Much of the variation in financial time series is driven by market-wide shocks that cannot be predicted from an asset's own history. Per-asset self-supervised learning treats this variation as irreducible noise. Under a latent factor model, we show that conditioning prediction on the realized market factor makes the asset's market exposure necessary for optimal prediction, while reducing the noise against which the asset-specific component is learned. Building on this insight, we introduce Market-Conditioned JEPA (MC-JEPA), a joint-embedding predictive architecture for financial time series. During training, we construct a leave-one-out market condition for each asset from the future target embeddings of other assets and incorporate it through factor loadings derived from the asset's own representation. On 11 years of minute-level Chinese A-share data, MC-JEPA improves over per-asset JEPA across nine targets spanning returns, market exposure, risk, and liquidity, with the strongest and most statistically significant gains in exposure, risk, and liquidity. It achieves the best RankIC on all liquidity targets and on return horizons from two hours to five days, outperforming time-series foundation models and self-supervised baselines, and delivers the best portfolio performance in a historical backtest. Ablations show that the return and exposure gains require the condition to be aligned with the realized market movement. After restoring the volatility scale removed by normalization, the predictor's factor loadings rank stocks by market beta nearly as well as a supervised probe, without labels. A synthetic factor-model study with known parameters shows that conditioning improves the recovery of both market exposure and the asset-specific component.
Effective search and rescue (SAR) operations require autonomous systems capable of coordinating multiple heterogeneous agents, adapting to dynamic hazards, and aligning with human mission intent. Existing language-guided reinforcement learning (RL) methods primarily focus on single-agent instruction following and lack mechanisms for team-level coordination in complex, partially observable environments. This paper presents a Cognitive Multi-Agent Framework based on Language-Grounded Hierarchical Reinforcement Learning (LG-HRL) that integrates natural-language understanding, hierarchical policy decomposition, and a shared cognitive workspace to achieve cohesive multi-agent behavior in SAR scenarios. Human instructions are interpreted by a large language model (LLM) and transformed into structured semantic cues that guide high-level strategy selection and role assignment across UAV and UGV agents. A formal Language-Grounded Multi-Agent Hierarchical Decision Process (LG-MAHDP) is introduced to model the interplay between semantic grounding, hierarchical control, and distributed coordination. Comprehensive experiments in a simulated disaster environment show that LG-HRL improves learning speed by 2.3 times, increases coordination coherence by 37%, and enhances subgoal accuracy and hazard avoidance by 46% and 31%, respectively. The system achieves 20-30% higher victim rescue rates, demonstrates emergent role specialization, and adapts immediately to human verbal updates. Ablation studies confirm that both the shared cognitive workspace and language grounding are critical to overall system performance. Overall, this work establishes a new paradigm for language-guided multi-agent SAR robotics, demonstrating that semantic grounding combined with hierarchical reasoning enables safer, more efficient, and more interpretable autonomous rescue operations.
Neural operators (NOs) have been introduced as deep learning-powered solutions to the computational bottleneck of solving families of problems. Once trained, an NO can rapidly output approximate solutions, avoiding the need to rerun classical solvers. However, standard NO architectures cannot guarantee static no-arbitrage when predicting European call-price surfaces from market or model features and, as we verify experimentally, can yield negative PnL in downstream trading tasks. We introduce a certifiably arbitrage-free (AF) and universal encoder-decoder NO framework, continuously mapping inputs from a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ over any fixed subset of $[0,\infty)^2$ to a convex combination of arbitrage-free European call-price surfaces by continuously solving an approximate nearest-neighbour problem. We show that a nearest arbitrage-free correction of an unconstrained predicted surface need not exist, implying that no-arbitrage cannot, in general, be restored through post-processing. Further, we show that standard NOs, such as the FNO and certain encoder-decoder NOs, admit parameter configurations whose outputs violate static no-arbitrage. Thus, out-of-the-box NOs generally cannot be certifiably restricted to arbitrage-free configurations, but may only be guided towards them through PINN-type regularization during training.
