We establish last-iterate mean-square residual bounds for nonexpansive stochastic approximation (SA), or stochastic Krasnoselskii-Mann (KM) iterations. In particular, we consider fixed-point mappings that are nonexpansive with respect to the Euclidean norm, and focus on polynomially decaying stepsizes. We study three conditions on the conditional second moment of the noise, and obtain bounds that are optimal up to logarithmic factors in each case. When it scales linearly with the squared residual, the best rate is $O(1/k^{1-ε})$ for any $ε>0$. In this case, for all considered stepsizes, our bounds match those of the noiseless KM iteration. When it is bounded by a constant, the best rate is $O(\log^2 k/\sqrt{k})$. When it scales affinely with the squared norm of the iterate, the best rate is $O(1/k^{1/2-ε})$, and the mean-square residual can diverge if the stepsizes are not square-summable. Thus, unlike for contractive SA, square-summable stepsizes are necessary for nonexpansive SA. We demonstrate how various algorithms with cocoercive maps, such as stochastic gradient descent, linear SA, and learning in cocoercive games, fit into our framework, and how the different noise conditions arise in each of them.
Coding agents are increasingly proposed as autonomous builders of biomedical models, but existing benchmarks are small, near saturation or open to leaked information. We present BioXArena-Pro, 64 research-level modelling tasks from eight biomedical domains, each rebuilt from a published study; most hold out whole biological units such as species or cohorts. Across 22 agent configurations, the best scores 55.1 of 100, and the scaffold matters almost as much as the model. We re-ran a published method for every task: where the published recipe applies unchanged, the best agent and the methods tie; on rebuilt tasks the methods trail by 8.2 points, suggesting that agents gain by adapting to new data. Pretrained models (including biological foundation models) matter where the strongest agent uses them: forbidding them decreases its score on those tasks by 9 points. Every task was audited in several AI-assisted rounds and a final human review.
Reinforcement learning from formal specifications often separates task definition, reward shaping, curriculum design, and policy diagnostics into different mathematical objects. This fragmentation requires additional conversion steps and discards structure already present in the specification, such as subtask boundaries, ordering constraints, and quantitative measures. We introduce TBTCL (Temporal Behavior Tree Centric Learning), a framework that uses Temporal Behavior Trees (TBTs) as a unified interface for specification-guided reinforcement learning. A single TBT specifies the task, induces dense robustness-based rewards, defines a curriculum, and supports better understanding of learned policies. By adapting TBT syntax and semantics for specification-guided reinforcement learning, we provide a formalism that is more expressive than popular specification languages such as LTL and inherently hierarchical. We present algorithms to automatically extract a curriculum DAG and derive dense, robustness-based rewards directly from TBT semantics. Furthermore, we utilize TBT trace segmentation to build understandable competence profiles and automatically adapt the reward toward bottlenecks. We evaluate TBTCL on six specifications across discrete and continuous domains and show that Temporal Behavior Trees can serve as a specification, a reward, a curriculum, and a diagnostic.
Remote photoplethysmography (rPPG) has been proposed as a physiological cue for deepfake detection, based on the premise that synthesized faces lack a genuine cardiac signal. We examine what rPPG-style detectors learn on Celeb-DF++ (22 forgery methods) and FaceForensics++ (FF++), using one identically sampled window per real and fake video. On talking-face forgeries, simple chrominance traces reach an AUC of 0.998, exceeding a dedicated rPPG extractor (0.87). Controlled experiments indicate that this signal is not physiological in origin. On fully synthesized forgeries, it is equally discriminative when extracted from background regions or from full frames without face detection, and it is concentrated above the 0.7 to 4 Hz heart-rate band. It is largely removed by shuffling frame order but persists after normalizing resolution, frame rate and encoding, and an independent reimplementation reproduces these findings. Removing high-frequency content makes most synthesized videos appear real, adding it makes real videos appear fake, and injecting a synthetic pulse has little effect. In controlled self-reenactment experiments with two generators, animating a face from a single frame introduces the same high-frequency signal, whereas reconstructing each frame from its own source does not. Face-based chrominance detectors trained on Celeb-DF++ classify over 99% of real FF++ videos as fake, indicating that they largely encode video source rather than manipulation, and a CLIP-based detector exhibits the same behavior. A frozen CLIP backbone matches or exceeds fusions of CLIP with rPPG and frequency features. Finally, we show that the official Celeb-DF and Celeb-DF++ splits share identities and source-video content between training and test, and that custom protocols reusing test videos and identities in training inflate weaker detectors by up to 0.30 AUC.
