Papers

Locating periodic solutions of chaotic dynamical systems normally requires an initial guess close enough to the target orbit for numerical continuation or gradient-based search to converge. We show that Physics-Informed Neural Networks (PINNs) trained on sparse, noisy observations without initial conditions recover periodic orbits of the gravitational three-body problem, including orbit families absent from the training data. The method rests on a second-order ODE formulation, fixed-frequency Fourier features, percentile-based adaptive refinement, and a trainable scaling parameter, each validated on forward problems. Across two 100-seed ensembles, $23$–$25\%$ of runs converge to families not present in the training data. We then ask what determines which family emerges. Two $\chi^2$ tests give a consistent answer: changing the training data source significantly shifts the distribution of recovered families ($p < 0.001$, Cramér's $V = 0.339$), whereas switching between the two initialization distributions tested does not ($p = 0.620$, $V = 0.094$). The random seed selects which family a given run recovers; the distribution the weights are drawn from does not shift the aggregate frequencies, but the training data does. The evidence is empirical: we do not characterize the loss landscape analytically, and PINNs remain slower than conventional integrators on well-posed initial-value problems. What the experiments establish is that the recovered orbits are verifiable rather than merely plausible: the identified ones refine to genuine periodic solutions, a network trained on Lagrange data recovers the figure-eight choreography (Li–Liao class I.A.1, matched to seven significant digits in $T^*$), and one trained on figure-eight data recovers a Broucke–Hadjidemetriou–Hénon orbit closing to $\delta_T < 10^{-9}$.

Concept erasure techniques (CETs) edit text-to-image diffusion models to erase undesired targets such as NSFW content or copyrighted styles, while preserving model utility on benign concepts. Current CETs face a trade-off between erasure robustness and utility: stronger edits erase the target more reliably but degrade utility on non-target concepts, and vice versa. This stems from how existing methods define what to erase and what to preserve. Many CETs rely on static concept banks specified manually, generated by LLMs, or selected by CLIP image-text similarity. Such banks do not model how prompts steer the model during denoising, leaving it vulnerable to triggers that reintroduce the target while suppressing nearby benign concepts. We present Preservation-aware Adaptive Ranked Subspace Expansion (PARSE), a training-free framework for robust concept erasure in latent diffusion models. Given a target, PARSE queries the diffusion model with classifier-free guidance to dynamically discover target-inducing erase concepts and nearby retain concepts in the model vocabulary. It then edits the cross-attention value space with a preservation-aware projection that removes target directions while leaving retain directions intact. For triggers beyond this vocabulary-indexed space, PARSE iteratively searches for re-emergence triggers by textual inversion and adaptively expands the erased subspace only when a new trigger direction does not conflict with retain semantics. We also introduce the Balanced Erasure Utility Score (BEUS), which combines robustness (ASR under multiple attacks) and utility preservation (FID) via bounded monotone transforms and harmonic mean aggregation. Experiments on NSFW, artistic style, and object erasure, with a large-scale robustness-utility analysis over many CET baselines, show that PARSE erases multiple concepts robustly without sacrificing post-edit utility.

Text-to-image diffusion models expose many inference-time sampling parameters, including prompts, negative prompts, classifier-free guidance scales, and noise schedules. These parameters are typically manually chosen once and then held fixed across prompts and denoising timesteps, even though different prompts and stages of generation can benefit from different parameter values. We introduce LeSAMP, a framework for learning prompt-conditioned, timestep-varying sampling parameters. We formulate parameter selection as a reinforcement learning problem: Given a user prompt, a large language model is trained to emit schedules for the chosen sampling parameters. We optimize our model using rewards from human preference models and VLM-as-a-judge. We evaluate our model on Flux.1 [dev] and Stable Diffusion 3.5, and find that compared to baselines, LeSAMP has a win rate of up to 68.12% using human preference scores and 73.37% using VLM-as-a-judge. These gains are validated in a user study where we achieve win rates of up to 59.46% over previous baselines. Our results suggest that learned sampling-parameter policies provide a complementary approach to existing post-training methods for improving diffusion model outputs.

