This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily relied on theoretical foundations provided by mathematics and statistics. However, recent developments in AI, particularly in reinforcement learning (RL) and large language models (LLMs), have demonstrated the potential for AI to contribute back to mathematics by offering flexible algorithmic frameworks and powerful inductive reasoning capabilities that support various aspects of mathematical research. This survey aims to establish a bridge between AI and mathematics, providing insights into the mutual benefits and fostering deeper interdisciplinary understanding. In particular, we argue that while current AI and LLMs may struggle with complex deductive reasoning, their "inherent creativity", the ability to generate outputs at high throughput based on recognition of shallow patterns, holds significant potential to support and inspire mathematical research. This creative capability, often overlooked, could be the key to unlocking new perspectives and methodologies in mathematics. Furthermore, we address the lack of cross-disciplinary communication: mathematicians may not fully comprehend the latest advances in AI, while AI researchers frequently prioritize benchmark performance over real-world applications in frontier mathematical research. This paper seeks to close that gap, offering a detailed exploration of AI fundamentals, its strengths, and its emerging applications in the mathematical sciences.

Vision-language models (VLMs), such as CLIP and SigLIP, have found remarkable success in classification, retrieval, and generative tasks. For this, VLMs deterministically map images and text descriptions to a joint latent space in which their similarity is assessed using the cosine similarity. However, a deterministic mapping of inputs fails to capture uncertainties over concepts arising from domain shifts when used in downstream tasks. In this work, we propose post-hoc uncertainty estimation in VLMs that does not require additional training. Our method leverages a Bayesian posterior approximation over the last layers in VLMs and analytically quantifies uncertainties over cosine similarities. We demonstrate its effectiveness for uncertainty quantification and support set selection in active learning. Compared to baselines, we obtain improved and well-calibrated predictive uncertainties, interpretable uncertainty estimates, and sample-efficient active learning. Our results show promise for safety-critical applications of large-scale models.

Accurate short-term precipitation forecasting is critical for weather-sensitive decision-making in agriculture, transportation, and disaster response. Existing deep learning approaches often struggle to balance global structural consistency with local detail preservation, especially under complex meteorological conditions. We propose DuoCast, a dual-diffusion framework that decomposes precipitation forecasting into low- and high-frequency components modeled in orthogonal latent subspaces. We theoretically prove that this frequency decomposition reduces prediction error compared to conventional single branch U-Net diffusion models. In DuoCast, the low-frequency model captures large-scale trends via convolutional encoders conditioned on weather front dynamics, while the high-frequency model refines fine-scale variability using a self-attention-based architecture. Experiments on four benchmark radar datasets show that DuoCast consistently outperforms state-of-the-art baselines, achieving superior accuracy in both spatial detail and temporal evolution.

Monocular 3D object detection has attracted great attention due to simplicity and low cost. Existing methods typically follow conventional 2D detection paradigms, first locating object centers and then predicting 3D attributes via neighboring features. However, these methods predominantly rely on progressive cross-scale feature aggregation and focus solely on local information, which may result in a lack of global awareness and the omission of small-scale objects. In addition, due to large variation in object scales across different scenes and depths, inaccurate receptive fields often lead to background noise and degraded feature representation. To address these issues, we introduces MonoASRH, a novel monocular 3D detection framework composed of Efficient Hybrid Feature Aggregation Module (EH-FAM) and Adaptive Scale-Aware 3D Regression Head (ASRH). Specifically, EH-FAM employs multi-head attention with a global receptive field to extract semantic features for small-scale objects and leverages lightweight convolutional modules to efficiently aggregate visual features across different scales. The ASRH encodes 2D bounding box dimensions and then fuses scale features with the semantic features aggregated by EH-FAM through a scale-semantic feature fusion module. The scale-semantic feature fusion module guides ASRH in learning dynamic receptive field offsets, incorporating scale priors into 3D position prediction for better scale-awareness. Extensive experiments on the KITTI and Waymo datasets demonstrate that MonoASRH achieves state-of-the-art performance.