Partial differential equation (PDE) solvers underpin modern computer graphics, geometry processing, and scientific computing. Classical Monte Carlo PDE solvers such as Walk-on-Spheres (WoS) provide mesh-free estimations that are unbiased, but with accuracy limited by sampling and numerical approximation. Learned solvers are fast but biased and brittle under distribution shift. We therefore present MC$^2$, a hybrid Neural Network-Monte Carlo PDE solver that treats a low-budget Monte Carlo solution as a structured estimator of the true field and learns a single-pass neural correction to recover a high-fidelity solution. MC$^2$ matches the accuracy of solutions using over $1000\times$ more Monte Carlo samples, outperforming all evaluated mesh-free classical, denoising, and neural-operator baselines. To enable reproducible study of finite-compute PDE solving, we additionally release PDEZoo, the largest standardized elliptic PDE benchmark to date: 2 million PDEs spanning 5 elliptic families and unlimited geometric compositions, with analytic ground truth and multi-budget Monte Carlo trajectories. Together, MC$^2$ and PDEZoo (1) empirically establish that finite-sample Monte Carlo error is structured, learnable, and correctable in a single forward pass, (2) show that we can solve PDEs $\sim$218$\times$ faster than WoS at matched accuracy and achieve a $\sim$171$\times$ reduction in inference time relative to state-of-the-art diffusion methods while attaining higher accuracy, and (3) provide the reproducible evaluation infrastructure the field has so far lacked. Code & Data: https://mc-error-correction.github.io
In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in EBMs is challenging for conventional inference methods. This work is a review paper that brings together these different methodological contributions within a unified framework, highlighting the connections among noise contrastive estimation (NCE), reverse logistic regression (RLR), Bennett's acceptance-ratio (BAR) method, multiple importance sampling (MIS), and bridge sampling within the context of EBMs. Some of them are equivalent under specific conditions. This unified perspective clarifies relationships among existing methods and enables the development of new estimators, with the potential to improve statistical and computational efficiency. Furthermore, this study helps elucidate the success of NCE in terms of its flexibility and robustness, while also identifying scenarios in which its performance can be further improved. Our aim is to provide a self-contained and accessible treatment, with clear and straightforward derivations, that brings together these contributions within a common framework and makes the main results and their underlying ideas understandable to a broader readership. The contribution is twofold. First, this work serves as a comprehensive tutorial for researchers entering the field, introducing the fundamental concepts and derivations. Second, it offers a thorough review for experienced practitioners. The code used in the numerical experiments is available to support the reproducibility of the results.
Neural surrogates for engineering models are often trained on large collections of simulated solutions. We investigate whether physics-informed neural networks (PINNs) can achieve accurate predictions from scarce labelled observations by incorporating governing equations and prescribed initial and boundary conditions. We introduce hierarchical loss weighting (H-PINN) and its gradient-direction-aware extension (HO-PINN), which adjust the emphasis on physical constraints according to higher-priority losses. Hierarchical PINNs are compared with Vanilla PINN, tuned gradient boosting, support-vector regression, and Gaussian-process regression on a heat equation and three heterogeneous two-phase-flow benchmarks. Experiments use 20--1000 labelled states and ten paired seeds. Each label is one coordinate--state observation, not a complete simulation. At least one PINN variant achieves the highest mean primary-target \(R^2\) in each interpolation and equation-assisted forecasting comparison at 20 and 50 labels. The advantage for water saturation persists across all tested budgets. Hierarchical weighting reduces variability across runs in selected settings. These results demonstrate that known physics can support accurate neural surrogate predictions from very few solution observations, at substantially higher fitting cost than the tested classical regressors.
