Classroom dynamics depend on various elements that influence teaching performance and learning activities. A key challenge is to determine the most effective seating plan, where students will seat in a specific classroom setting to achieve the best learning environment. This paper introduces the Student Seat Allocation Problem (SSAP) for strategically organizing student seating in traditional classrooms to minimize interpersonal conflicts. We propose a mathematical model and an Iterated Local Search (ILS) heuristic to solve the SSAP. Computational experiments demonstrated that ILS outperformed in more complex scenarios when compared to the results obtained by a commercial solver on the introduced mathematical model. ILS was particularly efficient in real and artificial instances that exhibited a higher number of conflicts.

Many-Shot In-Context Learning (ICL) has emerged as a promising paradigm, leveraging extensive examples to unlock the reasoning potential of Large Language Models (LLMs). However, existing methods typically rely on a predetermined, fixed number of shots. This static approach often fails to adapt to the varying difficulty of different queries, leading to either insufficient context or interference from noise. Furthermore, the prohibitive computational and memory costs of long contexts severely limit Many-Shot's feasibility. To address the above limitations, we propose AdapShot, which dynamically optimizes shot counts and leverages KV cache reuse for efficient inference. Specifically, we design a probe-based evaluation mechanism that utilizes output entropy to determine the optimal number of shots. To bypass the redundant prefilling computation during both the probing and inference phases, we incorporate a semantics-aware KV cache reuse strategy. Within this reuse strategy, to address positional encoding incompatibilities, we introduce a decoupling and re-encoding method that enables the flexible reordering of cached key-value pairs. Extensive experiments demonstrate that AdapShot achieves an average performance gain of around 10% and a 4.64x speedup compared to state-of-the-art DBSA.

Several applications demand the timely detection of critical situations, such as threats to safety and transparency, over high-velocity streams of symbolic events. This demand has motivated the development of (i) event specification languages, which define composite events via temporal patterns over simpler events, and (ii) stream reasoning frameworks, evaluating patterns expressed in these languages. However, event specification languages are typically studied in isolation, complicating their comparison in terms of expressivity and obscuring the scope of their associated stream reasoners. To mitigate this issue, we map practical fragments of prominent event specification languages into Temporal Datalog->-, a temporal Datalog with stratified negation and no future dependencies. To support efficient stream reasoning over Temporal Datalog->-, we propose Streaming Trigger Graphs, an extension of a state-of-the-art technique for Datalog materialisation. Our approach yields a uniform composite event recognition mechanism that has the potential to generalise across a wide range of practical event specification languages.

A systematic algebraic framework for composing and decomposing logic programs is currently missing, limiting our ability to analyze and construct programs in a modular way. In this paper, we introduce set-like operations for (propositional Horn) logic programs that allow for a structured manipulation of rule bodies. Our main technical result shows that programs can be decomposed into simpler components in such a way that their least model semantics can be reconstructed or approximated from the semantics of these components. In particular, we prove that every minimalist program can be decomposed into Krom programs -- consisting only of rules with at most one body atom -- such that its least model can be computed from the least models of its components. For arbitrary programs, we obtain corresponding approximation results. These results provide a new algebraic perspective on logic programs and lay the groundwork for compositional reasoning and program construction.

Cross-lingual topic modeling aims to discover shared semantic structures across languages, yet existing models depend on sparse bilingual resources and often yield incoherent or weakly aligned topics. Recent LLM-based refinements improve interpretability but are costly, document-level, and prone to hallucination, with prior white-box approaches requiring inaccessible token probabilities. We propose LLM-XTM, a framework that integrates LLM-guided topic refinement with self-consistency uncertainty quantification, enabling black-box, stable, and scalable enhancement of cross-lingual topic models. Experiments on multilingual corpora show that LLM-XTM achieves superior topic coherence and alignment while reducing reliance on bilingual dictionaries and expensive LLM calls.

