Papers

Long-context and agentic LLM workloads push the KV cache past any fixed memory budget, forcing the inference stack to permanently evict tokens at every step of a continuous-inference stream. Existing methods all share the same template, a per-step direct-attention score followed by deterministic top-$K$ selection, which converts a single below-cutoff step into an irreversible verdict and permanently erases any subtly important token that direct attention cannot single out from noise. To address this challenge, we propose Nexus Sampling, a training-free eviction method that pairs Nexus scoring, an iterative walk over direct attention that surfaces bridge tokens, with weighted reservoir sampling, which retains tokens with inclusion probability in place of deterministic top-$K$. Theoretically, we show that Nexus Sampling dominates deterministic top-$K$ in long-run survival of subtly important tokens. Empirically, at 80% KV cache eviction, Nexus Sampling matches dense attention within 1% on LongBench while outperforming top-$K$ baselines on retrieval-heavy tasks, with up to 10x smaller per-sequence cache memory.

Because mathematics is highly abstract, a single statement can take very different forms depending on what subfield it is framed in. There are many examples where breakthroughs occurred after researchers discovered that a question had already been answered in a different field. At the same time, the growth of new resources related to formalization has increased the need for tools that enable efficient and reliable navigation between mathematical 'languages' (e.g., from Lean to natural language). In this paper, we investigate whether current embedding models capture mathematical equivalence. To do this, we introduce the Mathematically Equivalent but Lexically Different Pairs (MELD) Dataset, a collection of mathematically equivalent statements that are expressed in very different language. We show that current state-of-the-art embedding models tend to group statements by the terminology used to make them instead of the underlying math. Motivated by this, we propose a contrastive approach to learning embeddings of mathematical text that focuses on aligning informal statements with different formalizations. Our experiments demonstrate that this leads to improvements not only on informal-formal retrieval tasks but also on MELD, which only contains natural language statements.

Learning Koopman operators with autoencoders enables linear prediction in a latent space, but long-horizon rollouts often drift off the learned manifold, leading to phase and amplitude errors on systems with switching, continuous spectra, or strong transients. We introduce two complementary components that make Koopman predictors more robust. First, we add an attention-free latent memory (AFT) block that aggregates a short window of past latents to produce a corrected latent before each Koopman update. Unlike multi-head attention, AFT operates in linear time and adds only $\approx$30k parameters ($3d^2 + T^2$, fewer than matched multi-head attention), yet captures the local temporal context needed to suppress error divergence. Second, we propose dynamic re-encoding: lightweight, online change-point triggers (EWMA, CUSUM, and sequential two-sample tests) that detect latent drift and project predictions back onto the autoencoder manifold. Across three benchmark systems – Duffing oscillator, Repressilator, IRMA – our model consistently reduces error accumulation compared to a Koopman autoencoder and matched-capacity multi-head attention. We also compare against GRU and Transformer autoencoders, evaluated both from initial conditions and with a 50-step context, and find that Koopman+AFT (with optional re-encoding) attains markedly lower long-horizon error while maintaining lower inference latency. We report improvements over horizons up to 1000 steps, together with ablations over trigger policies. The result is a fast, compact predictor that stays on the learned manifold over long horizons.

State–space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state–space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation–Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state–space modeling and SAEM-based inference in interference-dominated imaging scenarios.

We present a large-scale empirical study isolating the contributions of the Derivative Regularization penalty (DREG). Across a fully-crossed factorial sweep of 960 experiments spanning 4 activations, 6 regularizers, 8 datasets, and 5 random seeds, we ask: when, where, and why does DREG work? Our results establish three principal findings. First, DREG achieves the highest overall and clean-regime accuracy among all regularizers evaluated (significantly so against the unregularized baseline, Weight Decay, and IGPen; Wilcoxon $p \leq 0.031$). It ranks second in noise robustness behind Spectral Normalization (SN) - the only two layer-wise regularizers in the study. Second, DREG is globally the best-performing regularizer under GELU, the default activation in modern transformer architectures, particularly on both messy vision and messy NLP benchmarks, suggesting direct applicability to frontier deep learning settings. Third, DREG's advantage over competing regularizers is most pronounced under data scarcity, consistent with its role as a geometric inductive bias that substitutes for the regularizing effect of data volume. Throughout, DREG is applied with a single fixed hyperparameter $\lambda = 10^{-2.5}$ and no per-dataset tuning, supporting its characterization as a plug-and-play regularizer for neural networks with nontrivial Jacobian structure. These findings are consistent with DREG's design: concentrating regularization pressure on layers where the activation derivative is largest, rather than constraining the network uniformly.

Droplet impact on solid surfaces is a complex fluid dynamics problem with applications in spray cooling, inkjet printing, and pharmaceutical processing. Although numerical simulations are widely used to investigate these dynamics, their computational cost becomes significant when multiple parametric variations are considered. In this work, we investigate the use of a Video Vision Transformer (ViViT) architecture to predict the temporal evolution of viscoelastic droplets impacting solid surfaces using volume fraction fields obtained from the Volume of Fluid (VOF) method. In Newtonian fluids, impact dynamics are mainly characterized by the Reynolds number $Re$, representing the ratio of inertial to viscous forces, and the Weber number $We$, representing the ratio of inertial to surface tension forces. For viscoelastic fluids, additional parameters are required to account for elastic effects, namely the solvent viscosity ratio $\beta$ and the Weissenberg number $Wi$, increasing simulation complexity and cost. Instead of simulating the entire droplet dynamics, the proposed approach uses only the initial 10% to 20% of the simulation to predict the remaining evolution. Depending on the prediction configuration, this strategy reduces computational cost by approximately 80% to 90% compared to full numerical simulations. The ViViT produces physically consistent predictions across different parameters and prediction horizons, successfully capturing both spreading and bouncing regimes while preserving geometric features and structural similarity. Since volume fraction fields can also be extracted from experimental videos, the proposed framework could be extended to incorporate experimental data during training, potentially improving the physical fidelity of the predicted dynamics.

Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a constrained variable-projection framework for data-science models, where the remaining variables are subject to convex constraints and the eliminated variables arise from a lower-level least-squares problem. In particular, by interpreting variable projection as a collapsed bilevel optimization problem, we derive exact reduced-gradient formulas compatible with automatic differentiation and propose a conditional-gradient algorithm for the resulting constrained reduced problem. We establish convergence guarantees under standard smoothness and compactness assumptions, and discuss extensions to structured lower-level variables. Numerical experiments on sparse autoencoding, dictionary learning, blind deconvolution, and few-shot learning suggest that the method can improve wall-clock efficiency and data efficiency relative to natural joint-optimization baselines.

Exact-match retrieval recall is often used as a proxy for whether a retriever supplies useful policy context to a downstream decision model. We test this proxy for pre-action policy classification in $\tau$-bench using Qwen2.5-3B/7B classifiers. Under gold-policy conditioning, a compact structured state improves macro-F1 over raw trajectories by $0.20$ after tuning at 3B, with the same ordering at 7B under shared hyperparameters. We then replace the benchmark-designated governing rule with the top-ranked benchmark assertion retrieved from decision-time context. Although the exact governing rule is retrieved at rank 1 for only $7\%$ of airline states, the primary 3B classifier obtains macro-F1 $0.58$ with retrieved assertions versus $0.60$ with the gold rule ($\Delta=-0.02$, task-cluster 95% CI $[-0.23,+0.21]$); random non-gold and no-assertion controls score $0.32$ and $0.21$. We do not detect a macro-F1 difference between retrieved assertions and the gold rule in this configuration, although the interval remains too wide to establish non-inferiority. The same qualitative pattern appears with a second retriever and at 7B, while varying across fine-tuning configurations. These results show that exact-match recovery of the benchmark-designated rule can underestimate the downstream utility of retrieved benchmark assertions in this setting. Retrieval should therefore be evaluated inside the classification loop rather than by exact-match recall alone.

