Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient arrives. Vanilla ASGD applies each arriving gradient with the same weight. When local data distributions are heterogeneous, this becomes problematic: faster workers contribute more updates, and we show theoretically that the method is biased toward a frequency-weighted average of the local objectives rather than the desired global objective. Existing remedies typically move away from the simple ASGD template by introducing gathering phases, buffering, or extra memory. We show that this is unnecessary. Keeping the standard ASGD mechanism, we recover the correct objective by rescaling worker-specific stepsizes in proportion to their computation times, so that each worker contributes the same aggregate learning rate over a cycle. In the non-convex setting, under smoothness and bounded heterogeneity assumptions, we prove that the resulting method, Rescaled ASGD, converges to stationary points of the correct global objective in the fixed-computation model. Its time complexity matches the known lower bound in the leading term, while the effects of staleness and data heterogeneity appear only in lower-order terms. Experiments confirm that the method converges to the correct objective and is competitive with state-of-the-art baselines.

Computing a minimum $s$-$t$ cut in a graph is a solution to a wide range of computer vision problems, and is often done using the Boykov-Kolmogorov (BK) algorithm. In this paper, we revisit the BK algorithm from both a theoretical and practical point of view. We improve the analysis of the time complexity of the BK algorithm to $O(mn|C|)$ and propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of $O(m|C|)$, where $m$, $n$, and $|C|$ are the number of edges, number of vertices, and the capacity of the cut, respectively. We additionally propose a compact graph representation that allows our implementation to find a minimum $s$-$t$ cut in a graph with upwards of $10^9$ vertices and $10^{10}$ edges on a machine with 128 GB of memory. We find our implementation of the BK algorithm to be the fastest available implementation of the BK algorithm when evaluating on a comprehensive set of benchmark datasets, highlighting the importance of memory-efficient implementations. We make our implementations publicly available for further research and implementation development within minimum $s$-$t$ cut algorithms.

Scalable compression is essential for bandwidth-adaptive transmission, yet most learned codecs are optimized for a fixed rate-distortion point, making rate adaptation costly due to re-encoding or maintaining multiple bitstreams. In this work, we propose TAFA-GSGC, a scalable learned point cloud geometry codec that enables multi-quality decoding from a single bitstream and a single trained model. TAFA-GSGC combines layered residual refinement with channel-group entropy coding, and introduces a Target-Aligned Feature Aggregation module to reduce cross-layer redundancy in enhancement residuals. Our framework supports up to 9 decodable quality levels with monotonic quality improvement as more subbitstreams are received, while maintaining strong compression efficiency. Compared with the PCGCv2 baseline, TAFA-GSGC demonstrates improved RD performance, achieving average BD-rate reductions of 4.99% and 5.92% in terms of D1-PSNR and D2-PSNR, respectively.

Artificial students -- models that simulate how learners act and respond within educational systems -- are a promising tool for evaluating tutoring strategies and feedback mechanisms at scale. However, most existing approaches rely on prompting large, proprietary language models, limiting adaptability to specific courses and raising concerns around privacy, cost, and dependence. In this work, we propose a framework for training open-weight artificial programming learners directly from authentic student process data. Our approach serializes temporal log traces into a conversational format, representing each student's problem-solving process as a dialogue between the learner and their automated assessment system. Student code submissions and environment feedback, such as test outcomes, grades, and error traces, form alternating conversational turns, enabling models to learn from the iterative debugging process. We additionally introduce a training pipeline combining supervised fine-tuning with preference optimization to align models with authentic student debugging behavior. We evaluate our framework by training Qwen models at 4B and 8B scales on a large-scale dataset of real student submissions to Python programming assignments. Our results show that incorporating environment feedback strengthens models' ability to replicate student debugging behavior, improving over both prior code-only approaches and prompted large language models baselines in functional alignment and code similarity. We release our code to support reproducibility.

