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We present a new method of self-supervised learning and knowledge distillation based on the multi-views and multi-representations (MV-MR). The MV-MR is based on the maximization of dependence between learnable embeddings from augmented and non-augmented views, jointly with the maximization of dependence between learnable embeddings from augmented view and multiple non-learnable representations from non-augmented view. We show that the proposed method can be used for efficient self-supervised classification and model-agnostic knowledge distillation. Unlike other self-supervised techniques, our approach does not use any contrastive learning, clustering, or stop gradients. MV-MR is a generic framework allowing the incorporation of constraints on the learnable embeddings via the usage of image multi-representations as regularizers. Along this line, knowledge distillation is considered a particular case of such a regularization. MV-MR provides the state-of-the-art performance on the STL10 and ImageNet-1K datasets among non-contrastive and clustering-free methods. We show that a lower complexity ResNet50 model pretrained using proposed knowledge distillation based on the CLIP ViT model achieves state-of-the-art performance on STL10 linear evaluation. The code is available at: //github.com/vkinakh/mv-mr

This article aims to study efficient/trace optimal designs for crossover trials with multiple responses recorded from each subject in the time periods. A multivariate fixed effects model is proposed with direct and carryover effects corresponding to the multiple responses. The corresponding error dispersion matrix is chosen to be either of the proportional or the generalized Markov covariance type, permitting the existence of direct and cross-correlations within and between the multiple responses. The corresponding information matrices for direct effects under the two types of dispersions are used to determine efficient designs. The efficiency of orthogonal array designs of Type $I$ and strength $2$ is investigated for a wide choice of covariance functions, namely, Mat($0.5$), Mat($1.5$) and Mat($\infty$). To motivate these multivariate crossover designs, a gene expression dataset in a $3 \times 3$ framework is utilized.

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning.

We introduce GUIDE, a novel continual learning approach that directs diffusion models to rehearse samples at risk of being forgotten. Existing generative strategies combat catastrophic forgetting by randomly sampling rehearsal examples from a generative model. Such an approach contradicts buffer-based approaches where sampling strategy plays an important role. We propose to bridge this gap by incorporating classifier guidance into the diffusion process to produce rehearsal examples specifically targeting information forgotten by a continuously trained model. This approach enables the generation of samples from preceding task distributions, which are more likely to be misclassified in the context of recently encountered classes. Our experimental results show that GUIDE significantly reduces catastrophic forgetting, outperforming conventional random sampling approaches and surpassing recent state-of-the-art methods in continual learning with generative replay.

This paper presents a novel approach for constructing graph neural networks equivariant to 2D rotations and translations and leveraging them as PDE surrogates on non-gridded domains. We show that aligning the representations with the principal axis allows us to sidestep many constraints while preserving SE(2) equivariance. By applying our model as a surrogate for fluid flow simulations and conducting thorough benchmarks against non-equivariant models, we demonstrate significant gains in terms of both data efficiency and accuracy.

We introduce a method for computing immediately human interpretable yet accurate classifiers from tabular data. The classifiers obtained are short Boolean formulas, computed via first discretizing the original data and then using feature selection coupled with a very fast algorithm for producing the best possible Boolean classifier for the setting. We demonstrate the approach via 13 experiments, obtaining results with accuracies comparable to ones obtained via random forests, XGBoost, and existing results for the same datasets in the literature. In most cases, the accuracy of our method is in fact similar to that of the reference methods, even though the main objective of our study is the immediate interpretability of our classifiers. We also prove a new result on the probability that the classifier we obtain from real-life data corresponds to the ideally best classifier with respect to the background distribution the data comes from.

Semi-implicit spectral deferred correction (SDC) methods provide a systematic approach to construct time integration methods of arbitrarily high order for nonlinear evolution equations including conservation laws. They converge towards $A$- or even $L$-stable collocation methods, but are often not sufficiently robust themselves. In this paper, a family of SDC methods inspired by an implicit formulation of the Lax-Wendroff method is developed. Compared to fully implicit approaches, the methods have the advantage that they only require the solution of positive definite or semi-definite linear systems. Numerical evidence suggests that the proposed semi-implicit SDC methods with Radau points are $L$-stable up to order 11 and require very little diffusion for orders 13 and 15. The excellent stability and accuracy of these methods is confirmed by numerical experiments with 1D conservation problems, including the convection-diffusion, Burgers, Euler and Navier-Stokes equations.

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity of knowledge, with endeavours to extend this knowledge without targeting the original task resulting in a catastrophic forgetting. Continual learning shifts this paradigm towards networks that can continually accumulate knowledge over different tasks without the need to retrain from scratch. We focus on task incremental classification, where tasks arrive sequentially and are delineated by clear boundaries. Our main contributions concern 1) a taxonomy and extensive overview of the state-of-the-art, 2) a novel framework to continually determine the stability-plasticity trade-off of the continual learner, 3) a comprehensive experimental comparison of 11 state-of-the-art continual learning methods and 4 baselines. We empirically scrutinize method strengths and weaknesses on three benchmarks, considering Tiny Imagenet and large-scale unbalanced iNaturalist and a sequence of recognition datasets. We study the influence of model capacity, weight decay and dropout regularization, and the order in which the tasks are presented, and qualitatively compare methods in terms of required memory, computation time, and storage.

Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related, and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the Predictive, Descriptive, Relevant (PDR) framework for discussing interpretations. The PDR framework provides three overarching desiderata for evaluation: predictive accuracy, descriptive accuracy and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post-hoc categories, with sub-groups including sparsity, modularity and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often under-appreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods.