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Flexible continuous-time survival modeling is critical for capturing complex time-varying hazard dynamics in high-dimensional data; however, training such models remains challenging due to the intractable integral required for likelihood estimation. We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling without relying on time discretization or restrictive distributional assumptions. We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy while facilitating efficient end-to-end training via standard backpropagation. Furthermore, to effectively capture non-stationary hazard dynamics in complex architectures, we introduce time-conditioned low-rank adaptation, a mechanism that conditions general neural backbones on time by dynamically modulating weights via low-rank updates. We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation. Comprehensive experiments across synthetic benchmarks, large-scale real-world tabular datasets, and high-dimensional medical imaging tasks demonstrate that QSurv achieves competitive predictive performance with advantages in instantaneous hazard function estimation, enabling more interpretable characterization of time-varying risk patterns.

Anomaly detection in multivariate time series remains a critical challenge in large-scale distributed systems, where related entities may exhibit transferable precursor behavior prior to anomaly onset. Existing methods typically operate independently on each data stream and therefore remain fundamentally reactive. To address this limitation, we introduce Distributed Hierarchical Temporal Memory (D-HTM), a neuromorphic framework that enables cross-entity preemptive warning through a Shared Associative Memory (SAM). D-HTM combines a Spatial Pooler (SP) that projects observations into a common Sparse Distributed Representation (SDR) space, Temporal Memory (TM) modules that learn entity-specific dynamics online, and a Shared Associative Memory that stores recurring pre-anomaly signatures. By reusing precursor knowledge across related entities, D-HTM can issue warnings prior to local anomaly onset while preserving HTM's online learning capabilities. We evaluate D-HTM on the Server Machine Dataset (SMD), the Soil Moisture Active Passive (SMAP) dataset, the Mars Science Laboratory (MSL) dataset, and a synthetic cascade benchmark designed to isolate precursor transfer. Experimental results demonstrate effective cross-entity warning propagation while maintaining competitive reactive anomaly detection performance. Across the real-world datasets, D-HTM provides an average warning lead time of 8.1 samples prior to anomaly onset. These findings demonstrate that transferable precursor structure can emerge within a shared SDR space and be reused for preemptive warning generation, extending HTM beyond isolated reactive detection toward distributed predictive reasoning.

Unsupervised 3D seismic horizon tracking faces a key limitation: signal-based propagators provide accurate trace-level alignment but often fail near faults, whereas texture-driven deep models are more robust to discontinuities, typically at the cost of labeled data requirements and reduced trace-level precision. We propose a self-supervised fusion of both paradigms in which signal-derived local horizon correspondences act as domain-specific priors to train a texture-based deep learning model. Specifically, we estimate reliable trace-to-trace flows from reflector slopes and use them to form positive pairs in a contrastive objective, while restricting training to high-confidence neighborhoods, optionally augmented with a fault mask. The objective is not to infer ambiguous correspondences close to discontinuities, but to preserve horizon identity across them. As a result, the network learns voxel-wise embeddings that preserve local signal continuity while enabling horizon propagation beyond discontinuities through similarity search. Experiments on the public F3 dataset and a faulted synthetic dataset achieve lower mean absolute error (MAE) than unsupervised baselines and competitive performance against a semi-supervised method using a single labeled slice.

While generative modeling has achieved remarkable success on tasks like natural language-conditioned image generation, enabling model adaptation from example data points remains a relatively underexplored and challenging problem. To this end, we propose Function Projection for Flow Matching (FP-FM), an algorithm that directly conditions generation on samples from the target distribution. FP-FM learns basis functions to span the velocity fields corresponding to a set of training distributions, and adapts to new distributions by computing a simple least-squares projection onto this basis. This enables efficient generation of samples from diverse target distributions without additional training at inference time. We further introduce multiple variants of FP-FM that provide a trade-off in expressivity and compute by enriching the coefficient calculation, e.g., by making the coefficients dependent on time. FP-FM achieves greatly improved precision and recall relative to baselines across synthetic and image-based datasets, with especially strong gains on unseen distributions.

ClinicalEncoder26AM is a multilingual Diagnosable ColBERT for clinical and biomedical texts, which aligns at multiple levels its token-level semantic with ClinicalMap25, a clinical latent space inspired by BioLORD-2023 and enriched with synthetic and annotated supervision. The post-training recipe builds upon BGE-M3, and combines synthetic clinical notes, patient--doctor conversations, and annotated resources such as MedMentions, while considering both named-entity-level and sentence-level representations in a multi-adapter distillation, along with a ColBERT-style retrieval objective. In this system demonstration paper, we evaluate the model in the MultiClinNER shared task by finetuning it as a BIO tagger for patient symptoms, disorders, and procedure spans, using a lightweight two-layer CNN head to improve local boundary detection. The resulting system remains simple, processes most documents in a single 8192-token window, and achieves state-of-the-art multilingual entity recall, while achieving Top 5 overall across all entity types and languages in Character-weighted F1 scores. Training curves further show that ClinicalEncoder26AM is markedly more data-efficient than the base M3 model, supporting the usefulness of its clinical post-training for downstream information extraction. The model can be downloaded on https://huggingface.co/Parallia/ClinicalEncoder26AM-Diagnosable-Colbert-L2-for-multilingual-medical-texts

Scheduling activities in business processes can improve efficiency (e.g., reduce makespan), but is challenging because the exact sequence of activities required to complete a case is often uncertain due to decisions based on data that emerges during execution. Nevertheless, probabilistic information regarding such decisions can often be estimated or derived from historical execution logs, and can help anticipate which execution paths are likely to lead to successful completion. Planning with particular execution paths affects feasibility, i.e., the probability of successful completion, and the expected number of superfluous activities that are planned but never executed. We frame the problem as a chance-constrained optimization problem and present two formulations: A decomposed approach with two stages, a planning stage that minimizes the expected number of superfluous activities subject to a feasibility constraint, and a scheduling stage that minimizes the makespan over the planned activities; and an integrated approach that combines planning and scheduling into a single formulation. Evaluation on two real-world and one synthetic dataset shows that the integrated approach yields superior makespans but is intractable at scale, while the decomposed approach scales to large settings.

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new dynamics on the fly. Transformer-based foundation models increasingly rely on in-context learning for time series forecasting, tabular prediction, and continuous control. As these models are deployed in non-stationary environments, understanding their ability to detect and adapt to regime shifts is important. We formalize this as an in-context change-point detection problem and formally establish the existence of transformer models that solve this problem. Our construction demonstrates that model complexity, in layers and parameters, depends on the level of information available about the change-point location, from no knowledge to knowing exact timing. We validate our results with experiments on synthetic linear regression and linear dynamical systems, where trained transformers match the performance of optimal baselines across information levels. We also show that encoding and incorporating changepoint knowledge indeed improves the real-world performance of a pretrained foundation models on infectious disease forecasting and on financial volatility forecasting around Federal Open Market Committee (FOMC) announcements without retraining, demonstrating practical applicability to real-world regime changes.

Symbolic regression aims to uncover explicit scientific laws from data. Recent methods use LLMs to guide mutation from background text, which is more directed than random genetic programming. However, exact symbolic recovery requires both semantic guidance and explicit structure, so that domain-informed search are carried out through valid symbolic representation. Current LLM-driven systems remain structure-blind: they select among opaque candidates, lack explicit mechanisms for local mutation, and rely on brittle coefficient fitting that can undervalue correct skeletons. We propose FunctionEvolve, an evolutionary framework using expression trees to organize the whole search: structural summaries promote diverse parent selection, local tree edits preserve useful subexpressions, and structure-aware fitting decomposes, constrains, and simplifies coefficients for more reliable scoring. It uses only elementary function families, without additional domain-specific rules limiting generalization. On the 129-task synthetic subset of LLM-SRBench, FunctionEvolve with \emph{Claude Opus 4.6} recovers 107 exact forms, reaching 82.9% SA@50, 4.5x above same-backbone baselines, and 55.8% SA@1, 3.6x above the strongest previously published top-1 result. Ablations show that structure-visible search is central to reliable recovery, with LLM-guided refinements and structure-aware coefficient optimization serving as essential proposal and scoring mechanisms. We also audit the benchmark and show that collinearity in its materials-science subset creates identifiability issues.