This paper presents an overview of the NTIRE 2026 Second Challenge on Day and Night Raindrop Removal for Dual-Focused Images. Building upon the success of the first edition, this challenge attracted a wide range of impressive solutions, all developed and evaluated on our real-world Raindrop Clarity dataset~\cite{jin2024raindrop}. For this edition, we adjust the dataset with 14,139 images for training, 407 images for validation, and 593 images for testing. The primary goal of this challenge is to establish a strong and practical benchmark for the removal of raindrops under various illumination and focus conditions. In total, 168 teams have registered for the competition, and 17 teams submitted valid final solutions and fact sheets for the testing phase. The submitted methods achieved strong performance on the Raindrop Clarity dataset, demonstrating the growing progress in this challenging task.

Low-Rank Adaptation (LoRA) is the dominant parameter-efficient fine-tuning method due to its favorable compute-performance trade-off, yet it suffers from catastrophic forgetting. We study forgetting through a tractable _mean-field self-attention_ toy model, where tokens evolve as an interacting particle system and LoRA acts as a low-rank perturbation. Using tools from partial differential equations and dynamical systems, we characterize regimes suggesting a phase transition between forgetting and non-forgetting behavior. We show that one phase transition appears with respect to the norm of the perturbation, and the other with respect to the depth of the Transformers. We further bound the time-to-deviation in terms of the perturbation size and spectral quantities, and corroborate the predicted trends with experiments and exploratory analyses on real models under LoRA fine-tuning.

For real-world applications, autonomous mobile robotic platforms must be capable of navigating safely in a multitude of different and dynamic environments with accurate and robust localization being a key prerequisite. To support further research in this domain, we present the INSANE data sets - a collection of versatile Micro Aerial Vehicle (MAV) data sets for cross-environment localization. The data sets provide various scenarios with multiple stages of difficulty for localization methods. These scenarios range from trajectories in the controlled environment of an indoor motion capture facility, to experiments where the vehicle performs an outdoor maneuver and transitions into a building, requiring changes of sensor modalities, up to purely outdoor flight maneuvers in a challenging Mars analog environment to simulate scenarios which current and future Mars helicopters would need to perform. The presented work aims to provide data that reflects real-world scenarios and sensor effects. The extensive sensor suite includes various sensor categories, including multiple Inertial Measurement Units (IMUs) and cameras. Sensor data is made available as raw measurements and each data set provides highly accurate ground truth, including the outdoor experiments where a dual Real-Time Kinematic (RTK) Global Navigation Satellite System (GNSS) setup provides sub-degree and centimeter accuracy (1-sigma). The sensor suite also includes a dedicated high-rate IMU to capture all the vibration dynamics of the vehicle during flight to support research on novel machine learning-based sensor signal enhancement methods for improved localization. The data sets and post-processing tools are available at: https://sst.aau.at/cns/datasets

We study robot construction problems where multiple autonomous robots rearrange stacks of prefabricated blocks to build stable structures. These problems are challenging due to ramifications of actions, true concurrency, and requirements of supportedness of blocks by other blocks and stability of the structure at all times. We propose a formal hybrid planning framework to solve a wide range of robot construction problems, based on Answer Set Programming. This framework not only decides for a stable final configuration of the structure, but also computes the order of manipulation tasks for multiple autonomous robots to build the structure from an initial configuration, while simultaneously ensuring the stability, supportedness and other desired properties of the partial construction at each step of the plan. We prove the soundness and completeness of our formal method with respect to these properties. We introduce a set of challenging robot construction benchmark instances, including bridge building and stack overhanging scenarios, discuss the usefulness of our framework over these instances, and demonstrate the applicability of our method using a bimanual Baxter robot.