Ultrasonic guided wave (UGW) inspection has become an effective method in structural health monitoring (SHM). While machine learning has enhanced damage detection capabilities, purely data-driven models remain constrained by extensive labeled datasets and limited physical interpretability. Standard multi-layer perceptrons (MLPs) further suffer from spectral bias (F-Principle) in high-frequency regimes, prioritizing low-frequency components while failing to resolve the high-frequency oscillations critical for UGW reconstruction. Physics-Informed Sinusoidal Representation Networks (PI-SIRENs) address these limitations by embedding governing partial differential equations directly into the training process. Building upon SIRENs, which utilize periodic activation functions to inherently capture high-frequency spectral content, the proposed framework is designed to operate effectively in sparse ultrasonic measurement regimes. This work introduces a frequency-domain PI-SIREN framework tailored for the Mindlin-Reissner plate theory to reconstruct ultrasonic wavefields without temporal discretization. The model parameters are optimized using a hybrid strategy comprising three phases: first-order Adam, residual-adaptive refinement (RAR) and quasi-Newton L-BFGS. Numerical and experimental evaluations confirm that the model serves as a physics-consistent baseline derived from sparse data, functioning as a computationally efficient surrogate for damage identification in SHM and non-destructive testing (NDT). Integrating the surrogate into a damage identification pipeline detects and localizes a milled notch from sparse experimental measurements with a localization error of 1 % of the plate diagonal. In contrast, data-driven benchmarks and MLPs with hyperbolic tangent activation functions, with and without Fourier feature embedding, are unable to identify damage due to higher reconstruction errors.
Large language models and the multi-agent systems built around them could accelerate materials discovery by connecting scientific knowledge with experimental decisions. Existing benchmarks establish capabilities in domain knowledge, multimodal interpretation and scientific tool use. As language models increasingly support materials research workflows, their ability to distinguish closely related material states and reason accurately with quantitative evidence remains insufficiently evaluated. These abilities are essential for comparing material responses, assessing mechanisms and maintaining reliable judgements as experimental evidence accumulates. We introduce MatScope to evaluate three connected capabilities. M1 tests unaided, condition-specific reasoning through 200 tasks spanning ten research functions, using aluminium and high-entropy alloys as representative material systems. M2 tests agent-assisted transfer of related knowledge to unresolved materials questions. MatEvoBench-20 tests initial forecasts across scientific dependency chains and revisions of still-hidden responses as observations accumulate. Across eleven model deployments, including GPT-6 Astra and Claude Fable 5.1, given-input calculations and many physical explanations are handled well. Fine-grained response estimates, comparisons between similar states and quantitatively supported choices remain substantially weaker. Related literature improves selected estimates, while condition and baseline mismatches limit transfer. Progressive observations calibrate some downstream responses and destabilize earlier accurate predictions. MatScope establishes measurable targets for developing reliable scientific reasoning in future self-evolving materials laboratories and materials-aware world models.
Protein variant effect prediction is central to understanding protein function and guiding protein engineering, yet experimental labels remain costly. In many protein experiments, the variants that can be assayed are dictated by protocol constraints, while the variants that need accurate prediction may lie in a different or broader region of the landscape. This assay-prediction mismatch makes candidate-local criteria such as predicted function, uncertainty, or exploration value insufficient for measurement design. Given a protocol-defined accessible space and a limited budget, we ask which variants should be assayed so that the resulting data best improves landscape prediction. We propose TALK, which estimates each candidate's contribution through posterior coupling between accessible and target variants and reduces redundant information within the batch. Across retrospective ProteinGym and FLIP protocols, TALK generally improves target-space prediction under limited measurement budgets. These results point to a practical two-stage workflow: first, spend a limited assay budget on variants selected to be informative for the target landscape and train a predictive model from the measured labels; then use this model to score and prioritize high-potential variants. Code is available at https://github.com/joehuang618/TALK.