Dissolved gas analysis (DGA) is crucial for diagnosing early power transformer failures. Traditional DGA interpretation methods like Duval Triangle, IEC ratio, Roger ratio, Doernenburg ratio and Key Gas are inconsistent and vary in accuracy, especially for multiple fault conditions. We propose an Adaptive Multi-Fuzzy Logic (AMFL) model integrating multiple DGA methods with fuzzy logic and a dynamic weight adjustment mechanism. Unlike existing approaches with fixed weights, this system iteratively evaluates each method's diagnostic performance, identifies multiple fault types, and adjusts weights based on fault prediction accuracy. A feedback-based optimization recalibrates weights after each cycle to ensure optimal solution convergence. The model, implemented in MATLAB/Simulink, is validated against DGA datasets with known error conditions. Results show the AMFL model significantly improves diagnostic accuracy, especially in complex error scenarios, and enhances adaptability to new datasets. Comparative analysis demonstrates the proposed method outperforms traditional fixed weight multi-fuzzy systems in accuracy, consistency, and reliability of error detection. This work provides a robust, flexible diagnostic tool for transformer condition monitoring and supports more accurate asset management decisions.

Accurate State-of-Health estimation is essential for safe battery operation and cost-effective maintenance. Although numerous health indicators have been derived from constant-current (CC) and constant-voltage (CV) charging phases, their effectiveness under realistic cross-battery validation remains insufficiently studied. This work addresses this gap through a systematic comparison of CC-only, CV-only, and combined indicator sets using rigorous Leave-One-Battery-Out (LOBO) validation on the NASA battery aging dataset. Four CV-phase indicators and CC phase duration are evaluated individually and in combination. Results show that the combined CC+CV approach achieves the best performance (R2 = 0.874), confirming that CC and CV phases capture complementary degradation information. Moreover, a 119% performance gap is observed between standard 5-fold cross-validation and LOBO validation, indicating that conventional evaluation overestimates practical accuracy. Based on these findings, practical guidelines are provided for indicator selection under data and computational constraints.

Variational autoencoders (VAEs) transform high-dimensional, often noisy data into a compact latent representation, making downstream optimization more tractable. Three challenges persist in VAE-based constrained optimization: (i) sampling effectively within the latent space, (ii) identifying the active decision variables that actually influence the objective and constraints, and (iii) enforcing constraints without destabilizing training. We propose a Multi-stage Constrained Optimization Framework (MCOF). First, an entropy-constrained VAE (EC-VAE) coupled with a feature selector embeds objective and constraint information into a designated subset of latent variables, so that optimization proceeds over a low-dimensional subspace while the remaining coordinates supply solution diversity. Second, a Uniform Transformation (UT) module applies a per-dimension probability integral transform, replacing the irregular aggregate posterior with a uniform distribution over a bounded box and mitigating posterior collapse and Gaussian mixture bias. Third, a constraint-priority filter method (CPFM) solves the resulting surrogate problem by alternating violation-reduction and objective-reduction steps under a filter acceptance test, returning solutions that are feasible for the learned surrogate to a specified tolerance without requiring multiplier estimation. Finally, unselected latent coordinates are resampled to generate diverse decodings of a single optimized solution. We validate MCOF on a synthetic problem, where we ablate each stage and recover the analytic optimum, and on a ZINC250k drug design task, where the generated molecules satisfy the imposed constraints and are entirely novel relative to the training set.

Fully homomorphic encryption (FHE) lets a server run inference on encrypted data with strong privacy guarantees, but running a Transformer under FHE is expensive. Its non-linear operations, such as softmax, normalization, and activation, must be replaced with polynomial approximations that the CKKS scheme supports, and the depth of these approximations dominates inference cost. Existing FHE Transformers use hand-tuned approximation settings, such as iteration count and polynomial degree, applied uniformly across layers, models, and tasks. Hand-tuning is slow and error-prone. Even a single uniform setting has about $10^7$ choices, and manual search cannot exploit layer-wise variation. AutoFHE, the only automated method with multi-objective search, targets ReLU-only CNNs and needs full fine-tuning per candidate, which is too costly for Transformers. Per-layer settings also push the search space to about $10^{85}$ for BERT and ViT and $10^{228}$ for LLaMA3, beyond both manual and fine-tuning-based search. We present ATLAS, a training-free framework that automates this search by treating each layer's approximation setting as a multi-objective optimization over latency and accuracy. The problem is hard: the decision space is large (96 or 256 variables), each configuration takes 70 to 1,000 seconds to evaluate even in cleartext, and 85 to 90 percent of configurations are invalid. ATLAS handles this with a two-stage optimization strategy and a surrogate model, completing the search in about one hour. Compared to an iterative softmax baseline, ATLAS cuts multiplicative depth and end-to-end latency by about 35 percent with little accuracy loss, and works across encoder-only, decoder-only, and vision Transformers, complementing parallel work on packing and matrix multiplication.