We present DEtection in phase-folded Light curves with cOntrastive Scoring (DELOS), a contrastive-learning-based framework designed to search for shallow transits in Kepler photometry. DELOS combines GPU-accelerated phase folding, optimized phase binning, and a custom one-dimensional convolutional encoder to assign a transit-likeness score to each folded light curve, thereby producing a score periodogram over trial periods without relying on pre-detected threshold-crossing events. Focusing on intermediate-to-long-period signals with orbital periods of 100-150 days, DELOS was trained on 20 million synthetic light curves generated with realistic transit models and Kepler-like noise properties, achieving a validation accuracy of 99.3 percent on the synthetic validation set. In controlled injection-recovery experiments, DELOS improves the combined precision-recall performance by 15.5 percent relative to Box-fitting Least Squares (BLS) and 11.25 percent relative to Transit Least Squares (TLS) in the low Signal-to-Noise Ratios (low-SNR) regime. It also accelerates the search by factors of approximately 3-5 and 74-80 compared with BLS and TLS, respectively. Applied to a selected Kepler validation sample, DELOS recovered all known shallow intermediate-to-long-period transit signals in the tested period range. These results demonstrate that DELOS provides an efficient and sensitive framework for low-SNR transit searches and represents a practical step toward future searches for longer-period terrestrial planets in Kepler, K2, TESS, PLATO, and Earth 2.0 data. Accordingly, this work is intended as a methodological development and validation study, with the detailed astrophysical validation of newly identified candidates deferred to future work.

Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples. We ask whether the geometric algebra structure itself contributes anything beyond exact equivariance. We compare against a minimal scalarization baseline: invariant dot products fed to a small MLP that outputs coefficients on the equivariant basis {v_i, v_i x v_j}, which is also exactly equivariant. On single-stage laws (rotation by axis-angle, cross product, central force), scalarization matches or beats the Cl(3,0) network at a fraction of the training cost, so the geometric algebra adds nothing there. On compositional targets whose computation graph nests group operations (apply R2 R1 to a point; map a local force through an orientation, then take a torque), the Cl(3,0) network beats scalarization by an order of magnitude in the low-data regime, reaching with 100 samples what the baseline needs 3000 for, and the gap survives strengthening the baseline with the triple-product invariant and 17x more parameters, external Vector Neurons and e3nn baselines, and a multiplicative coefficient network. Ablations show the required network depth tracks the rotation chain length, and scalarization falls below the constant predictor on chains of four rotations. The advantage is not composition per se: on a rotation-free nested cross product, which flattens into polynomial invariant coefficients, scalarization wins by 24x. No tested model, equivariant or not, extrapolates invariant magnitudes: on radius and separation shifts every model is worse than a constant predictor once errors are normalized. We conclude that geometric algebra layers are not a general shortcut for low-data 3D learning, but become useful precisely when the target composes group elements in depth.

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Neural networks transform data through learned representations whose geometry affects separation, contraction, and generalization. Recent work studies this geometry using discrete curvature on neighborhood graphs, suggesting Ricci-flow-like behavior across layers. We develop a smooth operator-theoretic alternative for feedforward representation snapshots. Each feature cloud induces a Gaussian-kernel diffusion Markov operator, and transport, spectral, label-boundary, and local-scale observables are derived from this single object via Bakry-Emery $Γ$-calculus. In a balanced Gaussian class-conditional snapshot model with shared covariance, the population operator has closed-form class affinities, leakage, and coarse spectra, all controlled by pairwise regularized Mahalanobis separations $c_\varepsilon^{(a,b)}$. We also prove that the resulting operator observables vary smoothly under feature perturbations, while hard neighborhood-graph diagnostics can change discontinuously. Synthetic experiments validate the closed-form Gaussian bridge, while learned MNIST experiments show that the same operator observables track training, width, and perturbation stability. Together, these results give a stable operator-geometric framework for analyzing feedforward representation geometry.

Non-Intrusive Load Monitoring (NILM) offers a cost-effective method to obtain fine-grained appliance-level energy consumption in smart homes and building applications. However, the increasing adoption of behind-the-meter (BTM) energy sources such as solar panels and battery storage poses new challenges for conventional NILM methods that rely solely on at-the-meter data. The energy injected from the BTM sources can obscure the power signatures of individual appliances, leading to a significant decrease in NILM performance. To address this challenge, we present DualNILM, a deep multi-task learning framework designed for the dual tasks of appliance state recognition and injected energy identification. Using a Transformer-based architecture that integrates sequence-to-point and sequence-to-sequence strategies, DualNILM effectively captures multiscale temporal dependencies in the aggregate power consumption patterns, allowing for accurate appliance state recognition and energy injection identification. Extensive evaluation on self-collected and synthesized datasets demonstrates that DualNILM maintains an excellent performance for dual tasks in NILM, much outperforming conventional methods. Our work underscores the framework's potential for robust energy disaggregation in modern energy systems with renewable penetration. Synthetic photovoltaic augmented datasets with realistic injection simulation methodology are open-sourced at https://github.com/MathAdventurer/PV-Augmented-NILM-Datasets.