Pareto set learning (PSL) is an emerging paradigm in multi-objective optimization that trains neural networks to map preference vectors to Pareto optimal solutions. However, existing PSL methods primarily focus on solving a single multi-objective optimization problem at a time. This limitation not only increases computational costs in multi-objective multitask optimization scenarios by requiring a separate model for each task, but also fails to exploit the inter-task correlations across tasks. To address this, we propose a Cross-tAsk correlation-aware Pareto Set Learning (CoAction) framework, which leverages task-aware transformer to handle multiple tasks simultaneously. Specifically, by assigning task-specific embedding vectors to individual tasks, the model effectively distinguishes between tasks while facilitating knowledge sharing among them. We utilize a Transformer encoder as the backbone architecture to leverage its self-attention mechanism for capturing complex task dependencies. The proposed approach is evaluated on comprehensive multitask test suites covering both benchmark problems and real-world applications, demonstrating effectiveness and competitive performance in Hypervolume, Range, and Sparsity.

In robotics systems, vast amounts of visual data are easily captured at high resolution using low-cost, low-power hardware. Yet, limited bandwidth and on-device compute resources prevent full utilization when transmitted via conventional codecs like JPEG/MPEG. Newer codecs, like AV1/AVIF, improve the rate-distortion trade-off, but demand far more resources for encoding, impractical without custom ASICs. Recent asymmetric autoencoders deliver high quality under extreme power and bandwidth constraints, but add prohibitive decoding cost and use bespoke formats that ignore decades of infrastructure built around standards like JPEG. To address these limitations, we introduce a compression framework for cloud robotics based on a Sensor Embedded Autoencoder paired with a One-Time Transcode for Efficient Reconstruction (SEAOTTER). Because the sensor, cloud, and consumer stages face very different power and bandwidth budgets, SEAOTTER combines the compactness of a learned latent with the broad usability of a standard JPEG file. Since naive transcoding degrades performance, we propose a learnable JPEG color and quantization transform that enables increased accuracy for global, dense, and vision-language-based perception. Using SEAOTTER, we train both general-purpose and task-aware transcoding pipelines for a pre-trained, frozen encoder. At a compression ratio of 200:1 and compared to AVIF, we observe 7 times faster encoding, 3.5 times faster decoding, and +8% ImageNet top-1 accuracy, while retaining compatibility with JPEG infrastructure. Our code is available at https://github.com/UT-SysML/seaotter .

Recently, industrial pioneers like Amazon, Tencent, ByteDance, and Huawei have been adopting BBR as their congestion control algorithm for live-streaming applications, including TikTok Live. However, BBR, originally crafted for bulk data transmission, faces multiple challenges in live-streaming scenarios. In this paper, we first explore two key issues associated with BBR due to inaccurate bandwidth estimation in live-streaming scenarios: (i) BBR cannot easily exit its startup phase, resulting in a fierce self-inflicted loss. (ii) BBR sends data at a lower rate than the available bandwidth during its stable phase. We then propose BBR-Copilot, an auxiliary congestion control component that cooperates with BBR, making BBR better adapt to live-streaming scenarios. BBR-Copilot allows for proactively generating accurate bandwidth measurement samples by smartly creating and sending extra data. We implement the BBR-Copilot prototype upon QUIC and evaluate it via testbed. Experimental evaluation results show that BBR-Copilot effectively enhances BBR's performance in live-streaming scenarios.

Recently, diffusion models operating on VAE latents or mel-spectrograms have become the dominant paradigm for zero-shot TTS. Although these compressed representations improve generation efficiency, they inevitably suffer from information loss and non-end-to-end training. Theoretically, directly modeling raw waveforms circumvents these issues; however, this direction remains underexplored and is often deemed difficult due to the extremely long sequence length of audio signals. To overcome this, we propose WavTTS, the first raw waveform generative TTS model that substantially narrows the gap with latent-space generative models. Built upon the flow matching with Diffusion Transformer (DiT), WavTTS directly models speech waveforms via a simple patchification strategy, while integrating multi-scale mel-spectrogram supervision to provide perceptual guidance during training. Furthermore, we investigate the impact of prediction targets and noise scheduling in waveform diffusion, and develop an effective schedule design to improve generation quality. Evaluations on open-source benchmarks demonstrate that WavTTS closely approaches the performance of current state-of-the-art latent generative zero-shot TTS models, while substantially outperforming previous end-to-end speech generation models. Our findings demonstrate the feasibility of scaling diffusion-based TTS directly in the waveform space, opening a new direction for end-to-end speech generation.

