arXiv:2605.09454v2 Announce Type: replace-cross Abstract: We study the $\textit{single-index bandit}$ problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function. This model extends linear and generalized linear bandits to a nonparametric setting, and is particularly relevant when the reward function is not known in advance. While optimal regret guarantees are known for monotone reward functions, the general non-monotone case remains poorly understood, with the best known bound being $\tilde{\mathcal{O}}(T^{3/4})$ (under standard boundedness and Lipschitz assumptions on the reward function [Kang et al., 2025]). We close this gap by establishing the optimal regret for general single-index bandits. We propose a simple two-phase algorithm, namely, Zoomed Single Index Bandit with Upper Confidence Bound ($\texttt{ZoomSIB-UCB}$), that first estimates the projection direction via a normalized Stein estimator, and then reduces the problem to a one-dimensional bandit using discretization and finally use UCB. This approach achieves a regret of $\tilde{\mathcal{O}}(T^{2/3})$, and improves significantly upon prior work without any additional assumptions. We also prove a matching minimax lower bound of $\tilde{\Omega}(T^{2/3})$, showing that the upper bound is essentially tight. Our upper and lower bounds together provide a sharp characterization of the regret in single-index bandits. Moreover, the empirical results further demonstrate the effectiveness and robustness of our approach.
Science Journals
arXiv:2606.01357v2 Announce Type: replace-cross Abstract: Hypergraphs provide a natural framework for representing neurophysiological interactions distributed across sets of sensors. A key methodological question is how hyperedges should be defined from frequency-resolved electroencephalography/magnetoencephalography (EEG/MEG) data. We demonstrate a construction strategy in which hyperedges are obtained from canonical coherence (caCOH), an extension of coherence that estimates coupling between multidimensional signal spaces. To our knowledge, this is the first work to construct hypergraphs directly from a multivariate connectivity measure specifically designed for frequency-resolved neurophysiological analysis. We propose two caCOH-based representations: a one-to-space hypergraph, where each external signal defines a hyperedge over the EEG/MEG sensor space, and a space-to-space hypergraph, where two multidimensional signal spaces are represented by a single hyperedge. We evaluate the approach in controlled simulations with known coupling frequencies and varying signal-to-noise ratio (SNR). Compared with graphs based on magnitude-squared coherence (MSC), caCOH-based hypergraphs showed statistically higher target-baseline contrasts at almost all SNR levels, indicating stronger recovery of coupling frequencies. They also recovered sensor-level spatial patterns associated with the simulated sources. In addition, one-to-space and space-to-space representations reduced 610 MSC edges per frequency to 10 and 1 hyperedges, respectively. These results establish multivariate spectral connectivity as a natural methodological basis for EEG/MEG hypergraphs.
arXiv:2606.04210v2 Announce Type: replace-cross Abstract: Randomized smoothing (RS) certifies robustness in the vector space where Gaussian noise is added. In audio classification, this space is often not uniquely defined as standard pipelines normalize, range-control, and transform waveforms into log-mel or other spectral features. We show that direct RS is therefore under-specified unless the certified object and preprocessing policy are explicit. On two audio benchmarks, keyword spotting and environmental-sound classification, we study waveform, feature-space, and post-processed smoothing. Our diagnostics show why representation-aware reporting is necessary: at the same smoothing level $\sigma=0.0025$, the two datasets share the same median raw radius $.007996$, but different waveform energies yield different SNR-equivalent scales ($83.98$ vs. $90.97$ dB); log-mel smoothing gives higher positive-radius certified accuracy on environmental sounds ($68.42\%$ vs. $65.53\%$), certifying more examples with nonzero radius but over features rather than waveforms; and clipping or peak normalization changes the effective perturbation norm by roughly $230$--$351\times$. We therefore recommend that audio RS studies choose and report the task-specific certified object and perturbation model, including the perturbation location, gain policy, raw radius, and any post-noise geometry changes.