We prove universal approximation for metaplectic neural operators on nonempty bounded Lipschitz domains. The nonlocal branches are whole-space metaplectic multipliers with zero extension and restriction, associated with any fixed free symplectic matrix. Assuming a smooth, globally Lipschitz, nonpolynomial activation, we obtain compact-uniform approximation of continuous operators from $C^s$ to $C^r$ and from $H^s$ to $H^r$ in the respective output norms, for arbitrary nonnegative integers $s,r$ and finite input and output channel dimensions. In the Sobolev setting, compact input sets must additionally be uniformly bounded in $L^\infty$. One hidden operator layer with one nonlocal branch suffices. A single scalar symbol atom and finitely many positional features are prescribed by the transform and domain independently of the target operator, compact set and accuracy. The proof combines averaging neural operator theory with an exact chirp-conjugated averaging identity and derivative estimates. The result includes Fourier and fixed nondegenerate fractional Fourier multiplier constructions.
Federated learning enables multiple clients to collaboratively train a machine-learning model without directly sharing their local datasets. However, as prior works have shown, the gradients exchanged during training may reveal sensitive information about client data. Most existing attacks usually optimize dummy inputs to match the true client gradients (Gradient Inversion Attacks), while some attempt to reconstruct them based on the observation that aggregate gradients from a fully connected (FC) layer are a linear combination of its inputs. In this work, we extend this observation by showing that aggregate gradients from an FC layer with the correct scaling are actually an affine combination of its inputs. We evaluate a gradient inversion attack that leverages either known linear-subspace information or its affine-subspace counterpart at each FC layer to improve reconstruction accuracy. Our results show that subspace-based methods can substantially improve reconstruction quality over the chosen baselines in certain settings. We further demonstrate that moderate overestimation of the batch size can generally improve or preserve reconstruction quality, even when the true batch size is unknown. We additionally examine reconstruction under gradient perturbations introduced by a differential privacy (DP) mechanism, providing insight into the effectiveness of the considered formulations under noisy conditions.
We consider the problem of estimating the power spectral density of a Vector-valued Autoregressive Moving-Average (VARMA) process. A well-established approach to accomplishing this task consists of formulating a moment problem that selects the spectral density maximizing an entropy-like index while matching certain moments of the underlying process. However, existing methods assume that the moving-average (MA) component is either fixed or scalar, thereby reducing the class of ARMA models over which the optimal spectral density is sought. In this paper, we propose a new moment problem, based on the notion of transportation entropy, for learning the spectral density of a VARMA process without fixing the MA component or restricting it to be scalar.
Modern recommender systems increasingly consider diverse data modalities to enhance model performance. However, the quality of the underlying multimodal data (e.g. data from social media platforms) has received limited attention so far. Focusing on tourism recommendation, we examine real-world challenges encountered when using datasets from Yelp and Instagram. Issues include noise from fake reviews, hallucinated content from LLMs, modality contradictions, and demographic bias. We outline future directions such as quality-aware fusion, structured and controlled LLM-based content generation to reduce hallucinations, and user group differentiation to improve the robustness and reliability of multimodal recommendation systems.
Text-guided segmentation models receive an image and a short caption about the lesion, and on public benchmarks the caption improves accuracy considerably. On colonoscopy and breast ultrasound, however, the size, count and location words of each caption were computed from the mask that later scores the prediction, and the chest X-ray captions were written by benchmark annotators. We tested what two published models take from them. On colonoscopy and chest X-ray, it is mostly the lesion's extent. Keeping only the size word or the lung-zone phrase recovers 84 to 98 percent of the improvement over an empty caption, and removing it loses 52 to 77 percent. The rest matters little, and a polyp called a rock is segmented just as well. We call this extent leakage. On breast ultrasound, nearly half the captions also name the diagnosis, which carries part of the benefit. Retraining on three datasets shows that models pick up this habit from their training captions, though only partly on breast ultrasound, and that it weakens their segmentation from the image alone. The leak can be measured without training a model, since caption words alone predict lesion area (coefficient of determination 0.54 to 0.77 on six of seven test sets). Without the test mask, the best method we tested, which estimates extent from the image, reaches 74.59 Dice on colonoscopy against the published 77.23. We propose an evaluation protocol that keeps what a caption says about the image apart from what it copies from the label.
