Contrastive Learning Can Find An Optimal Basis For Approximately View-Invariant Functions

Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning kernel functions that approximate a fixed positive-pair kernel. We then prove that a simple representation obtained by combining this kernel with PCA provably minimizes the worst-case approximation error of linear predictors, under a straightforward assumption that positive pairs have similar labels. Our analysis is based on a decomposition of the target function in terms of the eigenfunctions of a positive-pair Markov chain, and a surprising equivalence between these eigenfunctions and the output of Kernel PCA. We give generalization bounds for downstream linear prediction using our Kernel PCA representation, and show empirically on a set of synthetic tasks that applying Kernel PCA to contrastive learning models can indeed approximately recover the Markov chain eigenfunctions, although the accuracy depends on the kernel parameterization as well as on the augmentation strength.Comment: Published at ICLR 202

Stein Variational Gradient Descent with Multiple Kernel

Stein variational gradient descent (SVGD) and its variants have shown promising successes in approximate inference for complex distributions. In practice, we notice that the kernel used in SVGD-based methods has a decisive effect on the empirical performance. Radial basis function (RBF) kernel with median heuristics is a common choice in previous approaches, but unfortunately this has proven to be sub-optimal. Inspired by the paradigm of Multiple Kernel Learning (MKL), our solution to this flaw is using a combination of multiple kernels to approximate the optimal kernel, rather than a single one which may limit the performance and flexibility. Specifically, we first extend Kernelized Stein Discrepancy (KSD) to its multiple kernels view called Multiple Kernelized Stein Discrepancy (MKSD) and then leverage MKSD to construct a general algorithm Multiple Kernel SVGD (MK-SVGD). Further, MKSVGD can automatically assign a weight to each kernel without any other parameters, which means that our method not only gets rid of optimal kernel dependence but also maintains computational efficiency. Experiments on various tasks and models demonstrate that our proposed method consistently matches or outperforms the competing methods

Client-server multi-task learning from distributed datasets

A client-server architecture to simultaneously solve multiple learning tasks from distributed datasets is described. In such architecture, each client is associated with an individual learning task and the associated dataset of examples. The goal of the architecture is to perform information fusion from multiple datasets while preserving privacy of individual data. The role of the server is to collect data in real-time from the clients and codify the information in a common database. The information coded in this database can be used by all the clients to solve their individual learning task, so that each client can exploit the informative content of all the datasets without actually having access to private data of others. The proposed algorithmic framework, based on regularization theory and kernel methods, uses a suitable class of mixed effect kernels. The new method is illustrated through a simulated music recommendation system

Kernel Modulation: A Parameter-Efficient Method for Training Convolutional Neural Networks

Deep Neural Networks, particularly Convolutional Neural Networks (ConvNets), have achieved incredible success in many vision tasks, but they usually require millions of parameters for good accuracy performance. With increasing applications that use ConvNets, updating hundreds of networks for multiple tasks on an embedded device can be costly in terms of memory, bandwidth, and energy. Approaches to reduce this cost include model compression and parameter-efficient models that adapt a subset of network layers for each new task. This work proposes a novel parameter-efficient kernel modulation (KM) method that adapts all parameters of a base network instead of a subset of layers. KM uses lightweight task-specialized kernel modulators that require only an additional 1.4% of the base network parameters. With multiple tasks, only the task-specialized KM weights are communicated and stored on the end-user device. We applied this method in training ConvNets for Transfer Learning and Meta-Learning scenarios. Our results show that KM delivers up to 9% higher accuracy compared to other parameter-efficient methods on the Transfer Learning benchmark

Kernel Modulation: A Parameter-Efficient Method for Training Convolutional Neural Networks