This paper develops an online, off-policy policy-iteration framework for reinforcement learning (RL), based on sparse Gaussian-mixture-model Q-functions (S-GMM-QFs). The framework reconciles streaming, non-stationary data with the Riemannian structure of the parameter space while handling distributional mismatch through experience replay. S-GMM-QFs are introduced via Hadamard overparametrization, enabling interpretable sparsification through smooth regularization that facilitates Riemannian-based optimization. Overparametrization allows the framework to adaptively identify meaningful components from a large initial pool, yielding sparse models where interpretability emerges naturally from geometry: each component's parameters (means and covariances) explicitly encode its geometric role in the ambient state-action space. These geometric roles are learned through online gradient descent on a smooth objective over a (Cartesian-product) Riemannian manifold. Numerical tests demonstrate that S-GMM-QFs match or exceed deep RL methods while using substantially fewer parameters and achieving faster improvement per observed transition. Notably, parameter efficiency and interpretability combine to maintain strong generalization in low-parameter regimes where sparsified deep RL approaches degrade.

Photonic-crystal surface-emitting lasers (PCSELs) can combine high-power operation with narrow-divergence surface emission, but optimizing coupled parameters requires costly full-wave simulations. Deep Q-network (DQN) optimization can reuse simulated transitions to guide edits, yet which value-learning mechanisms remain reliable under tight simulation budgets is unknown. We address this gap by comparing baseline DQN and six value-based variants for a seven-variable PCSEL design under a shared objective, simulator, 83-call budget, and four matched initializations. Beyond endpoints, we analyze sample efficiency, policy behavior, and physical response to separate learning gains from favorable starts or exploratory jumps. Dueling DQN is the only variant to improve all four seeds. Relative to the first evaluated designs, its selected structures increase the mean quality factor () from to (), reduce wavelength error by 64%, and increase upward power by 47%; compared with baseline DQN, they achieve a higher mean under the same budget. Other variants yield no consistent improvement; Double DQN reproduces baseline trajectories, while Rainbow-lite shows high upside but strong seed dependence. These results identify Dueling DQN as the most reliable configuration tested for simulation-budget-limited PCSEL inverse design and provide a reproducible framework for attributing algorithmic gains in scientific optimization. The source code is publicly available at https://github.com/Longying-Wen/PCSEL-RL.

We study an integrated pickup-and-delivery problem on sparse, non-Euclidean networks that jointly optimizes cyclic routing, cargo flow allocation, and cross-cycle service. The tight coupling of these operational constraints creates a complex discrete-continuous decision space with highly restricted feasible regions. To overcome these computational challenges, we propose Double-Channel Graph Attention (DCGA), an end-to-end reinforcement learning framework. DCGA isolates network reachability and demand-service logic into separate graph channels and constructs valid routes using a simulator-coupled, constraint-informed decoder. Experiments on LinerLib benchmarks demonstrate that DCGA achieves seconds-level inference and delivers state-of-the-art solution quality on instances beyond a specific scale, with its advantage over existing baselines widening significantly as problem size increases. Supported by extensive stability and ablation analyses, our results demonstrate that this structure-aware learning approach provides an effective, low-latency engine for realistic routing-and-flow optimization.

Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited. We extend Fourier neural operators (FNOs) with minimal architectural modifications along two directions. For parameterized dynamics, we propose a hypernetwork-based modulation that conditions the operator on physical parameters. For coupled systems, we conduct a systematic exploration of architectural choices, examining how operator components can be adapted to balance shared structure with cross-variable interactions while retaining the efficiency of standard FNOs. Evaluations on benchmark PDEs, including the one-dimensional capacitively coupled plasma equations and the Gray-Scott system, show that our methods achieve up to 55-72% lower errors than strong baselines, demonstrating the effectiveness of principled modulation and systematic design exploration.

Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive. Practitioners currently lack principled guidance on how many failure examples suffice for a given model and accuracy target. This paper develops a sample complexity framework for RUL prediction comprising seven main results organised around three themes. First, we establish fundamental learning rates: a distribution-free generalization bound shows that the uniform deviation of the mean squared error decreases as $O(B^{2}\sqrt{p/n})$, where $p$ is the model complexity and $n$ the number of trajectories, and a minimax lower bound proves that the $\Theta(p/n)$ rate is unimprovable.} \rev{Second, we quantify how domain knowledge accelerates learning: incorporating degradation physics reduces data requirements by up to two orders of magnitude for deep networks, a Bernstein-type analysis achieves the minimax-optimal $O(p/n)$ rate under high signal-to-noise conditions, and closed-form penalties reveal when an incorrectly assumed physics model hurts rather than helps. Third, we characterise the impact of data quality: fleet variability induces an irreducible bias$-$variance tradeoff, while right-censored observations suffer an efficiency loss that depends critically on the degradation class.} Closed-form expressions are provided for exponential, power-law, and stretched-exponential degradation. \rev{Cross-domain validation against published turbofan, battery, and bearing benchmarks confirms the theoretical predictions within a factor of 2$-$3 on average. The results yield practical guidelines for planning data collection, selecting model complexity, and evaluating physics model assumptions in prognostics applications.

Local regularization assigns each hypothesis a test-point-dependent score and predicts with a minimum-score hypothesis consistent with the sample. Asilis et al. asked whether this principle characterizes multiclass PAC learnability. We give a negative answer. There is a countable class of Daniely–Shalev-Shwartz dimension at most two with realizable PAC sample complexity \[ O\!\left(\frac{1}{\varepsilon}\log\frac{1}{\delta}\right), \] that no local regularizer learns. Hypotheses are edges of complete graphs and instances are tournaments. At a test tournament, the scores fix an edge ranking while the training sample independently removes competitors. Cyclic triangles force enough inversions that surviving competitors produce constant population error at arbitrarily large sample sizes.

Expensive constrained optimization problems in real-world industry design often involve constraint thresholds that are difficult to determine in advance. Engineers may need to adjust constraint thresholds to explore different feasibility-performance trade-offs, requiring solutions under a wide range of threshold settings. However, existing constrained Bayesian optimization methods treat each threshold configuration independently, leading to repeated optimization and failing to exploit the shared relationship among continuously varying thresholds. To address this challenge, we propose constraint-bound agnostic Bayesian optimization (CBA-BO), a learning-based framework that learns a parametric constraint model mapping thresholds to optimal solutions. Once learned, CBA-BO directly predicts solutions for arbitrary unseen threshold configurations without additional optimization, with a one-step Bayesian optimization refinement further improving solution quality. Experiments on benchmark and engineering problems demonstrate that CBA-BO learns a transferable threshold-solution mapping, enabling efficient prediction and optimization for arbitrary threshold queries. An intent-guided constraint-bound recommendation mechanism is further developed to improve objective performance while satisfying user-specified constraint preferences.

Predicting cellular responses to unseen chemical perturbations is challenging due to unknown targets and mechanisms, high-dimensional expression responses, and limited experimental coverage of the large small-molecule design space. We propose PerturbPFN, a PFN-style amortized model for unknown-target perturbation prediction under a hierarchical synthetic structural prior. Instead of directly regressing high-dimensional expression responses, PerturbPFN infers a latent system graph, sparse atomic intervention targets, and intervention strengths, then propagates their effects through an SCM decoder. The model is trained entirely on prior-predictive synthetic episodes generated from biologically motivated graph and expression simulators, enabling structured in-context learning without test-time gradient updates. We evaluate PerturbPFN on both real single-cell perturbation data and synthetic benchmarks, covering effect prediction, target identification, and regulatory structure discovery. Our results show that PerturbPFN offers a complementary trade-off to specialized baselines, achieving competitive perturbation prediction with low inference cost while exposing interpretable intermediate estimates of targets, strengths, and system structure.

We propose a neural representation for minimal surfaces. Unlike prior approaches based on discretization or Physics-Informed Neural Networks (PINNs), where meshes or neural fields are optimized to approximate the governing equations, our method builds on an exact representation, similar to the classical Weierstrass–Enneper parameterization, yielding minimal surfaces up to negligible quadrature error in evaluation. We formulate a training objective for the Plateau problem that optimizes over this representation.