MeanFlow enables one-step generation in continuous spaces by learning an average velocity over a time interval rather than the instantaneous velocity field of flow matching. However, discrete state spaces do not have smooth trajectories or spatial derivatives, so the continuous formulation does not directly apply. We introduce Discrete MeanFlow, which replaces the motion of a point with the transport of probability mass over finite states. Our key object is the conditional transition kernel of a continuous-time Markov chain (CTMC), from which we define a mean discrete rate that measures the average change in transition probability over a time interval. We prove a Discrete MeanFlow identity that relates this finite-interval rate to the instantaneous CTMC generator at the endpoint, with the Kolmogorov forward equation replacing the spatial chain rule of continuous MeanFlow. Based on this identity, we parameterize the transition kernel directly using a boundary-by-construction design that guarantees valid probability outputs and exact boundary conditions without auxiliary losses. Since the learned kernel is itself a probability distribution, generation reduces to a single forward pass followed by one categorical draw meaning no iterative denoising, ODE integration, or multi-step refinement is required. We validate the framework on exact finite-state Markov chains, where the learned kernel recovers the analytical ground truth to high precision, and on factorized synthetic sequence generation tasks with varying alphabet sizes and sequence lengths.

Hybrid machine learning combines physical knowledge with data-driven models to enhance interpretability and performance. In this context, Port-Hamiltonian Systems (PHS), which generalize Hamiltonian mechanics to describe open, non-autonomous dynamical systems, have been successfully integrated with neural networks under the name Port-Hamiltonian Neural Networks (PHNNs). While the ability of PHNNs to identify Hamiltonian ordinary differential equation (ODE) systems has already been demonstrated, their application to learning Hamiltonian partial differential equation (PDE) systems remains largely unexplored. This limitation restricts their use in musical acoustics, where instruments are typically modeled as distributed parameter systems governed by PDEs. In this work, we demonstrate how to learn the nonlinear string dynamics from data in a physically-consistent framework through a PHNN extension to PDEs. By constructing structured neural network architectures based on PHS, we can recover both the Hamiltonian governing the string and the dissipation affecting it. This approach outperforms baseline, non-physics-informed methods in terms of both accuracy and interpretability. Numerical experiments using synthetic data demonstrate the ability of the proposed PHNN model to identify and emulate the nonlinear dynamics of the system.

Multi-agent debate has emerged as a promising approach for improving LLM reasoning on ground-truth tasks, yet current methodologies face certain structural limitations: debate tends to induce a martingale over belief trajectories, majority voting accounts for most observed gains, and LLMs exhibit confidence escalation rather than calibration across rounds. We argue that the genuine value of debate, and dialectic systems as a whole, lies not in ground-truth tasks but in defeasible domains, where every position can in principle be defeated by better reasoning. We present the Council of Hierarchical Agentic Language (CHAL), a multi-agent dialectic framework that treats defeasible argumentation as an engine for belief optimization. Each agent maintains a CHAL Belief Schema (CBS), a graph-structured belief representation with a Bayesian-inspired architecture, that facilitates belief revision through a gradient-informed dynamic mechanism by leveraging the strength of the belief's thesis as a differentiable objective. Meta-cognitive value systems spanning epistemology, logic, and ethics are elevated to configurable hyperparameters governing agent reasoning and adjudication outcomes. We provide a series of ablation experiments that demonstrate systematic and interpretable effects: the adjudicator's value system determines the debate's overall trajectories in latent belief space, council diversity refines beliefs for all participants, and the framework generalizes across broad fields. CHAL is, to our knowledge, the first framework to treat multi-agent debate as structured belief optimization over defeasible domains. Further, the auditable belief artifacts it produces establish the foundation for dedicated evaluation suites for defeasible argumentation, with broader implications for building AI systems whose reasoning and value commitments are transparent, aligned, and subject to human oversight.