Deep Neural Networks, particularly Convolutional Neural Networks (ConvNets), have achieved incredible success in many vision tasks, but they usually require millions of parameters for good accuracy performance. With increasing applications that use ConvNets, updating hundreds of networks for multiple tasks on an embedded device can be costly in terms of memory, bandwidth, and energy. Approaches to reduce this cost include model compression and parameter-efficient models that adapt a subset of network layers for each new task. This work proposes a novel parameter-efficient kernel modulation (KM) method that adapts all parameters of a base network instead of a subset of layers. KM uses lightweight task-specialized kernel modulators that require only an additional 1.4% of the base network parameters. With multiple tasks, only the task-specialized KM weights are communicated and stored on the end-user device. We applied this method in training ConvNets for Transfer Learning and Meta-Learning scenarios. Our results show that KM delivers up to 9% higher accuracy than other parameter-efficient methods on the Transfer Learning benchmark.Comment: Accepted at 2022 26th International Conference on Pattern Recognition (ICPR

Generalizing Supervised Deep Learning MRI Reconstruction to Multiple and Unseen Contrasts using Meta-Learning Hypernetworks

Meta-learning has recently been an emerging data-efficient learning technique for various medical imaging operations and has helped advance contemporary deep learning models. Furthermore, meta-learning enhances the knowledge generalization of the imaging tasks by learning both shared and discriminative weights for various configurations of imaging tasks. However, existing meta-learning models attempt to learn a single set of weight initializations of a neural network that might be restrictive for multimodal data. This work aims to develop a multimodal meta-learning model for image reconstruction, which augments meta-learning with evolutionary capabilities to encompass diverse acquisition settings of multimodal data. Our proposed model called KM-MAML (Kernel Modulation-based Multimodal Meta-Learning), has hypernetworks that evolve to generate mode-specific weights. These weights provide the mode-specific inductive bias for multiple modes by re-calibrating each kernel of the base network for image reconstruction via a low-rank kernel modulation operation. We incorporate gradient-based meta-learning (GBML) in the contextual space to update the weights of the hypernetworks for different modes. The hypernetworks and the reconstruction network in the GBML setting provide discriminative mode-specific features and low-level image features, respectively. Experiments on multi-contrast MRI reconstruction show that our model, (i) exhibits superior reconstruction performance over joint training, other meta-learning methods, and context-specific MRI reconstruction methods, and (ii) better adaptation capabilities with improvement margins of 0.5 dB in PSNR and 0.01 in SSIM. Besides, a representation analysis with U-Net shows that kernel modulation infuses 80% of mode-specific representation changes in the high-resolution layers. Our source code is available at https://github.com/sriprabhar/KM-MAML/.Comment: Accepted for publication in Elsevier Applied Soft Computing Journal, 36 pages, 18 figure

Efficient Multi-Template Learning for Structured Prediction

Conditional random field (CRF) and Structural Support Vector Machine (Structural SVM) are two state-of-the-art methods for structured prediction which captures the interdependencies among output variables. The success of these methods is attributed to the fact that their discriminative models are able to account for overlapping features on the whole input observations. These features are usually generated by applying a given set of templates on labeled data, but improper templates may lead to degraded performance. To alleviate this issue, in this paper, we propose a novel multiple template learning paradigm to learn structured prediction and the importance of each template simultaneously, so that hundreds of arbitrary templates could be added into the learning model without caution. This paradigm can be formulated as a special multiple kernel learning problem with exponential number of constraints. Then we introduce an efficient cutting plane algorithm to solve this problem in the primal, and its convergence is presented. We also evaluate the proposed learning paradigm on two widely-studied structured prediction tasks, \emph{i.e.} sequence labeling and dependency parsing. Extensive experimental results show that the proposed method outperforms CRFs and Structural SVMs due to exploiting the importance of each template. Our complexity analysis and empirical results also show that our proposed method is more efficient than OnlineMKL on very sparse and high-dimensional data. We further extend this paradigm for structured prediction using generalized $p$-block norm regularization with $p>1$, and experiments show competitive performances when $p \in [1,2)$