Unexpected shocks recur in global operations, requiring decision rules that adapt as market and operating conditions change. Many operational systems also have hierarchical structures in which long-term and short-term decisions pursue a shared objective. We study how hierarchical reinforcement learning can strengthen resilience by adapting these interdependent rules jointly. We develop a two-timescale hierarchical reinforcement learning framework that adapts long-term and short-term policies at their respective time scales. Because the policies are interdependent, we synchronize their updates and prove, to our knowledge, the first convergence guarantees for coupled two-timescale learning. Over $T$ periods, our policies' average gap from an optimal policy pair is $O(T^{-1/2})$, improving to $O(\log T/T)$ when poor decisions produce clearer profit losses. In a used-car case study, inventory replenishment is the long-term decision and customer-arrival pricing the short-term decision. Relative to the strongest partially adaptive benchmark, the framework increases mean profit by $9.2\%$ under joint demand-supply shocks and by $11.8\%$ under a prolonged shock scenario, while maintaining a more stable profit trajectory over time. Short-term adaptation addresses routine seasonality and one-sided disruptions by responding immediately to changing conditions. Under joint demand-supply shocks, however, it is insufficient alone; long-term adaptation is also needed to create favorable conditions for short-term decisions. Joint adaptation thus yields higher and more stable profits through disruption and recovery. Because many organizations already use hierarchical planning, the framework strengthens operational resilience without altering existing decision structures.

Decision-makers in learning environments face a dilemma when their short-term optimal actions may not favor their long-term benefits the most. To understand the fundamental tradeoff behind the dilemma, we study adaptive experimentation with post-commitment reward shifts. During an experiment phase, the decision-maker may adaptively test multiple options; during a subsequent commitment phase, the decision-maker must commit to a single option, whose reward may differ from its pre-commitment reward. We propose the Reserved Arm Eliminations for Commitment (RAEC) algorithm, which reserves a predetermined portion of the experiment phase to identify the best post-shift option while using the remaining rounds to minimize short-run regret. We establish regret upper bounds for RAEC across all parameter regimes and matching minimax lower bounds, providing a tight characterization of the cost of balancing short-term performance and long-term commitment. A key implication is that deciding in advance how much of the experiment phase to reserve for the commitment decision is sufficient to achieve the best possible worst-case regret rate; adapting this amount as more data are observed does not improve the rate. We further study extensions with structural knowledge of reward shifts and with concave commitment rewards and portfolio choice. Numerical experiments confirm that our proposed algorithms achieve the regret predicted by our theory and outperform other baselines.

Electrocardiograms (ECGs) are widely used for cardiovascular risk prediction, yet models often fail to transfer across hospitals because of protocol, population, and measurement differences. We benchmark cross-dataset generalization on three tasks - heart failure classification, 30-day all-cause mortality, and 30-day mortality among sinus-rhythm ECGs - using two large cohorts (MIMIC-IV and the Alberta Cohort). To reduce vendor-specific measurement mismatch, we build a harmonized, interpretable feature representation computed directly from raw waveforms: FeatureDB morphology/heart-rate-variability summaries plus compact time-frequency descriptors (autoregressive and wavelet features). We train XGBoost models on this unified feature space and evaluate with patient-disjoint internal and bidirectional external testing. We pre-specify two hypotheses: (H1) external AUROC retains at least 90% of source-site internal AUROC under transfer, and (H2) internal AUROC of the harmonized feature set stays within 10% of dataset-native machine-measurement models. Across tasks, internal AUROC is 0.79-0.82 and cross-dataset AUROC is 0.74-0.78, with larger and direction-dependent AUPRC shifts under transfer. As an exploratory benchmark, an end-to-end ConvNeXt model trained directly on raw ECG waveforms with age and sex achieves higher internal AUROC, while the harmonized representation remains competitive in relative cross-dataset transfer stability. These findings show that a consistent waveform-derived feature interface preserves performance, supports realistic external validation, and provides a transparent alternative for cross-site clinical prediction.

