This paper introduces Quantum-PEFT that leverages quantum computations for parameter-efficient fine-tuning (PEFT). Unlike other additive PEFT methods, such as low-rank adaptation (LoRA), Quantum-PEFT exploits an underlying full-rank yet surprisingly parameter efficient _quantum unitary parameterization_. With the use of Pauli parameterization, the number of trainable parameters grows only logarithmically with the ambient dimension, as opposed to linearly as in LoRA-based PEFT methods. Quantum-PEFT achieves vanishingly smaller number of trainable parameters than the lowest-rank LoRA as dimensions grow, enhancing parameter efficiency while maintaining a competitive performance. We apply Quantum-PEFT to several transfer learning benchmarks in language and vision, demonstrating significant advantages in parameter efficiency.

Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the general population. We present a new efficient method for fair spectral clustering (Fair SC) by casting the Fair SC problem within the difference of convex functions (DC) framework. To this end, we introduce a novel variable augmentation strategy and employ an alternating direction method of multipliers type of algorithm adapted to DC problems. We show that each associated subproblem can be solved efficiently, resulting in higher computational efficiency compared to prior work, which required a computationally expensive eigendecomposition. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world benchmarks, showing significant speedups in computation time over prior art, especially as the problem size grows. This work thus represents a considerable step forward towards the adoption of fair clustering in real-world applications.

Training data mixtures greatly impact the generalization performance of large language models. Existing domain reweighting methods often rely on costly weight computations and require retraining when new data is introduced. To this end, we introduce a flexible and efficient data mixing framework, Chameleon, that employs leverage scores to quantify domain importance within a learned embedding space. We first construct a domain affinity matrix over domain embeddings. The induced leverage scores determine a mixture that upweights domains sharing common representations in embedding space. This formulation allows direct transfer to new data by computing the new domain embeddings. In experiments, we demonstrate improvements over three key scenarios: (i) our computed weights improve performance on pretraining domains with a fraction of the compute of existing methods; (ii) Chameleon can adapt to data changes without proxy retraining, boosting few-shot reasoning accuracies when transferred to new data; (iii) our method enables efficient domain reweighting in finetuning, consistently improving test perplexity on all finetuning domains over uniform mixture. Our code is available at https://github.com/LIONS-EPFL/Chameleon.

Linear Transformers and State Space Models have emerged as efficient alternatives to softmax Transformers for causal sequence modeling, enabling parallel training via matrix multiplication and efficient RNN-style inference. However, despite their success in causal tasks, no unified framework exists for applying Linear Transformers to bidirectional sequence modeling. We introduce LION, the first framework to systematically extend Linear Transformers to the bidirectional setting. LION generalizes three core representations commonly used in the causal case—full Linear Attention , bidirectional RNN, and chunkwise parallel form—to the bidirectional setting. These forms are theoretically equivalent and enable models to exploit the strengths of each during training and inference. We prove that a broad class of Linear Transformers can be extended using LION and validate our framework via three core examples based on the choice of decay type: LION-LIT, the bidirectional extension of [25]; LION-D, based on [44]; and LION-S, a variant using selective decay [34, 13]. Across standard bidirectional tasks, LION enables models to match or exceed the performance of softmax Transformers, while offering significantly faster training and more efficient inference than existing State Space Models.

The high inference demands of transformer-based Large Language Models (LLMs) pose substantial challenges in their deployment. To this end, we introduce *Neural Block Linearization* (NBL), a novel framework for accelerating transformer model inference by replacing self-attention layers with linear approximations derived from Linear Minimum Mean Squared Error estimators. NBL leverages Canonical Correlation Analysis to compute a theoretical upper bound on the approximation error. Then, we use this bound as a criterion for substitution, selecting the LLM layers with the lowest linearization error. NBL can be efficiently applied to pre-trained LLMs without the need for fine-tuning. In experiments, NBL achieves notable computational speed-ups while preserving competitive accuracy on multiple reasoning benchmarks. For instance, applying NBL to 12 self-attention layers in *DeepSeek-R1-Distill-Llama-8B* increases the inference speed by 32% with less than 1% accuracy trade-off, making it a flexible and promising solution to improve the inference efficiency of LLMs.

We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. The method is built of two main types of blocks: (i) We introduce unsupervised kernel machine layers propagating the node features in a one-hop neighborhood, using implicit node feature mappings. (ii) We specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. We derive an effective initialization scheme and efficient end-to-end training algorithm in the dual variables for the full architecture. The main idea underlying GCKM is that, because of the unsupervised core, the final model can achieve higher performance in semi-supervised node classification when few labels are available for training. Experimental results demonstrate the effectiveness of the proposed framework.

While the great capability of Transformers significantly boosts prediction accuracy, it could also yield overconfident predictions and require calibrated uncertainty estimation, which can be commonly tackled by Gaussian processes (GPs). Existing works apply GPs with symmetric kernels under variational inference to the attention kernel; however, omitting the fact that attention kernels are in essence asymmetric. Moreover, the complexity of deriving the GP posteriors remains high for large-scale data. In this work, we propose Kernel-Eigen Pair Sparse Variational Gaussian Processes (KEP-SVGP) for building uncertainty-aware self-attention where the asymmetry of attention kernels is tackled by Kernel SVD (KSVD) and a reduced complexity is acquired. Through KEP-SVGP, i) the SVGP pair induced by the two sets of singular vectors from KSVD w.r.t. the attention kernel fully characterizes the asymmetry; ii) using only a small set of adjoint eigenfunctions from KSVD, the derivation of SVGP posteriors can be based on the inversion of a diagonal matrix containing singular values, contributing to a reduction in time complexity; iii) an evidence lower bound is derived so that variational parameters and network weights can be optimized with it. Experiments verify our excellent performances and efficiency on in-distribution, distribution-shift and out-of-distribution benchmarks.

In contrast with Mercer kernel-based approaches as used e.g. in Kernel Principal Component Analysis (KPCA), it was previously shown that Singular Value Decomposition (SVD) inherently relates to asymmetric kernels and Asymmetric Kernel Singular Value Decomposition (KSVD) has been proposed. However, the existing formulation to KSVD cannot work with infinite-dimensional feature mappings, the variational objective can be unbounded, and needs further numerical evaluation and exploration towards machine learning. In this work, i) we introduce a new asymmetric learning paradigm based on coupled covariance eigenproblem (CCE) through covariance operators, allowing infinite-dimensional feature maps. The solution to CCE is ultimately obtained from the SVD of the induced asymmetric kernel matrix, providing links to KSVD. ii) Starting from the integral equations corresponding to a pair of coupled adjoint eigenfunctions, we formalize the asymmetric Nyström method through a finite sample approximation to speed up training. iii) We provide the first empirical evaluations verifying the practical utility and benefits of KSVD and compare with methods resorting to symmetrization or linear SVD across multiple tasks.

Large vision-language models (VLLMs) exhibit promising capabilities for processing multi-modal tasks across various application scenarios. However, their emergence also raises significant data security concerns, given the potential inclusion of sensitive information, such as private photos and medical records, in their training datasets. Detecting inappropriately used data in VLLMs remains a critical and unresolved issue, mainly due to the lack of standardized datasets and suitable methodologies. In this study, we introduce the first membership inference attack (MIA) benchmark tailored for various VLLMs to facilitate training data detection. Then, we propose a novel MIA pipeline specifically designed for token-level image detection. Lastly, we present a new metric called MaxRényi-K%, which is based on the confidence of the model output and applies to both text and image data. We believe that our work can deepen the understanding and methodology of MIAs in the context of VLLMs. Our code and datasets are available at https://github.com/LIONS-EPFL/VL-MIA.