Machine learning algorithms in socially sensitive domains (e.g., credit decisions) often focus on equalizing predictive outcomes. However, satisfying these metrics does not guarantee that models use the same reasoning for different groups. We show that existing outcome-fair models can still apply fundamentally different reasoning to individuals, a ``hidden procedural bias'' missed by standard fairness metrics and algorithms. We propose Counterfactual Explanation Consistency (CEC), a framework that detects and mitigates this bias by aligning feature attributions between individuals and their counterfactual counterparts. Key contributions include a nearest-neighbor counterfactual generation method, a modified baseline for integrated gradient comparisons, an individual-level procedural fairness metric, and a corresponding training loss. We introduce a taxonomy identifying ``Regime B'' (same outcome, different reasoning) as a critical blind spot. Experiments on synthetic data, German Credit, Adult Income, and HMDA mortgage data demonstrate that outcome-fair baselines exhibit substantial hidden bias, while CEC substantially reduces it with modest utility cost.

As autonomous vehicles move from a simplified research setting to practical use, there exists a large gap between the dynamic behavior of a human driving and an autonomous system. Risk-aware behavior needs to naturally develop in order to scale to the demands of the real world. A major issue for risk-aware planning and control has been predicting how dynamical uncertainty evolves through time and optimizing plans that account for this without being overly conservative. Here, we present a learning framework to predict distributional dynamics that can be optimized in real time for Model Predictive Control (MPC). We explore the importance of structure when learning distributional dynamics for use in MPC. A rigorous ablation study is conducted on a large dataset of real world off-road driving that shows the impact of deviations from our proposed structure. Furthermore, we deploy our learned model and planning stack on a full sized vehicle in challenging off-road conditions. Our planning architecture is able to naturally regulate the speed of the vehicle based on the environment and consistently demonstrates intelligent behavior over miles of diverse terrain.

Recent research work on fashion outfit generation focuses on promoting visual consistency of garments by leveraging key information from reference image and text prompt. However, the potential of outfit generation remains underexplored, requiring comprehensive e-commercial dataset and elaborative utilization of multi-modal condition. In this paper, we propose a brand-new e-commerce dataset, named Fashion130k, with various occasions, models, and garment types. For the consistent generation of garment, we design a framework with Unified Multi-modal Condition (UMC) to align and integrate the text and visual prompts into generation model. Specifically, we explore an embedding refiner to extract the unified embeddings of multi-modal prompts, within which a Fusion Transformer is proposed to align the multi-modal embeddings by adjusting the modality gap between text and image. Based on unified embeddings, the attention in generation model is redesigned to emphasis the correlations between prompts and noise image, inducing that the noise image can select the pivotal tokens of prompts for consistent outfit generation. Our dataset and proposed framework offer a general and nuanced exploration of multi-modal prompts for generation models. Extensive experiments on real-world applications and benchmark demonstrate the effectiveness of UMC in visual consistency, achieving promising result than that of SoTA methods.

The rapid evolution of generative paradigms has enabled the creation of highly realistic imagery, which escalating the risks of identity fraud and the dissemination of disinformation. Most existing approaches frame face forgery detection as a fully supervised binary classification problem. Consequently, these models typically exhibit significant performance decay when tasked with detecting forgeries from previously unseen generative paradigms. Furthermore, these methods focus exclusively on either DeepFakes or fully synthesized faces, thereby failing to provide a generalized framework for universal face forgery detection. In this paper, we address this challenge by introducing FADNet (Face Authenticity Detector Net), % a self-supervised framework that which reformulates face forgery detection as a one-class classification (OCC) task. By training exclusively on authentic facial data to capture their intrinsic representations, FADNet flags any image whose feature embedding deviates significantly from the learned distribution of real faces as a forgery. The framework incorporates Evidential Deep Learning (EDL) to quantify predictive uncertainty and utilizes a plug-and-play pseudo-forgery image generator (PFIG) to tighten decision boundaries around authentic data. Extensive experimental evaluations on the DF40 and ASFD benchmarks demonstrate that FADNet achieves superior performance and generalization capabilities. Specifically, FADNet substantially outperforms existing state-of-the-art (SOTA) methods, yielding a remarkable average accuracy of 96.63\% and an average precision of 98.83\%.