Continuous cuffless blood pressure (BP) monitoring is essential for connected health systems and wearable devices, enabling early detection, longitudinal tracking, and personalized management of cardiovascular disease. Many prior approaches attempt to estimate BP indirectly by reconstructing electrocardiography (ECG) from photoplethysmography (PPG), assuming ECG provides a stronger physiological link to BP. However, ECG sensing is less accessible in wearable settings and may introduce unnecessary complexity. In this work, we first perform a large-scale physiological correlation analysis on the MIMIC-III waveform database, revealing that PPG exhibits substantially stronger coupling with arterial blood pressure (ABP) ($|r|=0.247$, $p<0.001$) than ECG does ($r=0.018$, $p=0.187$), challenging the assumption that ECG provides a superior intermediate representation. Motivated by this insight, we conduct a systematic comparison between direct PPG-to-BP prediction and ECG-mediated pipelines using multiple state-of-the-art deep learning models. Across 1.74M segments from 3,127 patients, direct PPG-to-BP prediction achieves British Hypertension Society Grade A performance ($\mathrm{MAE}_{\mathrm{SBP}} = 4.82 mmHg$, $\mathrm{MAE}_{\mathrm{DBP}} = 4.31 mmHg$), outperforming all ECG-mediated approaches, which achieve only Grade B accuracy. Our findings suggest that accurate continuous BP monitoring can be achieved directly from wearable PPG signals, enabling simpler, more efficient pipelines for real-world connected health systems.

Self-driving laboratories increasingly rely on multi-fidelity Bayesian optimization (MFBO) to balance cheap, approximate evaluations against scarce, expensive ones, with a predictive surrogate at its core. Gaussian processes (GPs) are the default choice, but they scale poorly as data accumulate and assume a smooth landscape that molecular and materials search spaces routinely violate. Transfer learning offers an alternative suited to this regime: it learns a representation from abundant cheap data and adapts it to sparse expensive data. Despite its use in property prediction, transfer learning has not been tested as the engine of a closed-loop optimization. Here we benchmark eleven transfer-learning surrogates against four GP methods under an identical selection rule, fidelity budget, and model size, across nine tasks spanning synthetic functions to real chemistry and materials problems. GPs win on smooth, low-dimensional functions but perform worst on molecular and materials problems, where transfer-learning surrogates reach substantially better solutions using far less computation. Because acquisition policy is held fixed across surrogates, this advantage is attributable to the surrogate itself. Uncertainty-driven exploration is not reliably beneficial, and calibration does not predict optimization performance, so greedy exploitation of the transfer-learned mean is the more robust default. Transfer learning is therefore the surrogate of choice for molecular and materials MFBO.

Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood. In the infinite-width limit, two different theoretical frameworks have been proposed. One reduces deep learning to kernel regression with a fixed kernel by assuming that the parameters remain close to their initialization, whereas the other allows the parameters to move away from their initialization, requiring the kernel itself to be optimized. In this paper, we study a three-layer neural network with a finite but large number of hidden units. We show that training the input-to-hidden weights yields a smaller generalization error than keeping them fixed. Furthermore, the latter setting exhibits singularities in the parameter space, whereas the former does not. These findings indicate that singularities play an essential role even in wide neural networks.

Adaptive optimizers are commonly parameterized by a fixed power of the second-moment estimate. Existing partially adaptive methods study exponents between momentum-like updates and the standard Adam square root, while the interaction between this exponent and the global learning rate is less understood. We perform a controlled cross-environment study using a paired four-environment classification problem with stable sparse features, environment-dependent spurious sparse features, dense features, and high-dimensional noise. Across \NumRuns{} source-training runs covering 21 preconditioning exponents $p\in[-0.5,0.5]$ and five learning rates $\eta\in[10^{-4},10^{-2}]$, we find that the exponent maximizing cross-environment accuracy decreases almost linearly with $\log_{10}\eta$. The fitted slopes range from $-0.270$ to $-0.300$, with $R^2$ between $0.972$ and $0.996$. At $\eta=10^{-2}$, source-validation selection still prefers positive exponents in all four environments, whereas cross-environment and worst-environment criteria prefer negative exponents. Checkpoint decomposition shows that lower $p$ reduces the learned spurious-to-stable and noise-to-stable weight ratios; under reversed correlation, it also reduces the magnitude of the harmful spurious margin. Negative $p$ is therefore not a universally optimal setting. It is a high-step-size allocation regime produced by the joint action of learning rate and preconditioning. The study also exposes a model-selection conflict: source-domain validation systematically selects a different preconditioning regime from the one that maximizes robustness to environmental change. The results are a single-seed, finite-budget mechanism study rather than a broad benchmark claim.