Generative Synthetic Populations (GSP) -- the convergence of population synthesis, agent-based modelling, and LLM agents -- are attracting growing interest for urban simulation and institutional communication research. Before any GSP instrument is used on a real population, a more basic question must be answered: does it respond to stimuli of known valence in an ordered, replicable, group-structured way? We call this controllability. We ask not whether a synthetic population tracks humans, but whether it tracks itself: whether the latent structure we impose on it is recovered in its own responses. This internal-validity question is logically prior to any claim about external validity, just as characterising an instrument's response function must precede using it to test a theory. We report SIVE (Synthetic Instrument Validation Experiment): a fictional municipality (Montelago) with 120 synthetic personas of known latent structure, exposed to seven conditions spanning strongly positive to strongly negative institutional communications about a water network. Seven pre-registered criteria, evaluated across a temperature sweep, jointly assess fidelity, stability, noise floor, specificity, sensitivity, and ordering. All seven pass at every temperature. A central finding turns a calibration failure into a diagnostic success: a message designed as "weakly positive" was identified by the instrument as functionally negative, traced to unresolved problems, uncertainty, and institutional passivity in its text; a redesigned version restored the expected ordering and interacts with agents' latent trust in unanticipated ways. A noise sub-experiment shows the instrument's intrinsic noise is roughly half the cross-agent estimate and stable across temperatures. Individual trajectories reveal coherent micro-dynamics that summary statistics obscure. Full data are available via an interactive explorer.

Complex-valued Neural Networks (CVNNs) are often motivated by domains where information is naturally encoded in magnitude and phase. Yet complex-valued inputs alone do not determine when complex arithmetic improves learning: the label signal may lie in amplitude, phase, their coupling, or a symmetry that real-valued models can also represent under suitable coordinates. We study this through a representation-first evaluation of CVNNs against Cartesian real, polar, phase-only, magnitude-only, parameter-matched real, and FLOP-matched real baselines. Across synthetic RF tasks, complex representations are useful but not universally superior. PSK-only tasks favor phase-aware and complex-valued models, QAM-only tasks favor magnitude-based models, mixed PSK+QAM gives only a small complex-valued advantage, and unseen carrier-phase rotations break coordinate-dependent models without augmentation. Similar patterns appear beyond RF: in quantum-wavefunction prediction, momentum is invisible to $|ψ|$ but recoverable from phase, while EEG analytic-signal experiments show that phase locking, amplitude bursts, and phase-amplitude coupling each favor different coordinate views. We also identify a benchmarking artifact on RadioML 2018.01A. Under matched-shared-trial selection, a CReLU complex model exceeds the best real baseline by 22.94 PP; under independent per-family tuning on the same data and 16-trial search space, the gap collapses to 2.46 PP. Gradient analysis traces the inflated gap to high-learning-rate first-step instability in real baselines, while complex parameter coupling distributes the loss signal more robustly. A learning-rate $\times$ activation factorial confirms the failure is primarily hyperparameter-driven. Overall, CVNNs are best viewed as structured inductive biases whose gains depend on representation, symmetry, and optimization, not as universally superior architectures.