With the rapid development of deep generative models, forged facial images are massively exploited for illegal activities. Although existing synthetic face detection methods have achieved significant progress, they suffer from the inherent limitation of overconfidence due to their reliance on the Softmax activation function. Thus, these methods often lead to unreliable predictions when encountering unknown Out-of-Distribution (OOD) images, and cannot ascertain the model's uncertainty in its prediction. Meanwhile, most existing methods require massive high-quality annotated data, which greatly limits their practicability across diverse scenarios. To address these limitations, we propose EMSFD (Evidence-based decision Modeling for Synthetic Face Detection with uncertainty-driven active learning), an approach designed to enhance detection reliability and generalizability. Specifically, EMSFD models class evidence using the Dirichlet distribution and explicitly incorporates model uncertainty into the prediction process. Furthermore, during training, the estimated uncertainty is exploited to prioritize more informative samples from the unlabeled pool for annotation, thereby reducing labeling cost and improving model generalization. Extensive experimental evaluations demonstrate that our method enhances the interpretability of synthetic face detection. Meanwhile, our method yields a 15\% increase in accuracy compared to existing state-of-the-art (SOTA) baselines, which demonstrates the superior detection performance and generalizability of our approach. Our code is available at: https://github.com/hzx111621/EMSFD.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the standard paradigm for LLM mathematical reasoning, where Group Relative Policy Optimization (GRPO) serves as the mainstream algorithm. We point out two understudied inefficiencies existing in GRPO. First, the fixed KL penalty coefficient overly restricts policy exploration at stages where the model requires significant deviation from the reference policy. Second, uniform sampling of training questions ignores that moderately difficult problems provide the most informative gradient signals for optimization. We propose Exploration-Prioritized Policy Optimization (EXPO) with two lightweight plug-in modules. The Accuracy-Conditioned KL Scaling (AKL) dynamically adjusts KL regularization strength through a smooth nonlinear function of batch average accuracy, relaxing the penalty when the model underperforms and strengthening it when the model achieves good results. The Gaussian Curriculum Sampling (GCS) assigns sampling weights to questions following a Gaussian distribution centered at moderate accuracy around 0.5, focusing training on the model's learning frontier. We conduct extensive experiments on DeepSeek-R1-Distill-Qwen-1.5B and Qwen3-8B-Base over six mathematical reasoning benchmarks. The results show EXPO steadily surpasses vanilla GRPO. It obtains an absolute gain of 13.34 on AIME 2025 pass@32, rising from 63.33 percent to 76.67 percent, and achieves an average pass@32 improvement of 2.66 on the 8B model. The much larger performance gains on pass@32 compared with pass@1 demonstrate that EXPO effectively enlarges the model's exploration boundary under a fixed inference cost budget.

Generative models have emerged as a promising paradigm for offline multi-agent reinforcement learning (MARL), but existing approaches require many iterative sampling steps. Recent few-step acceleration methods either distill a joint teacher into independent students or apply averaged velocity fields independently to each agent. Unfortunately, these few-step approaches hurt inter-agent coordination. We show that the efficiency-coordination trade-off is not inherent: single-pass multi-agent generation can preserve coordination when the velocity field is natively joint-coupled. We propose Coordinated few-step Flow (CoFlow), an architecture that combines Coordinated Velocity Attention (CVA) with Adaptive Coordination Gating. A finite-difference consistency surrogate further replaces memory-prohibitive Jacobian-vector product backpropagation through the averaged velocity field with two stop-gradient forward passes. Across 60 configurations spanning MPE, MA-MuJoCo, and SMAC, CoFlow matches or surpasses Gaussian policies, value-based methods, transformer policies, diffusion models, and prior flow baselines on episodic return. Three independent coordination probes confirm that CoFlow's improvements arise from inter-agent coordination rather than per-agent capacity. A denoising-step sweep shows that single-pass inference suffices on every configuration. CoFlow reaches state-of-the-art coordination quality in 1-3 denoising steps under both centralized and decentralized execution. Project Page: https://guowei-zou.github.io/coflow/

