Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fréchet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256 × 256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.
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We study non-linear bandit optimization where the learner maximizes a black-box function with zeroth order function oracle, which has been successfully applied in many critical applications such as drug discovery and materials design. Existing works have showed that with the aid of quantum computing, it is possible to break the classical Ω(√T) regret lower bound and achieve the new O(poly log T) upper bound. However, they usually assume that the objective function sits within the reproducing kernel Hilbert space and their algorithms suffer from the curse of dimensionality. In this paper, we propose the new Q-NLB-UCB algorithm which enjoys an input dimension-free O(poly log T) upper bound, making it applicable for high-dimensional tasks. At the heart of our algorithm design are quantum Monte Carlo mean estimator, parametric function approximation technique, and a new quantum non-linear regression oracle, which can be of independent interests in more quantum machine learning problems. Our algorithm is also validated for its efficiency compared with other quantum algorithms on both high-dimensional synthetic and real-world tasks.
While large language models (LLMs) have recently made tremendous progress towards solving challenging AI problems, they have done so at increasingly steep computational and API costs. We propose a novel strategy where we combine multiple LLM models with varying cost/accuracy tradeoffs in an agentic manner, where models and tools are run in sequence as determined by an orchestration model to minimize cost subject to a user-specified level of reliability; this constraint is formalized using conformal prediction to provide guarantees. To solve this problem, we propose Conformal Constrained Policy Optimization (CCPO), a training paradigm that integrates constrained policy optimization with off-policy reinforcement learning and recent advances in online conformal prediction. CCPO jointly optimizes a cost-aware policy (score function) and an adaptive threshold. Across two multi-hop question answering benchmarks, CCPO achieves up to a 30% cost reduction compared to other cost-aware baselines and LLM-guided methods without compromising reliability. Our approach provides a principled and practical framework for deploying LLM agents that are significantly more cost-effective while maintaining reliability.
Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong potential in such tasks due to its capacity to embed hierarchical structures with minimal distortion. Previous evidence indicates that the hyperbolic representation capacity can be further enhanced through kernel methods. However, existing hyperbolic kernels still suffer from mild geometric distortion or lack adaptability. This paper addresses these issues by introducing a curvature-aware de Branges–Rovnyak space, a reproducing kernel Hilbert space (RKHS) that is isometric to a Poincaré ball. We design an adjustable multiplier to select the appropriate RKHS corresponding to the hyperbolic space with any curvature adaptively. Building on this foundation, we further construct a family of adaptive hyperbolic kernels, including the novel adaptive hyperbolic radial kernel, whose learnable parameters modulate hyperbolic features in a task-aware manner. Extensive experiments on visual and language benchmarks demonstrate that our proposed kernels outperform existing hyperbolic kernels in modeling hierarchical dependencies.
Vision modeling has advanced rapidly with Transformers, whose attention mechanisms capture visual dependencies but lack a principled account of how semantic information propagates spatially. We revisit this problem from a wave-based perspective: feature maps are treated as spatial signals whose evolution over an internal propagation time (aligned with network depth) is governed by an underdamped wave equation. In this formulation, spatial frequency—from low-frequency global layout to high-frequency edges and textures—is modeled explicitly, and its interaction with propagation time is controlled rather than implicitly fixed. We derive a closed-form, frequency–time decoupled solution and implement it as the Wave Propagation Operator (WPO), a lightweight module that models global interactions in O(NlogN) time—far lower than attention. Building on WPO, we propose a family of WaveFormer models as drop-in replacements for standard ViTs and CNNs, achieving competitive accuracy across image classification, object detection, and semantic segmentation, while delivering up to 1.6× higher throughput and 30% fewer FLOPs than attention-based alternatives. Furthermore, our results demonstrate that wave propagation introduces a complementary modeling bias to heat-based methods, effectively capturing both global coherence and high-frequency details essential for rich visual semantics.
