Enhancing defense through model ensemble is an emerging trend, where the challenge lies in how to use ensemble knowledge to counter Out-of-Distribution (OOD) attacks. In this paper, we propose the Reliable Defense Ensemble (REE) to address this issue. REE optimizes the ensemble knowledge of models through aggregation and enhances multidimensional robust performance through collaboration. It employs the Dynamic Synergy Amplification for weight allocation and strategy adjustment. Furthermore, we design a new Kernel Anomaly Smoothing Detection Module, which detects anomalous attacks using a smoothing feature function based on Gaussian kernel mean embedding and a multi-layer feedback structure. Particularly, we build a framework that uses reinforcement learning to iteratively fine-tune the parameters of inter-model communication and consensus. Extensive experimental results show that REE outperforms current state-of-the-art methods by a large margin in defending against OOD attacks.
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Error Bounds for Gaussian Process Regression Under Bounded Support Noise with Applications to Safety Certification
PDF ↗Gaussian Process Regression (GPR) is a powerful and elegant method for learning complex functions from noisy data with a wide range of applications, including in safety-critical domains. Such applications have two key features: (i) they require rigorous error quantification, and (ii) the noise is often bounded and non-Gaussian due to, e.g., physical constraints. While error bounds for applying GPR in the presence of non-Gaussian noise exist, they tend to be overly restrictive and conservative in practice. In this paper, we provide novel error bounds for GPR under bounded support noise. Specifically, by relying on concentration inequalities and assuming that the latent function has low complexity in the reproducing kernel Hilbert space (RKHS) corresponding to the GP kernel, we derive both probabilistic and deterministic bounds on the error of the GPR. We show that these errors are substantially tighter than existing state-of-the-art bounds and are particularly well-suited for GPR with neural network kernels, i.e., Deep Kernel Learning (DKL). Furthermore, motivated by applications in safety-critical domains, we illustrate how these bounds can be combined with stochastic barrier functions to successfully quantify the safety probability of an unknown dynamical system from finite data. We validate the efficacy of our approach through several benchmarks and comparisons against existing bounds. The results show that our bounds are consistently smaller, and that DKLs can produce error bounds tighter than sample noise, significantly improving the safety probability of control systems.
Black box optimization (BBO) focuses on optimizing unknown functions in high-dimensional spaces. In many applications, sampling the unknown function is expensive, imposing a tight sample budget.Ongoing work is making progress on reducing the sample budget by learning the shape/structure of the function, known as kernel learning. We propose a new method to learn the kernel of a Gaussian Process. Our idea is to create a continuous kernel space in the latent space of a variational autoencoder, and run an auxiliary optimization to identify the best kernel. Results show that the proposed method, Kernel Optimized Blackbox Optimization (KOBO), outperforms state of the art by estimating the optimal at considerably lower sample budgets. Results hold not only across synthetic benchmark functions but also in real applications. We show that a hearing aid may be personalized with fewer audio queries to the user, or a generative model could converge to desirable images from limited user ratings.
Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to capture complex learning dynamics, particularly in few-shot learning scenarios. To address this limitation, we propose Stiefel-MAML, which integrates Riemannian geometry by optimizing within the Stiefel manifold, a space that naturally enforces orthogonality constraints. By leveraging the geometric structure of the Stiefel manifold, we improve parameter expressiveness and enable more efficient optimization through Riemannian gradient calculations and retraction operations. We also introduce a novel kernel-based loss function defined on the Stiefel manifold, further enhancing the model’s ability to explore the parameter space. Experimental results on benchmark datasets—including Omniglot, Mini-ImageNet, FC-100, and CUB—demonstrate that Stiefel-MAML consistently outperforms traditional MAML, achieving superior performance across various few-shot learning tasks. Our findings highlight the potential of Riemannian geometry to enhance meta-learning, paving the way for future research on optimizing over different geometric structures.
Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks
PDF ↗Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.