In this paper, we study whether an off-the-shelf LLM can be adapted into a discrete, variable-length token compressor and decompressor for long-context processing. To this end, we design a self-expressive autoencoding framework that fine-tunes a pretrained LLM with lightweight LoRA adapters to map long texts into compact sequences of learned latent codes, termed Z-tokens, and to decode them back into natural language or task outputs. The resulting representation is content-adaptive: less predictable or information-dense segments can receive more Z-tokens, while redundant regions can be represented more compactly through a budget-aware length regularizer. Our method is evaluated on long-context datasets such as Wikipedia, CNN/DailyMail, HotpotQA, and QuALITY, showing that it preserves reconstruction quality and downstream performance while reducing effective context length, generation-stage memory usage, and end-to-end latency. This simple design supports both direct decoding from compressed contexts and autoregressive generation in the Z-token space, providing a practical interface for efficient long-context inference.

Many European languages possess rich biblical translation histories, yet existing corpora - in prioritizing linguistic breadth - often fail to capture this depth. To address this gap, we introduce a multilingual corpus of 651 New Testament translations, of which 334 are unique, spanning five languages with 2.4-5.0x more translations per language than any prior corpus: English (194 unique versions from 390 total), French (41 from 78), Italian (17 from 33), Polish (29 from 48), and Spanish (53 from 102). Aggregated from 12 online biblical libraries and one preexisting corpus, each translation is annotated with metadata that maps the text to a standardized identifier for the work, its specific edition, and its year of revision. This canonicalization allows researchers to define "uniqueness" for their own needs: they can perform micro-level analyses on translation families, such as the KJV lineage, or conduct macro-level studies by deduplicating closely related texts. By providing the first multilingual resource with sufficient depth per language for flexible, multilevel analysis, the corpus fills a gap in the quantitative study of translation history.

Reinforcement learning with verifiable rewards (RLVR) has become a practical route to improve large language model reasoning, and Group Relative Policy Optimization (GRPO) is a widely used optimizer in this setting. However, RLVR training is typically performed with limited control over generalization. We revisit GRPO through a robustness-based generalization view, where the generalization loss is upper bounded by a combination of the empirical loss and a sharpness surrogate measured by the gradient norm. Building on this perspective, we propose Sharpness-Guided GRPO (GRPO-SG), a simple token-weighted variant of GRPO that downweights tokens likely to cause overly large gradients, reducing sharp updates and stabilizing optimization, thereby improving generalization. Experiments across mathematical reasoning, logic puzzles and tool-augmented question answering show consistent improvements over GRPO, along with smoother gradient-norm trajectories, supporting GRPO-SG as a simple and effective generalization-oriented upgrade to GRPO for RLVR.

Independent on-policy policy gradient algorithms are widely used for multi-agent reinforcement learning (MARL) in cooperative and no-conflict games, but they are known to converge sub-optimally when each agent's individual policy gradient points away from an optimal joint equilibrium. Going beyond prior work, we observe that sub-optimal convergence can still arise even when the expected individual policy gradients of each agent point toward the optimal joint solution. After collecting a finite set of trajectories, stochasticity in independent action sampling can cause the joint data distribution to deviate from the expected joint on-policy distribution. This \textit{sampling error} w.r.t. the joint on-policy distribution produces inaccurate gradient estimates that can make agents converge sub-optimally. We hypothesize that joint sampling error can be reduced through coordinated action selection and that doing so will increase the reliability of policy gradient learning in MARL (i.e., the probability of converging to an optimal joint policy). To test this hypothesis, we first introduce an adaptive action sampling approach to reduce joint sampling error in the Centralized Training with Decentralized Execution setting. Our method, Cooperative Sampling Error Reduction (CoSER), continually adapts a centralized behavior policy to place higher probability on joint actions that are under-sampled w.r.t. the current joint policy. We then empirically evaluate CoSER on a diverse set of multi-agent games and demonstrate that (1) CoSER reduces joint sampling error more efficiently than independent on-policy sampling and (2) this reduction increases the reliability of independent policy gradient algorithms.