We study non-stationary linear contextual bandits where the reward model drifts over time, rendering classical contextual bandit algorithms brittle because historical data becomes systematically biased. We propose Flow-Corrected Thompson Sampling (fcTS), a Bayesian method that reuses experience by transporting past rewards to the present using an explicit drift model and incorporating each transported observation with a confidence weight that reflects transport reliability. This yields a unified template that specializes in (i) linear parameter drift via online slope estimation and reward correction, (ii) periodic variation via phase-aware reuse across cycles, and (iii) recurring regime switches via changepoint detection and regime-specific posterior memory. The resulting posterior updates remain closed-form under a linear Gaussian model and can be implemented efficiently with truncated, incrementally updated sufficient statistics. Across five controlled case studies and a semi-synthetic portfolio-selection benchmark with multiple overlapping non-stationarities, fcTS outperforms standard forgetting-based baselines (discounting, sliding windows, and periodic restarts), with the largest gains in settings exhibiting recurring temporal structure. These results demonstrate that when non-stationarity is structured, correcting and reweighting historical observations can be substantially more sample-efficient than uniformly discarding them.

Proximal Policy Optimization (PPO) is the standard policy-gradient algorithm for on-policy reinforcement learning. The literature presents it in two forms, a clipped surrogate that bounds the importance ratio between successive policies and a Kullback-Leibler penalty between them. These forms are treated as separate algorithms with their own gradients, their own hyperparameters, and their own reference implementations, and a sizeable body of empirical work compares them. We show that the gradient of the clipped surrogate is reproduced exactly by a Kullback-Leibler surrogate whose coefficient varies per sample, with closed-form dependence on the importance ratio and the advantage. The identity holds at every minibatch step and across the entire inner loop, and on five MuJoCo continuous-control benchmarks the two losses produce indistinguishable training curves. The reformulation exposes a structural feature of the clipped surrogate that the min notation hides. PPO-Clip's implicit per-sample penalty is a step function at the boundary of the trust region, and the shape of this coefficient is the natural design axis for generalising the algorithm. We sketch the resulting follow-up directions in the discussion.

The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.

Practice often treats automatic metrics for attribution in LLM retrieval-augmented generation as interchangeable. We audit eight automatic scorers – lexical, embedding, and BERTScore baselines alongside entailment/grounding-trained models (clean and FEVER NLI, the checker MiniCheck) – across three evaluation constructs (provenance/topicality, generated-answer attribution, and fact-check entailment), asking whether any scorer transfers: stays within the 95% confidence interval of the best audited scorer on every dataset of a multi-dataset construct. In the construct with the most multi-dataset human-labeled coverage – generated-answer attribution (AttributionBench's four source datasets, n = 1,610, with independent HAGRID, n = 2,150) – none of the audited automatic scorers does: the per-dataset metric rankings invert (Kendall tau = -0.64, p = 0.031 on AttributedQA vs. LFQA), and an off-the-shelf NLI scorer that is best on short-claim AttributedQA (AUROC 0.90) collapses to AUROC 0.53 (chance) on long-form LFQA, where BERTScore wins (0.91); the reversal persists under the tested truncation settings. This instability has a concrete decision cost: a naive "best-on-average" rule for choosing an evaluator fails leave-one-dataset-out (mean held-out regret 0.172 AUROC, worse than fixing one scorer), so metric choice should be validated on the target dataset rather than assumed from performance elsewhere. A prompt-based LLM judge avoids the chance-level collapses the automatic scorers suffer (no LFQA collapse) but is not uniformly best, ~100x costlier, and non-deterministic – relocating, not removing, the validation burden.