Latent diffusion models decode approximately correct latents, making decoder sensitivity to perturbations relevant to image quality. After whitening, forward diffusion corrupts every direction at the same signal-to-noise ratio (SNR), despite unequal decoder sensitivities. We study an invertible linear layer between the encoder and diffusion process that shifts each direction's log-SNR. Its linear minimum mean-square-error (LMMSE) recovery risk has an exact spectral expression for any whitened latent distribution. Under an energy budget and a floor ensuring invertibility, minimizing decoder-sensitivity-weighted LMMSE risk integrated over the diffusion schedule yields a unique optimal allocation. The layer aligns with the decoder's expected pullback metric and equalizes marginal risk reduction across directions, computed by a deterministic spectral solver. At large budgets, the allocation follows a power law in sensitivity whose exponent is determined by the low-SNR tail of the loss weighting: one half for noise prediction and two thirds for data prediction under the cosine schedule, with a crossover on truncated schedules. We instantiate this principle as RB-LDC using Jacobian-based sensitivity estimates. On ImageNet at 256 x 256 resolution with SD-VAE and VA-VAE, trained RB-LDC improves reconstruction from noisy latents over budget-matched isotropic coding in all four metrics and five coding configurations, averaged over 15 SNRs and three pipeline seeds. It reduces average perturbed FID by 17.1 for VA-VAE block-local coding while preserving clean reconstruction. We also report intermediate SNRs where perturbed FID worsens. With a frozen diffusion model, RB-LDC yields lower FID point estimates in all 12 tested combinations of sampling progress and channel SNR under corruption during sampling.
On bounded Euclidean domains, we study how hidden-parameter geometry affects shallow ReLU$^k$ networks through results on approximation rates, saturation-type lower bounds, Gram and stiffness matrix spectra, Bernstein and Marcinkiewicz--Zygmund inequalities, discrete least-squares recovery, and inverse approximation. Our analysis uses smooth localization and dyadic Fourier estimates. We quantify parameter geometry by the fill distance $h$ and antipodal separation distance $\underline h$. For the prescribed network space $L_n^k$, representative approximation estimates take the form \begin{equation*} \begin{aligned} \inf_{g_n\in L_n^k}\|f-g_n\|_{\mathcal L^2(Ω')}&\lesssim h^r\|f\|_{\mathcal H^r(Ω)},\\ \inf_{g_n\in L_n^k}\|f-g_n\|_{\mathcal L^2(Ω)}&\gtrsim \underline h^{\frac{d+2k+1}{2}}\|f\|_{\mathcal L^2(Ω')}. \end{aligned} \end{equation*} The upper bound exploits target regularity up to the critical order $\frac{d+2k+1}{2}$, while the lower bound applies asymptotically to fixed targets smoother than this order. The upper estimate holds on an interior subdomain $Ω'$, whereas the lower estimate concerns the larger domain $Ω$. We also obtain geometry-dependent spectral estimates that quantify conditioning and coefficient stability. Further results establish norm discretization and regularized recovery from function values, and infer target regularity from approximation rates under coefficient or separation conditions. Altogether, these results describe how parameter geometry governs approximation accuracy, the stability of coefficient representations, discrete recovery, and the regularity information contained in convergence rates.
Molecular property prediction is fundamental to computational chemistry and drug formulation research, yet existing benchmarks remain fragmented across datasets, properties, and evaluation protocols, limiting systematic evaluation of model generalization. We introduce Chem World, a large-scale benchmark integrating 17 public datasets with over 800,000 molecular and chemical-system instances across 10 property tracks, covering single-molecule and multi-component systems, including drug solubility. Chem World provides a unified testbed for evaluating molecular representations and compositional modeling across diverse chemical properties. Building on the benchmark, we propose PACM (Physics-Aware Compositional Modeling), which combines molecular representations with composition-aware modeling and domain-specific physical constraints. Extensive experiments show that molecular language models provide strong and transferable representations, while PACM consistently improves prediction across diverse chemical systems. Chem World and our PACM-powered drug-property prediction Agent support generalizable chemical modeling and offer a foundation for AI-assisted biomedical research and drug formulation development.
Estimating precipitation at the global scale is vital for Earth system science and disaster response, yet observational coverage and measurement precision remain constrained. Existing solutions provide options that trade off desirable traits such as skill, latency, geographical coverage, temporal coverage, and spatial and temporal resolution. We present PARDIG, an artificial intelligence framework based on a spherical graph-mesh transformer architecture that produces near-real-time global precipitation estimates. PARDIG is trained on dense multi-modal inputs, including atmospheric state analyses and multi-spectral geostationary satellite imagery, to predict sparse, high-precision precipitation measurements from spaceborne radar. At inference, the trained model is applied densely across the globe at $0.1^\circ$ spatial and 15-minute temporal resolution, producing complete near-real-time precipitation fields from 2016 to the present, alongside a historical variant extending the record back to 1999. Evaluation against three independent radar networks (over the US, Europe, and Japan) and against over 36,000 surface stations worldwide shows that PARDIG consistently outperforms IMERG V07 (Final and Early), MSWEP V3, ERA5, and HRES across precipitation thresholds and regions, with the largest improvements at extreme intensities. Case studies of extreme precipitation events demonstrate that PARDIG successfully captures their spatial structure and timing. The improvements also extend to forecasting: WeatherNext 3, a global weather model, produces more skillful precipitation forecasts when trained to predict PARDIG. Both the historical and near-real-time PARDIG datasets are openly available under a CC BY 4.0 license.
Tensor wheel decomposition captures complex correlations in high-dimensional data through interactions between outer-ring factors and a high-order central core. However, updating these components requires the explicit construction and manipulation of large-scale matrices, which limits computational efficiency and incurs particularly high computational and memory costs for the central-core update. To address these limitations, we propose dual-core tensor wheel decomposition (DCTW), which factorizes the central core into two lower-order cores linked by a shared latent bond. Each core is coupled to a different group of outer-ring factors. We further propose a structure-cached acceleration strategy that avoids explicit large-scale matrix multi- plications and caches intermediate tensors generated during tensor network contractions for reuse across block updates. This reuse reduces redundant computation and avoids the explicit construction of large matrices. Complexity analysis and experiments show that the strategy based on structural caching accelerates optimization compared with explicit and implicit up- date schemes while limiting the increase in peak memory as the ranks grow. Experiments on color video completion and robust denoising show that DCTW matches or outperforms representative tensor network methods in reconstruction quality, computational efficiency, and scalability.
This paper develops a dual-space preconditioning framework for variational inequalities and root-finding problems beyond classical cocoercivity and Lipschitz continuity assumptions. To this end, we introduce both a novel cocoercivity-type condition and a relaxed Lipschitz continuity condition, and derive convergence of deterministic and stochastic methods under these generalized conditions. For isotropic preconditioners, the resulting algorithms can be interpreted as variable-stepsize variants of classical methods, extending recent analyses based on $(L_0, L_1)$-type growth conditions while allowing simpler proofs and larger stepsize ranges. We also show that the framework naturally handles variational inequalities through weak Minty-type arguments. Finally, we study the associated continuous-time dynamics and derive a variational and optimal control interpretation of the preconditioned flow. Overall, the results show that dual-space preconditioning provides a flexible mechanism for designing and analyzing operator methods beyond the standard Euclidean Lipschitz setting.
A run that stops at its first wrong decision shows the queries and their correct labels up to and including that decision, and nothing after it. We study how many such runs are needed for learning. Each run tests a hypothesis, the pilot, chosen beforehand from a fixed binary class of VC dimension at most $d$, on a fresh record of at most $D$ queries drawn from one unknown distribution that does not depend on the pilot. The terminal information of a record is shown only if the pilot makes no discrepancy, and a bounded loss, fixed in advance, is attached to the position where a hypothesis stops. If the discrepancy probabilities of members of the class have infimum at most $f$ and their risks have infimum at most $r$, one learner uses $\widetilde O((d+1)[D(f+\varepsilon)+r]/\varepsilon^2)$ runs and $\widetilde O(D(1+f/\varepsilon))$ distinct pilots on every history. It returns a member of the class and an interval of width at most $\varepsilon$ containing, with probability at least $1-δ$, both the output's risk and the optimal risk. We also treat unknown ceilings and expected costs. Lower bounds for finite classes show that each order is necessary in the worst case, possibly on different instances, at positive dimension, small accuracy and fixed confidence. The learner enumerates label patterns of the class on displayed queries, possibly in exponential time; the results, under standard measurability conditions, concern statistical resources only. The proof combines a gain computable from stopped displays, exponential weights, a sparse depth-robust graph and a harmonic-mean bound.