Machine vision and image processing are often used with sensors for situation awareness in autonomous systems, from industrial robots to self-driving cars. The 3D depth sensors, such as LiDAR (Light Detection and Ranging), Radar, are great invention for autonomous systems. Due to the complexity of the setup, LiDAR may not be suitable for some operational environments, for example, a space environment. This study was motivated by a desire to get real-time volumetric and change information with multiple 2D cameras instead of a depth camera. Two cameras were used to measure the dimensions of a rectangular object in real-time. The R-C-P (row-column-pixel) method is developed using image processing and edge detection. In addition to the surface areas, the R-C-P method also detects discontinuous edges or volumes. Lastly, experimental work is presented for illustration of the R-C-P method, which provides the equations for calculating surface area dimensions. Using the equations with given distance information between the object and the camera, the vision system provides the dimensions of actual objects.

Large vision models (LVMs) have recently proven to be surprisingly effective time series forecasters, simply by rendering temporal data as images. This success, how ever, rests on a largely unexamined premise: the rendered time series images are sufficiently close to natural images for knowledge in pre-trained models to transfer effectively. We argue that two gaps still remain, i.e., spectral and structural gaps, fundamentally limiting the potential of LVMs for time series forecasting. Spectrally, we systematically reveal that rendered time series images exhibit a markedly shallower power spectrum than the natural images LVMs are pre-trained to recognize. Structurally, reshaping 1D temporal sequences into 2D grids fabricates spurious spatial adjacencies while severing genuine temporal continuities, misleading the spatial inductive biases of pre-trained LVMs. To bridge these gaps, we propose SSDA, a dual-branch network that spectrally and structurally adapts to unlock the full potential of LVMs for time series forecasting. At the data level, a Spectral Magnitude Aligner (SMA) applies 2D FFT to selectively enhance the magnitude spectrum toward natural-image statistics while preserving phase. At the model level, a Structural-Guided Low-Rank Adaptation (SG-LoRA) injects position-aware temporal encodings into patch embeddings and adapts at tention via low-rank updates. The two branches are further adaptively fused to produce the final forecast. Extensive experiments on seven real-world benchmarks demonstrate that SSDA consistently outperforms strong LVM- and LLM-based baselines under both full-shot and few-shot settings. Code is publicly available at https://anonymous.4open.science/r/SSDA-8C5B.

We consider fully connected and feedforward deep neural networks with dependent and possibly heavy-tailed weights, as introduced in [26], to address limitations of the standard Gaussian prior. It has been proved in [26] that, as the number of nodes in the hidden layers grows large, according to a sequential and ordered limit, the law of the output converges weakly to a Gaussian mixture. In this paper, we study the neural network through the lens of the posterior distribution with a Gaussian likelihood. If the random covariance matrix of the infinite-width limit is positive definite under the prior, we identify the posterior distribution of the output in the wide-width limit according to a sequential regime. Remarkably, we provide mild sufficient conditions to ensure the aforementioned invertibility of the random covariance matrix under the prior, thereby extending the results in [8]. Among our results, we present sufficient conditions on some model parameters (the activation function and the associated Lévy measures) which ensure that the sequential limits are independent of the order. We illustrate our findings with examples and numerical simulations.