Alzheimer's disease (AD) poses significant global health challenges due to its increasing prevalence and associated societal costs. Early detection and diagnosis of AD are critical for delaying progression and improving patient outcomes. Traditional diagnostic methods and single-modality data often fall short in identifying early-stage AD and distinguishing it from Mild Cognitive Impairment (MCI). This study addresses these challenges by introducing a novel approach: multImodal enseMble via class BALancing diversity for iMbalancEd Data (IMBALMED). IMBALMED integrates multimodal data from the Alzheimer's Disease Neuroimaging Initiative database, including clinical assessments, neuroimaging phenotypes, biospecimen and subject characteristics data. It employs an ensemble of model classifiers, each trained with different class balancing techniques, to overcome class imbalance and enhance model accuracy. We evaluate IMBALMED on two diagnostic tasks (binary and ternary classification) and four binary early detection tasks (at 12, 24, 36, and 48 months), comparing its performance with state-of-the-art algorithms and an unbalanced dataset method. IMBALMED demonstrates superior diagnostic accuracy and predictive performance in both binary and ternary classification tasks, significantly improving early detection of MCI at 48-month time point. The method shows improved classification performance and robustness, offering a promising solution for early detection and management of AD.

Generating physically feasible dynamics in a data-driven context is challenging, especially when adhering to physical priors expressed in specific equations or formulas. Existing methodologies often overlook the integration of physical priors, resulting in violation of basic physical laws and suboptimal performance. In this paper, we introduce a novel framework that seamlessly incorporates physical priors into diffusion-based generative models to address this limitation. Our approach leverages two categories of priors: 1) distributional priors, such as roto-translational invariance, and 2) physical feasibility priors, including energy and momentum conservation laws and PDE constraints. By embedding these priors into the generative process, our method can efficiently generate physically realistic dynamics, encompassing trajectories and flows. Empirical evaluations demonstrate that our method produces high-quality dynamics across a diverse array of physical phenomena with remarkable robustness, underscoring its potential to advance data-driven studies in AI4Physics. Our contributions signify a substantial advancement in the field of generative modeling, offering a robust solution to generate accurate and physically consistent dynamics.

Time Series Forecasting (TSF) has long been a challenge in time series analysis. Inspired by the success of Large Language Models (LLMs), researchers are now developing Large Time Series Models (LTSMs)-universal transformer-based models that use autoregressive prediction-to improve TSF. However, training LTSMs on heterogeneous time series data poses unique challenges, including diverse frequencies, dimensions, and patterns across datasets. Recent endeavors have studied and evaluated various design choices aimed at enhancing LTSM training and generalization capabilities. However, these design choices are typically studied and evaluated in isolation and are not benchmarked collectively. In this work, we introduce LTSM-Bundle, a comprehensive toolbox, and benchmark for training LTSMs, spanning pre-processing techniques, model configurations, and dataset configuration. It modularized and benchmarked LTSMs from multiple dimensions, encompassing prompting strategies, tokenization approaches, training paradigms, base model selection, data quantity, and dataset diversity. Furthermore, we combine the most effective design choices identified in our study. Empirical results demonstrate that this combination achieves superior zero-shot and few-shot performances compared to state-of-the-art LTSMs and traditional TSF methods on benchmark datasets.

Data distribution shift is a common problem in machine learning-powered smart city applications where the test data differs from the training data. Augmenting smart city applications with online machine learning models can handle this issue at test time, albeit with high cost and unreliable performance. To overcome this limitation, we propose to endow test-time adaptation with a systematic active fine-tuning (SAF) layer that is characterized by three key aspects: a continuity aspect that adapts to ever-present data distribution shifts; intelligence aspect that recognizes the importance of fine-tuning as a distribution-shift-aware process that occurs at the appropriate time to address the recently detected data distribution shifts; and cost-effectiveness aspect that involves budgeted human-machine collaboration to make relabeling cost-effective and practical for diverse smart city applications. Our empirical results show that our proposed approach outperforms the traditional test-time adaptation by a factor of two.