The rapid advancement of instruction-guided audio generation has highlighted the critical need for robust alignment evaluation. Current automated evaluation methods heavily rely on holistic scoring from general-purpose large language models, which struggle to decouple complex instructions, lack interpretability, and fail to capture fine-grained attribute mismatches. To address this, we introduce a novel dynamic rubric-based evaluation paradigm that adaptively decomposes complex audio captions into a variable number of independent, verifiable binary rubric items. To rigorously benchmark this capability, we propose the AnyAudio-Judge Bench, a comprehensive, bilingual benchmark comprising 7,920 meticulously curated samples across four diverse audio domains (speech, sound, music, and mixed), featuring deliberately constructed hard negatives. Furthermore, we construct a large-scale corpus of 105K samples with explicit Chain-of-Thought (CoT) rationales to train our dedicated evaluator, the AnyAudio-Judge model. By employing a training pipeline that combines Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO), our model successfully aligns its reasoning paths with the rubric-based scoring mechanism. Extensive experiments demonstrate that AnyAudio-Judge not only significantly enhances zero-shot alignment detection compared to state-of-the-art baselines, but also provides precise and interpretable reward signals that substantially improve instruction alignment in downstream reinforcement learning for audio generation.

In this study, we conduct a comprehensive comparative analysis of generative and discriminative deep learning-based speech enhancement methods, specifically in noise reduction tasks. Our investigation focuses on evaluating their effectiveness under high and low signal-to-noise ratio conditions, considering both matched and mismatched training scenarios. We further investigate the impact of training data volume, model convergence speed, and interpret the performance differences in terms of objective results for the considered training paradigms. Additionally, we compare the complexity-performance trade-off and the practical viability of these approaches. To further strengthen the evaluation, we study the hallucination characteristics of generative approaches in terms of word error rate and phoneme similarity. The insights derived from this study provide empirical evidence to assist researchers and practitioners in understanding whether the perceptual gains of different approaches justify their computational cost in practical applications.

We introduce D^3S Consensus, a physics-based, closed-form algorithm that unifies depth-from-defocus (DfD) and stereo to achieve highly accurate depth estimation throughout an extended working range beyond the depth-of-field (DoF) of cameras. Given a pair of dual-defocus stereo images, the method estimates an overdetermined set of depth using a novel DfD theory, Dual Differential Defocus (D^3), and (S)tereo in a coupled fashion. It then picks the most confident depth prediction from the set by enforcing consensus between these physically independent cues to reject unreliable estimates. Analysis shows that D^3S achieves a comparable working range under the same error tolerance with 10x smaller baseline than previous triangulation-based depth estimation systems. This enables compact passive binocular rangefinders with substantially smaller form factors than conventional stereo and DfD designs. We demonstrate the first D^3S prototype with only 4 mm baseline and 12 mm EFL. It generates up to 900 x 1800-pixel depth maps with 1-cm mean absolute error over 0.3-1.64 m from a snapshot acquisition. This has surpassed the reported accuracy of certain commercially available stereo cameras with much larger form factors.

Accurate precipitation nowcasting is vital for disaster mitigation, but deep learning methods face a key trade-off: regression models produce over-smoothed, spectrally decaying predictions that blur convective details and violate turbulence power laws; diffusion models generate realistic yet unanchored hallucinations lacking physical grounding. We propose Spectral-Decoupled Iterative Refinement (SDIR), a deterministic framework that reformulates nowcasting as progressive frequency-decoupled refinement. SDIR first extracts a stable low-frequency synoptic skeleton, then iteratively refines high-frequency textures under physical constraints, eliminating both blurring and hallucinations. It features a dual-path design: the Synoptic Frequency-Guided Former (SFG-Former) with Scale-Adaptive Transformers for global structure, and the Fourier Residual Refiner (FR-Refiner) with Scale-Conditioned Fourier Neural Operators for fine residuals. A Physically Consistent Power Spectral Density (PCPSD) loss with dynamic masking enforces a turbulence-consistent spectral distribution. Experiments on three benchmarks show SDIR significantly outperforms SOTA methods in spatial accuracy while achieving spectral fidelity competitive with diffusion-based methods, enabling reliable high-resolution operational nowcasting. Code link: https://github.com/RuntimeWarning/SDIR.