This article develops an architecture that creates a formally verifiable reward signal to train legal AI, adapting the LLM proposes, verifier disposes paradigm from mathematical AI to the distinctive demands of law. We present an architecture comprising LLM-driven autoformalization into a formal legal calculus extending Catala, a verification kernel, and explanation generation grounded in formal proof traces. For the computational components of law, the architecture provides provable correctness. For open-textured legal analysis, it provides structural guarantees: every required stage of the legal argument is addressed, argumentation is exercised at the correct stages and not omitted, and the deductive links between steps are valid. We demonstrate the architecture on procedural deadline calculations in German law, Commerce Clause analysis in U.S. constitutional law, and cross-jurisdictional sanction proportionality. We further show that the same architecture has a structural advantage for legal AI training: a deterministic external verifier supplies verifiable outcomes for legal problems and thereby closes the traditional reinforcement-learning loop gap in law.

Distilling conditional diffusion models aims to transfer the behavior of a large teacher to a smaller student while preserving alignment across conditioning inputs. Unlike recognition tasks, knowledge distillation in conditional diffusion often struggles to transfer knowledge beyond the training distribution, since the predicted noise strongly depends on the conditioning signal. As a result, effective distillation requires exploring a large conditioning space. In practical settings, this creates a major bottleneck. Paired image-condition data may be limited, and generating synthetic images for every available condition is often computationally infeasible, while the pool of conditions, such as text prompts, can be extremely large. Recent work addresses this issue by switching conditions during training, exposing the student to a broader conditioning space without changing the distillation objective. Yet this raises a complementary question: once a large conditioning corpus is available, how should the training effort be allocated? In this work, we introduce ARIA, a framework that adaptively allocates training effort across coarse regions of the conditioning space. By maintaining online estimates of teacher-student discrepancy at the region level, ARIA focuses updates where misalignment persists while preserving the original distillation objective. Empirically, ARIA improves over RC across most architectures and settings, with the clearest gains observed in unseen and underrepresented regimes. We also provide a theoretical analysis showing that the proposed tracking mechanism follows the evolving discrepancy during training under bounded variance and drift assumptions.

From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE ($\textbf{G}$ated $\textbf{R}$efinement for $\textbf{A}$ccurate $\textbf{C}$ausal $\textbf{E}$dge discovery), which refines constraint-based discovery using Hard Concrete gates with $L_0$ regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by $L_1$ and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erdős-R'enyi, small-world) and dimensionalities up to $d=100$, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost ($75\times$ faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive ($F_1 = 0.86$, AUROC${} = 0.99$), reducing the skeleton's 106 false positives by 99%.

As generative models increasingly produce samples that are indistinguishable from human-created content, it becomes difficult to determine whether a given data point was part of a model's natural training set or was generated by the model itself, especially when models memorize and reproduce training data. We formalize this challenge as Member vs Generated Inference (MGI): given a sample and a target generative model, infer whether the sample is a true training member or a generated output of that model. Focusing on image generation, we show that existing membership inference methods systematically misclassify generated samples as training members, while attribution-based methods often misclassify true members as generated. This failure arises because both approaches rely on likelihood-related signals that are similarly elevated for training examples and for the model's own outputs. To address MGI, we propose Data Circuit Breaker (DCB), a three-stage method that combines complementary signals from a generative model's autoencoder and latent generator to distinguish training members from generated samples. Across multiple generative models, including image autoregressive and diffusion models, DCB consistently addresses the shortcomings of membership inference and attribution methods, remains effective even when models reproduce near-duplicates of training samples, and generalizes to challenging model derivative settings in which new models are trained on generated data.

Survival analysis is central to clinical decision-making, yet reliable time-to-event models require large, diverse cohorts that are rarely available at a single institution, while privacy regulations restrict the centralization of patient data. Federated learning (FL) offers a privacy-preserving alternative by training shared models without exchanging raw data, but its effectiveness for survival modeling under realistic, heterogeneous conditions remains insufficiently understood. This paper presents a systematic, multi-model evaluation of federated survival analysis on a cross-institutional breast cancer cohort with naturally heterogeneous distributed clients. Three representative survival models, the Cox Proportional Hazards model, DeepSurv, and Random Survival Forest (RSF), are compared across centralized, local, and federated training, and three federated optimization strategies (FedAvg, FedProx, and FedAdam) are assessed for the gradient-based models. Results show that FL consistently outperforms local training and approaches, and occasionally exceeds, centralized performance, while RSF offers the best overall balance of discrimination, calibration, and robustness across heterogeneous clients. We further find that performance depends on the diversity of client distributions, and that FedAvg and FedProx are stronger and more stable than FedAdam. Based on these findings, we derive practical, decision-oriented guidelines mapping data, privacy, interpretability, and resource constraints to recommended model and training-paradigm choices for federated survival modeling in healthcare.