arXiv:2606.19317v2 Announce Type: replace Abstract: A longstanding goal of research on interpretable deep learning is to replace opaque neural computations with human-meaningful symbolic descriptions. In this paper, we propose an approach for approximating the behavior of components of deep networks with executable programs. We focus on attention heads in transformer language models. For a given head, we first compute its associated attention matrices on a collection of randomly selected training examples. Next, we prompt a pre-trained language model with a summary of these matrices, and instruct it to generate a set of Python programs that can reproduce the associated attention patterns given only text from the input sentence. Finally, we re-rank programs according to how well our final set of programs predict behavior on held-out inputs. We demonstrate that a set of fewer than 1,000 such generated programs can reproduce the attention patterns of heads in GPT-2, TinyLlama-1.1B, and Llama-3B, achieving an average Intersection-over-Union similarity above 75% on TinyStories. Moreover, the best-fit programs can replace neural attention heads without substantially affecting model behavior: replacing 25% of attention heads with programmatic surrogates across the three models incurs only a 16% average perplexity increase, while maintaining performance on a variety of downstream question answering benchmarks. This work contributes a scalable pipeline for reverse-engineering attention heads in transformer models using human-readable, executable code, advancing a path toward symbolic transparency in neural models.
arXiv:2606.06179v2 Announce Type: replace-cross Abstract: Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score error while perfectly matching the target distribution. By decomposing score errors into a gradient and a solenoidal component (a Helmholtz-Hodge decomposition), we identify the geometric reason behind this: only the gradient component enters the marginal Fokker-Planck dynamics, while the solenoidal component is structurally invisible. We make this precise in three results. First, building on the corrected geometry, we prove an impossibility result: no monotone function of the $L^2$ score error can uniformly lower bound any divergence between the learned and target distributions. Second, we derive an upper bound on the Kullback-Leibler divergence that depends only on the observable gradient component of the error, tightening the standard Girsanov bound for generic score networks, and identifying its looseness as the cost of operating on path-space rather than marginal-space dynamics. Third, we give a tractable estimator of the gradient component via a dual Sobolev identity, which is shown to empirically correlate substantially better with sample quality than the full $L^2$ error.
arXiv:2606.20724v2 Announce Type: replace Abstract: Long-horizon web agents often fail in ways hidden by final-answer evaluation: they may visit useful pages, produce a well-formed answer, and terminate confidently while still missing fields, over-including unsupported items, or relying on stale evidence. We study these failures with Parallel WebBench, a parallel web-exploration benchmark containing 1,679 verified records: 350 manually curated parallel tasks and 1,329 reconstructed records with verified URL-based trajectories. We train WebExplorer-style agents with GRPO under human-only, balanced human-synthetic, and synthetic-heavy data mixtures. At 16k context and 16 interaction rounds, the best GRPO model improves completion over WebExplorer-8B from 50.7% to 96.0% and GPT-4.1-mini-judged element-wise F1 from 0.2489 to 0.4529, but binary accuracy remains far below completion. Trace-level analysis identifies three persistent failure modes: context-bound search loops, premature termination on partial answers, and synthesis collapse after relevant evidence has already been retrieved. These results show that synthetic-data GRPO reduces abstention and improves partial correctness, but leaves a completion-correctness gap that requires evidence-grounded coverage and synthesis diagnostics.
arXiv:2606.23244v2 Announce Type: replace Abstract: We motivate an axiomatic definition of probabilistic algorithms (PAs) by four postulates covering random branching time, abstract states, background, and random bounded exploration. Then, we introduce probabilistic Abstract State Machines (pASMs) and show that they specify PAs. Finally, we prove that every PA satisfying these postulates can be simulated step-by-step by a behaviourally equivalent pASM with the same signature and background.
arXiv:2606.24516v2 Announce Type: replace Abstract: A growing family of training-free solvers -- FlowDPS, FLOWER, PnP-Flow and their diffusion ancestors (DPS, DAPS) -- repurpose a pretrained flow-matching prior to solve imaging inverse problems by adding a measurement-guidance term to the deterministic probability-flow ODE. Despite strong empirical results, what these per-step corrections actually approximate -- and how far the resulting samples are from the true posterior $p(x\mid y)$ -- has not been characterized. We give a posterior-transport account of flow-based inverse problem solving. Our starting point is a simple but consequential fact: for a \emph{deterministic} flow prior, Bayesian conditioning is realized entirely by a \emph{reweighting of the source distribution}, not by a drift correction; pushing the reweighted source through the \emph{unmodified} velocity field yields exact posterior samples. From this we show that trajectory-guidance solvers can be read as the minimum-kinetic-energy \emph{correction} field needed to morph the unconditional source into the posterior, and that FlowDPS / FLOWER / PnP-Flow correspond to distinct zeroth-order / Gaussian / proximal approximations of this single object; we bound the resulting posterior bias in Wasserstein distance. A controlled $2$D study with a closed-form posterior confirms the theory decisively: source reweighting matches the true posterior to the Monte-Carlo floor on every metric, whereas trajectory guidance incurs $200$--$800\times$ larger error and collapses posterior modes, \emph{regardless of guidance strength}. Guided by the analysis we propose a cheap, principled velocity-correction solver that is competitive across two in-domain priors (AFHQ, CelebA) and two out-of-distribution settings while, unlike point-estimate source-space optimizers, producing diverse posterior samples with uncertainty that correlates with reconstruction error.
arXiv:2606.08916v3 Announce Type: replace-cross Abstract: Chemical substitution offers an effective route to tune magnetic ordering and magnetocaloric performance in rare-earth oxides for cryogenic refrigeration. Here we investigate the structural evo lution, magnetic properties, and magnetocaloric effect of polycrystalline zircon-type Gd1-xErxVO4 (x=0, 0.1, 0.25, 0.5, and 0.75). Powder X-ray diffraction confirms that all samples crystallize in the tetragonal zircon structure without detectable impurity phases. Substitution of Gd3+ by the smaller Er3+ ion produces a systematic lattice contraction and modifies the magnetic behavior of the rare-earth sublattice. In particular, the magnetic ordering temperature is suppressed from 3.65(2) K in GdVO4 to 2.76(2) K in Gd0.9Er0.1VO4 , accompanied by a weakening of the spin-flop-like field-induced anomaly observed in the parent compound. A low Er concentration correspondingly improves the low-temperature magnetocaloric performance, with Gd0.9Er0.1VO4 exhibiting a max imum magnetic entropy change of 45.1 J kg-1 K-1 for mu_0 Delta H=7T. These results demonstrate that weak Er substitution effectively tunes the competition among exchange interactions, dipolar coupling, and magnetic anisotropy, optimizing the balance between magnetic ordering and available spin entropy in zircon-type rare-earth vanadates, which is crucial for developing efficient cryogenic refrigeration materials.
arXiv:2606.09820v2 Announce Type: replace-cross Abstract: We generalize the universal approximation theorem for functional input neural networks (FNN) to differentiable maps by including the approximation of the derivatives. A FNN maps the input from a possibly infinite-dimensional weighted manifold to the real-valued hidden layer, on which a non-linear scalar activation function is applied, and then returns the output into a Banach space via some linear readouts. By proving a weighted Nachbin theorem, we establish a universal approximation theorem for differentiable maps, which goes beyond the usual formulation on compact sets and also includes the approximation of the derivatives. This leads us to approximation results for non-anticipative functionals including the horizontal and vertical derivatives. As a further application, we show that linear functions of the signature are able to approximate path space functionals including their directional derivatives.
arXiv:2606.15083v2 Announce Type: replace-cross Abstract: Quantum computing has rapidly emerged as a powerful paradigm for tackling computationally demanding problems. In particular, quantum optimization shows strong promise for hard combinatorial problems in power systems, where increasing distributed energy penetration heightens the need for intentional islanding to maintain grid reliability and resilience. However, power system islanding is an NP-hard combinatorial optimization problem that becomes computationally prohibitive for classical solvers as network size grows, motivating the use of quantum computing as a promising alternative pipeline. This study develops a resource-efficient hybrid QAOA islanding framework that brings physics-constrained power-system partitioning into the quantum optimization workflow. The framework combines coherency-informed graph reduction, physics-aware constraint modeling, and structured post-processing to efficiently convert shallow-circuit QAOA samples into high-quality feasible islanding decisions without deep circuits or large shot budgets. The proposed framework is validated on the standard IEEE benchmark systems (9-, 14-, 24-, 30-, 39-, and 57-bus), demonstrating that the hybrid workflow achieves Gurobi-optimal solution quality with a clear quantum resource advantage over vanilla QAOA, while the resulting islanding solutions satisfy all physical feasibility requirements after network separation. This study establishes QAOA-based islanding as a viable quantum approach for critical infrastructure, with structured post-processing as the key enabler of quantum resource efficiency.
arXiv:2606.18438v2 Announce Type: replace-cross Abstract: In this paper, we study a sequential workforce management problem in a contingent labor setting with uncertainty in both worker production and labor supply. A firm seeks to maximize cumulative profit by maintaining an active team of fixed size while learning worker productivity over time. We emphasize two critical operational frictions in this problem: replacing workers is costly, and workers may not be available immediately for hiring because of, for example, prior job commitments, scheduling constraints, or onboarding procedures. Thus, hiring decisions take effect only after a random delay. We formulate this problem as a stochastic multi-play bandit with costly switching and delayed actions, and develop a learning-based hiring policy, DR-UCB (DelayedReplacement-UCB), that makes replacement and hiring decisions sequentially through learning cycles. In each cycle, the policy uses real-time production data to determine when to initiate workforce changes and which workers to replace and hire. We show that the leading-order regret of the proposed policy matches its lower bound in its dependence on the time horizon. Our numerical experiments show that DR-UCB outperforms benchmark policies.
arXiv:2606.26744v2 Announce Type: replace Abstract: We present HyperDFlash, a block-parallel speculative decoding framework tailored to DeepSeek-V4's Hyper-Connections (HC). Despite the strong performance of DeepSeek-V4's native Multi-Token Prediction (MTP) module on initial token drafting, its draft accuracy degrades sharply at later positions, as error accumulation from unverified intermediate tokens harms draft acceptance rates. Although the original DFlash method supports efficient one-pass block drafting, it cannot be seamlessly adapted to the HC paradigm, since DeepSeek-V4's multi-path residual stream induces inherent feature misalignment with conventional drafting designs. To resolve this architectural mismatch, we propose two dedicated, model-aligned optimizations for HC residual streams. First, we adopt pre-collapse residual states as the exclusive conditioning signal, preserving complete multi-path structural information and better aligning the drafter with the target's native prediction pathway. Second, we replace the heavy generic linear compressor with a lightweight gated residual reducer, whose parameters are directly inherited from the target model's built-in hc_head module. This design yields input-aware path aggregation with three orders of magnitude fewer parameters while maintaining precise architectural alignment. We further enhance model training via a targeted KL distillation loss applied to the LM-head, regularizing predictions against the target distribution to improve early draft quality. Extensive experiments across math reasoning, code synthesis, and conversational benchmarks demonstrate that HyperDFlash consistently outperforms both the native MTP baseline and vanilla DFlash adaptation, achieving substantial gains in average accepted draft length and decoding speedup. These results validate HC alignment, gated reduction, and targeted distillation for high-performance speculative decoding.
arXiv:2105.09254v4 Announce Type: replace-cross Abstract: In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal effects. For binary treatments, efficient estimators for the direct and indirect effects are presented by Tchetgen Tchetgen and Shpitser (2012) based on the influence function of the parameter of interest. These estimators possess desirable properties such as multiple-robustness and asymptotic normality while allowing for slower than root-n rates of convergence for the nuisance parameters. However, in settings involving continuous treatments, these influence function-based estimators are not readily applicable without making strong parametric assumptions. In this work, utilizing a kernel smoothing approach, we propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimation strategy. Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter. Additionally, similar to influence function-based estimators, our proposed estimator is multiply robust and asymptotically normal, allowing for inference in settings where parametric assumptions may not be justified.
arXiv:2603.12598v2 Announce Type: replace Abstract: Large Vision-Language Models (LVLMs) have shown remarkable potential across a wide array of vision-language tasks, leading to their adoption in critical domains such as finance and healthcare. However, their growing deployment also introduces significant security and privacy risks. Malicious actors could potentially exploit these models to extract sensitive information, highlighting a critical vulnerability. Recent studies show that LVLMs often fail to consistently refuse instructions designed to compromise user privacy. While existing work on privacy protection has made meaningful progress in preventing the leakage of sensitive data, they are constrained by limitations in both generalization and non-destructiveness. They often struggle to robustly handle unseen privacy-related queries and may inadvertently degrade a model's performance on standard tasks. To address these challenges, we introduce Neural Gate, a novel method for mitigating privacy risks through neuron-level model editing. Our method improves a model's privacy safeguards by increasing its rate of refusal for privacy-related questions, crucially extending this protective behavior to novel sensitive queries not encountered during the editing process. Neural Gate operates by learning a feature vector to identify neurons associated with privacy-related concepts within the model's representation of a subject. This localization then precisely guides the update of model parameters. Through comprehensive experiments on MiniGPT and LLaVA, we demonstrate that our method significantly boosts the model's privacy protection while preserving its original utility. The code is available at https://github.com/Xiangkui-Cao/Neural-Gate.