Multivariable time series forecasting methods can integrate information from exogenous variables, leading to significant prediction accuracy gains. The transformer architecture has been widely applied in various time series forecasting models due to its ability to capture long-range sequential dependencies. However, a naïve application of transformers often struggles to effectively model complex relationships among variables over time. To mitigate against this, we propose a novel architecture, termed Spectral Operator Neural Network (Sonnet). Sonnet applies learnable wavelet transformations to the input and incorporates spectral analysis using the Koopman operator. Its predictive skill relies on the Multivariable Coherence Attention (MVCA), an operation that leverages spectral coherence to model variable dependencies. Our empirical analysis shows that Sonnet yields the best performance on 34 out of 47 forecasting tasks with an average mean absolute error (MAE) reduction of 2.2% against the most competitive baseline. We further show that MVCA can remedy the deficiencies of naïve attention in various deep learning models, reducing MAE by 10.7% on average in the most challenging forecasting tasks.
Adaptive LiDAR Scanning: Harnessing Temporal Cues for Efficient 3D Object Detection via Multi-Modal Fusion
PDF ↗Multi-sensor fusion using LiDAR and RGB cameras significantly enhances 3D object detection task. However, conventional LiDAR sensors perform dense, stateless scans, ignoring the strong temporal continuity in real-world scenes. This leads to substantial sensing redundancy and excessive power consumption, limiting their practicality on resource-constrained platforms. To address this inefficiency, we propose a predictive, history-aware adaptive scanning framework that anticipates informative regions of interest (ROI) based on past observations. Our approach introduces a lightweight predictor network that distills historical spatial and temporal contexts into refined query embeddings. These embeddings guide a differentiable mask generator network, which leverages Gumbel-Softmax sampling to produce binary masks identifying critical ROIs for the upcoming frame. Our method significantly reduces unnecessary data acquisition by concentrating dense LiDAR scanning only within these ROIs and sparsely sampling elsewhere. Experiments on nuScenes and Lyft benchmarks demonstrate that our adaptive scanning strategy reduces LiDAR energy consumption by over 65% while maintaining competitive or even superior 3D object detection performance compared to traditional LiDAR-camera fusion methods with dense LiDAR scanning.
Graph neural networks (GNNs) have shown promise on combinatorial problems such as Max-Clique, yet it remains unclear what algorithmic principles they actually learn. This paper introduces a concept-driven framework for evaluating and interpreting GNNs on such tasks. We begin with a principled benchmark based on synthetic graphs with known difficulty levels—easy, medium, and hard—derived from theoretical thresholds for planted cliques. Using this setup, we show that GNNs reliably learn a simple yet powerful concept: degree-based ranking. This insight motivates a new decoder, Least-Probable Removal (LPR), which significantly outperforms the common top-k strategy, especially on harder and real-world instances. Our analysis pipeline connects latent representations to classical heuristics, improving both interpretability and performance. Finally, we demonstrate cross-domain generalization to sparse PCA, showing that the same GNN architecture and decoding strategy succeed in recovering sparse principal components, revealing a shared underlying principle across domains.
Message passing is the core operation in graph neural networks, where each node updates its embeddings by aggregating information from its neighbors. However, in deep architectures, this process often leads to diminished expressiveness. A popular solution is the use of residual connections, where the input from the current (or initial) layer is added to the aggregated neighbor information to preserve embeddings across layers. Following a recent line of research, we investigate an adaptive residual scheme in which different nodes have varying residual strengths. We prove that this approach prevents oversmoothing; particularly, we show that the Dirichlet energy of the embeddings remains bounded away from zero. This is the first theoretical guarantee not only for the adaptive setting, but also for static residual connections (where residual strengths are shared across nodes) with activation functions. Furthermore, based on an extensive set of experiments, this adaptive approach is shown to outperform the standard and state-of-the-art message passing mechanisms, especially on heterophilic graphs. To improve the time complexity of our approach, we introduce a variant in which residual strengths are not learned but instead set heuristically, a choice that performs as well as the learnable version.