The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.g., Lasso) has been historically limited by the cubic scaling walls of manifold-constrained projection and volume integration. At each step of the geometric Propose-and-Project Metropolis–Hastings (PPMH) sampler, evaluating the projection operator requires inverting an $(N+k) \times (N+k)$ generalized KKT matrix, while calculating the volume factor requires the determinant of an $(N-k) \times (N-k)$ Gram matrix. This paper presents an exact, mathematically equivalent formulation that bypasses both bottlenecks by utilizing the block Schur complement and Sylvester's determinant identity. We prove that the computational complexity of both operations collapses from $\mathcal{O}(N^3)$ to $\mathcal{O}(k^3 + N^2 k)$ per step. We generalize this reduction to Sparse Support Vector Machines (SVMs), Elastic Net, and Group Lasso. Finally, we provide a rigorous numerical stability analysis and evaluate the sampler's efficiency using the Effective Sample Size (ESS) per second. Our empirical benchmarks on high-dimensional datasets confirm a constant speedup exceeding $14{,}100\times$ while maintaining double-precision numerical equivalence, rendering exact non-smooth NML estimation highly tractable for large-scale statistical inference.

A primary challenge in AI safety is the existence of adversarial examples – slightly distorted inputs that cause a neural network (NN) to misclassify. To mitigate this problem, recent research focuses on the computation of robustness certifications, which, for a given input, determine the largest distortion the input may receive without breaking the network's prediction. Robustness certifications can be interpreted as an axis-aligned hyper-rectangle (multi-dimensional intervals). Most existing approaches focus on maximizing the certification's volume, but recent intractability results prohibit the computation of volume-optimal certifications in reasonable time. We introduce the apothem measure and show how to compute apothem-optimal certifications in a linear number of calls to a NN verifier (oracle) w.r.t. the input domain's diameter. Moreover, we prove that we cannot have a volume-optimal, oracle-based algorithm, even if we discard the oracle costs. Also, we introduce dual certifications – an interval including all instances of a class – thus providing apothem-minimum upper bounds to a robustness certification. Further, we present the ParallelepipedoNN system, which we evaluate on the standard MNIST and Fashion MNIST benchmarks. A preliminary comparison with existing work on the same datasets reveals at least two-fold improvement w.r.t. the minimum edge length.

Generative molecular models for drug design are a promising direction with much active research. In the next phase of computational drug design, such models will need to understand small molecule structure and protein-ligand interactions, and they will need to possess the machinery to generate molecules de novo. Incorporating each feature poses a critical challenge. Equally important, yet often treated as secondary, is the ability to grow a molecule from a partial starting point – a scaffold or fragment supplied by a chemist – which is the central operation of lead optimization. We present Sesame (Spatial Evoformer for a Structure-Aware Molecular Engine), a diffusion-based molecular generation model that leverages a novel spatial pairformer module to condition on partial molecular structure and the surrounding protein pocket, both expressed as continuous spatial density maps. This single conditioning mechanism supports both de novo generation and fragment-conditioned lead optimization, letting a medicinal chemist prune a hit to a scaffold and have Sesame grow it in productive ways. In addition to this module, we also introduce a diffusion framework for joint denoising of atom types, bond types, and positions, along with a trajectory finetuning scheme that trains on the model's own sampling rollouts to improve generation quality. Sesame is trained on a large corpus of ligand-only and protein-ligand datasets.