Despite the success of audio-visual large-language models (LLMs), they can produce plausible but ungrounded outputs, termed hallucination. Existing benchmarks focus on environmental sounds (e.g., dog barking) to indicate event occurrence. In contrast, human speech carries fundamentally different, rich semantics and temporal structures, yet it remains unexplored whether current models can accurately align speech content with corresponding visual signals. In this work, we show that speech content can induce hallucinations in audio-visual LLMs. To systematically study this, we introduce SVHalluc, the first comprehensive benchmark for evaluating speech-vision hallucination in audio-visual LLMs. Our benchmark diagnoses speech-vision hallucinations from two critical and complementary aspects: semantic and temporal. Experimental results demonstrate that state-of-the-art open-source audio-visual LLMs struggle with aligning speech content with corresponding visual signals, with a near-random accuracy on multiple tasks. In contrast, Gemini 2.5 Pro significantly outperforms the open-source models. Our analysis suggests that their failures stem from limited ability in cross-modality understanding, despite strong performance in single-modality perception. Our work uncovers a new and fundamental limitation of current audio-visual LLMs and highlights the need for speech-grounded video comprehension. Project page: https://chenshuang-zhang.github.io/projects/svhalluc/.

We identify and resolve a previously unreported failure mode in TensoRF when applied to X-ray attenuation fields: the default density shift of -10, originally introduced for RGB scene reconstruction, suppresses density gradients and prevents sparse-view medical reconstruction regardless of learning rate or regularization strategy. Setting the density shift to zero restores gradient flow and enables stable volumetric reconstruction of pulmonary nodules from only three orthogonal X-ray projections. Building on this, we propose AReT, an anatomy-regularized tensorial radiance field framework for lung nodule reconstruction using coronal, sagittal, and axial projections from the LIDC-IDRI dataset (19 patients, radiologist-annotated nodules). Unlike existing NeRF approaches requiring dense multi-view acquisition, AReT is designed for sparse-view thoracic imaging and incorporates chest-anatomy-aware regularization combining L1 sparsity and total variation smoothness. A systematic comparison across 11 reconstruction strategies shows anatomy-aware regularization consistently outperforms generative-prior-guided approaches. Evaluated against radiologist consensus segmentations, AReT achieves Pearson r=0.983 (p<0.0001) for clinically actionable nodules >=10 mm (n=14), median absolute volumetric error of 11.4%, near-zero systematic bias of -77.3 mm^3, and 8.4x improvement over spherical volume approximation.

We introduce Echo-POSED, a self-supervised framework for real-time transthoracic echocardiography (TTE) guidance that recommends probe adjustments directly from 2D ultrasound images, without the need for expert-labelled views or tracked probe trajectories. Instead, it trains on 2D views sliced from routinely acquired 3D echocardiography volumes, enforcing equivariance to probe motions while remaining invariant to cardiac phase, yielding a pose representation on $\mathrm{SO}(3)\times\mathrm{SO}(3)$. Across a held-out split and public external 3D--TTE datasets (including vendor shift), Echo-POSED maintains geometric consistency under virtual perturbations and enables intra- and inter-patient guidance simulations, achieving a combined mean angular error of 8.2 degrees between the guided and target views in intra-patient simulations with cardiac motion.

This paper studies whether audio, images, and video can share a common wavelet token schema rather than relying on separate modality-specific latent grids. It introduces a preliminary continuous-token model built around a one-level Haar DWT/IDWT frontend, a shared coefficient-token layout, optional structural metadata, lightweight modality value adapters, and a shared token-wise encoder-decoder trunk. On Speech Commands, EuroSAT RGB, and DAVIS 2017 data, a dense shared model reaches 39.92 dB audio, 29.37 dB image, and 23.93 dB video PSNR. A matched-rate sweep under continuous latent scalar budgets indicates that the visual gains are not explained solely by latent capacity, while also showing that additive metadata embeddings are not a universal source of improvement. Finally, fixed-rate energy selection provides a strong non-parametric baseline: energy_global improves average PSNR over uniform selection by 16.73 dB for audio, 16.90 dB for images, and 15.86 dB for video under compressed keep ratios. Masked sparse training reaches 34.45 dB video PSNR with 50% of dense tokens. The results support a unified wavelet token schema and sparse token interface, while stopping short of establishing a universal discrete vocabulary.