arXiv:2403.20044v4 Announce Type: replace-cross Abstract: The nonlinear electrodynamics proposed by Bandos, Lechner, Sorokin and Townsend is a remarkable theory that unifies Maxwell, Bialynicki-Birula and ModMax theories, which are known theories invariant under conformal transformations and electromagnetic duality transformations. In the Bandos-Lechner-Sorokin-Townsend nonlinear electrodynamics, we calculate the energy flux density, dispersion relations, refractive indices, phase and group velocities of plane waves as well as the changes of the photon wavelength in the Compton scattering process in the presence of a constant uniform electromagnetic background. Our results are useful for testing and constraining this new theory of nonlinear electrodynamics.
arXiv:2405.09203v2 Announce Type: replace-cross Abstract: In this paper, we propose a new randomized method for numerical integration on a compact complex manifold with respect to a continuous volume form. Taking for quadrature nodes a suitable determinantal point process, we build an unbiased Monte Carlo estimator of the integral of any $\mathscr{C}^1$ function, and show that the estimator satisfies a central limit theorem, with a faster rate than under independent sampling. In particular, seeing a complex manifold of dimension $d$ as a real manifold of dimension $d_\mathbb{R}=2d$, the mean squared error for $N$ quadrature nodes decays as $N^{-1-2/d_{\mathbb{R}}}$; this is faster than previous DPP-based quadratures and reaches the optimal worst-case rate investigated by \cite{Bak} in Euclidean spaces. The determinantal point process we use is characterized by its kernel, which is the Bergman kernel of a holomorphic Hermitian line bundle, and we build heavily on the work of Berman that led to the central limit theorem in \citep{Ber7}. We provide numerical illustrations for the Riemann sphere.
arXiv:2411.19088v3 Announce Type: replace-cross Abstract: We study the Goppa construction of linear codes from algebraic curves as a morphism of moduli stacks. For integers $g,n,d$ with $n>d>2g-2$ and $k:=1-g+d$, let $\mathfrak{LS}_{g,n,d}$ be the stack of rank-one level structures $(X,p_1,\dots,p_n,L,\gamma_1,\dots,\gamma_n)$, where $X$ is a smooth genus-$g$ curve with $n$ marked points, $L$ a degree-$d$ line bundle, and $\gamma_i$ a trivialization of $L$ at $p_i$. We construct the Goppa morphism $\operatorname{Goppa}_{g,n,d}:\mathfrak{LS}_{g,n,d}\to\operatorname{Gr}(k,n)$. We prove that, if $n>d>2g-1$, the extended morphism $\Phi_{g,n,d}:\mathfrak{LS}_{g,n,d}\to\operatorname{Gr}(k,n)\times\mathfrak{M}_{g,n}$ is an immersion of stacks, and that $\operatorname{Goppa}_{g,n,d}$ is universally injective if $n/2>d>2g+1$. If $n>d>2g+1$, we identify the fiber over a non-degenerate code $C$ with the moduli stack of $n$-pointed smooth genus-$g$ curves of degree $d$ in $\mathbb{P}_C$ whose marked points lie at the distinguished points determined by the coordinate projections of $C$, recovering the classical incidence problem of curves of fixed degree and genus through assigned points. For a fixed $n$-pointed curve $(X,D)$, $D=p_1+\dots+p_n$, with $n=2(1-g+d)$, we show that the self-dual level structures form the fixed-point subscheme of a natural involution on $\mathfrak{LS}_{X,D,d}$, isomorphic to the $2$-torsion subscheme of $\mathfrak{LS}_{X,D,0}$ whenever it has a $\mathbb{K}$-rational point. In genus zero we identify $\mathfrak{LS}_{0,n,d}$ with $\mathbb{G}_m^{n-1}\times\mathfrak{M}_{0,n}$ and prove that, for $2\leq d\leq n-3$, the morphism $\operatorname{Goppa}_{0,n,d}$ is an immersion. Its restriction to each $\lambda\in\mathbb{G}_m^{n-1}$ is then a map $\mathfrak{M}_{0,n}\hookrightarrow\operatorname{Gr}(k,n)$, giving a canonical $\mathbb{G}_m^{n-1}$-family of immersions of $\mathfrak{M}_{0,n}$ into the Grassmannian.