Video face swapping has no natural paired supervision: no real footage exists of one person's face performing another person's video. The strongest current answer, DreamID-V's SyncID-Pipe, mints pairs by replacing the identity in exactly two frames of a real clip -- the first and the last -- and regenerating the rest from a pose sequence alone. Pose carries no appearance evidence of the swapped-in identity, so over long clips, occlusions, and extreme pose excursions the synthesized identity has a long unanchored span on which to drift; no published ablation examines anchor count or placement. We propose Adaptive Identity Anchoring (AIA): (i) generalize the synthesizer to arbitrary anchor sets, architecturally natural for diffusion-forcing-style transformers where conditioning on a frame is clamping its tokens to zero noise; (ii) place anchors by a closed feedback loop that scores every generated frame against the real reference identity and inserts an image-face-swapped anchor at the worst-scoring frame until the pair passes a threshold or exhausts a budget; (iii) reuse the loop's verdict as an automatic data filter. A second pathology, the beauty-filter look of over-smoothed skin, has the same root cause: micro-texture, like identity, is priced by none of the pipeline's objectives. We therefore pair AIA with Reality-Referenced Texture Restoration: matched re-graining from each real frame's non-face regions, band-split transfer of sub-identity micro-texture from the real footage, and a second, spectral acceptance channel refereed by the footage's own spectrum. Identity-anchor density, we argue, is a controllable quality dial, and we specify falsifiable experiments -- drift-versus-gap curves, uniform-versus-adaptive placement at matched budgets, student training on AIA-minted data, and texture ablations with a human beauty-filter study -- that would validate or refute the proposal.

While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives. We develop conservation laws based on generalized extrinsic information transfer (GEXIT) functions for a broad class of memoryless noise processes, showing that the data--model cross-entropy (CE) can be characterized exactly as an integral of local information-theoretic derivatives along the noise path. This yields a unified characterization of the likelihood for discrete and continuous diffusion, with the Gaussian case reducing to the well-known mutual information--minimum mean-square error (I-MMSE) relationship. An immediate implication is a locality property: one can compute the information-theoretic derivatives using only the marginal posteriors along the noise path. As a result, training reduces to learning the marginal posteriors by minimizing the negative log-likelihood. While the conservation law implies that the entropy does not depend on the noise path, finite-capacity denoisers approximate the posteriors with varying accuracy across noise types, leading to differences in performance. We validate these predictions on synthetic Markov sources and standard benchmarks, including text8 and CIFAR-10.

Continuous-time event data, in which entities emit instantaneous events over time, arises naturally across many domains such as neuroscience, seismology, and social networks. Non-negative matrix factorization (NMF) is a natural tool to uncover interpretable structure in such data, but it has so far only been applied after binning or smoothing the entity-level counting measures. This preprocessing step comes with the risk of erasing entity-level heterogeneities and fine-grained temporal features. In this paper, we introduce EventNMF, a continuous-time non-negative factorization model that operates directly on event times: each entity's events are modeled as a Poisson process whose intensity factorizes through a non-negative B-spline basis, and a simple estimation procedure recovers interpretable temporal templates shared across entities. The resulting method is mathematically principled, easy to implement, and computationally efficient. We further show that standard binned-count approaches arise as the special case of degree-zero splines, explore bias-variance tradeoffs and compare against existing methods on a synthetic latent factor model, and demonstrate the effectiveness of EventNMF on several real-world applications.

Graph neural networks (GNNs) achieve strong performance on relational data, but real-world graphs are often distributed across organizations that cannot share raw data due to privacy and policy constraints. Existing federated GNN methods either ignore cross-client links, leading to degraded accuracy, or require frequent embedding exchanges, incurring substantial communication and privacy costs. We propose CE-FedGNN, a communication-efficient and privacy-preserving federated GNN framework for learning over such coupled graphs. Our approach avoids sharing raw data or per-round embeddings by infrequently exchanging aggregated node representations. To handle cross-client dependency and staleness, we introduce a moving-average estimator that continuously tracks node representations and enables their stable reuse across rounds. To provide formal privacy guarantees for the released representations, we adopt the metric differential privacy (metric-DP) framework, which measures privacy with respect to distances in the learned embedding space rather than worst-case input perturbations. This yields meaningful guarantees at noise levels where standard differential privacy becomes overly conservative. We establish convergence to a stationary point at a rate of $O(1/\sqrt{T})$ with $O(T^{3/4})$ communication complexity. In addition, we derive $(\varepsilon,δ)$-metric-DP guarantees via Rényi differential privacy composition under a public-cohort threat model. Experiments on synthetic interbank anti-money laundering benchmarks and citation networks demonstrate that CE-FedGNN achieves strong performance while significantly reducing communication and maintaining robustness under privacy-preserving noise.

