Dataset distillation methods learn a representative summary of the full dataset such that training on the distilled data is more efficient in terms of time and space. The current state-of-the-art methods exploit the correspondence between infinitely wide neural networks (NNs) and kernel ridge regression to design distillation methods that result in high-quality summaries of the data. In this work, we leverage the correspondence between infinitely wide networks and Gaussian Processes(GPs) for learning a distilled dataset. We investigate the feasibility of using the inducing points method for Gaussian Processes, as a data distillation method. While most of the existing dataset distillation methods are based on loss or gradient matching, our method looks at the function space approximation, facilitated by the NN-GP correspondence. Additionally, using recent theoretical results on GP regression and neural tangent kernels(NTKs), we also provide an upper bound on the size of the distilled data. We demonstrate the utility of inducing points as distilled data on a set of datasets empirically.
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Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent (Abstract Reprint)
PDF ↗This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For classification problems, this approach allows us to learn bounded geometric structures around given data points and hence solve the global model learning problem in an efficient way by exploiting convexity properties of the related optimisation problem in a Reproducing Kernel Hilbert Space (RKHS). In this way, we can reduce classification problems to determining the closest bounded geometric structure from a given data point. Further advantages that come with our solution is that our approach does not require clients to perform multiple epochs of local optimisation using stochastic gradient descent, nor require rounds of communication between client/server for optimising the global model. We highlight that numerous experiments have shown that the proposed method is a competitive alternative to the state-of-the-art.
Improving Day-Ahead Grid Carbon Intensity Forecasting by Joint Modeling of Local-Temporal and Cross-Variable Dependencies Across Different Frequencies
PDF ↗Accurate forecasting of the grid carbon intensity factor (CIF) is critical for enabling demand-side management and reducing emissions in modern electricity systems. Leveraging multiple interrelated time series, CIF prediction is typically formulated as a multivariate time series forecasting problem. Despite advances in deep learning-based methods, it remains challenging to capture the fine-grained local-temporal dependencies, dynamic higher-order cross-variable dependencies, and complex multi-frequency patterns for CIF forecasting. To address these issues, we propose a novel model that integrates two parallel modules: 1) one enhances the extraction of local-temporal dependencies under multi-frequency by applying multiple wavelet-based convolutional kernels to overlapping patches of varying lengths; 2) the other captures dynamic cross-variable dependencies under multi-frequency to model how inter-variable relationships evolve across the time-frequency domain. Evaluations on four representative electricity markets from Australia, featuring varying levels of renewable penetration, demonstrate that the proposed method outperforms the state-of-the-art models. An ablation study further validates the complementary benefits of the two proposed modules. Designed with built-in interpretability, the proposed model also enables better understanding of its predictive behavior, as shown in a case study where it adaptively shifts attention to relevant variables and time intervals during a disruptive event.
Zero-shot stance detection (ZSSD) seeks to determine the stance of text toward previously unseen targets, a task critical for analyzing dynamic and polarized online discourse with limited labeled data. While large language models (LLMs) offer zero-shot capabilities, prompting-based approaches often fall short in handling complex reasoning and lack robust generalization to novel targets. Meanwhile, LLM-enhanced methods still require substantial labeled data and struggle to move beyond instance-level patterns, limiting their interpretability and adaptability. Inspired by cognitive science, we propose the Cognitive Inductive Reasoning Framework (CIRF), a schema-driven method that bridges linguistic inputs and abstract reasoning via automatic induction and application of cognitive reasoning schemas. CIRF abstracts first-order logic patterns from raw text into multi-relational schema graphs in an unsupervised manner, and leverages a schema-enhanced graph kernel model to align input structures with schema templates for robust, interpretable zero-shot inference. Extensive experiments on SemEval-2016, VAST, and COVID-19-Stance benchmarks demonstrate that CIRF not only establishes new state-of-the-art results, but also achieves comparable performance with just 30% of the labeled data, demonstrating its strong generalization and efficiency in low-resource settings.
The high memory demands of the Key-Value (KV) Cache during the inference of Large Language Models (LLMs) severely restrict their deployment in resource-constrained platforms. Quantization can effectively alleviate the memory pressure caused by KV Cache. However, existing methods either rely on static one-size-fits-all precision allocation or fail to dynamically prioritize critical KV in long-context tasks, forcing memory-accuracy-throughput tradeoffs. In this work, we propose a novel mixed-precision quantization method for KV Cache named KVmix. KVmix leverages gradient-based importance analysis to evaluate how individual Key and Value projection matrices affect the model loss, enabling layer-specific bit-width allocation for mix-precision quantization. It dynamically prioritizes higher precision for important layers while aggressively quantizing less influential ones, achieving a tunable balance between accuracy and efficiency. KVmix introduces a dynamic long-context optimization strategy that adaptively keeps full-precision KV pairs for recent pivotal tokens and compresses older ones, achieving high-quality sequence generation with low memory usage. Additionally, KVmix provides efficient low-bit quantization and CUDA kernels to optimize computational overhead. On LLMs such as Llama and Mistral, KVmix achieves near-lossless inference performance with extremely low quantization configuration (Key 2.19bit Value 2.38bit), while delivering a remarkable 4.9× memory compression and a 5.3× speedup in inference throughput.
Demystifying GNN-to-MLP Knowledge Transfer: Theoretical Grounding and Dual-Stream Distillation Method
PDF ↗Graph Neural Networks (GNNs) have shown remarkable effectiveness across various applications, but their computational complexity poses significant scalability challenges. To this end, GNN-to-MLP Knowledge Distillation (KD) methods transfer relational inductive biases from GNNs to MLPs, equipping MLPs with graph-aware capabilities that rival or even surpass those of their teacher GNNs. However, a theoretical foundation for understanding GNN-to-MLP KD is still missing. In this paper, we provide a theoretical analysis of how knowledge distillation unlocks the potential of MLPs for graph tasks from the perspective of training dynamics. We demonstrate that label alignment in KD fundamentally reshapes the Neural Tangent Kernel (NTK) matrix of student MLPs, enabling them to learn the teacher model’s implicit graph bias. We further investigate finer-grained distillation paradigms and reveal that conventional layer-wise output alignment fails to effectively align the deep-layer graph propagation outcomes. To address this, we propose Dual-Stream Aligned MLP (DA-MLP), which incorporates complementary graph filters in a dual-stream architecture. This approach simultaneously enhances feature space dimensionality for improved representation alignment and preserves graph signals across different frequency bands. Comprehensive experiments on seven benchmark datasets validate that DA-MLP can be seamlessly integrated into existing knowledge distillation frameworks for performance enhancements in both transductive and inductive settings.
Gaussian Processes (GPs), as a nonparametric learning method, offer flexible modeling capabilities and calibrated uncertainty quantification for function approximations. Additionally, GPs support online learning by efficiently incorporating new data with polynomial-time computation, making them well-suited for safety-critical dynamical systems that require rapid adaptation. However, the inference and online updates of exact GPs, when processing streaming data, incur cubic computation time and quadratic storage memory complexity, limiting their scalability to large datasets in real-time settings. In this paper, we propose a streaming kernel-induced progressively generated expert framework of Gaussian processes (SkyGP) that addresses both computational and memory constraints by maintaining a bounded set of experts, while inheriting the learning performance guarantees from exact Gaussian processes. Furthermore, two SkyGP variants are introduced, each tailored to a specific objective, either maximizing prediction accuracy (SkyGP-Dense) or improving computational efficiency (SkyGP-Fast). The effectiveness of SkyGP is validated through extensive benchmarks and real-time control experiments demonstrating its superior performance compared to state-of-the-art approaches.
The KV cache in self-attention has emerged as a major bottleneck in long-context and large-batch inference for LLMs. Existing approaches often treat sparsity prediction and compression as separate modules—relying on auxiliary index structures to select relevant tokens, and on complex quantization schemes to reduce memory usage. This fragmented design introduces redundant overhead and limits scalability. In this paper, we propose a novel paradigm: treating the compressed key representation not merely as storage, but as a self-indexing structure that directly enables efficient sparse attention. By designing a sign-based 1-bit vector quantization (VQ) scheme, our method unifies compression and retrieval in a single, hardware-friendly format. This approach eliminates the need for external indices or learning-based predictors, offering a lightweight yet robust solution for memory-constrained inference. All components are designed to be hardware-efficient and easy to implement. By implementing custom CUDA kernels, our method integrates seamlessly with FlashAttention, minimizing additional runtime and memory overhead. Experimental results demonstrate that our approach delivers both effectiveness and efficiency.