This work investigates the implementation of artificial intelligence and machine learning (AI/ML) for real-time monitoring in laser powder bed fusion (LPBF) additive manufacturing. We developed a binary image classification framework for distinguishing normal and abnormal melt pool images using a balanced dataset of 1,200 images collected from Nickel superalloy 625 on the NIST AMMT platform. The study evaluates accuracy and inference time based on control requirements and hardware limitations of open-architecture LPBF machines. We benchmark three transfer learning architectures (ResNet50, EfficientNetB0, and MobileNetV2) against two Random Forest approaches: one trained on EfficientNetB0 feature embeddings (hybrid) and one trained on raw pixel features (baseline). Images are stratified into 80/20 train-test splits, with a further 90/10 validation split on the training set, and undergo standardized resizing, normalization, and label-preserving data augmentation to emulate realistic process variability. Each model is evaluated using accuracy, precision, recall, F1 score, and area under the receiver operating characteristic curve (AUC), along with training time, inference latency, and CPU & GPU usage to capture deployability constraints relevant to factory-floor monitoring. The hybrid EfficientNetB0-plus-Random Forest approach achieves the best performance on the held-out test set, with an F1 score of 0.9451, accuracy of 0.9458, and AUC of 0.9904, while maintaining sub-millisecond per-image inference (1.15 ms). In contrast, purely deep learning models exhibit significantly higher inference times with lower accuracy. These results demonstrate that combining pre-trained convolutional features with classical ensemble methods provides a robust, computationally efficient route to real-time melt pool anomaly detection in data-limited additive manufacturing environments.

When two or more parameters or labels produce similar data, they are degenerate, or hard to distinguish. Degeneracies render both label prediction and inverse problems difficult, since both machine learning algorithms and probabilistic samplers rely on the distinguishability of data and its gradients with respect to parameters. However, identifying degeneracies in physical models or real-world datasets can be elucidating about the choice of model or the underlying process that produces the data. We present the degeneracy distillery, a method that (1) detects and (2) resolves degenerate parameter combinations (a) automatically and (b) symbolically, from parameter-data (or parameter-simulation) pairs alone, through estimation and flattening of the Fisher information matrix. By exploring the information geometry of the likelihood, we characterize degeneracies as an intrinsic property of the physical model, requiring no realised data observation. We demonstrate our approach on a range of synthetic and real-world problems, discovering symbolic coordinate transformations that identify the combinations of parameters of a model which yield independent effects on the data. The resulting coordinates flatten the Fisher information in expectation globally, in contrast to posterior-based methods that flatten only at a single point, and substantially reduce the simulation budget required for downstream neural posterior estimation. In test cases we require up to $10\times$ fewer simulations for posterior estimation at matched validation calibration whilst simultaneously gaining physical insight on the system.

Terrestrial water storage (TWS) integrates snow, soil moisture, surface water, and groundwater and is a key indicator of how climate variability and human activity reshape the global water cycle. The GRACE and GRACE-FO satellite missions provide the only direct, globally consistent observations of TWS change, but their record only begins in 2002 which is too short for many climate-scale analyses. We present a deep learning application that reconstructs monthly GRACE-like TWS anomalies (TWSA) back to 1940 by learning the relationship between daily ERA5 meteorological forcing (precipitation, evapotranspiration, runoff) and monthly GRACE observations. In contrast to prior reconstruction approaches based on grid-cell-wise regression, CNNs, or LSTMs, we adapt a multi-variate time series graph neural network (MTGNN) architecture, which was originally developed for mobility and traffic forecasting on urban sensor networks to this satellite-geodesy task. Spatial dependencies are encoded in a static, interpretable hybrid adjacency matrix that combines geodesic proximity with lagged correlations of climatic time series, capturing both local hydrological coupling and large-scale teleconnections. The reconstruction achieves a grid-cell Pearson correlation of 0.69, a basin-mean correlation of 0.94, and a near-zero bias, and it reproduces the spatial fingerprints of the 2015/16 El Niño and 2020/21 La Niña events. A systematic comparison with established reconstruction approaches (GTWS-MLrec, RM-REC, GRAiCE) shows that the graph-based model is statistically competitive at basin scale, reaching a correlation within 0.025 of the best baseline while using only roughly half to a tenth of the predictors the other models require and revealing characteristic weaknesses in arid regions in all models. The complete implementation is publicly available at github.com/hcu-cml/MTGNN-TWS-Reconstruction-GRACE