Large Language Models (LLMs) exhibit approximate recall: they retain coarse associations about past events while losing fidelity on specific details. Past research on LLMs has quantified different models' forecasting ability in real-world events using prediction markets, but has not studied how losing said fidelity impacts their forecasting abilities. For example: while an LLM correctly recalls that the answer to: ''Did Anna Sawai win the Best Drama Actress in the 76th Emmy Awards?'' is ''Yes,'' it incorrectly states the event date as September 22 rather than September 15. In this paper, we introduce a novel metric called the Recall Fidelity Score to study how imprecision in internalized knowledge propagates to forecasting capability on future events. On resolved historical markets, we find that higher local recall fidelity around semantically similar past events predicts lower forecasting error on resolved markets, and the same signal predicts smaller distance from open markets prices.
Gaussian basis functions provide an efficient and flexible alternative to spline activations in Kolmogorov-Arnold networks (KANs), but their performance is sensitive to the Gaussian scale parameter \epsilon. We introduce the partition-of-unity Gaussian KAN (PU-GKAN), a kernel-based normalization framework that transfers the Shepard partition-of-unity principle to trainable KAN edge functions. Each Gaussian edge basis is normalized by its local sum over fixed centers, preserving the standard edge-based architecture and essentially the same trainable coefficient structure as GKAN. The resulting feature map reproduces constants exactly at the edge level and admits an explicit normalized finite-feature kernel interpretation. Numerical experiments show that PU-GKAN reduces sensitivity to \epsilon, improves validation accuracy for most smooth and moderately non-smooth targets, and provides more stable training behavior. These benefits persist across variations in sample size and number of centers, higher-dimensional architectures, and Matern RBF bases. PU-GKAN also improves physics-informed neural networks for Helmholtz and wave equations, with validation-error reductions of up to 90%. These results establish partition-of-unity normalization as a mathematically grounded and broadly applicable framework for improving the reliability and accuracy of radial basis function KANs.
Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic Attention, a lightweight sample-average inference-time modification that randomizes attention by replacing softmax weights with normalized multinomial samples controlled by a single concentration parameter, and produces predictive ensembles without retraining. To set this parameter, we introduce a calibration objective that matches the stochastic attention output with the target, yielding an efficient univariate post-hoc tuning problem. We evaluate this mechanism on scientific foundation models for weather and time-series forecasting, as well as a regression task. Across benchmarks against baseline methods, Stochastic Attention achieves the strongest native calibration and the sharpest prediction intervals at comparable calibration, with adaptation costs nearly three orders of magnitude lower than the next-best baseline. Code is available at https://github.com/UQUH/StochasticAttention.
Dynamic prediction of locomotor capacity after stroke could enable more individualized rehabilitation, yet current assessments largely provide static impairment scores and do not indicate whether patients can perform specific tasks such as slope walking or stair climbing. Here, we present a wearable-informed data-physics hybrid generative framework that reconstructs a stroke survivor's locomotor control from wearable inertial sensing and predicts task-conditioned post-stroke locomotion in new environments. From a single 20 m level-ground walking trial recorded by five IMUs, the framework personalizes a physics-based digital avatar using a healthy-motion prior and hybrid imitation learning, generating dynamically feasible, patient-specific movements for inclined walking and stair negotiation. Across 11 stroke inpatients, predicted postures achieved approximately 95% of the practically attainable accuracy for slope ascent and 80% for stair climbing, respectively, demonstrating reliable task-specific gait prediction. In a multicenter randomized pilot feasibility study (n = 21; 28 days), access to scenario-specific locomotion predictions to support task selection and difficulty titration was associated with larger gains in Fugl-Meyer lower-extremity scores than the control group (mean change 6.0 vs 3.7 points; p < 0.05). These results suggest that wearable-informed generative digital avatars may augment individualized gait rehabilitation planning and provide a pathway toward dynamically personalized post-stroke motor recovery strategies.