Continual learning (CL) learns a sequence of tasks incrementally. This paper studies the challenging CL setting of class-incremental learning (CIL). CIL has two key challenges: catastrophic forgetting (CF) and inter-task class separation (ICS). Despite numerous proposed methods, these issues remain persistent obstacles. This paper proposes a novel CIL method, called Kernel Linear Discriminant Analysis (KLDA), that can effectively avoid CF and ICS problems. It leverages only the powerful features learned in a foundation model (FM). However, directly using these features proves suboptimal. To address this, KLDA incorporates the Radial Basis Function (RBF) kernel and its Random Fourier Features (RFF) to enhance the feature representations from the FM, leading to improved performance. When a new task arrives, KLDA computes only the mean for each class in the task and updates a shared covariance matrix for all learned classes based on the kernelized features. Classification is performed using Linear Discriminant Analysis. Our empirical evaluation using text and image classification datasets demonstrates that KLDA significantly outperforms baselines. Remarkably, without relying on replay data, KLDA achieves accuracy comparable to joint training of all classes, which is considered the upper bound for CIL performance.
Understanding causality is challenging and often complicated by changing causal relationships over time and across environments. Climate patterns, for example, shift over time with recurring seasonal trends, while also depending on geographical characteristics such as ecosystem variability. Existing methods for discovering causal graphs from time series either assume stationarity, do not permit both temporal and spatial distribution changes, or are unaware of locations with the same causal relationships. In this work, we therefore unify the three tasks of causal graph discovery in the non-stationary multi-context setting, of reconstructing temporal regimes, and of partitioning datasets and time intervals into those where invariant causal relationships hold. To construct a consistent score that forms the basis of our method, we employ the Minimum Description Length principle. Our resulting algorithm SPACETIME simultaneously accounts for heterogeneity across space and non-stationarity over time. Given multiple time series, it discovers regime changepoints and a temporal causal graph using non-parametric functional modeling and kernelized discrepancy testing. We also show that our method provides insights into real-world phenomena such as river-runoff measured at different catchments and biosphere-atmosphere interactions across ecosystems.
High-level synthesis (HLS) is a widely used tool in designing Field Programmable Gate Array (FPGA). HLS enables FPGA design with software programming languages by compiling the source code into an FPGA circuit. The source code includes a program (called ``kernel'') and several pragmas that instruct hardware synthesis, such as parallelization, pipeline, etc. While it is relatively easy for software developers to design the program, it heavily relies on hardware knowledge to design the pragmas, posing a big challenge for software developers. Recently, different machine learning algorithms, such as GNNs, have been proposed to automate the pragma design via performance prediction. However, when applying the trained model on new kernels, the significant domain shift often leads to unsatisfactory performance. We propose a more domain-generalizable model structure: a two-level hierarchical Mixture of Experts (MoE), that can be flexibly adapted to any GNN model. Different expert networks can learn to deal with different regions in the representation space, and they can utilize similar patterns between the old kernels and new kernels. In the low-level MoE, we apply MoE on three natural granularities of a program: node, basic block, and graph. The high-level MoE learns to aggregate the three granularities for the final decision. To stably train the hierarchical MoE, we further propose a two-stage training method. Extensive experiments verify the effectiveness of the hierarchical MoE.
Distributionally Robust Policy Evaluation and Learning for Continuous Treatment with Observational Data
PDF ↗Using offline observational data for policy evaluation and learning allows decision-makers to evaluate and learn a policy that connects characteristics and interventions. Most existing literature has focused on either discrete treatment spaces or assumed no difference in the distributions between the policy-learning and policy-deployed environments. These restrict applications in many real-world scenarios where distribution shifts are present with continuous treatment. To overcome these challenges, this paper focuses on developing a distributionally robust policy under a continuous treatment setting. The proposed distributionally robust estimators are established using the Inverse Probability Weighting (IPW) method extended from the discrete one for policy evaluation and learning under continuous treatments. Specifically, we introduce a kernel function into the proposed IPW estimator to mitigate the exclusion of observations that can occur in the standard IPW method to continuous treatments. We then provide finite-sample analysis that guarantees the convergence of the proposed distributionally robust policy evaluation and learning estimators. The comprehensive experiments further verify the effectiveness of our approach when distribution shifts are present.