In many practical reinforcement learning tasks, feedback is only provided at the end of a long horizon, leading to sparse and delayed rewards. Existing reward redistribution methods typically assume that per-step rewards are independent, thus overlooking interdependencies among state–action pairs. In this paper, we propose a Gaussian Process-based Likelihood Reward Redistribution (GP-LRR) framework that addresses this issue by modeling the reward function as a sample from a Gaussian Process (GP), which explicitly captures dependencies between state–action pairs through the kernel function. By maximizing the likelihood of the observed episodic return via a leave-one-out strategy that leverages the entire trajectory, our framework inherently introduces uncertainty regularization. Moreover, we show that the conventional mean squared error (MSE)-based reward redistribution arises as a special case of our GP-LRR framework when using a degenerate kernel without observation noise. When integrated with an off-policy algorithm such as Soft Actor-Critic, GP-LRR yields dense and informative reward signals, resulting in superior sample efficiency and policy performance on several MuJoCo benchmarks.
The Area Under the ROC Curve (AUC) is an important evaluation metric for both linear and, in particular, nonlinear classification models, owing to its robustness against class imbalance. Sparse learning with an ℓ₀ constraint can enhance model interpretability and generalization. Prior work has shown that, in the linear setting, the pairwise formulation of AUC maximization can be reformulated as a standard pointwise empirical risk minimization problem, which enables efficient optimization using hard-thresholding gradient descent for ℓ₀-constrained AUC maximization. Extending this approach to the nonlinear setting remains largely unexplored, even though we establish that pairwise AUC maximization in this setting is equivalent to a pointwise compositional optimization problem; however, designing a compositional optimization algorithm compatible with hard-thresholding operators remains an open challenge. To address this challenge, in this paper, we propose a novel algorithm—Compositional Stochastic Hard Thresholding (CSHT)—for nonlinear sparse AUC maximization. Specifically, CSHT integrates stochastic variance-reduced gradient techniques with hard-thresholding projections to effectively reduce gradient estimation variance while enforcing sparsity. Notably, we provide a rigorous convergence analysis and prove that CSHT achieves linear convergence up to a tolerance bound. To the best of our knowledge, this is the first stochastic hard-thresholding algorithm tailored for nonlinear sparse AUC maximization. Extensive experiments on (a) nonlinear sparse AUC maximization using Random Fourier Feature-based kernel approximation and (b) universal adversarial attack scenarios demonstrate the superior performance of CSHT over existing methods, attributed to its unified treatment of nonlinearity and sparsity.
ST-TPP: Learning Semi-Transductive Temporal Point Processes with Gromov-Wasserstein Barycentric Regularization
PDF ↗The generative mechanisms behind real-world event sequences are often heterogeneous, leading to data that possesses inherent clustering structures. However, most existing temporal point processes (TPPs) treat different event sequences independently, without leveraging the clustering structures when predicting events. In this study, we design and learn a novel semi-transductive temporal point process (ST-TPP), which explicitly improves prediction performance by co-training sequence clusters. In particular, given a set of event sequences, our method learns a neural TPP together with cluster centers of the sequences. Besides maximizing the likelihood of the event sequences, we leverage a data-based kernel matrix and prior knowledge to regularize the sequence embeddings, leading to a Gromov-Wasserstein barycentric (GWB) regularizer. Based on the optimal transport plans associated with the GWB regularizer, we derive the cluster centers by the push-forward of the sequence embeddings. When a new sequence comes, the learned model first assigns a cluster center to the sequence and then jointly encodes the sequence and the cluster center to predict future events, leading to a semi-transductive prediction scheme. Experiments demonstrate that ST-TPP achieves competitive sequence clustering results and strong prediction performance.