Few-shot prompting provides an effective way to adapt auditory large language models to low-resource tasks such as children's speech recognition. However, most auditory large language models are not explicitly trained to perform inference in this demonstration-conditioned format, limiting the extent to which they can benefit from few-shot prompting. To address this limitation, we introduce Few-Shot Aware GRPO (FSA-GRPO), an RL-based post-training recipe that uses a specially designed reward to encourage the model to leverage few-shot demonstrations, thereby strengthening its few-shot adaptation ability. Notably, training with only high-resource adult ASR data improves the model's general few-shot adaptation ability, yielding gains not only in children's speech recognition but also in speech translation and audio understanding. We further study data selection and auxiliary reward weighting to identify an effective training recipe. Our experiments show that when in-domain data are unavailable or cannot be used for training, FSA-GRPO is more effective than direct tuning on related out-of-domain data.

Advertising platforms use randomized lift tests to measure incrementality, but privacy-preserving reporting systems degrade the observed signal through match-rate loss, linkability loss, attribution-window loss, aggregation-threshold suppression, randomized reporting noise, and segment-heterogeneous signal loss. This paper formulates privacy-constrained advertising measurement as a robust causal decision problem under the mentioned signal losses. Given a randomized experiment and an ambiguity set for privacy-induced degradation, the framework projects the observation-compatible fiber of clean/unfiltered experimental worlds onto the incrementality functional and returns certified, rejected, and unresolved decisions. The main result gives a sharp decision frontier. Reports outside the frontier support uniformly valid certification or rejection, whereas reports inside it contain too little information for any method to uniformly distinguish above-threshold incrementality from non-incrementality. Supporting results give finite-sample certification, sample-complexity guarantees, a minimax lower bound showing that signal loss reduces effective information, and a reporting-granularity tradeoff. On 2.0M Criteo Uplift rows and the 64K-row Hillstrom email experiment, clean conversion lift is positive in both datasets, with lifts 0.00112 and 0.00495, respectively. Population certification survives mild degradation in Criteo and severe degradation in Hillstrom, while all considered finite-sample stress settings in both datasets remain unresolved after simultaneous uncertainty and reporting noise are included. Overall, the research contributes a decision-theoretic layer for privacy-aware incrementality measurement whose output is the strongest causal-claim justified by degraded ads signals.

We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps. Focusing on trajectory distillation for the probability-flow ODE, we show that local approximation errors can be strongly amplified in low-noise multimodal regimes, where the underlying dynamics become stiff. In an analytically tractable Gaussian-mixture Ornstein--Uhlenbeck setting, we separate two core difficulties: approximating the time-dependent score field and controlling the dynamical amplification governed by the time-integrated Jacobian bound of the probability-flow ODE. On the approximation side, we prove constructive L^p(p_t) guarantees showing that ReLU--ReQU networks approximate the Gaussian-mixture score uniformly over time, with depth and width scaling polylogarithmically in the target accuracy and explicitly with the mixture geometry. On the stability side, we derive an explicit bound L(t) for the spatial Lipschitz constant of the probability-flow velocity and convert it into a flow map stability estimate governed by \int_s^t L(u)\,du, making late-time amplification in stiff regimes computable. Building on these estimates, we prove that deep residual compositions efficiently approximate the long-horizon transport, with global error controlled by the stability amplification factor, and identify a Lipschitz-mismatch regime in which one-step distillation is structurally unfavorable. The resulting theory yields a stability-balanced non-uniform time grid obtained by uniform partitioning in the cumulative stability coordinate. Experiments support the prediction and reduce end-to-end relative MSE by up to 51.9\% with 8 segments compared with uniform grids.

Resource-constrained pricing controllers can make fixed-price inference impossible: the controller's resource state may remove the target price neighborhood from the feasible set, even when every realized action has a known positive density. We formalize this support-exclusion failure through a local non-identification result and a realized information clock. We then design a target-aware pricing controller that certifies feasible target bands and logs continuous local densities. Localized debiasing gives studentized intervals whose width is governed by this clock. The resulting regret--information accounting, stated up to pilot re-solving error, shows that cheap exploration can be insufficient for inference: polynomial target mass gives polynomial rates, while a pure $1/t$ target branch does not yield shrinking fixed-target intervals without additional local movement. Experiments show calibration in certified bands and diagnostic abstention when the resource state collapses target support.

Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate $1-2α$ coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired $1-α$ coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.

This work proposes a novel solution to predict pulsar timing residuals with limited data, addressing the critical challenge of data scarcity across spin-frequency subgroups of millisecond pulsars in PTA datasets. The proposed solution applies a Long Short-Term Memory (LSTM) network optimized using the model-agnostic meta-learning algorithm, enabling rapid adaptation to new frequency domain by fine-tuning the LSTM network with only a few-shot of ground truth timing residuals. Particle swarm optimization algorithm is also used for automatic hyperparameter optimization, leading to improved prediction accuracy. Our solution, evaluated on the second data release of the International Pulsar Timing Array (IPTA), demonstrates robust generalization with accurate predictions in three metrics across high-frequency test frequency domains, while requiring only 10% of the timing residuals from these domains for model fine-tuning. Furthermore, our lightweight structure only costs 16.86 MB CPU memory and 18 milliseconds for single-step residual prediction. All these characteristics make our solution highly suitable for real-world applications, where effective and real-time predictions of pulsar timing residuals are essential-particularly in resource-constrained environments with limited computational power, memory, or energy availability.

While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data. Existing methods address this by promoting sparsity through explicit $\ell_1$-penalties, but these are not obvious to tune due to the unsupervised nature of the task. In contrast, we propose Adversarial PCA (AdvPCA), which leverages robust optimization to achieve sparsity by optimizing the reconstruction objective against bounded, worst-case latent space perturbations. We show that this formulation admits a closed-form reduction, leading to a practical iterative algorithm that alternates between adversarial linear regression-style updates for the sparse encoder and orthogonal updates for the decoder. By theoretically characterizing the solution, we derive a data-adaptive parameterization that allows the algorithm to perform effectively out of the box. We validate these claims through numerical experiments on synthetic and real-world genomics data.

Many systems used in real-world environments require adding new categories and incorporating new information without forgetting what was previously learnt by the classification model. This is known as class-incremental continual learning, and in the case of multivariate time-series, is further complicated by the temporal structure of the data. In this paper, we present a novel approach for performing class incremental continual learning for the classification of multivariate time series data based upon the construction of a dual-stream feature extraction pipeline (using both deep temporal embedding features generated via a pre-trained frozen foundation model and application of statistical features). Evaluated on five benchmark datasets, the proposed system achieves competitive average accuracy across all datasets while maintaining low forgetting rates across all experimental configurations.

Concepts of calibration formalize the compatibility between probabilistic predictions and the respective outcomes. In a nutshell, the outcomes ought to be indistinguishable from random draws from the predictive distributions. In this paper, we review, extend, and bridge notions of calibration that have been proposed for classification and regression tasks. Particular emphasis is given to hierarchical relations between the various notions, as they apply to general real-valued data, continuous outcomes, count data, nominal classes, and binary outcomes. To highlight a number of contributions, we introduce the notion of modal calibration for nominal outcomes, we distinguish full, partial, and average calibration in this setting, and we show that double probability integral transform (PIT) calibration is logically independent of previously proposed concepts of calibration for discrete outcomes. Furthermore, we generalize extant results on concepts of calibration that are expressed in terms of properties or functionals of the predictive distributions, such as means, quantiles, or event probabilities. Throughout the paper, we illustrate the concepts and their hierarchical relations in worked examples, and we provide algorithmic tools that support the construction of instructive examples and counterexamples.

Chain-of-thought (CoT) reasoning has become a widely used mechanism for eliciting multi-step reasoning in large language models by generating intermediate reasoning steps at inference time. Yet the scaling behavior of generalization with CoT depth remains poorly understood. To address this question, we study a theoretically solvable model of CoT for in-context weight prediction in linear regression, where test-time reasoning is represented as an iterative refinement of the weight-parameter estimate. Using tools from random matrix theory under high-dimensional asymptotics, we derive an exact formula for the generalization error as a function of reasoning depth, pretraining data amount, and context length. Our analysis reveals a sharp phase transition separating exponential and polynomial improvement, saturation, and overthinking, and characterizes how the optimal reasoning depth scales. We further show that deeper reasoning is most effective with sufficiently rich pretraining and in-context information, whereas limited pretraining or context makes longer reasoning prone to error amplification or saturation. We also validate these predictions through experiments on fully learned linear attention and softmax attention models. Our results provide a unified theoretical account of how test-time CoT depth affects generalization.