Urban cellular activity forecasting requires jointly modeling heterogeneous spatiotemporal signals, including SMS usage, mobile network traffic, and call activity. Existing methods often separate temporal modeling, spatial relation learning, and multi-signal prediction, relying on fixed graph structures or static multi-task learning schemes, which limits their adaptability to changing urban scenes. We propose SCRR-Net, a scene-conditioned spatial relation routing framework in which urban contextual information jointly controls spatial dependency selection and cross-task knowledge transfer. SCRR-Net includes a context encoder, a spatial graph expert routing module, a temporal Transformer encoder, and a task knowledge routing module. Experiments on the Milano and Trento datasets demonstrate that SCRR-Net consistently outperforms competing methods on SMS, network traffic, and call activity forecasting, while providing interpretable routing behaviors.

Cognitive workload reflects the mental effort required during task performance and is central to the design of adaptive human-machine systems. The use of biosignals to measure cognitive workload has been extensively researched and documented; however, studies examining the effects of combining heterogeneous biosignal modalities for this purpose remain limited. To provide insight into this area, we developed a unified, modality-agnostic, hierarchical Transformer-based architecture to process heterogeneous biosignal modalities within a single model. We use this framework in a pilot study evaluating all $31$ possible combinations of five modalities: Electrocardiogram (ECG), Electrodermal Activity (EDA), Respiration (RESP), Peripheral Oxygen Saturation (SpO$_2$), and Electroencephalogram (EEG), under leave-one-subject-out validation across three cognitively distinct tasks: abstract reasoning (IQ), arithmetic problem solving (MATH), and a game task (GAME). In this pilot setting, the results suggest that: (i) EEG is the strongest single modality, ranking highest in IQ, GAME, and the pooled ALL setting, where samples from all three tasks are combined; (ii) adding more modalities does not consistently improve performance; (iii) the full five-modality combination achieves the highest Average score of $73.02%$ on IQ and $68.08%$ when the Average scores are averaged over the four evaluation settings: IQ, MATH, GAME, and ALL; and (iv) the proposed method reduces model size by approximately $50%$ compared with late-fusion alternatives while maintaining a lower inference time.

Physics-informed neural networks (PINNs) use automatic differentiation to impose differential-equation residuals, but good agreement in function values does not necessarily imply accurate derivatives. This paper formulates derivative fidelity as a failure mode of PINNs and tests it with one-dimensional benchmarks. Multilayer perceptrons are trained only on function values for sin(x) and exp(x), while second derivatives obtained by automatic differentiation are evaluated separately. The hypothesis is strengthened by additional tests over training-point density, activation functions, endpoint-dense evaluation, and both L2 and maximum-error diagnostics. The results show that visually accurate function approximation can coexist with substantially larger second-derivative errors, especially near high-curvature boundary regions. The experiment provides a diagnostic protocol for distinguishing value accuracy from physics-residual reliability.

Source apportionment from sparse urban air-quality sensors is an inverse problem limited by sensor placement, wind-driven transport, background variation, and noise. Known or proxy emission inventories make attribution meaningful by restricting the unknown source field to a finite set of candidate groups, but do not guarantee those groups are distinguishable from the observations. We represent time-varying source activity with a low-dimensional nonnegative temporal basis and formulate inventory-based apportionment as a wind-conditioned lagged inverse problem in which each source–basis coefficient produces a sensor-time fingerprint. After projecting out a separate low-dimensional background space, the relevant object is the projected lagged response matrix $\widetilde H_\Phi$: exact identifiability at the chosen basis resolution requires its full column rank, while noise-robust attribution is controlled by its singular values, coefficient visibility, background absorption, pairwise coherence, and ray distance. We propose an identifiability-aware apportionment (IASA) framework that estimates nonnegative source–basis coefficients, reconstructs activity trajectories, and reports uncertainty and conservative grouping recommendations for indistinguishable sources. We instantiate it on a New Delhi platform built from government PM$_{2.5}$ and wind records, regulatory sensor locations, and four proxy source groups, and define controlled and observed evaluations of recovery, ambiguity, wind diversity, background stress, transport error, inventory robustness, and residual adequacy. IASA reports the attribution resolution defensible under the declared inventories, transport, background, lag, and noise rather than the most detailed possible vector.