Although time-series foundation models (TSFMs) achieve strong zero-shot transferability across high-information-density physical systems, applying overparameterized TSFMs to quantitative finance is fundamentally constrained by low signal-to-noise ratios, non-stationarity, and prohibitive autoregressive decoding latency. To reconcile representation learning with institutional operational constraints, this study presents TailDART, a dense 2.68 million-parameter foundation model engineered for financial time-series forecasting. By integrating grouped-query attention into a lightweight backbone, the architecture drastically reduces Key-Value cache memory bandwidth overhead, achieving major inference acceleration (up to 48.1%) over prevailing state-of-the-art TSFMs to enable low-latency, high-throughput streaming execution. Furthermore, multi-asset benchmarks across varying temporal resolutions show that a compact model can remain competitive for market forecasting: TailDART matches the predictive fidelity of substantially larger baselines while demonstrating superior error resilience in high-volatility regimes.
Quantitative strategy optimization remains largely manual, requiring domain experts to identify weak signals, tune risk-control rules, and repeatedly validate iterative revisions. Large language models can accelerate this process, but directly relying on them to rewrite trading strategies often introduces hallucinated edits, strategy drift, and backtest overfitting. We propose EVOQUANT, a self-Evolving Verifier-guided framework for strategy Optimization in Quantitative trading. Our method utilizes LLMs to deeply diagnose performance bottlenecks, generates semantically controlled candidate edits, selects the best strategy through a multi-stage verification pipeline, and distills optimization experience into reusable knowledge for continual self-improvement. We evaluate our method using seven representative strategies: four from the A-share market and three from the Crypto market. Experimental results show that our method significantly improves the Sharpe ratio across all tested strategies: the average test Sharpe increases from -0.298 to 0.538, and the best-performing strategy achieves a 199% relative improvement. Ablation studies and stress tests under stricter conditions further validate the effectiveness and robustness of the framework. Overall, this work transforms quantitative strategy optimization from costly manual trial and error into an automated and verifiable iterative paradigm, offering a new path for applying large language models to financial strategy research.
This work develops a locally adaptive jackknife+ conformal prediction framework for polynomial chaos expansions. Therein, the non-conformity scores are normalized with an auxiliary polynomial chaos expansion trained on the log-transformed leave-one-out residuals of the base model. We show that the coverage guarantee of jackknife+ conformal prediction carries over to the adaptive intervals if the leave-one-out auxiliary models are trained on nested leave-one-out residuals. For fixed-basis polynomial chaos expansions fitted by ordinary least squares, all required quantities are derived in closed form and the guarantee-preserving adaptive intervals are obtained from a single model fit, without any model retraining. For sparse polynomial chaos expansions, where multiple model fits are necessary, we propose a heuristic simplification that limits the computational overhead of adaptivity at the cost of the formal coverage guarantee. Numerical experiments on an academic benchmark with known heteroscedastic noise and on an engineering simulation dataset show that the suggested method attains the target coverage while providing intervals that adapt to local prediction uncertainty, therefore being considerably more statistically efficient. These advantages are particularly prominent in high-uncertainty regions of the input space, where the performance of non-adaptive methods degrades substantially.
The growing reliance on high-fidelity, state-of-the-art machine learning based models for engineering decision-making necessitates robust and systematic approaches for model selection. While high predictive accuracy at untrained points is a necessary trait in the final model, other attributes such as model complexity, forecastability, explainability, scalability, and physics-awareness may be equally important or relevant criteria depending on application context and user requirements. In this work, we propose a novel composite performance metric, Surrogate Quality Score (SQS) for model selection based on predictive accuracy and model complexity simultaneously. SQS heuristically integrates these two attributes through a weighted product of normalized measures, yielding a unified score to reflect overall model quality. A user-specified parameter in SQS enables explicit control over the accuracy-complexity trade-off, thereby incorporating human judgement and preference in the model selection process. We extensively discuss and justify the formulation of SQS and demonstrate its utility through an illustrative example. By combining predictive accuracy and model complexity, SQS offers a systematic and objective approach for model selection based on both attributes.