Text-Attributed Graphs (TAGs) are graphs where both nodes and edges are associated with text attributes. To leverage their semantic richness, recent efforts have integrated large language models (LLMs) with graph neural networks, leading to the development of GraphLLMs. However, many real-world datasets remain inaccessible, and processing text-attributed graphs while ensuring privacy and efficiency remains a challenge. To address this, we place TAGs within a federated environment, referred to as TAG-FGL. Despite its potential, TAG-FGL remains largely underexplored in the face of adversarial threats. In this work, we introduce GTAE, a novel attack framework that cascades influence-guided topological perturbations and embedding-level text refinements to generate transferable, modality-agnostic adversarial inputs. To defend against these threats, we propose STRUM, a defense strategy that combines local adversarial training with robustness-aware aggregation, enhancing resilience at both the node and system levels. Extensive experiments on five real-world datasets with diverse model backbones demonstrate that GTAE significantly degrades model performance, while STRUM consistently improves robustness.
Modern deep learning techniques focus on extracting intricate information from data to achieve accurate predictions. However, the training datasets may be crowdsourced and include sensitive information, such as personal contact details, financial data, and medical records. As a result, there is a growing emphasis on developing privacy-preserving training algorithms for neural networks that maintain good performance while preserving privacy. In this paper, we investigate the generalization and privacy performances of the differentially private gradient descent (DP-GD) algorithm, which is a private variant of the gradient descent (GD) by incorporating additional noise into the gradients during each iteration. Moreover, we identify a concrete learning task where DP-GD can achieve superior generalization performance compared to GD in training two-layer Huberized ReLU convolutional neural networks (CNNs). Specifically, we demonstrate that, under mild conditions, a small signal-to-noise ratio can result in GD producing training models with poor test accuracy, whereas DP-GD can yield training models with good test accuracy and privacy guarantees if the signal-to-noise ratio is not too small. This indicates that DP-GD has the potential to enhance model performance while ensuring privacy protection in certain learning tasks. Numerical simulations are further conducted to support our theoretical results.
The success of large-scale pre-training paradigm, exemplified by Large Language Models (LLMs), has inspired the development of Time Series Foundation Models (TSFMs). However, their application to financial candlestick (K-line) data remains limited, often underperforming non-pre-trained architectures. Moreover, existing TSFMs often overlook crucial downstream tasks such as volatility prediction and synthetic data generation. To address these limitations, we propose Kronos, a unified, scalable pre-training framework tailored to financial K-line modeling. Kronos introduces a specialized tokenizer that discretizes continuous market information into token sequences, preserving both price dynamics and trade activity patterns. We pre-train Kronos using an autoregressive objective on a massive, multi-market corpus of over 12 billion K-line records from 45 global exchanges, enabling it to learn nuanced temporal and cross-asset representations. Kronos excels in a zero-shot setting across a diverse set of financial tasks. On benchmark datasets, Kronos boosts price series forecasting RankIC by 93% over the leading TSFM and 87% over the best non-pre-trained baseline. It also achieves a 9% lower MAE in volatility forecasting and a 22% improvement in generative fidelity for synthetic K-line sequences. These results establish Kronos as a robust, versatile foundation model for end-to-end financial time series analysis.