Speech Large Language Models (SLLMs) enable high-level emotion reasoning but often produce ungrounded, text-biased judgments without verifiable acoustic evidence. In contrast, self-supervised speech encoders such as WavLM provide strong acoustic representations yet remain opaque discriminative models with limited interpretability. To bridge this gap, we introduce ADEPT (Agentic Decoding of Emotion via Evidence Probing Tools), a framework that reframes emotion recognition as a multi-turn inquiry process rather than a single-pass prediction. ADEPT transforms an SLLM into an agent that maintains an evolving candidate emotion set and adaptively invokes dedicated semantic and acoustic probing tools within a structured pipeline of candidate generation, evidence collection, and adjudication. Crucially, ADEPT enables a paradigm shift from consensus learning to ambiguity-driven emotion reasoning. Since human affect exhibits inherent complexity and frequent co-occurrence of emotions, we treat minority annotations as informative perceptual signals rather than discarding them as noise. Finally, we integrate Group Relative Policy Optimization (GRPO) with an Evidence Trust Gate to explicitly couple tool-usage behaviors with prediction quality and enforce evidence-grounded reasoning. Experiments show that ADEPT improves primary emotion accuracy in most settings while substantially improving minor emotion characterization, producing explanations grounded in auditable acoustic and semantic evidence.

Retrieval-augmented generation (RAG) has become a dominant paradigm for grounding large language models (LLMs) with external evidence in knowledge-intensive question answering. A core design choice is how to fuse retrieved samples into the LLMs, where existing internal fusion approaches broadly fall into query-based fusion, parametric fusion, and latent-based fusion. Despite their effectiveness at modest retrieval scales, these methods often fail to scale gracefully as the number of retrieved candidates k increases: Larger k improves evidence coverage, yet realistic top-k retrieval inevitably contains irrelevant or redundant content and increases the inference cost. To address these limitations, we propose ReFilter, a novel latent-based fusion framework that performs token-level filtering and fusion. ReFilter consists of three key components: a context encoder for encoding context features, a gated filter for weighting each token, and a token fusion module for integrating the weighted token feature into the LLM's hidden states. Our experiments across four general-domain QA benchmarks show that ReFilter consistently achieves the best average performance under both in-domain adaptation and out-of-domain transfer. ReFilter further generalizes to five biomedical QA benchmarks in zero-shot transfer without domain fine-tuning, reaching 70.01% average accuracy with Qwen2.5-14B-Instruct.

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data regimes and under unseen (out-of-distribution) input functions that are not represented in the training data. To address these limitations, we propose the Physics-Informed Laplace Neural Operator (PILNO), which enhances the Laplace Neural Operator (LNO) by embedding governing physics into training through PDE, boundary condition, and initial condition residuals. To improve expressivity, we first introduce an Advanced LNO (ALNO) backbone that retains a pole-residue transient representation while replacing the steady-state branch with an FNO-style Fourier multiplier. To make physics-informed training both data-efficient and robust, PILNO further leverages (i) virtual inputs: an unlabeled ensemble of input functions spanning a broad spectral range that provides abundant physics-only supervision and explicitly targets out-of-distribution (OOD) regimes; and (ii) temporal-causality weighting: a time-decaying reweighting of the physics residual that prioritizes early-time dynamics and stabilizes optimization for time-dependent PDEs. Across four representative benchmarks -- Burgers' equation, Darcy flow, a reaction-diffusion system, and a forced KdV equation -- PILNO consistently improves accuracy in small-data settings (e.g., N_train <= 27), reduces run-to-run variability across random seeds, and achieves stronger OOD generalization than purely data-driven baselines.

Previous speech restoration (SR) primarily focuses on single-task speech restoration (SSR), which cannot address general speech restoration problems. Training specific SSR models for different distortions is time-consuming and lacks generality. In addition, most studies ignore the problem of model generalization across unseen domains. To overcome those limitations, we propose DisSR, a Disentangling Speech Representation based general speech restoration model with two properties: 1) Degradation-prior guidance, which extracts speaker-invariant degradation representation to guide the diffusion-based speech restoration model. 2) Domain adaptation, where we design cross-domain alignment training to enhance the model's adaptability and generalization on cross-domain data, respectively. Experimental results demonstrate that our method can produce high-quality restored speech under various distortion conditions. Audio samples can be found at https://itspsp.github.io/DisSR.

Depth control of underwater vehicles in engineering applications must simultaneously satisfy requirements for rapid tracking, low overshoot, and actuator constraints. Traditional fuzzy PID tuning often relies on empirical methods, making it difficult to achieve a stable and reproducible equilibrium solution between performance enhancement and control cost. This paper proposes a constrained particle swarm optimization (PSO) method for tuning six-parameter fuzzy PID controllers. By adjusting the benchmark PID parameters alongside the fuzzy controller's input quantization factor and output proportional gain, it achieves synergistic optimization of the overall tuning strength and dynamic response characteristics of the fuzzy PID system. To ensure engineering feasibility of the optimization results, a time-weighted absolute error integral, adjustment time, relative overshoot control energy, and saturation occupancy rate are introduced. Control energy constraints are applied to construct a constraint-driven comprehensive evaluation system, suppressing pseudo-improvements achieved solely by increasing control inputs. Simulation results demonstrate that, while maintaining consistent control energy and saturation levels, the proposed method significantly enhances deep tracking performance: the time-weighted absolute error integral decreases from 0.2631 to 0.1473, the settling time shortens from 2.301 s to 1.613 s, and the relative overshoot reduces from 0.1494 to 0.01839. Control energy varied from 7980 to 7935, satisfying the energy constraint, while saturation occupancy decreased from 0.004 to 0.003. These results validate the effectiveness and engineering significance of the proposed constrained six-parameter joint tuning strategy for depth control in underwater vehicle navigation scenarios.

Training and evaluating vision encoders on Multi-Channel Imaging (MCI) data remains challenging as channel configurations vary across datasets, preventing fixed-channel training and limiting reuse of pre-trained encoders on new channel settings. Prior work trains MCI encoders but typically evaluates them via full fine-tuning, leaving probing with frozen pre-trained encoders comparatively underexplored. Existing studies that perform probing largely focus on improving representations, rather than how to best leverage fixed representations for downstream tasks. Although the latter problem has been studied in other domains, directly transferring those strategies to MCI yields weak results, even worse than training from scratch. We therefore propose Channel-Aware Probing (CAP), which exploits the intrinsic inter-channel diversity in MCI datasets by controlling feature flow at both the encoder and probe levels. CAP uses Independent Feature Encoding (IFE) to encode each channel separately, and Decoupled Pooling (DCP) to pool within channels before aggregating across channels. Across three MCI benchmarks, CAP consistently improves probing performance over the default probing protocol, matches fine-tuning from scratch, and largely reduces the gap to full fine-tuning from the same MCI pre-trained checkpoints. Code can be found in https://github.com/umarikkar/CAP.

Split conformal prediction provides distribution-free prediction intervals with finite-sample marginal coverage, but produces constant-width intervals that overcover in low-variance regions and undercover in high-variance regions. Existing adaptive methods require training auxiliary models. We propose Leverage-Weighted Conformal Prediction (LWCP), which weights nonconformity scores by a function of the statistical leverage -- the diagonal of the hat matrix -- deriving adaptivity from the geometry of the design matrix rather than from auxiliary model fitting. We prove that LWCP preserves finite-sample marginal validity for any weight function; achieves asymptotically optimal conditional coverage at essentially no width cost when heteroscedasticity factors through leverage; and recovers the form and width of classical prediction intervals under Gaussian assumptions while retaining distribution-free guarantees. We further establish that randomized leverage approximations preserve coverage exactly with controlled width perturbation, and that vanilla CP suffers a persistent, sample-size-independent conditional coverage gap that LWCP eliminates. The method requires no hyperparameters beyond the choice of weight function and adds negligible computational overhead to vanilla CP. Experiments on synthetic and real data confirm the theoretical predictions, demonstrating substantial reductions in conditional coverage disparity across settings.