Tabular data poses unique challenges due to its heterogeneous nature, combining both continuous and categorical variables. Existing approaches often struggle to effectively capture the underlying structure and relationships within such data. We propose GFTab (Geodesic Flow Kernels for Semi-Supervised Learning on Mixed-Variable Tabular Dataset), a semi-supervised framework specifically designed for tabular datasets. GFTab incorporates three key innovations: 1) Variable-specific corruption methods tailored to the distinct properties of continuous and categorical variables, 2) A Geodesic flow kernel based similarity measure to capture geometric changes between corrupted inputs, and 3) Tree-based embedding to leverage hierarchical relationships from available labeled data. To rigorously evaluate GFTab, we curate a comprehensive set of 21 tabular datasets spanning various domains, sizes, and variable compositions. Our experimental results show that GFTab outperforms existing ML/DL models across many of these datasets, particularly in settings with limited labeled data.
Unsupervised Kernel-based Multi-view Feature Selection with Robust Self-representation and Binary Hashing
PDF ↗Unsupervised multi-view feature selection involves selecting a subset of crucial features across diverse views to diminish feature dimensionality without leveraging label information. While numerous studies have delved into this area, current solutions predominantly rely on linear multi-view data or employ weakly supervised learning to aid in feature selection. These approaches may risk losing semantic information when applied to real-world multi-view datasets. In this study, we introduce a novel model, Unsupervised Kernel-based Multi-view Feature selection with Robust self-representation and Binary hashing (UKMFS), which aims to identify robust consistent graph representation across views and leverage binary hashing codes to guide feature selection. Specifically, we first explore the underlying geometry by unifying the dimension of multi-view data with non-linear kernel mapping. Then, we search the consistent graph across views by fusing unique graph representations of each view in a self-representation manner. Additionally, we impose low-rank constraints on the graph of each view to mitigate noise and unimportant parts for preserving the main structures and patterns. Furthermore, we design an unsupervised hashing feature selection model to exploit reliable binary labels across views and weighted matrices from each view. Finally, an effective optimization method is customised to solve the formulated problem iteratively. Comprehensive experiments on public multi-view datasets indicate that our proposed method achieves state-of-the-art performance compared with the representative comparison methods regarding the clustering and the feature selection task.
Existing Multiple Kernel Clustering (MKC) algorithms commonly utilize the Nyström method to handle large-scale datasets. However, most of them employ uniform sampling for kernel matrix approximation, hence failing to accurately capture the underlying data structure, leading to large approximation errors. Additionally, they often use the same landmark points for all kernel matrix approximations, reducing kernel diversity. Moreover, in scenarios where approximate kernel matrices emerge over time, these methods require storing historical kernel information and recalculating, resulting in inefficient resource utilization. To address these issues, we propose a novel MKC algorithm, termed Incremental Nyström-based Multiple Kernel Clustering (INMKC). Specifically, leverage score sampling is utilized to reduce kernel approximation errors and enhance kernel diversity. Furthermore, we employ a consensus clustering structure that aligns with the newly emerged base kernel matrix for updates, avoiding recalculating previous kernel matrices, thus saving substantial computational resources. Additionally, we tackle the challenge of aligning incremental approximate kernels with different landmark points. Extensive experiments on the proposed INMKC demonstrate its effectiveness and efficiency compared to state-of-the-art methods.