arXiv:2412.19897v3 Announce Type: replace-cross Abstract: We introduce a local surrogate approach for explainable time-series forecasting. An initially non-interpretable predictive model to improve the forecast of a classical time-series 'base model' is used. 'Explainability' of the correction is provided by fitting the base model again to the data from which the error prediction is removed (subtracted), yielding a difference in the model parameters which can be interpreted. We provide illustrative examples to demonstrate the potential of the method to discover and explain underlying patterns in the data.
arXiv:2404.05062v4 Announce Type: replace-cross Abstract: We present four new mathematical methods, two exact and two approximate, along with open-source software, to compute the cdf, pdf and inverse cdf of the generalized chi-square distribution. Some methods are geared for speed, while others are designed to be accurate far into the tails, using which we can also measure large values of the discriminability index $d'$ between multivariate normal distributions. We compare the accuracy and speed of these and previous methods, characterize their advantages and limitations, and identify the best methods to use in different cases.
arXiv:2512.09849v3 Announce Type: replace-cross Abstract: We demonstrate deterministic preparation of arbitrary two-component product states of fermionic $^6$Li atoms in an 8$\times$8 optical tweezer array, achieving motional ground-state fidelities above $98.5\,\%$. Leveraging the large differential magnetic moments for spin-resolution, with parallelized site- and number-resolved control, our approach addresses key challenges for low-entropy quantum state engineering. Combined with high-fidelity spin-, site-, and density-resolved readout within a single $20\,\mathrm{\mu s}$ exposure, and $3\,\mathrm{s}$ experimental cycles, these advances establish a fast, scalable, and programmable architecture for fermionic quantum simulation.
arXiv:2512.08444v2 Announce Type: replace-cross Abstract: Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation algorithms for solving variational problems. While the underlying algorithm is usually formulated in the functional analytic setting, learned approaches are often viewed as purely discrete. In this survey we present a unified operator view for learned iterative networks. Specifically, we formulate a learned reconstruction operator, defining how to compute, and separately the learning problem, which defines what to compute. In this setting we present common approaches and show that many approaches are closely related in their core. We review linear as well as non-linear inverse problems in this framework and present a short numerical study to conclude.
arXiv:2603.19130v2 Announce Type: replace-cross Abstract: Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE has mostly focused on sparse matrices; less effort has been devoted to data-sparse (e.g., rank-structured) matrices. In this work we examine a particular case of rank structure, namely, one-pair semiseparable matrices. We present a new block encoding approach that relies on a suitable factorization of the given matrix as the product of triangular and diagonal factors. To encode the matrix, the algorithm needs $2\log(N)+7$ ancillary qubits. Assuming that the data input oracles can be implemented with polylogarithmic depth, or that a QRAM input model is available, our proposed method requires $\mathcal{O}({\rm polylog} (N))$ time and has an error of $\mathcal{O}(N^2)$, where $N$ is the matrix size.
arXiv:2602.02992v2 Announce Type: replace-cross Abstract: We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next, combining this characterization with behavioral theory, we establish a necessary and sufficient condition for the noisy data to be informative for quadratic stabilization. This condition is formulated in terms of linear matrix inequalities, whose solutions yield a stabilizing controller. Finally, we characterize data informativity for system identification in the noise-free setting.
arXiv:2606.18729v3 Announce Type: replace-cross Abstract: Data valuation quantifies the intrinsic quality of individual samples to enable principled data curation, quality control, and robust learning. For time series in critical domains such as healthcare, finance, and industrial monitoring, effective valuation methods are essential yet fundamentally lacking. Existing approaches are either model-dependent, limiting their generalizability, or designed for i.i.d. data and thus fail to capture temporal dependencies, multi-scale patterns, and non-stationary dynamics inherent to sequential data. We introduce TimeLAVA, a learning-agnostic framework that values temporal segments by their marginal contribution to minimizing distributional discrepancy between evaluated and reference data. At its core is a novel Selective Wavelet-based Wasserstein discrepancy combining multi-scale wavelet transforms for temporal localization with unbalanced optimal transport for robustness to distributional shifts. Segment values are efficiently computed via sensitivity analysis without requiring model training and aggregated into point-wise scores. We provide theoretical guarantees linking valuation to model-agnostic generalization and prove bounded sensitivity to outlier contamination. Extensive experiments across anomaly detection, data pruning, and label noise detection demonstrate that TimeLAVA produces significantly more informative value scores than existing methods on diverse real-world datasets.