Sparse-Linear Attention (SLA) combines sparse and linear attention to accelerate diffusion models and has shown strong performance in video generation. However, (i) SLA relies on a heuristic split that assigns computations to the sparse or linear branch based on attention-weight magnitude, which can be suboptimal. Additionally, (ii) after formally analyzing the attention error in SLA, we identify a mismatch between SLA and a direct decomposition into sparse and linear attention. We propose SLA2, which introduces (I) a learnable router that dynamically selects whether each attention computation should use sparse or linear attention, (II) a more faithful and direct sparse-linear attention formulation that uses a learnable ratio to combine the sparse and linear attention branches, and (III) a sparse + low-bit attention design, where low-bit attention is introduced via quantization-aware fine-tuning to reduce quantization error. Experiments show that on video diffusion models, SLA2 can achieve 97% attention sparsity and deliver an 18.6x attention speedup while preserving generation quality.

Knowledge Distillation (KD) for Large Language Models (LLMs) has become increasingly important as models grow in size and complexity. While existing distillation approaches focus on imitating teacher behavior, they often overlook the original learning environment that shaped the teacher's knowledge. Inspired by the experiential learning theory and inverse reinforcement learning, we propose Experiential Knowledge Distillation ($\mathcal{X}$-KD), a novel and general framework that enables student models to learn in the teacher's original learning environment. $\mathcal{X}$-KD adopts the Approximated Variational Reward Imitation Learning (AVRIL) framework to jointly model the teacher's original reward function and perform policy distillation, encouraging consistency between the student policy and the original reward function. Our derivation demonstrates that $\mathcal{X}$-KD follows the supervised learning framework and applies to both sequence-level and divergence-based distillation methods, underlining the simplicity and flexibility of our approach. Empirical results show that $\mathcal{X}$-KD outperforms the generalized KD and MiniLLM baselines on abstractive summarization, machine translation, and arithmetic reasoning tasks. Additionally, $\mathcal{X}$-KD achieves better performance-diversity trade-off and data efficiency than baseline KD approaches.

Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine satisfiability. We introduce a diagnostic benchmark for 2-SAT built from parameterized families of structured 2--CNF formulas, where satisfiability is characterized by the implication graph and can be tuned along interpretable axes. Our generators isolate distinct competencies and failure modes: (i) contradiction-cycle UNSAT cores with controllable size and imbalance, (ii) SAT instances with a prescribed fraction of free variables to control solution multiplicity, (iii) planted backbones that modulate propagation, (iv) late bridge clauses that couple otherwise monotone regions to probe sensitivity to ordering and revision, and (v) symmetry/duplication variants that test abstraction under renaming and redundant structure. We evaluate LLM-based reasoners on decision accuracy and assignment validity, and quantify robustness under semantics-preserving perturbations such as clause reordering, filler clauses, and variable renaming. Across models, we observe sharp performance transitions under targeted structural interventions even when surface statistics are held fixed, revealing brittleness regimes that are invisible to aggregate SAT accuracy.

Large language models (LLMs) are increasingly deployed as autonomous agents for multi-turn decision-making tasks. However, current agents typically rely on fixed cognitive patterns: non-thinking models generate immediate responses, while thinking models engage in deep reasoning uniformly. This rigidity is inefficient for long-horizon tasks, where cognitive demands vary significantly from step to step, with some requiring strategic planning and others only routine execution. In this paper, we introduce CogRouter, a framework that trains agents to dynamically adapt cognitive depth at each step. Grounded in ACT-R theory, we design four hierarchical cognitive levels ranging from instinctive responses to strategic planning. Our two-stage training approach includes Cognition-aware Supervised Fine-tuning (CoSFT) to instill stable level-specific patterns, and Cognition-aware Policy Optimization (CoPO) for step-level credit assignment via confidence-aware advantage reweighting. The key insight is that appropriate cognitive depth should maximize the confidence of the resulting action. Experiments on ALFWorld and ScienceWorld demonstrate that CogRouter achieves state-of-the-art performance with superior efficiency. With Qwen2.5-7B, it reaches an 82.3% success rate, outperforming GPT-4o (+40.3%), OpenAI-o3 (+18.3%), and GRPO (+14.0%), while using 62% fewer tokens.