We introduce OmniMark, a novel and efficient fingerprinting method for Latent Diffusion Models (LDM). OmniMark can encode user-specific fingerprints across diverse dimensions of the weights of the LDM, including kernels, filters, channels, and spatial domains. The LDM is fine-tuned to encode the invisible fingerprint into generated images, which can be decoded by a decoder. By altering fingerprints and re-encoding the weights, OmniMark supports efficient and scalable ad-hoc generation (
Sharper Error Bounds in Late Fusion Multi-view Clustering with Eigenvalue Proportion Optimization
PDF ↗Multi-view clustering (MVC) aims to integrate complementary information from multiple views to enhance clustering performance. Late Fusion Multi-View Clustering (LFMVC) has shown promise by synthesizing diverse clustering results into a unified consensus. However, current LFMVC methods struggle with noisy and redundant partitions and often fail to capture high-order correlations across views. To address these limitations, we present a novel theoretical framework for analyzing the generalization error bounds of multiple kernel k-means, leveraging local Rademacher complexity and principal eigenvalue proportions. Our analysis establishes a convergence rate of O(1/n), significantly improving upon the existing rate in the order of O(sqrt(k/n)). Building on this insight, we propose a low-pass graph filtering strategy within a multiple linear K-means framework to mitigate noise and redundancy, further refining the principal eigenvalue proportion and enhancing clustering accuracy. Experimental results on benchmark datasets confirm that our approach outperforms state-of-the-art methods in clustering performance and robustness.
The Surprising Effectiveness of Infinite-Width NTKs for Characterizing and Improving Model Training
PDF ↗Developments in deep neural nets have trended towards increasingly larger overparameterized architectures, resulting in lengthy training sessions with ever more elusive training dynamics. Thus, ensuring these models learn accurate generalizable representations of data efficiently is challenging. Previous works have developed specialized techniques from data-pruning, architecture selection, pseudo-label generation, bias identification, or label refurbishment to improve downstream training. Problematically, most methods require prohibitively expensive iterative model training. In this paper, we demonstrate that we can exploit the recent neural tangent kernel (NTK) theory for understanding and improving model training behavior before ever training a model. First, we show a powerful signal derived from the NTK theory can be computed remarkably fast. We then leverage this signal for the design of a unified suite of surprisingly effective tools for the four important tasks of architecture selection, pseudo-label verification, bias identification, and label refurbishment, all requiring zero model training.
Unsupervised Skill Discovery aims at learning diverse skills without any extrinsic rewards and leverage them as prior for learning a variety of downstream tasks. Existing approaches to unsupervised reinforcement learning typically involve discovering skills through empowerment-driven techniques or by maximizing entropy to encourage exploration. However, this mutual information objective often results in either static skills that discourage exploration or maximise coverage at the expense of non-discriminable skills. Instead of focusing only on maximizing bounds on f-divergence, we combine it with Integral Probability Metrics to maximize the distance between distributions to promote behavioural diversity and enforce disentanglement. Our method, Hilbert Unsupervised Skill Discovery (HUSD), provides an additional objective that seeks to obtain exploration and separability of state-skill pairs by maximizing the Maximum Mean Discrepancy between the joint distribution of skills and states and the product of their marginals in Reproducing Kernel Hilbert Space. Our results on Unsupervised RL Benchmark show that HUSD outperforms previous exploration algorithms on state-based tasks.
The learnware paradigm aims to establish a learnware dock system of numerous well-trained machine learning models, enabling users to reuse existing helpful models for their tasks instead of starting from scratch. Each learnware in the system is a well-established model submitted by its developer, associated with a specification generated by the learnware dock system. The specification characterizes the specialty of the corresponding model, enabling it to be identified accurately for new task requirements. Existing specification generation methods are mostly based on the Reduced Kernel Mean Embedding (RKME) technique, which uses the Maximum Mean Discrepancy (MMD) in the Reproducing Kernel Hilbert Space (RKHS) to seek a reduced set that characterizes the model's capabilities. However, existing RKME-based methods mainly utilize feature information to generate specifications by assuming the existence of the ground-truth labeling function, while leaving the label information, which is capable of providing rich semantic characterization, untouched. Furthermore, the quality of the generated specifications heavily relies on the choice of the kernels, which makes it prohibitive to adapt to all real-world scenarios. In this paper, to overcome the above limitations, we propose a novel specification approach named LANE, i.e., Label-Aware Neural Embedding. In LANE, the neural embedding space is utilized to replace the RKHS, effectively circumventing the step of kernel selection and thereby addressing the dependency on kernels in existing RKME-based specification methods. More importantly, LANE uses the label information as additional supervision to enhance the generation process, resulting in specifications of superior quality. Extensive experiments demonstrate the effectiveness and superiority of the proposed LANE approach in the learnware paradigm.