Molecular surfaces encode the geometric and physicochemical patterns that determine antibody-antigen recognition, central to epitope prediction. However, existing methods rely on sequences or backbone structures and struggle to capture discontinuous, surface-driven epitopes. This study presents SurfBind, a surface-centric learning framework for epitope prediction that operates directly on molecular surface representations. SurfBind integrates geometric and physicochemical cues through a Transformer-based architecture with patch-level surface modeling, binder-aware cross-attention, and a hierarchical coarse-to-fine prediction paradigm. Experiments on challenging epitope identification benchmarks, including SAbDab and DB5.5, demonstrate that SurfBind achieves state-of-the-art performance and strong generalization across unseen antibodies and conformational states, highlighting the value of interaction-aware surface modeling for understanding the crucial mechanisms of protein-protein interactions.

A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradients, and Hessians of the value function, where Hessian information is obtained from a matrix Riccati equation along optimal trajectories. These quantities augment a weighted least-squares regression over sparse polynomial bases on hyperbolic cross index sets, with gradients and Hessians contributing additional linear equations per sample and substantially reducing sample complexity compared to value-only regression. Feedback laws are recovered analytically from the learned value function. In high dimensions, a partial Hessian strategy controls the cost of data generation. The approach is validated on problems of increasing state dimension, where second-order data augmentation is shown to improve approximation accuracy and closed-loop performance, with up to an order-of-magnitude reduction in the number of training samples required relative to lower-order methods.

Headline accuracies on the Tuebingen cause-effect pairs are routinely compared across papers even though each is measured under its authors' own protocol – different pair subsets, weightings, model-selection, and decision rates. We argue this is the wrong comparison and run the right one: a same-hands re-evaluation in which every method is run by us on the identical 102 pairs, with one strict rule – no tuning and a decision forced on every pair. As a clean reference point we introduce a deliberately minimal baseline: sorted-conditional compression, which feeds quantized, sorted, first-differenced data to an off-the-shelf compressor (bz2) and has zero fitted parameters. Under the common ruler the ranking differs sharply from the literature. Our baseline reaches 74.7% weighted accuracy (p = 3.7e-7); on the same 100 pairs that SLOPE is evaluated on it scores 76.0%, a 1.2-point gap below the authors' own forced-decision SLOPE (77.2%) that is well inside noise (McNemar p = 0.39). A faithful re-run of RECI lands at 70.7% – inside the original authors' reported error bar, not the 77.5% often quoted (which we trace to a mis-copied cell). SLOPE's published 82.4% is a decided-subset figure: scoring the authors' own stored output only on the pairs its significance test chose to answer reproduces 81.7%. Under the common ruler the methods cluster in the low-to-mid 70s and the zero-parameter compressor ties the strongest of them. We document the mechanisms that inflate published figures (test-set model selection, significance-gated abstention) and contribute two further results: compression score magnitude is a model-free confounding flag (p = 2.8e-68), and a pre-registered falsification test fails in an instructive way that bounds the method's theoretical interpretation. Code, pre-registrations, and per-pair outputs are released.