Execution algorithms are calibrated asset by asset, because the queues, trade rates and bid-ask spreads they face differ by orders of magnitude across assets. For reinforcement learning this is zero-shot generalisation across contexts of very different scales, and microstructure invariance proposes a normalisation fixed by theory: measured in each asset's own units of time, size and price, markets look alike. In an exact order-by-order replay of public Nasdaq data, we train policies once, on 954 stocks in 2019, to choose between waiting in the queue and crossing the spread, and evaluate them unchanged on 1,964 unseen stocks in 2020-21, 2,629 stocks in 2025-26, crypto pairs and a second exchange. First, a policy that sees a stock only through its recent trade rate, trade size, spread and price increment (tick) costs within 0.015 spreads per share (a fifth of what learning saves) of a policy whose training data included the stock, and the stock's own history does not help it; it comes within a similar margin of policies trained on the second exchange when every episode counts equally, and within a wider one on crypto. Second, in mean cost before fees, invariant units beat raw units, z-scores and asset descriptors, but by under a basis point: most of their advantage is information and a common cost scale that a learner can also take as plain inputs, and none of the representations tested extrapolates to unseen spread regimes. Third, a near-zero transfer gap to a pooled comparator is weak evidence that a representation is right: we show that such a comparator detects only a small share of what a poor representation loses, and confirm it in synthetic markets and on pendulums.
Capturing sheet-metal localisation physics with a trained surrogate inside a finite element (FEM) solver requires the surrogate to deliver consistent predictions irrespective of the solver's strain-increment count, which is difficult to control in non-linear explicit codes. We address this by re-implementing a trained recurrent neural network (RNN) damage criterion in Fortran and embed it as a live, increment-by-increment fracture criterion inside an Abaqus/Explicit user material subroutine (VUMAT), advancing the network state alongside the solver. Two architectures are compared: a SimpleRNN and the proposed Consistent RNN (ConsRNN), whose transition function is designed so that predictions converge as the strain path is refined rather than drifting with the increment count. Both are trained on bilinear strain paths and evaluated under varying temporal discretisations and nonlinear histories. SimpleRNN predictions drift as the increment count increases, which disqualifies it for embedding; ConsRNN converges under refinement, at a substantial fixed-resolution accuracy cost relative to SimpleRNN on multilinear paths. Deployed at structural scale, the embedded ConsRNN surrogate governs element deletion in a clamped steel plate and reaches the same peak force and peak displacement as an established two-parameter fracture criterion. This pre-peak agreement is expected by construction, since no element is deleted before the peak and the two runs therefore share an identical constitutive path; the responses diverge only on the post-peak softening branch. The results establish discretisation consistency as the decisive property for embedding recurrent surrogates in explicit FEM solvers, and report the first embedding of a customised, non-standard-transition recurrent cell at structural scale.
Climate change threatens maize yields worldwide, yet identifying which genetic traits sustain productivity under future conditions requires exploring an enormous space of genotype, soil, and climate combinations that process-based crop models are too costly to simulate at scale. Here we develop an integrated probabilistic emulation framework that transforms a mechanistic crop simulator (APSIM) into a fast, uncertainty-aware discovery engine. Built from two million simulations and coupled to a generative weather model that produces realistic climate sequences, the emulator reproduces thirteen maize growth outputs with high fidelity while returning calibrated confidence for every prediction, at a fraction of the original computational cost. Applying it across 100,000 trait configurations, six locations, and future climate projections extending to the year 2100, we identify 1,114 trait combinations that remain resilient under the 2100 future conditions and a stricter subset of 246 configurations that remain resilient across four future projection periods: 2040, 2060, 2080, and 2100. These resilient configurations occupy a distinct region of trait space, combining high radiation use efficiency with characteristic shifts in developmental and reproductive traits. Trait-importance analysis further identifies radiation use efficiency as the dominant driver of yield under future climate, while projected yields vary widely across locations and climate models, indicating strong spatial heterogeneity in the maize response to climate change.