When Can We Approximate Wide Contrastive Models with Neural Tangent Kernels and Principal Component Analysis?
PDF ↗Contrastive learning is a paradigm for learning representations from unlabelled data and several recent works have claimed that such models effectively learn spectral embeddings and show relations between (wide) contrastive models and kernel principal component analysis (PCA). However, it is not known if trained contrastive models indeed correspond to kernel methods or PCA. In this work, we analyze the training dynamics of two-layer contrastive models, with non-linear activation, and answer when these models are close to PCA or kernel methods. It is well known in the supervised setting that neural networks are equivalent to neural tangent kernel (NTK) machines, and that the NTK of infinitely wide networks remains constant during training. We provide the first constancy results of NTK for contrastive losses, and present a nuanced picture: NTK of wide networks remains almost constant for cosine similarity based contrastive losses, but not for losses based on dot product similarity. We further study the training dynamics of contrastive models with orthogonality constraints on output layer, which is implicitly assumed in works relating contrastive learning to spectral embedding. Our deviation bounds suggest that representations learned by contrastive models are close to the principal components of a certain matrix computed from random features.
With the advancements of artificial intelligence (AI), emerging scenarios involving close collaboration between AI and other unknown agents are becoming increasingly common. This requires sometimes training AI agents to collaborate with unknown agents in the absence of a reward function -- which may be unavailable to the AI agents or even undefined by the unknown agents themselves -- thus posing news challenges to existing learning algorithms that often require knowing the shared reward. In this paper, we show that effective teaming with unknown agents can be achieved in the absence of a reward function, through actively modeling other unknown agents and reasoning about their latent rewards from available interaction/observation history. In particular, we propose a novel framework that leverages a kernel density Bayesian inverse learning method for active reward/goal inference and prove that multi-agent reinforcement learning guided by the inferred reward signals can converge to an optimal policy teaming with unknown agents. The result enables us to develop an adaptive policy update strategy, through the use of a family of pre-trained, goal-conditioned policies, further eliminating the need for online retraining. The proposed solution is evaluated using a wide range of diverse unknown agents of latent and even non-stationary reward. Our solution significantly increases the teaming performance between AI and unknown agents in the absence of reward.
Decomposing and Fusing Intra- and Inter-Sensor Spatio-Temporal Signal for Multi-Sensor Wearable Human Activity Recognition
PDF ↗Wearable Human Activity Recognition (WHAR) is a prominent research area within ubiquitous computing. Multi-sensor synchronous measurement has proven to be more effective for WHAR than using a single sensor. However, existing WHAR methods use shared convolutional kernels for indiscriminate temporal feature extraction across each sensor variable, which fails to effectively capture spatio-temporal relationships of intra-sensor and inter-sensor variables. We propose the DecomposeWHAR model consisting of a decomposition phase and a fusion phase to better model the relationships between modality variables. The decomposition creates high-dimensional representations of each intra-sensor variable through the improved Depth Separable Convolution to capture local temporal features while preserving their unique characteristics. The fusion phase begins by capturing relationships between intra-sensor variables and fusing their features at both the channel and variable levels. Long-range temporal dependencies are modeled using the State Space Model (SSM), and later cross-sensor interactions are dynamically captured through a self-attention mechanism, highlighting inter-sensor spatial correlations. Our model demonstrates superior performance on three widely used WHAR datasets, significantly outperforming state-of-the-art models while maintaining acceptable computational efficiency.