Graph-level clustering (GLC), which aims to group entire graphs according to their structural and attribute-based similarities, represents a fundamental yet challenging task in various practical applications. Existing GLC methods primarily fall into two main paradigms: 1) deep graph clustering approaches based on Graph Neural Networks (GNNs), and 2) kernel-based methods that utilize predefined kernels to perform fine-grained structural comparison for clustering. However, GNN-based methods typically learn graph-level representations by aggregating node embeddings through pooling operations, which inevitably leads to substantial information loss and suboptimal clustering performance. In contrast, kernel methods, despite their theoretical expressiveness, suffer from prohibitive computational costs that hinder their scalability to large-scale settings. To solve these issues, we propose a novel graph learning framework named Anchor-driven Nyström for Deep Graph-Level Clustering (ANGC), which computes graph similarity via kernel methods while retaining the scalability of GNNs. Specifically, we first employ GNNs to encode individual graphs into sets of node embeddings. Rather than relying on pooling operations, we compute graph similarities in a kernel space constructed from these embeddings. To enhance both scalability and representational power, we introduce learnable graph Nyström anchors, which support end-to-end optimization and significantly accelerate kernel computations. To further improve the discriminative capability of these anchors, we propose the concept of anchor response discrepancy, that is, the variation in a given anchor’s responses across different samples. By maximizing this discrepancy, the anchors are encouraged to strengthen inter-graph distinctions for better clustering. Extensive experiments demonstrate the effectiveness and superiority of ANGC over existing state-of-the-art methods.
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.
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds, most existing approaches require access to specific input features, and rely on posterior mean and variance estimates or the tuning of hyperparameters. These limitations hinder robustness and fail to capture the model’s global behavior in expectation. To address these limitations, we propose a chaining-based framework for estimating upper and lower bounds on the expected extreme values over unseen data, without requiring access to specific input features. We provide kernel-specific refinements for commonly used kernels such as RBF and Matérn, in which our bounds are tighter than generic constructions. We further improve numerical tightness by avoiding analytical relaxations. In addition to global estimation, we also develop a novel method for local uncertainty quantification at specified inputs. This approach leverages chaining geometry through partition diameters, adapting to local structures without relying on posterior variance scaling. Our experimental results validate the theoretical findings and demonstrate that our method outperforms existing approaches on both synthetic and real-world datasets.
Bipartite learning is a machine learning task that aims to predict interactions between pairs of instances. It has been applied to various domains, including drug-target interactions, RNA-disease associations, and regulatory network inference. Despite being widely investigated, current methods still present drawbacks, as they are often designed for a specific application and thus do not generalize to other problems or present scalability issues. To address these challenges, we propose Oxytrees: proxy-based biclustering model trees. Oxytrees compress the interaction matrix into row- and column-wise proxy matrices, significantly reducing training time without compromising predictive performance. We also propose a new leaf-assignment algorithm that significantly reduces the time taken for prediction. Finally, Oxytrees employ linear models using the Kronecker product kernel in their leaves, resulting in shallower trees and thus even faster training. Using 15 datasets, we compared the predictive performance of ensembles of Oxytrees with that of the current state-of-the-art. We achieved up to 30-fold improvement in training times compared to state-of-the-art biclustering forests, while demonstrating competitive or superior performance in most evaluation settings, particularly in the inductive setting. Finally, we provide an intuitive Python API to access all datasets, methods and evaluation measures used in this work, thus enabling reproducible research in this field.
Bayesian optimization (BO) has been widely used to optimize expensive and gradient-free objective functions across various domains. However, existing BO methods have not addressed the objective where both inputs and outputs are functions, which increasingly arise in complex systems as advanced sensing technologies. To fill this gap, we propose a novel function-on-function Bayesian optimization (FFBO) framework. Specifically, we first introduce a function-on-function Gaussian process (FFGP) model with a separable operator-valued kernel to capture the correlations between function-valued inputs and outputs. Compared to existing Gaussian process models, FFGP is modeled directly in the function space. Based on FFGP, we define a scalar upper confidence bound (UCB) acquisition function using a weighted operator-based scalarization strategy. Then, a scalable functional gradient ascent algorithm (FGA) is developed to efficiently identify the optimal function-valued input. We further analyze the theoretical properties of the proposed method. Extensive experiments on synthetic and real-world data demonstrate the superior performance of FFBO over existing approaches.