The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors. In order to leverage the geometry of the space, we formulate the learning of such matrices as optimization on a Riemannian quotient manifold. We propose a novel block-diagonal Riemannian metric derived from the pullback of the Frobenius inner product. The metric is shown to be invariant under these symmetries. We develop a Riemannian gradient descent algorithm that uses a tuning-free Gauss--Newton step size and scales linearly in the number of observed entries per iteration. The versatile framework of Riemannian quotient optimization enables both first-order and second-order Riemannian methods, the latter through a closed-form connection and the Riemannian Hessian. Experiments on real and synthetic datasets illustrate the efficacy of our proposed Riemannian approach.

Synthetic control (SC) matches a treated unit's pre-treatment trajectory to a weighted combination of donor units. We study Spectral SC, which instead matches the treated unit in coordinates defined by the leading temporal singular vectors of the donor panel, and a hybrid estimator that places separately tunable weight on retained and discarded directions, nesting raw-path SC and truncated Spectral SC as endpoints. We prove that the family reduces exactly to raw-path SC at full rank, that exact balance on $K$ retained dimensions with $N_0$ donors is underdetermined whenever $N_0>K+1$, with an affine solution set of dimension $N_0-K-1$, and that spectral imbalance maps to treatment-effect bias through a finite-sample best-linear-predictor decomposition. We evaluate the estimators across eleven data-generating regimes, using $400$ replications per regime and donor-only placebo validation to select regularization and the mixing weight. Truncated Spectral SC has significantly higher RMSE than tuned raw-path SC in every regime, with paired differences equal to $4$ to $11$ Monte Carlo standard errors. The hybrid estimator selects raw-path matching in most replications and is statistically indistinguishable from tuned SC in most regimes. The result is highly sensitive to preprocessing. With raw inputs, the performance gap is large; after removing unit and time fixed effects before spectral decomposition, as suggested by the assumptions behind our bound, the gap nearly disappears and placebo validation begins to favor truncation. We interpret these findings diagnostically rather than as evidence that Spectral SC should replace raw-path SC. Basis-estimation noise, balancing underdetermination, and fixed-effects contamination determine when spectral matching can help.

Clinical B-mode images are widely available as potential data sources for quantitative ultrasound (QUS) analysis for tissue characterization. However, standard clinical ultrasound devices apply unknown log-compression to RF envelope data before display and storage. Previous work has demonstrated estimation of the underlying RF envelope statistics in the presence of an unknown compression law. Using Fisher information analysis, we show that finite-offset log compression causes severe information loss when estimating the Rayleigh scale $σ$, which controls diffuse speckle. For a single image window, unknown compression raises the minimum achievable variance for unbiased estimation of $σ$ by a compression-independent factor of approximately $\FisherMinInflation$. When $M$ equal-sized windows share the same unknown compression settings, the excess variance decays as $1/M$; even in the most favorable regime, reducing the variance inflation factor below $1.1$ requires $\FisherBestCaseWindows$ windows. Our analysis treats the contrast parameter $a$ as unknown and the boundary offset $b$ as known; estimating $b$ experimentally shows even larger variance. We validate this theory using synthetic estimation experiments and demonstrate RF-scale recovery on real RF-envelope windows from the OASBUD dataset. Together, these results clarify the limitations of using routine B-mode images for QUS.

Reconstructing physics-based 3D assets -- geometry, materials, and illumination -- from multi-view images is a core problem in computer graphics and vision, and a prerequisite for realistic relighting and editing. Physics-based inverse rendering offers an accurate image-formation model, but is severely underconstrained: without strong priors, illumination is baked into materials, and reconstructions generalize poorly to novel views and lighting. Data-driven diffusion models, in contrast, predict visually plausible materials, yet their predictions rarely satisfy the rendering equation and are not directly usable for physics-based rendering. We bridge these two paradigms rather than replacing either. Our key idea is to treat the predictions of a state-of-the-art diffusion model not as target material values but as a similarity kernel for optimization: we introduce a regularization loss that penalizes deviations in the optimized material over surface regions where the diffusion predictions are near-constant, while leaving the optimization free to match the input images. Built on this regularizer, our end-to-end pipeline jointly reconstructs geometry, materials, and illumination, yielding high-quality assets that drop into standard rendering pipelines and relight faithfully. On the Synthetic4Relight, Stanford-ORB, and DTC-Synthetic datasets, our method significantly outperforms state-of-the-art baselines in both reconstruction accuracy and relighting quality.