Vision-Language Models (VLMs) are known to inherit and amplify societal biases from their web-scale training data with Indian being particularly misrepresented. Existing fairness-aware datasets have significantly improved demographic balance across global race and gender groups, yet they continue to treat Indian as a single monolithic category. The oversimplification ignores the vast intra-national diversity across 28 states and 8 Union Territories of India and leads to representational and geographical bias. To address the limitation, we present IndicFairFace, a novel and balanced face dataset comprising 14,400 images representing geographical diversity of India. Images were sourced ethically from Wikimedia Commons and open-license web repositories and uniformly balanced across states and gender. Using IndicFairFace, we quantify intra-national geographical bias in prominent CLIP-based VLMs and reduce it using post-hoc Iterative Nullspace Projection debiasing approach. We also show that the adopted debiasing approach does not adversely impact the existing embedding space as the average drop in retrieval accuracy on benchmark datasets is less than 1.5 percent. Our work establishes IndicFairFace as the first benchmark to study geographical bias in VLMs for the Indian context.

Cellular identity and function are linked to both their intrinsic genomic makeup and extrinsic spatial context within the tissue microenvironment. Spatial transcriptomics (ST) offers an unprecedented opportunity to study this, providing in situ gene expression profiles at single-cell resolution and illuminating the spatial and functional organization of cells within tissues. However, a significant hurdle remains: ST data is inherently noisy, large, and structurally complex. This complexity makes it intractable for existing computational methods to effectively capture the interplay between spatial interactions and intrinsic genomic relationships, thus limiting our ability to discern critical biological patterns. Here, we present CellScape, a deep learning framework designed to overcome these limitations for high-performance ST data analysis and pattern discovery. CellScape jointly models cellular interactions in tissue space and genomic relationships among cells, producing comprehensive representations that seamlessly integrate spatial signals with underlying gene regulatory mechanisms. This technique uncovers biologically informative patterns that improve spatial domain segmentation and supports comprehensive spatial cellular analyses across diverse transcriptomics datasets, offering an accurate and versatile framework for deep analysis and interpretation of ST data.w

We investigate additive skip fusion in U-Net architectures for image denoising and denoising-centric multi-task learning (MTL). By replacing concatenative skips with gated additive fusion, the proposed Additive U-Net (AddUNet) constrains shortcut capacity while preserving fixed feature dimensionality across depth. This structural regularization induces controlled encoder-decoder information flow and stabilizes joint optimization. Across single-task denoising and joint denoising-classification settings, AddUNet achieves competitive reconstruction performance with improved training stability. In MTL, learned skip weights exhibit systematic task-aware redistribution: shallow skips favor reconstruction, while deeper features support discrimination. Notably, reconstruction remains robust even under limited classification capacity, indicating implicit task decoupling through additive fusion. These findings show that simple constraints on skip connections act as an effective architectural regularizer for stable and scalable multi-task learning without increasing model complexity.

Diffusion models have emerged as the leading approach for text-to-image generation. However, their iterative sampling process, which gradually morphs random noise into coherent images, introduces significant latency that limits their applicability. While recent few-step diffusion models reduce the number of sampling steps to as few as one to four steps, they often compromise image quality and prompt alignment, especially in one-step generation. Additionally, these models require computationally expensive training procedures. To address these limitations, we propose ImageRAGTurbo, a novel approach to efficiently finetune few-step diffusion models via retrieval augmentation. Given a text prompt, we retrieve relevant text-image pairs from a database and use them to condition the generation process. We argue that such retrieved examples provide rich contextual information to the UNet denoiser that helps reduce the number of denoising steps without compromising image quality. Indeed, our initial investigations show that using the retrieved content to edit the denoiser's latent space ($\mathcal{H}$-space) without additional finetuning already improves prompt fidelity. To further improve the quality of the generated images, we augment the UNet denoiser with a trainable adapter in the $\mathcal{H}$-space, which efficiently blends the retrieved content with the target prompt using a cross-attention mechanism. Experimental results on fast text-to-image generation demonstrate that our approach produces high-fidelity images without compromising latency compared to existing methods.

