish a novel equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, rigorously justifying the use of finite-dimensional neural networks to approximate the true solution. Furthermore, we assess the robustness of the proposed framework by quantifying uncertainty in the learned stopping boundaries using deep ensembles and Monte Carlo dropout. The results show low variability across independent training runs and stochastic forward passes, indicating stable and consistent boundary estimates. We also compare our PINN results with reference numerical solutions where available and find close agreement.