Spectral-based machine learning models have been increasingly deployed in chemometrics and spectroscopy, where predictive accuracy is as important as explainability. Current employed eXplainable Artificial Intelligence (XAI) methods are largely adapted from tabular or generic multivariate domains, assigning relevance to isolated spectral variables rather than to the chemically meaningful spectral zones. Widely adopted tools such as SHapley Additive exPlanations (SHAP), Permutation Feature Importance (PFI), and Variable Importance in Projection scores (VIP) were not designed for the physical continuity and high collinearity of spectral data, and their variable-level outputs require post-hoc aggregation to recover zone-level information. This study introduces the Spectral Model eXplainer (SMX), a post-hoc, global, model-agnostic XAI framework that explains spectral classifiers through expert-informed spectral zones. SMX summarizes each zone via PCA, defines quantile-based logical predicates, estimates predicate relevance with perturbation in stochastic subsamples, and aggregates bag-wise rankings in a directed weighted graph summarized by Local Reaching Centrality. A key component is threshold spectrum reconstruction, which back-projects predicate boundaries to the original spectral domain in natural measurement units, enabling direct visual comparison with measured spectra. The method was evaluated on eight real spectral datasets (six based on X-ray Fluorescence--XRF and two based on Gamma-ray Spectrometry) and one synthetic benchmark with known gr

Credit-card fraud detection is difficult because fraudulent transactions are rare, costly, and unevenly distributed. Strong gradient-boosted tree models already perform well on structured transaction data, so the value of another fusion method is not obvious. This paper examines whether Combinatorial Fusion Analysis (CFA), which searches over model subsets and rank-score fusion rules, can still add value on the IEEE-CIS Fraud Detection benchmark. Using a leakage-free 60/20/20 train/validation/test protocol, we evaluate 480 fusion configurations built from seven base classifiers. The best test-set result comes from diversity-weighted score fusion of Random Forest, XGBoost, and LightGBM (DEF WtScore), with AUC-ROC = 0.9405, AUPRC = 0.6699, and F1 = 0.6373. Bootstrap confidence intervals from 1,000 resamples show that the gains over the strongest single model exclude zero for all three metrics. CFA matches soft voting on AUC-ROC, improves AUPRC and F1, and outperforms stacking in this setting. A CTGAN augmentation experiment gives a negative result: synthetic fraud samples degrade both individual models and CFA. Overall, CFA is most useful here not as a way to combine every classifier, but as a validation-stage method for choosing a small, complementary subset and assigning diversity-aware weights.

We study learning to learn through the lens of hyperparameter tuning. We propose the Langevin Gradient Descent Algorithm (LGD), which approximates the mean of the posterior distribution defined by the loss function and regularizer of a regression task with convex objective. For classification tasks, the LGD algorithm estimates the posterior probabilities of each class on the test set. We prove the existence of an optimal hyperparameter configuration for which the LGD algorithm achieves the Bayes' optimal solution for squared loss on regression tasks, and for which LGD closely approximates the posterior probabilities for well-specified classification tasks. Subsequently, we study generalization guarantees on meta learning optimal hyperparameters for the LGD algorithm from a given set of tasks in the data-driven setting. For a number of parameters $d$ and hyperparameter dimension $h$, we show a pseudo-dimension bound of $O(dh)$, up to logarithmic terms under mild assumptions on LGD. This matches the dependence of the bounds on number of parameters obtained in prior work for linear regression using the elastic net, which only allows for $h=2$ hyperparameters, and extends their bounds to regression on convex loss. Compared to bounds on regularized logistic regression that allow for only $h=1$ hyperparameter, our bounds improve greatly on the dependence on samples per task at the cost of worse dependence on the number of parameters by accounting for hardware-aware procedures. Finally, we show empirical evidence of the success of LGD and the meta learning procedure for few-shot learning on linear and logistic regression using synthetically created datasets.

Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural electrophysiological experiments. Standard low-rank estimators impose a single global latent geometry, which can recover average structure but may smooth away subgroup-specific variation, especially when observations are unevenly distributed across groups. We introduce Group-Aware Matrix Estimation (GAME), a convex estimator for overlapping subgroup-wise low-rank matrix estimation. GAME regularizes category-specific submatrices through overlapping nuclear-norm penalties, allowing related groups to borrow information while preserving local latent structure in a shared coordinate system. We provide finite-sample guarantees for both reconstruction error and subgroup-specific subspace recovery, showing how performance depends on sampling density, subgroup rank, and overlap structure. Experiments on synthetic, recommendation, ecological, and neuroscience datasets show that GAME is most beneficial in structured missingness regimes, where subgroup-aware regularization improves both reconstruction accuracy and latent subspace fidelity. Across these benchmarks, GAME is competitive or best among global low-rank, side-information, and modern imputation baselines, with the largest gains when subgroups exhibit distinct low-rank structure.