URaG: Unified Retrieval and Generation in Multimodal LLMs for Efficient Long Document Understanding
PDF ↗Recent multimodal large language models (MLLMs) still struggle with long document understanding due to two fundamental challenges: information interference from abundant irrelevant content, and the quadratic computational cost of Transformer-based architectures. Existing approaches primarily fall into two categories: token compression, which sacrifices fine-grained details; and introducing external retrievers, which increase system complexity and prevent end-to-end optimization. To address these issues, we conduct an in-depth analysis and observe that MLLMs exhibit a human-like coarse-to-fine reasoning pattern: early Transformer layers attend broadly across the document, while deeper layers focus on relevant evidence pages. Motivated by this insight, we posit that the inherent evidence localization capabilities of MLLMs can be explicitly leveraged to perform retrieval during the reasoning process, facilitating efficient long document understanding. To this end, we propose URaG, a simple-yet-effective framework that Unifies Retrieval and Generation within a single MLLM. URaG introduces a lightweight cross-modal retrieval module that converts the early Transformer layers into an efficient evidence selector, identifying and preserving the most relevant pages while discarding irrelevant content. This design enables the deeper layers to concentrate computational resources on pertinent information, improving both accuracy and efficiency. Extensive experiments demonstrate that URaG achieves state-of-the-art performance while reducing computational overhead by 44-56%.
Single-channel audio separation aims to separate individual sources from a single-channel mixture. Most existing methods rely on supervised learning with synthetically generated paired data. However, obtaining high-quality paired data in real-world scenarios is often difficult. This data scarcity can degrade model performance under unseen conditions and limit generalization ability. To this end, in this work, we approach this problem from an unsupervised perspective, framing it as a probabilistic inverse problem. Our method requires only diffusion priors trained on individual sources. Separation is then achieved by iteratively guiding an initial state toward the solution through reconstruction guidance. Importantly, we introduce an advanced inverse problem solver specifically designed for separation, which mitigates gradient conflicts caused by interference between the diffusion prior and reconstruction guidance during inverse denoising. This design ensures high-quality and balanced separation performance across individual sources. Additionally, we find that initializing the denoising process with an augmented mixture instead of pure Gaussian noise provides an informative starting point that significantly improves the final performance. To further enhance audio prior modeling, we design a novel time–frequency attention-based network architecture that demonstrates strong audio modeling capability. Collectively, these improvements lead to significant performance gains, as validated across speech–sound event, sound event, and speech separation tasks.
Not All Inconsistency Is Equal: Decomposing LVLM Uncertainty into Belief Divergence and Belief Conflict
PDF ↗Uncertainty Quantification (UQ) is critical for detecting hallucinations in black-box Large Vision-Language Models (LVLMs). However, prevailing methods like Discrete Semantic Entropy (DSE) are unreliable, as their scores are primarily dominated by the number of semantic clusters. This renders them incapable of distinguishing between benign semantic ambiguity (varied but coherent responses) and severe belief conflict (contradictory responses). We address this limitation by proposing a novel framework rooted in Dempster-Shafer theory of evidence, built on the premise that not all inconsistency is equal. Our method decomposes uncertainty into two complementary metrics: Belief Divergence, which quantifies ambiguity by measuring the separation between viewpoints, and Belief Conflict, which captures direct logical contradictions. Extensive experiments demonstrate that our framework provides a more reliable measure of uncertainty.
Momentum SGD (MSGD) serves as a foundational optimizer in training deep models due to momentum's key role in accelerating convergence and enhancing generalization. Meanwhile, asynchronous distributed learning is crucial for training large-scale deep models, especially when the computing capabilities of the workers in the cluster are heterogeneous. To reduce communication frequency, local updates are widely adopted in distributed learning. However, how to implement asynchronous distributed MSGD with local updates remains unexplored. To solve this problem, we propose a novel method, called ordered local momentum (OrLoMo), for asynchronous distributed learning. In OrLoMo, each worker runs MSGD locally. Then the local momentum from each worker will be aggregated by the server in order based on its global iteration index. To the best of our knowledge, OrLoMo is the first method to implement asynchronous distributed MSGD with local updates. We prove the convergence of OrLoMo for non-convex problems under arbitrary delays. Experiments validate that OrLoMo can outperform its synchronous counterpart and other asynchronous methods.