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success, but a framework for deep principal component analysis is still lacking. Here we develop a deep kernel PCA methodology (DKPCA) to extract multiple levels of the most informative components of the data. Our scheme can effectively identify new hierarchical variables, called deep principal components, capturing the main characteristics of high-dimensional data through a simple and interpretable numerical optimization. We couple the principal components of multiple KPCA levels, theoretically showing that DKPCA creates both forward and backward dependency across levels, which has not been explored in kernel methods and yet is crucial to extract more informative features. Various experimental evaluations on multiple data types show that DKPCA finds more efficient and disentangled representations with higher explained variance in fewer principal components, compared to the shallow KPCA. We demonstrate that our method allows for effective hierarchical data exploration, with the ability to separate the key generative factors of the input data both for large datasets and when few training samples are available. Overall, DKPCA can facilitate the extraction of useful patterns from high-dimensional data by learning more informative features organized in different levels, giving diversified aspects to explore the variation factors in the data, while maintaining a simple mathematical formulation.

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient gradient-based algorithms avoiding the expensive SVD of the Gram matrix. Particularly, we consider objective functions that can be written as Moreau envelopes, demonstrating how to promote robustness and sparsity within the same framework. The proposed method is evaluated on synthetic and realworld benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.

Recently, a new line of works has emerged to understand and improve self-attention in Transformers by treating it as a kernel machine. However, existing works apply the methods for symmetric kernels to the asymmetric self-attention, resulting in a nontrivial gap between the analytical understanding and numerical implementation. In this paper, we provide a new perspective to represent and optimize self-attention through asymmetric Kernel Singular Value Decomposition (KSVD), which is also motivated by the low-rank property of self-attention normally observed in deep layers. Through asymmetric KSVD, i) a primal-dual representation of self-attention is formulated, where the optimization objective is cast to maximize the projection variances in the attention outputs; ii) a novel attention mechanism, i.e., Primal-Attention, is proposed via the primal representation of KSVD, avoiding explicit computation of the kernel matrix in the dual; iii) with KKT conditions, we prove that the stationary solution to the KSVD optimization in Primal-Attention yields a zero-value objective. In this manner, KSVD optimization can be implemented by simply minimizing a regularization loss, so that low-rank property is promoted without extra decomposition. Numerical experiments show state-of-the-art performance of our Primal-Attention with improved efficiency. Moreover, we demonstrate that the deployed KSVD optimization regularizes Primal-Attention with a sharper singular value decay than that of the canonical self-attention, further verifying the great potential of our method. To the best of our knowledge, this is the first work that provides a primal-dual representation for the asymmetric kernel in self-attention and successfully applies it to modelling and optimization.

Detecting out-of-distribution (OOD) samples is an essential requirement for the deployment of machine learning systems in the real world. Until now, research on energy-based OOD detectors has focused on the softmax confidence score from a pre-trained neural network classifier with access to class labels. In contrast, we propose an unsupervised energy-based OOD detector leveraging the Stiefel-Restricted Kernel Machine (St-RKM). Training requires minimizing an objective function with an autoencoder loss term and the RKM energy where the interconnection matrix lies on the Stiefel manifold. Further, we outline multiple energy function definitions based on the RKM framework and discuss their utility. In the experiments on standard datasets, the proposed method improves over the existing energy-based OOD detectors and deep generative models. Through several ablation studies, we further illustrate the merit of each proposed energy function on the OOD detection performance.

We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on the latent variables to promote disentanglement and to make it possible to carry out optimization without first defining a stabilized objective. After discussing a number of algorithms for end-to-end training, we quantitatively evaluate the proposed method's effectiveness in disentangled feature learning. We demonstrate on four benchmark datasets that this approach performs similarly overall to β-VAE on several disentanglement metrics when few training points are available while being less sensitive to randomness and hyperparameter selection than β-VAE. We also present a deterministic initialization of Constr-DRKM's training algorithm that significantly improves the reproducibility of the results. Finally, we empirically evaluate and discuss the role of the number of layers in the proposed methodology, examining the influence of each principal component in every layer and showing that components in lower layers act as local feature detectors capturing the broad trends of the data distribution, while components in deeper layers use the representation learned by previous layers and more accurately reproduce higher-level features.