With the increasing scale and number of wind farms, wind turbines' daily operation and maintenance costs are increasing. To reduce operation and maintenance costs and enhance the reliability of wind turbine and system operation data before reaching catastrophic failures, monitoring the operating status of the equipment and detecting failures at an early stage is crucial. It is of great practical significance to utilize the working condition data for abnormal assessment of the operating status of wind turbines to realize abnormal monitoring of the operating status of wind turbines. However, the existing anomaly detection methods can neither perform effective relational modeling in data filled with a large amount of redundant information nor reasonably utilize the valuable anomaly data. For this reason, this paper proposes an anomaly detection model that fuses a Transformer and a generative adversarial network. Firstly, it reduces the leakage detection rate of minor deviation anomalies by amplifying the reconstruction error. Secondly, it uses autoregressive inference to extract multimodal features to enhance the stability and generalization ability of training. Finally, the temporal feature extraction module is constructed to promote the interactive learning between features of different time scales and effectively reduce the time redundancy. The results of multiple sets of experiments conducted on real WTG datasets show that TransGAN-WT achieves an average F1 score of 96.10% across multiple wind turbine datasets, which is 5.84% and 2.89% higher than several other state-of-the-art baseline methods. It also realizes a false positive rate (FPR) of 0.06%, and is verified by the Wilcoxon signed-rank test to have achieved a statistically significant performance enhancement compared to the state-of-the-art baseline methods, effectively ensuring the stable operation of wind turbines.

Modeling interactions among multimodal, high-dimensional data is intrinsically challenging due to ultra-high dimensionality and complex dependence structure with high level noise. Screening methods are effective for reducing dimensionality, but most existing approaches shrink only the predictor space while retaining all outcomes. In cross-modal analyses, different outcomes often select different predictor subsets, so the union remains large and the response dimension is unchanged, limiting the practical benefit of screening. This gives rise to heavy computational burdens and poor interpretability. To address these limitations, we propose a new screening framework, Graph Independence Dual Screening (GIDS), which simultaneously reduces the dimensionality of response variables and predictors. We design computationally efficient algorithms that facilitate downstream selection procedures, improving accuracy and scalability, and establish supporting theoretical results. Extensive simulation studies demonstrate that GIDS outperforms existing methods that screen only predictors. To illustrate its utility, we applied GIDS to the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, analyzing interactions between genome-wide 865,353 DNA methylation and 49,386 transcriptomic variables. GIDS reduced the feature space to approximately 9,000 CpGs and 2,000 transcripts, uncovering blockwise interaction structures: clusters of CpG sites and gene transcripts with strong associations. These findings not only improve computational tractability but also yield interpretable biological insights, highlighting coordinated regulatory mechanisms underlying Alzheimer's disease.

Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive. However, exact inference with $n$ function values and $n$ full gradients in $d$ dimensions scales cubically in the joint state size, imposing an intractable $\mathcal{O}(n^3 d^3)$ computational bottleneck. We introduce TERA, a highly scalable derivative GP method based on target-specific exact gradient reduction. We prove that for stationary kernels, the gradient components orthogonal to the directions connecting the target and conditioning points are conditionally independent of the target function value; consequently, the exact conditional density is fully characterized by at most $m^2$ directional derivatives once a conditioning set of size $m$ is specified. By using these reduced, dimension-free conditionals as local factors in a Vecchia approximation, TERA effectively decouples $n$ and $d$ from the dense matrix inversion. This reduces the per-target evaluation cost to $\mathcal{O}(dm^2 + m^6)$ time and $\mathcal{O}(dm^2 + m^4)$ memory, leaving the underlying derivative GP model mathematically unchanged. Empirical evaluations demonstrate that TERA achieves state-of-the-art predictive accuracy while operating orders of magnitude faster than standard derivative GPs. Crucially, both computation time and peak GPU memory remain essentially flat with respect to $d$, enabling highly scalable inference in high-dimensional spaces.