Mixed-reality (MR) P300 interfaces can register selectable destinations, such as wheelchair goals, directly in the user's surroundings. When the cues disappear between flashes, however, the user must retain an intended target that is no longer visible. We tested whether such an interface supports target selection and whether giving each cue a stable colour-shape identity improves it compared with visually uniform spheres. Six healthy adults completed four trials in each cue condition of a 5x5 row/column task on a head-mounted MR display, with EEG from Fz, Cz, and Pz. Shrinkage linear discriminant analysis was evaluated with nested validation in which complete trials were held out from class balancing, hyperparameter selection, and fitting. Both conditions evoked a parietal target-related positivity. The decoded cell was correct in 18 of 48 held-out trials, against 1.9 expected by chance (binomial p < 1e-12), and in three participants individually. Cue format made no detectable difference: complete-target accuracy was 9/24 in both conditions (paired difference 0.0 percentage points, 95% CI [-37, 37]), and held-out AUC was 0.609 for spheres and 0.585 for object cues. Disappearing-stimulus MR P300 selection is therefore feasible under strict trial-level evaluation, but the benefit of object identity, if any, is too small to resolve in a pilot of this size.
Artificial intelligence and machine learning (AI/ML)-based regression models support operational decision-making in optical networks but typically expose only point predictions, which carry no statistically controlled information about their reliability. This paper proposes a post-hoc conformal risk control (CRC) framework that keeps a pretrained AI/ML regressor fixed, provides a finite-sample guarantee on uncertainty band miscoverage, and maps the band to operational decisions through policy rules. The guarantee applies to interval miscoverage, while decision-error rates are evaluated empirically. We instantiate the framework for quality of transmission (QoT)-aware lightpath (LP) feasibility assessment, in which a regressor predicts optical signal-to-noise ratio (OSNR) under domain shifts caused by fiber, amplifier, and switching upgrades. Feature shift contribution scores identify the LP features whose relation to QoT changes the most across a technology transition, and two policies translate the bands into feasibility decisions, allowing operators to tune the trade-off between conservatively rejecting or aggressively accepting LP realizations. Experiments on open space-division multiplexing (SDM) QoT datasets over the CONUS topology show that, for a target coverage of 90%, the uncertainty bands meet the target in all 170 trials spanning 17 domain shifts and ten calibration-test partitions, whereas a source-only quantile regression (QR) baseline meets it in none. Under severe shifts, the efficiency-oriented (EO) policy empirically improves zero-shot (ZS) feasibility-decision accuracy from about 85% to above 99%, approaching a transfer learning (TL) policy while avoiding retraining. The framework provides finite-sample control of uncertainty band miscoverage for regression-based optical network decision support, with potential applications beyond QoT-aware LP feasibility assessment.
Interpretability demonstrations often show that intervening on a group of neurons changes a model's answer. A recent example removes an 18-neuron group in Qwen3-32B and the model answers "Simba" instead of "Scar" to a two-hop Lion King riddle. Such a demonstration establishes that the group matters, but not how much of it is necessary, whether other groups could do the same, or whether the effect carries over to other inputs. We ask: when intervening on a group of neurons changes a model's answer, how much of that group is actually necessary? For every selected group we measure all 4,096 subsets of 12 MLP neurons. On a two-alternative capital task (Qwen3-0.6B), zero-ablating 12 selected neurons lowers the answer margin by 27% while random neurons barely change it, yet replacing the same neurons with their values from other questions also barely changes it: their activations are nearly constant across questions, and we find no evidence that they carry question-specific content. On two-hop relation chains, patching 12 neurons with activations from the first-hop question shifts the answer to the bridge entity (from Scar to Simba): the greedy answer starts with the bridge in 9/11 chains for Qwen3-1.7B, 9/11 for Llama-3.2-1B and 8/10 for Gemma-3-1B; random neurons never do. The full group is rarely necessary: a few neurons often suffice, and in many chains disjoint subsets each flip the answer on their own, in an exploratory analysis most often when the model is less confident. Group effects transfer to rephrasings of the same chain but are much weaker on other tested chains. We study neuron-level causal interventions and alternative subsets; we do not recover the full connectivity of circuits.
We study how outliers affect the hard-margin linear support vector machine when the dimension grows while the sample sizes remain fixed. For one-sided contamination, the centered Gram matrix converges to a constant inlier block plus an outlier-diagonal component, and the limiting dual problem has a closed-form solution. All outliers act through one effective distance. This representation yields explicit thresholds for loss of inlier support, margin shrinkage. intercept displacement, and asymptotic misclassification. We then treat contamination in both classes. The limiting intercept is the multiplier of the class-balance constraint, and the two classes pull it in opposite directions. Consequently, at most one class can collapse or be asymptotically misclassified, whereas symmetric contamination leaves the limiting discriminant function unchanged even though the margin shrinks. Seven numerical experiments verify the dual allocation, phase transitions, and discriminant limits.