Electroencephalography (EEG) generation is essential for alleviating data scarcity and enabling large scale neural modeling in brain computer interface applications. However, existing flow based approaches assume that every channel and every time segment within a sample shares a single global time progression, overlooking the fact that not all EEG moments are equal. To address this overlooked heterogeneity, we propose an adaptive EEG generation framework built on conditional flow matching. The framework introduces Position-Adaptive Time Scheduling, which tracks per position reconstruction error to modulate a position specific time progress within the flow matching trajectory. It further incorporates Factorized Spatio-Temporal Attention and a frequency aligned multi resolution spectral consistency loss to model inter channel dependencies induced by volume conduction and compensate for the power law spectral bias of EEG, thereby improving the quality of generated signals. Extensive experiments on three EEG datasets with distinct acquisition protocols and task semantics show that our framework consistently outperforms the strongest baseline, reducing TS-FID by up to 62.2% and improving downstream classification accuracy gain by up to 6.77 percentage points. These results suggest that the proposed method represents a promising step toward scalable, high fidelity data augmentation for real world brain computer interface applications.

Accurate fracture risk prediction is important for osteoporosis management, but commonly used clinical tools may not fully use information available in electronic health records (EHRs) and dual-energy X-ray absorptiometry (DXA) reports. We developed and externally validated time-to-event fracture prediction models among adults aged 50 years or older with clinically obtained DXA reports in 2 US health care systems. The development cohort was derived from NewYork-Presbyterian/Weill Cornell Medical Center and the external validation cohort from the Indiana Network for Patient Care. Predictors included demographics, lifestyle factors, prior fracture, comorbidities, medication exposures, osteoporosis treatment history, and DXA-derived T-scores extracted from radiology reports. The outcome was time from index DXA to first incident fragility fracture identified from structured diagnosis codes. We evaluated penalized Cox regression, random survival forest, gradient-boosting survival, and XGBoost survival models using 2 prespecified predictor settings and compared discrimination with clinically reported FRAX major osteoporotic fracture probabilities. The development cohort included 11,510 adults, of whom 858 sustained incident fragility fractures; the external validation cohort included 1,932 adults, of whom 180 sustained fractures. In internal validation, the expanded Cox model achieved a mean Harrell C-index of 0.779, compared with 0.653 for FRAX. In external validation, the corresponding Cox model achieved a Harrell C-index of 0.714, compared with 0.590 for FRAX; gradient-boosting survival had the highest external discrimination (0.725). EHR- and DXA-enhanced models showed better discrimination than clinically reported FRAX scores in this DXA-tested population, but calibration assessment, prospective evaluation, and implementation workflow assessment are needed before clinical use.

A stochastic Gumbel-Top-K router defines, for every token of a mixture-of-experts (MoE) model, a routing law: a distribution over ordered expert lists and mixture weights. We ask which joint distributions over the routing choices of different tokens are reachable while every individual token's complete routing law is held exactly fixed. We give a two-sided construction, Hierarchical Copula-Gumbel-Top-K (CGA). Within a group of related tokens, an exchangeable Gaussian copula positively correlates the Gumbel perturbations at each expert coordinate, which can increase within-group expert-set coherence. Across disjoint pairs of groups, a tunable antithetic construction introduces a selectable amount of negative dependence. We prove that both operations leave each token's ordered Top-K sample, mixture weights, and inclusion probabilities identical in distribution to independent routing at a routing layer conditioned on its pre-routing logits; conditional expected expert traffic is preserved as a consequence. We characterize the resulting trade-off: positive within-group coupling can only inflate the variance of realized expert loads relative to independent routing, while nonnegative cross-group opposition can only reduce it relative to flat coupling at the same within-group strength. Coherence and load dispersion are thus controlled by two complementary dependence dials on the invariance constraint surface. Because the base model is untouched, the dials can be driven by a small controller over frozen features, trainable with a score-function estimator: the frozen network is evaluated only in the forward direction, and gradients are confined to the controller. An initial small-scale pilot validates the mechanism and the training route, but does not establish task-level fine-tuning gains.