The detection and atmospheric characterization of exoplanets have entered a new data-intensive era driven by the James Webb Space Telescope and the upcoming Ariel mission. Modern surveys produce millions of light curves and high-resolution spectra that overwhelm traditional pipelines, motivating the rapid integration of Machine Learning and Deep Learning methods into the exoplanet workflow. This review synthesizes the latest progress in applying ML/DL techniques to exoplanet detection (transit identification, candidate vetting, false-positive rejection) and atmospheric characterization (retrieval, detrending, cross-correlation, surrogate modelling) in the context of JWST and Ariel. We start with classical algorithms such as Random Forests and Convolutional Neural Networks, move through Transformers and Recurrent architectures, then survey modern simulation-based inference using Neural Posterior Estimation and Flow Matching Posterior Estimation with normalizing or continuous normalizing flows. We discuss benchmark efforts, including the Ariel Machine Learning Data Challenges (2019 to 2025) hosted with NeurIPS, and key JWST case studies such as the WASP-39b Early Release Science programme. Results indicate that DL approaches consistently match or exceed traditional pipelines in both speed and accuracy, while ML-driven retrievals reduce inference time from CPU-hours to seconds and can accelerate nested-sampling retrievals by factors of 3-8 without compromising Bayesian evidence. We identify outstanding challenges interpretability, calibration of uncertainties under noisy data, hybrid modelling, and the generalization of models across instruments and planet populations and outline a research roadmap spanning the JWST era and beyond into Ariel's launch in 2029.

Domain generalization learns from multiple source domains to generalize to unseen target domains. However, it often neglects the realistic case of label mismatch between source and target. Open set domain generalization is then proposed to recognize unseen classes in unseen domains. A simple approach trains one-vs-all classifiers to separate each class and detect outliers as unknown. Yet, the imbalance between few positive samples and many negative samples skews the decision boundary towards the positive ones, leading the model to over-reject out-of-distribution data, even from known classes in unseen domains. In this paper, we propose a novel meta-learning stategy called dualistic MEta-learning with joint DomaIn-Class matching (MEDIC), which considers implicit gradient matching towards inter-domain and inter-class task splits simultaneously to find optimal boundaries balanced for both domains and classes. Experimental results show that MEDIC not only outperforms prior methods in open set scenarios, but also maintains competitive close set generalization ability.

Extracting interpretable governing equations from sparse, noisy chemical time-series data remains difficult because discrete reaction topology and continuous kinetic parameters are tightly coupled. We present PC-MCMC-CIGP, a reproducible gray-box workflow that combines spike-and-slab topology sampling, hard conservation and thermodynamic screening, and a Chemical-Informed Gaussian Process (CIGP) residual model for parameter calibration and experimental design. The methodological contribution is not a new MCMC or GP family in isolation; rather, it is the integration of these components into a physically constrained workflow with explicit uncertainty-aware acquisition choices. On the H2 + Br2 benchmark, the constrained sampler distinguishes elementary radical pathways from deceptive phenomenological fits in our experiments. On styrene epoxidation, the CIGP optimization loop improves final yield by 12.5% over the reported GP-BO baseline. A new 10-seed acquisition study shows that EI, GWU, PC-EI, uncertainty sampling, discrepancy hunting, and random search have different trade-offs: PC-EI substantially reduces low-yield BO suggestions, while EI-style criteria give the strongest final-yield performance.

Deploying foundation models for robot control raises a central challenge: the expressive power that enables rich, multimodal perception also makes these models opaque and difficult to analyze formally, rendering them intractable for existing verification tools. In this paper, we present FEARL (Foundation-Enabled Assured Robot Learning), a framework that addresses this tension through a modular architectural decomposition. FEARL separates the policy into a large Controller (C) responsible for high-dimensional perception and task reasoning, and a small Safety module (S) that receives low-dimensional observations from dedicated safety sensors together with a bounded context embedding from C and produces the final action. Since many robot safety requirements, such as collision avoidance and workspace boundary constraints, can be expressed over these safety sensor observations, formal verification can be applied to S rather than to the full foundation-model backbone. This makes formal analysis tractable with existing tools while preserving the Controller's expressive power for task reasoning. To show that the decomposed policy remains capable of solving diverse tasks, we evaluate FEARL on three simulated robotic domains using multiple Controller backbones and training procedures, including pretrained off-the-shelf vision-language-action models. We further transfer the learned policy from one of our simulated tasks to a physical robot, suggesting that the low-dimensional safety interface supports practical sim-to-real transfer.