Designing suitable rewards poses a significant challenge in reinforcement learning (RL), especially for embodied manipulation. Trajectory success rewards are suitable for human judges or model fitting, but the sparsity severely limits RL sample efficiency. While recent methods have effectively improved RL via dense rewards, they rely heavily on high-quality human-annotated data or abundant expert supervision. To tackle these issues, this paper proposes Dual-granularity contrastive reward via generated Episodic Guidance (DEG), a novel framework to seek sample-efficient dense rewards without requiring human annotations or extensive supervision. Leveraging the prior knowledge of large video generation models, DEG only needs a small number of expert videos for domain adaptation to generate dedicated task guidance for each RL episode. Then, the proposed dual-granularity reward that balances coarse-grained exploration and fine-grained matching, will guide the agent to efficiently approximate the generated guidance video sequentially in the contrastive self-supervised latent space, and finally complete the target task. Extensive experiments on 18 diverse tasks across both simulation and real-world settings show that DEG can not only serve as an efficient exploration stimulus to help the agent quickly discover sparse success rewards, but also guide effective RL and stable policy convergence independently.

Inventory control is a fundamental operations problem in which ordering decisions are traditionally guided by theoretically grounded operations research (OR) algorithms. However, such algorithms often rely on rigid modeling assumptions and can perform poorly when demand distributions shift or relevant contextual information is unavailable. Recent advances in large language models (LLMs) have generated interest in AI agents that can reason flexibly and incorporate rich contextual signals, but it remains unclear how best to incorporate LLM-based methods into traditional decision-making pipelines. We study how OR algorithms, LLMs, and humans can interact and complement each other in a multi-period inventory control setting. We construct InventoryBench, a benchmark of over 1,000 inventory instances spanning both synthetic and real-world demand data, designed to stress-test decision rules under demand shifts, seasonality, and uncertain lead times. Through this benchmark, we find that OR-augmented LLM methods outperform either method in isolation, suggesting that these methods are complementary rather than substitutes. We further investigate the role of humans through a controlled classroom experiment that embeds LLM recommendations into a human-in-the-loop decision pipeline. Contrary to prior findings that human-AI collaboration can degrade performance, we show that, on average, human-AI teams achieve higher profits than either humans or AI agents operating alone. Beyond this population-level finding, we formalize an individual-level complementarity effect and derive a distribution-free lower bound on the fraction of individuals who benefit from AI collaboration; empirically, we find this fraction to be substantial.

Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers, the holistic design of sampling, specifically solver selection and scheduling, remains dominated by static heuristics. In this work, we revisit this challenge through a geometric lens, proposing SDM, a principled framework that aligns the numerical solver with the intrinsic properties of the diffusion trajectory. By analyzing the ODE dynamics, we show that efficient low-order solvers suffice in early high-noise stages while higher-order solvers can be progressively deployed to handle the increasing non-linearity of later stages. Furthermore, we formalize the scheduling by introducing a Wasserstein-bounded optimization framework. This method systematically derives adaptive timesteps that explicitly bound the local discretization error, ensuring the sampling process remains faithful to the underlying continuous dynamics. Without requiring additional training or architectural modifications, SDM achieves state-of-the-art performance across standard benchmarks, including an FID of 1.93 on CIFAR-10, 2.41 on FFHQ, and 1.98 on AFHQv2, with a reduced number of function evaluations compared to existing samplers. Our code is available at https://github.com/aiimaginglab/sdm.

