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Johan Suykens

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7 papers

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NeurIPS Conference 2025 Conference Paper

Rethinking PCA Through Duality

Jan Quan
Johan Suykens
Panagiotis Patrinos

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and provide new theoretical insights. In particular, we show the kernelizability and out-of-sample applicability for a PCA-like family of problems. Moreover, we uncover that simultaneous iteration, which is connected to the classical QR algorithm, is an instance of the difference-of-convex algorithm (DCA), offering an optimization perspective on this longstanding method. Further, we describe new algorithms for PCA and empirically compare them with state-of-the-art methods. Lastly, we introduce a kernelizable dual formulation for a robust variant of PCA that minimizes the $l_1$-deviation of the reconstruction errors.

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NeurIPS Conference 2023 Conference Paper

Primal-Attention: Self-attention through Asymmetric Kernel SVD in Primal Representation

Yingyi Chen
Qinghua Tao
Francesco Tonin
Johan Suykens

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.

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NeurIPS Conference 2022 Conference Paper

On the Double Descent of Random Features Models Trained with SGD

Fanghui Liu
Johan Suykens
Volkan Cevher

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF regression under both constant and polynomial-decay step-size SGD setting, and observe the double descent phenomenon both theoretically and empirically. Our analysis shows how to cope with multiple randomness sources of initialization, label noise, and data sampling (as well as stochastic gradients) with no closed-form solution, and also goes beyond the commonly-used Gaussian/spherical data assumption. Our theoretical results demonstrate that, with SGD training, RF regression still generalizes well for interpolation learning, and is able to characterize the double descent behavior by the unimodality of variance and monotonic decrease of bias. Besides, we also prove that the constant step-size SGD setting incurs no loss in convergence rate when compared to the exact minimum-norm interpolator, as a theoretical justification of using SGD in practice.

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NeurIPS Conference 2020 Conference Paper

A Theoretical Framework for Target Propagation

Alexander Meulemans
Francesco Carzaniga
Johan Suykens
João Sacramento
Benjamin F. Grewe

The success of deep learning, a brain-inspired form of AI, has sparked interest in understanding how the brain could similarly learn across multiple layers of neurons. However, the majority of biologically-plausible learning algorithms have not yet reached the performance of backpropagation (BP), nor are they built on strong theoretical foundations. Here, we analyze target propagation (TP), a popular but not yet fully understood alternative to BP, from the standpoint of mathematical optimization. Our theory shows that TP is closely related to Gauss-Newton optimization and thus substantially differs from BP. Furthermore, our analysis reveals a fundamental limitation of difference target propagation (DTP), a well-known variant of TP, in the realistic scenario of non-invertible neural networks. We provide a first solution to this problem through a novel reconstruction loss that improves feedback weight training, while simultaneously introducing architectural flexibility by allowing for direct feedback connections from the output to each hidden layer. Our theory is corroborated by experimental results that show significant improvements in performance and in the alignment of forward weight updates with loss gradients, compared to DTP.

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AAAI Conference 2020 Conference Paper

Random Fourier Features via Fast Surrogate Leverage Weighted Sampling

Fanghui Liu
Xiaolin Huang
Yudong Chen
Jie Yang
Johan Suykens

In this paper, we propose a fast surrogate leverage weighted sampling strategy to generate reﬁned random Fourier features for kernel approximation. Compared to the current state-ofthe-art method that uses the leverage weighted scheme (Li et al. 2019), our new strategy is simpler and more effective. It uses kernel alignment to guide the sampling process and it can avoid the matrix inversion operator when we compute the leverage function. Given n observations and s random features, our strategy can reduce the time complexity for sampling from O(ns2 +s3 ) to O(ns2 ), while achieving comparable (or even slightly better) prediction performance when applied to kernel ridge regression (KRR). In addition, we provide theoretical guarantees on the generalization performance of our approach, and in particular characterize the number of random features required to achieve statistical guarantees in KRR. Experiments on several benchmark datasets demonstrate that our algorithm achieves comparable prediction performance and takes less time cost when compared to (Li et al. 2019).

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AAMAS Conference 2018 Conference Paper

Valuing Knowledge, Information and Agency in Multi-agent Reinforcement Learning: A Case Study in Smart Buildings

Hussain Kazmi
Johan Suykens
Johan Driesen

Increasing energy efficiency in buildings can reduce costs and emissions substantially. Historically, this has been treated as a singleagent optimization problem. However, many buildings utilize the same types of thermal equipment e. g. electric heaters and hot water vessels. During operation, occupants in these buildings interact with the equipment differently thereby accelerating state-space exploration. Reinforcement learning agents learn from these interactions, recorded as sensor data, to optimize the overall energy efficiency. However, if these agents operate at a household level, they can not exploit the replicated structure in the problem. In this paper, we demonstrate that multi-agent collaboration can improve control by exploring the state-space better. We also investigate trade-offs between integrating human knowledge and additional sensors. Results show that savings of over 40% are possible with collaborative multi-agent systems making use of either expert knowledge or additional sensors with no loss of occupant comfort. We find that such multi-agent systems outperform comparable single agent systems.

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NeurIPS Conference 2007 Conference Paper

A Risk Minimization Principle for a Class of Parzen Estimators

Kristiaan Pelckmans
Johan Suykens
Bart Moor

This paper explores the use of a Maximal Average Margin (MAM) optimality principle for the design of learning algorithms. It is shown that the application of this risk minimization principle results in a class of (computationally) simple learning machines similar to the classical Parzen window classifier. A direct relation with the Rademacher complexities is established, as such facilitating analysis and providing a notion of certainty of prediction. This analysis is related to Support Vector Machines by means of a margin transformation. The power of the MAM principle is illustrated further by application to ordinal regression tasks, resulting in an $O(n)$ algorithm able to process large datasets in reasonable time.

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