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1,235篇论文匹配“Kernel methods”
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Deep Learning · Attention Mechanisms

Xiaodong Ji, Hailin Zhang, Fangcheng Fu, Bin Cui

Many advanced Large Language Model (LLM) applications require long-context processing, but the self-attention module becomes a bottleneck during the prefilling stage of inference due to its quadratic time complexity with respect to sequence length. Existing sparse attention methods accelerate attention computation by skipping less significant regions of the attention map. However, these approaches typically perform coarse-grained inspection of the attention map, resulting in their suboptimal performance. In this paper, we propose SALE, a fine-grained sparse attention method that accelerates the long-context prefilling stage of LLM with negligible loss in model accuracy. SALE achieves fast and accurate fine-grained attention map estimation using low-bit quantized query-key products to approximate attention weights, followed by the application of a novel Relative Attention Score metric to assess the importance of query-key pairs. This design enables us to accurately identify important regions in the attention map, thereby constructing a highly sparse attention mask. We implement a custom CUDA kernel in SALE optimized for hardware efficiency, reducing overhead to approximately 11% of the full attention latency. Notably, SALE requires no parameter training and can be seamlessly integrated into existing systems with trivial code modifications. Experiments on long-context benchmarks demonstrate that our method outperforms existing approaches in accuracy-efficiency trade-offs, achieving at least 3.36× speedups on Llama-3.1-8B for sequences longer than 64K while maintaining model quality.

Reinforcement Learning · Everything Else

Danlong Yuan, Wei Wu, Huishuai Zhang, Zhengren Wang, Xueliang Zhao, Dongyan Zhao

Reinforcement learning (RL) has become a key paradigm for training software engineering (SWE) agents, yet its practical accessibility and scalability is often constrained by container-based execution frameworks used for environment isolation. As the number of task instances increases, pre-cached container images introduce substantial storage overhead, limiting large-scale training under limited cotainer resources, and excludes users without container management privileges. We introduce SWE-MiniSandbox, a lightweight, container-free method that enables scalable RL training of SWE agents without sacrificing isolation. Instead of relying on per-instance containers, SWE-MiniSandbox executes each task in an isolated workspace backed by kernel-level mechanisms, substantially reducing system overhead. It leverages lightweight environment pre-caching techniques to eliminate the need for bulky container images. As a result, our approach lowers disk usage to approximately 5\% of that required by container-based pipelines and reduces environment preparation time to about 25\% of the container baseline. Empirical results demonstrate that SWE-MiniSandbox achieves evaluation performance comparable to standard container-based pipelines. Consequently, by removing the dependency on heavy container infrastructure, SWE-MiniSandbox offers a practical and accessible foundation for scaling RL-based SWE agents, particularly in resource-constrained research environments.

Deep Learning · Graph Neural Networks

Fan Li, Xiaoyang Wang, Chen Chen, Wenjie Zhang

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, going beyond traditional graph condensation (GC) methods limited to modeling pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose \textbf{A}nchor-guided \textbf{H}yper\textbf{G}raph \textbf{C}ondensation with \textbf{D}ual-level \textbf{D}iscrimination (\textbf{AHGCDD}), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis scheme based on feature-level association for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Deep Learning · Generative Models and Autoencoders

Yuehao Wang, Peihao Wang, Hanwen Jiang, Ziyi Yang, Qixing Huang, Zhangyang “Atlas” Wang

Diffusion models have shown remarkable performance on diverse generation tasks. Recent work finds that imposing representation alignment on the hidden states of diffusion networks can both facilitate training convergence and enhance sampling quality, yet the mechanism driving this synergy remains insufficiently understood. In this paper, we investigate the connection between self-supervised spectral representation learning and diffusion generative models through a shared perspective on perturbation kernels. On the diffusion side, samples (e.g., images, videos) are produced by reversing a stochastic noise-injection process specified by Gaussian kernels; on the spectral representation side, spectral embeddings emerge from contrasting positive and negative relations induced by random perturbation kernels. Motivated by this, we propose a self-supervised spectral representation alignment method to facilitate diffusion model training. In addition, we clarify how joint spectral learning can benefit diffusion training from a geometric perspective. Furthermore, we find that the optimization of the spectral alignment objective is in an equivalent form of diffusion score distillation in the representation space. Building on these findings, we integrate a spectral regularizer into diffusion training objectives to improve the performance of diffusion models on multiple datasets. Experiments across images and 3D point clouds show consistent gains in generation quality.

General Machine Learning · Kernel methods

Hachem Kadri, Joachim Tomasi, Yuka Hashimoto, Sandrine Anthoine

Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and have emerged as a centerpiece of quantum machine learning. The initial enthusiasm for quantum kernel machines has been tempered by recent studies suggesting that quantum kernels could not offer significant computational or statistical advantages when learning from classical data. However, most of the research in this area has been devoted to scalar-valued kernels in standard classification or regression settings for which classical kernel methods are efficient and effective, leaving very little room for improvement with quantum kernels. In this position paper, we argue that progress in this field requires moving beyond scalar-valued kernels toward more expressive kernel frameworks. Scalar-valued kernels lack the degrees of freedom necessary to fully exploit intrinsically quantum resources such as entanglement and are not rich enough to deal with complex learning tasks where classical learning methods struggle. Building on recent advances in operator-valued kernel learning and C*-algebraic kernel representations, we propose a roadmap for designing quantum kernels capable of leveraging entanglement and non-commutative structures to tackle complex structured prediction problems. To support this viewpoint, we present an initial proof-of-concept illustrating how quantum entangled operator-valued kernel formulations can reveal structural dependencies that remain difficult to access for scalar-valued kernel methods. This shift in focus could open a pathway toward a new generation of quantum kernel machines and a more faithful exploration of their potential advantages.

Applications · Computer Vision

Yin Tang, Jiawei Ma, Jinrui Zhang, Alex Jinpeng Wang, Deyu Zhang

Continuous prediction in complex environments is critical for Unmanned Aerial Vehicle (UAV). However, the existing Vision-Language Navigation (VLN) models follows the dead-reckoning, which iteratively predicts the next waypoint and updates its position, thereby constructing the complete trajectory. Then, such stepwise manner will inevitably lead to accumulated errors of position over time, resulting in misalignment between internal belief and objective coordinates, which is known as ``state drift'' and ultimately compromises the subsequent trajectory prediction. Drawing inspiration from classical control theory, we propose to correct for errors by formulating the continuous prediction as a recursive Bayesian state estimation problem. In this paper, we design NeuroKalman, a novel framework that decouples navigation into two complementary processes: a Prior Prediction, based on motion dynamic,s and a Likelihood Correction, from historical observation. We first mathematically associate Kernel Density Estimation of the measurement likelihood with the attention-based retrieval mechanism, which then allows the system to rectify the latent representation using retrieved historical anchors without gradient updates. Comprehensive experiments on TravelUAV benchmark demonstrate that, with only 10\% of the full training data fine-tuning, our method clearly outperforms strong baselines and regulates drift accumulation.

General Machine Learning · Kernel methods

Suleman Baloch, Kishlay Jha, Alberto Segre, Philip Polgreen, Bijaya Adhikari

Traditional comorbidity scores (e.g., Charlson and Elixhauser) are widely used for risk adjustment and patient stratification, but they have two key limitations: they are largely mortality-centric and do not align well with other outcomes, and their linear, rule-based structure cannot capture nonlinear, outcome-specific risk relationships. We propose a Machine-Learned Comorbidity Index (MLCI) that maps diagnosis codes to a single scalar by maximizing the normalized Hilbert–Schmidt Independence Criterion (nHSIC) between the score and multiple clinical outcomes. MLCI captures nonlinear risk–outcome dependence and is supported by a novel theory that characterizes when a unified, informative patient ordering can be achieved across outcomes. Empirical results on multiple benchmark electronic health record (EHR) datasets show that MLCI outperforms strong single-index baselines across multiple evaluation metrics.

Vasily Ilin, Peter Sushko, Ranjay Krishna

Estimating probability density and its score from samples remains a core problem in generative modeling, Bayesian inference, and kinetic theory. Existing methods are bifurcated: classical kernel density estimators (KDE) generalize across distributions but suffer from the curse of dimensionality, while modern neural score models achieve high precision but require retraining for every target distribution. We introduce DiScoFormer (Density and Score Transformer), a ``train-once, infer-anywhere" equivariant Transformer that maps i.i.d. samples to both density values and score vectors, generalizing across distributions and sample sizes. Analytically, we prove that self-attention can recover normalized KDE, establishing it as a functional generalization of kernel methods; empirically, individual attention heads learn multi-scale, kernel-like behaviors. The model converges faster and achieves higher precision than KDE for density estimation, and provides a high-fidelity plug-in score oracle for score-debiased KDE, Fisher information computation, and Fokker-Planck-type PDEs.

General Machine Learning · Kernel methods

Vasily Ilin, Peter Sushko, Ranjay Krishna

Estimating probability density and its score from samples remains a core problem in generative modeling, Bayesian inference, and kinetic theory. Existing methods are bifurcated: classical kernel density estimators (KDE) generalize across distributions but suffer from the curse of dimensionality, while modern neural score models achieve high precision but require retraining for every target distribution. We introduce DiScoFormer (Density and Score Transformer), a ``train-once, infer-anywhere" equivariant Transformer that maps i.i.d. samples to both density values and score vectors, generalizing across distributions and sample sizes. Analytically, we prove that self-attention can recover normalized KDE, establishing it as a functional generalization of kernel methods; empirically, individual attention heads learn multi-scale, kernel-like behaviors. The model converges faster and achieves higher precision than KDE for density estimation, and provides a high-fidelity plug-in score oracle for score-debiased KDE, Fisher information computation, and Fokker-Planck-type PDEs.

Social Aspects · Robustness

Amir Mehrpanah, Matteo Gamba, Hossein Azizpour

The adversarial robustness of attributions is a fundamental requirement for reliable explainability in deep learning, yet existing approaches typically rely on computationally expensive explicit regularization. In this work, we show that attribution robustness can arise implicitly from the learning dynamics of standard stochastic gradient descent. We theoretically motivate this effect through connections between parameter-space and input-space curvature, and validate it across architectures, datasets, and attribution methods, with negligible computational overhead. In contrast, we prove that such robustness gains often does not transfer to attention-based attribution under softmax normalization, due to inherent entropy constraints, and we validate this limitation experimentally. Finally, we show that replacing softmax attention with kernel-based attention restores the robustness gains in transformer models. Our results highlight learning dynamics as a principled and practical mechanism for robust explainability, and reveal fundamental limitations of attention-based attribution under normalization.

General Machine Learning · Scalable Algorithms

Nasib Ullah, Jinbin Zhang, Jean Lucien Randrianantenaina, Erik Schultheis, Rohit Babbar

Extreme multi-label classification (XMC) involves learning deep learning models over large output spaces with millions of labels, making the output layer of the network a major bottleneck in memory and compute. While sparsity-based methods reduce arithmetic complexity, they often fail to yield proportional wall-clock gains due to irregular memory access, poor hardware utilization, or reliance on auxiliary architectural components in extreme long-tailed regimes. We introduce group-shared fixed fan-in sparsity, a semi-structured output-layer design in which groups of semantically related labels share a common sparse input pattern while retaining independent weights. This grouping introduces a task-aligned inductive bias---encouraging related labels to attend to similar feature subsets---while simultaneously reducing index memory overhead, increasing feature reuse across labels, and enabling efficient GPU execution via custom CUDA kernels that leverage modern accelerator primitives. As an alternative to auxiliary objectives, we exploit the long-tailed structure of XMC datasets by decomposing the output layer into a small dense head over frequent labels and a group-shared sparse tail over the remainder, providing an informative gradient pathway while preserving the memory benefits of sparsity. Through kernel-level microbenchmarking, we show that group-shared fixed fan-in converts reductions in arithmetic complexity into proportional wall-clock gains, achieving up to $4.4\times$ speedup in the forward pass and up to $25\times$ speedup in backward passes compared to standard fixed fan-in sparsity, while operating within a few percent of a FLOPs-matched dense bottleneck. Across large-scale XMC benchmarks, our approach matches or improves precision@k compared to prior sparse baselines, while substantially narrowing the performance gap to dense.

General Machine Learning · Kernel methods

Louis Allain, Sébastien Da Veiga, Brian Staber

Conformal prediction (CP) is a distribution-free method to construct reliable prediction intervals that has gained significant attention in recent years. Despite its success and various proposed extensions, a significant practical feature which has been overlooked in previous research is the potential skewed nature of the noise, or of the residuals when the predictive model exhibits bias. In this work, we leverage recent developments in CP to propose a new asymmetric procedure that bridges the gap between skewed and non-skewed noise distributions, while still maintaining adaptivity of the prediction intervals. We introduce a new statistical learning problem to construct adaptive and asymmetric prediction bands, with a unique feature based on a penalty which promotes symmetry: when the penalty intensity varies, the intervals smoothly change from symmetric to asymmetric ones. This statistical learning problem is based on reproducing kernel Hilbert spaces and the recently introduced kernel sum-of-squares framework. First, we establish representer theorems to make our problem tractable in practice, and derive dual formulations which are essential for scalability to larger datasets. Second, the intensity of the penalty is chosen using a novel data-driven method which automatically identifies the symmetric nature of the noise. We show that consenting to some asymmetry can let the learned prediction bands better adapt to small sample regimes, outliers or biased predictive models. Finally, our experiments illustrate the efficiency of such penalized kernel sum-of-squares to construct adaptive prediction bands.

Social Aspects · Accountability, Transparency, and Interpretability

Florian Eichin, Yupei Du, Philipp Mondorf, Maria Matveev, Barbara Plank, Michael Hedderich

Post-hoc interpretability methods typically attribute a model’s behavior to its components, data, or training trajectory in isolation. This leads to explanations that lack a unified view and may miss key interactions. While combining existing methods or applying them at different training stages offers broader insights, such approaches usually lack theoretical support. In this work, we present ExPLAIND, a unified framework that integrates all these perspectives. First, we generalize recent work on gradient path kernels, which reformulate models trained by gradient descent as a kernel machine, to realistic settings like AdamW. We empirically validate that a CNN and a Transformer are accurately replicated by this reformulation. Second, we derive novel parameter- and step-wise influence scores from the kernel feature maps. Their effectiveness for parameter pruning is comparable to existing methods, demonstrating their value for model component attribution. Finally, jointly interpreting model components and data over the training process, we use ExPLAIND to analyze a Transformer that exhibits Grokking. Our findings support previously proposed stages of Grokking, while refining the final phase as one of alignment of the outer layers around a representation pipeline learned after the memorization phase. Overall, ExPLAIND provides a theoretically grounded, unified framework to interpret model behavior and training dynamics.

Applications · Everything Else

Huilai Chen, Yuanbo Wen, Liangfeng Li, Shaohui Peng, Jingzhe Zhu, Xuzhi Zhang, Jun Bi, Qi Guo, Ling Li, Yunji Chen

Optimizing OS kernels for specific applications is vital for peak performance, yet existing LLM-based methods struggle with a semantic mismatch between generalized reasoning and low-level system behaviors. As a result, these static, open-loop approaches suffer from runtime blindness, configuration fragmentation, and search drift, ultimately failing to unlock the system’s performance potential. To address this, we propose PerceptOS, an autonomous framework that shifts the paradigm to perception-driven tuning. PerceptOS integrates: (1) a Perception Module that aligns raw telemetry into high-fidelity semantic fingerprints; (2) a Global Search Module utilizing a Bi-level Hierarchical Induction Tree (BHIT) for global navigation and efficient pruning; and (3) a Posterior Enhancement Module to suppress hallucinations via trajectory synthesis. Experiments across Redis, Apache, PostgreSQL, and RAG show that PerceptOS achieves significant performance breakthroughs by optimizing kernel configurations, reaching 296.6% of default Redis throughput and surpassing SOTA baselines by 32.6% within only 15 iterations. By establishing a perception-driven closed-loop, PerceptOS provides new insights for fully automated, large-scale system optimization.

Lingyuan Meng, KE LIANG, Hao Li, Meng Liu, Weijia Shi, Miaomiao Li, Yang Gao, Xinwang Liu

Multi-modal brain network analysis aims to predict neuropsychiatric status from functional connectomes with heterogeneous phenotypes. However, most existing methods treat phenotypes as auxiliary features and perform late fusion, implicitly assuming that the connectome representation should be learned in the same way regardless of phenotype. However, in clinical neuroscience the same functional connectivity pattern may support different conclusions under different phenotype contexts. To bridge this gap, we propose PhenoBrain, a novel framework for multi-modal brain network analysis that injects phenotype information at the mechanism level rather than only at the classifier level. Specifically, we propose a phenotype-conditioned long-range routing mechanism, which learns a subject-specific multi-hop communication kernel to model long-range connectome interactions. Furthermore, we propose a phenotypic-guided attention mechanism regulation method, which uses phenotypic information as a conditional prior to regulate the learning process of attention in brain networks. To verify the effectiveness of our method, we constructed two multi-modal brain network analysis datasets based on open-source image data. Extensive experiments demonstrate that PhenoBrain achieves state-of-the-art performance.

Deep Learning · Large Language Models

Yash Akhauri, Xingyou Song, Arissa Wongpanich, Bryan Lewandowski, Mohamed Abdelfattah

We study \textbf{code-to-metric regression}: predicting numeric outcomes of code executions, a challenging task due to the open-ended nature of programming languages. While prior methods have resorted to heavy and domain-specific feature engineering, we show that a single unified Regression Language Model (RLM) can simultaneously predict directly from text, (i) the memory footprint of code across multiple high-level languages such as Python and C++, (ii) the latency of Triton GPU kernels, and (iii) the accuracy and speed of trained neural networks represented in ONNX. In particular, a relatively small 300M parameter RLM initialized from T5Gemma, obtains $>$0.9 Spearman-rank on competitive programming submissions from APPS, and a single unified model achieves $>$0.5 average Spearman-rank across 17 separate languages from CodeNet. Furthermore, the RLM can obtain the highest average Kendall-Tau of 0.46 on five classic NAS design spaces previously dominated by graph neural networks, and simultaneously predict architecture latencies on numerous hardware platforms.

Social Aspects · Fairness

Felix Störck, Fabian Hinder, CITEC Barbara Hammer

With the on-going integration of machine learning systems into the everyday social life of millions the notion of fairness becomes an ever increasing priority in their development. Fairness notions commonly rely on protected attributes to assess potential biases. Here, the majority of literature focuses on discrete setups regarding both target and protected attributes. The literature on continuous attributes especially in conjunction with regression - we refer to this as *continuous fairness* - is scarce. A common strategy is iterative null-space projection which as of now has only been explored for linear models or embeddings such as obtained by a non-linear encoder. We improve on this by extending this to kernel induced feature spaces by means of the ``empirical feature space''. We theoretically derive this as a direct transformation of the kernel matrix yielding a model and fairness-score agnostic method applicable to continuous protected attributes. We demonstrate that our novel approach in conjunction with Support Vector Regression (SVR) provides competitive or improved performance across multiple datasets in comparisons to other contemporary methods.

Deep Learning · Generative Models and Autoencoders

Gyeonghoon Ko, Juho Lee

Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a physics-informed neural network (PINN). Given an explicit manifold specification, we choose a coordinate system, derive the corresponding heat (Fokker--Planck) equation and a short-time asymptotic approximation, and then train a PINN to learn the log heat kernel. The resulting surrogate enables both forward noising (heat-kernel sampling) and conditional-score evaluation for denoising score matching. We demonstrate the method on diverse manifolds including $S^2$, $SO(3)$, $\mathrm{SPD}(n)$, and permutation-quotiented point clouds.

General Machine Learning · Scalable Algorithms

Alessandro Manenti, Kumar Avinava Dubey, Arijit Sehanobish, Cesare Alippi, Krzysztof Choromanski

We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate functions of feature vectors in the corresponding nodes. Those classes of graphs include several prominent examples, such as: *$\epsilon$-neighborhood* graphs, used on regular basis in machine learning. Rather than conducting walks on graphs' nodes, those methods rely on walks in continuous spaces, in which those graphs are embedded. To accurately and efficiently approximate original combinatorial calculations, SWING applies customized Gumbel-softmax sampling mechanism with linearized kernels, obtained via random features coupled with importance sampling techniques. This mechanism is of its own interest. SWING relies on the deep connection between implicitly defined graphs and Fourier analysis, presented in this paper. SWING is accelerator-friendly and does not require input graph materialization. We provide detailed analysis of SWING and complement it with thorough experiments on different classes of i-graphs.

Probabilistic Methods · Monte Carlo and Sampling Methods

Zonghao Chen, Toni Karvonen, Heishiro Kanagawa, Francois-Xavier Briol, Chris J Oates

Approximation of a target probability distribution using a finite set of points is a problem of fundamental importance in numerical integration. Several authors have proposed to select points by minimising a maximum mean discrepancy (MMD), but the non-convexity of this objective typically precludes global minimisation. Instead, we consider the concept of \emph{stationary points of the MMD} which, in contrast to points globally minimising the MMD, can be accurately computed. Our main contributions are two-fold and theoretical in nature. We first prove the (perhaps surprising) result that, for integrands in the associated reproducing kernel Hilbert space, the numerical integration error of stationary MMD points vanishes \emph{faster} than the MMD. Motivated by this \emph{super-convergence} property, we consider MMD gradient flows as a practical strategy for computing stationary points of the MMD. We then prove that MMD gradient flow can indeed compute stationary MMD points, based on a refined convergence analysis that establishes a novel non-asymptotic finite-particle error bound.