Internet of things (IoT) networks face increasing security threats due to their distributed nature and resource constraints. Although federated learning (FL) has gained prominence as a privacy-preserving framework for distributed IoT environments, current federated principal component analysis (PCA) methods lack the integration of personalization and robustness, which are critical for effective anomaly detection. To address these limitations, we propose an efficient personalized federated PCA (FedEP) method for anomaly detection in IoT networks. The proposed model achieves personalization through introducing local representations with the $\ell_1$-norm for element-wise sparsity, while maintaining robustness via enforcing local models with the $\ell_{2,1}$-norm for row-wise sparsity. To solve this non-convex problem, we develop a manifold optimization algorithm based on the alternating direction method of multipliers (ADMM) with rigorous theoretical convergence guarantees. Experimental results confirm that the proposed FedEP outperforms the state-of-the-art FedPG, achieving excellent F1-scores and accuracy in various IoT security scenarios. Our code will be available at \href{https://github.com/xianchaoxiu/FedEP}{https://github.com/xianchaoxiu/FedEP}.

Multimodal Large Language Models (MLLMs) incur significant computational cost from processing numerous vision tokens through all LLM layers. Prior pruning methods operate either before the LLM, limiting generality due to diverse encoder-projector designs or within the LLM using heuristics that are incompatible with FlashAttention. We take a different approach: rather than identifying unimportant tokens, we treat the LLM itself as the optimal guide for compression. Observing that deeper layers naturally transmit vision-to-text information, we introduce Attention-Driven Self-Compression (ADSC), a simple, broadly applicable method that progressively reduces vision tokens using only the LLM's attention mechanism. Our method applies uniform token downsampling at selected layers, forming bottlenecks that encourage the model to reorganize and compress information into the remaining tokens. It requires no score computation, auxiliary modules, or attention modification, and remains fully compatible with FlashAttention. Applied to LLaVA-1.5, ADSC reduces FLOPs by 53.7% and peak KV-cache memory by 56.7%, while preserving 98.2% of the original model performance. Across multiple benchmarks, it outperforms prior pruning approaches in both efficiency and accuracy. Crucially, under high compression ratios, our method remains robust while heuristic-based techniques degrade sharply.

This paper presents GeoAgent, a model capable of reasoning closely with humans and deriving fine-grained address conclusions. Previous RL-based methods have achieved breakthroughs in performance and interpretability but still remain concerns because of their reliance on AI-generated chain-of-thought (CoT) data and training strategies, which conflict with geographic characteristics. To address these issues, we first introduce GeoSeek, a new geolocation dataset comprising CoT data annotated by geographic experts and professional players. We further thoroughly explore the inherent characteristics of geographic tasks and propose a geo-similarity reward and a consistency reward assessed by a consistency agent to assist training. This encourages the model to converge towards correct answers from a geographic perspective while ensuring the integrity and consistency of its reasoning process. Experimental results show that GeoAgent outperforms existing methods and a series of general VLLMs across multiple grains, while generating reasoning that closely aligns with humans.

Temporal Graph Neural Networks (TGNNs) are pivotal in processing dynamic graphs. However, existing TGNNs primarily target one-time predictions for a given temporal span, whereas many practical applications require continuous predictions, that predictions are issued frequently over time. Directly adapting existing TGNNs to continuous-prediction scenarios introduces either significant computational overhead or prediction quality issues especially for large graphs. This paper revisits the challenge of { continuous predictions} in TGNNs, and introduces {\sc Coden}, a TGNN model designed for efficient and effective learning on dynamic graphs. {\sc Coden} innovatively overcomes the key complexity bottleneck in existing TGNNs while preserving comparable predictive accuracy. Moreover, we further provide theoretical analyses that substantiate the effectiveness and efficiency of {\sc Coden}, and clarify its duality relationship with both RNN-based and attention-based models. Our evaluations across five dynamic datasets show that {\sc Coden} surpasses existing performance benchmarks in both efficiency and effectiveness, establishing it as a superior solution for continuous prediction in evolving graph environments.