We study regression-based data fusion under uncertainty, where multiple noisy and biased measurement sources are available but ground-truth labels are absent during training. This setting arises in sensor networks, simulation ensembles, and scientific monitoring systems where supervision is costly or infeasible. We propose the Neural Conjugate Aggregation Model (NCAM), a hierarchical Bayesian framework that combines neural networks with conjugate Gaussian inference for unsupervised multi-source fusion. NCAM learns source-specific bias and reliability conditioned on contextual covariates, yielding an analytically tractable posterior over a latent target variable with decomposed epistemic and aleatoric uncertainty. Structural non-identifiability is resolved through sensor anchoring and variance regularization, enabling stable and interpretable posterior aggregation. To complement Bayesian uncertainty with finite-sample guarantees, we integrate locally adaptive Monte Carlo conformal prediction, producing heteroscedastic prediction intervals with coverage guarantees under exchangeability assumptions. Experiments on synthetic and real-world air-quality datasets demonstrate improved predictive accuracy and well-calibrated uncertainty compared to unsupervised baselines, including mean aggregation, probabilistic PCA, and Kalman filtering.

The emergence of Large Language Models (LLMs) offers a transformative interface for Web3, yet existing benchmarks fail to capture the complexity of translating high-level user intents into functionally correct, state-dependent on-chain transactions. We present \textsc{Intent2Tx}, a high-fidelity benchmark featuring 29,921 single-step and 1,575 multi-step instances meticulously derived from 300 days of real-world Ethereum mainnet traces. Unlike prior works that rely on synthetic instructions, \textsc{Intent2Tx} grounds natural language intents in real-world protocol interactions across 11 categories, including diverse long-tail Decentralized Finance (DeFi) primitives. To enable rigorous evaluation, we propose an execution-aware framework that transcends surface-level text matching by employing differential state analysis on forked mainnet environments. Our extensive evaluation of 16 state-of-the-art LLMs reveals that while scaling and retrieval-augmentation enhance logical consistency and parameter precision, current models struggle with out-of-distribution generalization and multi-step planning. Crucially, our execution-based analysis demonstrates that syntactically valid outputs often fail to achieve intended state transitions, highlighting a significant gap in current "reasoning-to-execution" capabilities. \textsc{Intent2Tx} serves as a critical foundation for developing autonomous, reliable agents in intent-centric Web3 ecosystems. Code and data: https://anonymous.4open.science/r/Intent2Tx_Bench-97FF .

Although multimodal large language models (MLLMs) have shown substantial potential in visual understanding and graphic code generation, editing scientific figures through code presents a greater challenge: a model must jointly recover visual structure, ground the requested change, generate compilable code, and preserve all unrelated content. While existing TikZ benchmarks mainly focus on figure reconstruction and generation, few systematically evaluate instruction-guided scientific figure editing with compilable code. We introduce Edit2TikZ, a comprehensive benchmark for scientific figure editing tasks, featuring 1,548 diverse and high-quality samples. Edit2TikZ combines real-world and controlled synthetic edit cases, supports both textual and visual localization request, and contains multi-step editing, each with step-level annotations. We further construct a human-aligned evaluation framework to measure whether a requested edit is completed while irrelevant content is preserved. Utilizing Edit2TikZ, we evaluate 14 mainstream MLLMs and find that current systems remain unreliable: on average, proprietary models achieve a compilation success rate of merely 75% and remain limited in both figure restoration and edit correctness, while compact models below 9B struggle further with instruction following and complete figure generation. Therefore, we build a mixed training set TikZEditMix and adopt reconstruction-then-editing curriculum learning for compact models. On Qwen3.5-4B, this training improves the compilation success rate from 45.35% to 83.40% and yields an average improvement of 18.7 points across our proposed evaluation metrics. The code and data will be released at https://github.com/Solunny/Edit2TikZ.