We introduce ProofGrid, a benchmark suite for evaluating LLM reasoning through machine-checkable proofs rather than final answers alone. ProofGrid contains 15 tasks spanning proof writing, proof checking, proof masking, and proof gap-filling. Tasks are expressed in minimal formal notation, especially NDL, a compact natural-deduction language that fits in short prompts and supports precise, auditable verification. This yields mechanical, reproducible, and fine-grained evaluation rather than judgments by humans or LLMs. ProofGrid covers a calibrated difficulty spectrum, from foundational reasoning tests to structurally rich challenge tasks that no current model solves, while minimizing reliance on domain knowledge, solver delegation, and long-context artifacts. We also develop a comparative framework for reasoning benchmarks and use it to situate ProofGrid relative to existing work in terms of representation, verification guarantees, and reasoning depth. Methodologically, we introduce an instrumented proof-checking pipeline that tolerates minor surface deviations while locating the first substantive reasoning failure, improving measurement resolution and separating proof planning from low-level execution noise. Using this pipeline, we evaluate a broad range of open and proprietary models. Results show rapid progress but substantial remaining limits: frontier models perform well on several foundational tasks, yet difficult tasks, especially those requiring global combinatorial reasoning or low-level proof synthesis, remain far from solved. We also identify epistemic instability, where models generate flawed proofs yet correctly reject those local inferences in isolation, and formalize this with an Epistemic Stability Index. Finally, we complement accuracy with 2PL IRT analyses, Wright maps, and a normalized task-discrimination measure based on Fisher information.

If S and S' are two finite sets of Coxeter generators for a right-angled Coxeter group W, then the Coxeter systems (W,S) and (W,S') are equivalent.

Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum of 2-dimensional torsion forms. This is obtained from a more general study of weakly isotropic forms over henselian valued fields and over function fields in one variable.

We present validated and forward-modelled galaxy luminosity functions and photometric predictions for the Vera C. Rubin Observatory Legacy Survey of Space and Time using the ASTRID cosmological hydrodynamical simulation. Galaxy magnitudes are computed by combining stellar population synthesis modeling with a physically motivated dust attenuation prescription in which the optical depth scales with metal surface density. The dust model is calibrated at z = 0 using SDSS luminosity functions and tested at intermediate redshifts (z = 0.5, 1.0, and 1.5) in rest-frame B, V , R, and I bands. We find that the attenuated luminosity functions reproduce observed galaxy statistics across multiple wavelengths and redshifts. Using this calibrated framework, we construct LSST-ready mock photometric catalogs over 0 <= z <= 2 in steps of Delta z = 0.1, containing ~378 million galaxies. We provide predicted apparent-magnitude luminosity functions in the LSST ugrizy bands, derive best-fit Schechter parameters as a compact analytic representation, and compute differential and cumulative galaxy number counts as a function of survey depth from Year 1 to Year 10.

Low-surface-brightness galaxies (LSBGs) are vital for understanding galaxy formation, but their diffuse nature makes them challenging to detect. Upcoming large-scale surveys are expected to uncover large numbers of LSBGs, requiring robust automated methods to identify them across heterogeneous datasets. As a precursor to the Legacy Survey of Space and Time (LSST) and Euclid, we explore domain adaptation techniques for cross-survey LSBG identification. Using models trained on the Dark Energy Survey (DES), we search for LSBGs in the Kilo-Degree Survey Data Release 5 (KiDS DR5). We used an ensemble consisting of one convolutional neural network (CNN) and two transformer models trained on DES cutouts and applied to KiDS DR5 imaging data. Structural parameters were estimated with galfitm, and photometric redshifts and stellar population properties were estimated through spectral energy distribution fitting with CIGALE. We identify 20,180 LSBGs and 434 ultra-diffuse galaxies (UDGs) in KiDS DR5. Their structural parameters are similar to known LSBGs from DES and the Hyper Suprime-Cam SSP Survey (HSC-SSP). The KiDS-LSBGs follow a continuous size-luminosity relation connecting classical dwarf galaxies and UDGs, and their colours are bimodal ($\sim73\%$ blue, $\sim27\%$ red). Cross-matching with spectroscopic and cluster catalogues provides redshifts for 4,913 systems, enabling a systematic characterisation of the star-forming main sequence of LSBGs. Strong environmental trends are evident, with cluster LSBGs and UDGs exhibiting redder colours and reduced star formation compared to non-cluster systems. We demonstrate that domain adaptation enables robust cross-survey LSBG identification with deep learning models, providing a scalable pathway for constructing homogeneous LSBG catalogues for the LSST and Euclid era.