Federated unlearning (FU) allows a participating client in a federated learning (FL) system to remove its contribution from the trained global model, thereby enforcing the client’s ``right to be forgotten'' (RTBF). However, from the perspective of a client that does not request unlearning, the activation of the FU process may disrupt ongoing FL training and introduce additional computational and time overhead. In such cases, a client opposed to unlearning may be incentivized to retaliate against the unlearning client(s). In this work, we take the first step toward demonstrating the feasibility of such retaliatory behavior by exploiting the information leakage introduced during the FU process. Specifically, we propose a novel unlearning-induced membership inference attack (MIA) model, followed by a coarse-to-fine data generation method that enables an adversarial client to locally reconstruct the unlearned data. Building on this reconstruction, we introduce two targeted retaliatory attacks: (1) Anti-Unlearning Attack (AUA), which hinders the global model from successfully forgetting the data intended for removal, and (2) Discrimination-Unlearning Attack (DUA), which specifically degrades the global model’s performance on the unlearned data. Extensive experiments across a variety of FU methods and settings validate the effectiveness of the proposed retaliatory attack framework.
Understanding the generalization behavior of in-context learning (ICL) in Transformers remains a fundamental challenge, as most existing theoretical analyses are based on the assumption that data are independently and identically distributed (i.i.d.), an assumption that often does not hold in practice. Motivated by the theoretical insight that ICL operates similarly to gradient-based optimization, we leverage the concept of gradient stability to establish generalization error bounds for ICL under a general non-i.i.d. setting. Our analysis shows that two factors play a central role in ICL generalization: the number of demonstrations in the prompt and their distributional alignment with the query. In particular, increasing the number of demonstrations and improving their alignment with the query distribution lead to better generalization, even without any parameter tuning. Under mild conditions, we further prove that the generalization error can achieve the optimal convergence rate of O(N^(-1/2)), where N is the number of demonstrations. Our empirical evaluations validate the effectiveness of our theoretical findings.
Diffusion models have shown great promise in data generation, yet generating time series data remains challenging due to the need to capture complex temporal dependencies and structural patterns. In this paper, we present TSGDiff, a novel framework that rethinks time series generation from a graph-based perspective. Specifically, we represent time series as dynamic graphs, where edges are constructed based on Fourier spectrum characteristics and temporal dependencies. A graph neural network-based encoder-decoder architecture is employed to construct a latent space, enabling the diffusion process to model the structural representation distribution of time series effectively. Furthermore, we propose the Topological Structure Fidelity (Topo-FID) score, a graph-aware metric for assessing the structural similarity of time series graph representations. Topo-FID integrates two sub-metrics: Graph Edit Similarity, which quantifies differences in adjacency matrices, and Structural Entropy Similarity, which evaluates the entropy of node degree distributions. This comprehensive metric provides a more accurate assessment of structural fidelity in generated time series. Experiments on real-world datasets demonstrate that TSGDiff generates high-quality synthetic time series data generation, faithfully preserving temporal dependencies and structural integrity, thereby advancing the field of synthetic time series generation.
Modeling normal behavior in dynamic, nonlinear time series data is challenging for effective anomaly detection. Traditional methods, such as nearest neighbor and clustering approaches, often depend on rigid assumptions, such as a predefined number of reliable neighbors or clusters, which frequently break down in complex temporal scenarios. To address these limitations, we introduce the Granular-ball One-Class Network (GBOC), a novel approach based on a data-adaptive representation called Granular-ball Vector Data Description (GVDD). GVDD partitions the latent space into compact, high-density regions represented by granular-balls, which are generated through a density-guided hierarchical splitting process and refined by removing noisy structures. Each granular-ball serves as a prototype for local normal behavior, naturally positioning itself between individual instances and clusters while preserving the local topological structure of the sample set. During training, GBOC improves the compactness of representations by aligning samples with their nearest granular-ball centers. During inference, anomaly scores are computed based on the distance to the nearest granular-ball. By focusing on dense, high-quality regions and significantly reducing the number of prototypes, GBOC delivers both robustness and efficiency in anomaly detection. Extensive experiments validate the effectiveness and superiority of the proposed method, highlighting its ability to handle the challenges of time series anomaly detection.