With the rise of vertical segmentation in real-world data, federated graph-level clustering has gained significant attention in recent years. However, the inherent missing attributes in graph datasets held by certain clients lead to suboptimal local parameter updates and misaligned global parameter consensus. This results in knowledge shifts during negotiation to ultimately impair overall clustering performance. This issue remains largely underexplored in the current advanced research. To bridge this gap, we propose a novel deep learning network called Federated Graph-level Clustering Network with Attribute Inference (FedAI), which utilizes high-confidence prior knowledge from each domain and multi-party collaborative optimization to achieve efficient reasoning of unknown features. Specifically, on the client, high-confidence graph samples are projected into a latent space. We then extract and upload irreversible path digest information and attribute-oriented inference signals from them. On the server, we first identify affinity relationships hierarchically via the improved graph kernel method. We then infer the features of clients lacking node attributes through a prior structure-guide recovery operator, facilitating inter-client knowledge transfer for better clustering. Experimental results on 15 cross-dataset and cross-domain non-IID graph datasets demonstrate that FedAI consistently outperforms existing methods.
Experience replay is a foundational technique in reinforcement learning that enhances learning stability by storing past experiences in a replay buffer and reusing them during training. Despite its practical success, its theoretical properties remain underexplored. In this paper, we present a theoretical framework that models experience replay using resampled U- and V-statistics, providing rigorous variance reduction guarantees. We apply this framework to policy evaluation tasks using the Least-Squares Temporal Difference (LSTD) algorithm and a Partial Differential Equation (PDE)-based model-free algorithm, demonstrating significant improvements in stability and efficiency, particularly in data-scarce scenarios. Beyond policy evaluation, we extend the framework to kernel ridge regression, showing that the experience replay-based method reduces the computational cost from the traditional cubic time to quadratic time in the sample size, while also reducing variance. Extensive numerical experiments validate our theoretical findings, demonstrating the broad applicability and effectiveness of experience replay in diverse machine learning tasks.
In supervised learning with distributional inputs in the two-stage sampling setup, relevant to applications like learning-based medical screening or causal learning, the inputs (which are probability distributions) are not accessible in the learning phase, but only samples thereof. This problem is particularly amenable to kernel-based learning methods, where the distributions or samples are first embedded into a Hilbert space, often using kernel mean embeddings (KMEs), and then a standard kernel method like Support Vector Machines (SVMs) is applied, using a kernel defined on the embedding Hilbert space. In this work, we contribute to the theoretical analysis of this latter approach, with a particular focus on classification with distributional inputs using SVMs. We establish a new oracle inequality and derive consistency and learning rate results. Furthermore, for SVMs using the hinge loss and Gaussian kernels, we formulate a novel variant of an established noise assumption from the binary classification literature, under which we can establish learning rates. Finally, some of our technical tools like a new feature space for Gaussian kernels on Hilbert spaces are of independent interest.
Large Language Models (LLMs) exhibit pronounced memory-bound characteristics during inference due to High Bandwidth Memory (HBM) bandwidth constraints. In this paper, we propose an L2 Cache-oriented asynchronous KV Cache prefetching method to break through the memory bandwidth bottleneck in LLM inference through computation-load overlap. By strategically scheduling idle memory bandwidth during active computation windows, our method proactively prefetches required KV Cache into GPU L2 cache, enabling high-speed L2 cache hits for subsequent accesses and effectively hiding HBM access latency within computational cycles. Extensive experiments on NVIDIA H20 GPUs demonstrate that the proposed method achieves 2.15× improvement in attention kernel efficiency and up to 1.97× end-to-end throughput enhancement, surpassing state-of-the-art baseline FlashAttention-3. Notably, our solution maintains orthogonality to existing optimization techniques and can be integrated with current inference frameworks, providing a scalable latency-hiding solution for next-generation LLM inference engines.