We present a new deep unfolding network for analysis-sparsity-based Compressed Sensing. The proposed network coined Decoding Network (DECONET) jointly learns a decoder that reconstructs vectors from their incomplete, noisy measurements and a redundant sparsifying analysis operator, which is shared across the layers of DECONET. Moreover, we formulate the hypothesis class of DECONET and estimate its associated Rademacher complexity. Then, we use this estimate to deliver meaningful upper bounds for the generalization error of DECONET. Finally, the validity of our theoretical results is assessed and comparisons to state-of-the-art unfolding networks are made, on both synthetic and real-world datasets. Experimental results indicate that our proposed network outperforms the baselines, consistently for all datasets, and its behaviour complies with our theoretical findings.

Unfolding networks have shown promising results in the Compressed Sensing (CS) field. Yet, the investigation of their generalization ability is still in its infancy. In this paper, we perform generalization analysis of a state-of-the-art ADMM-based unfolding network, which jointly learns a decoder for CS and a sparsifying redundant analysis operator. To this end, we first impose a structural constraint on the learnable sparsifier, which parametrizes the network's hypothesis class. For the latter, we estimate its Rademacher complexity. With this estimate in hand, we deliver generalization error bounds for the examined network. Finally, the validity of our theory is assessed and numerical comparisons to a state-of-the-art unfolding network are made, on synthetic and real-world datasets. Our experimental results demonstrate that our proposed framework complies with our theoretical findings and outperforms the baseline, consistently for all datasets.

Recent advances in the understanding of Generative Adversarial Networks (GANs) have led to remarkable progress in visual editing and synthesis tasks, capitalizing on the rich semantics that are embedded in the latent spaces of pre-trained GANs. However, existing methods are often tailored to specific GAN architectures and are limited to either discovering global semantic directions that do not facilitate localized control, or require some form of supervision through manually provided regions or segmentation masks. In this light, we present an architecture-agnostic approach that jointly discovers factors representing spatial parts and their appearances in an entirely unsupervised fashion. These factors are obtained by applying a semi-nonnegative tensor factorization on the feature maps, which in turn enables context-aware local image editing with pixel-level control. In addition, we show that the discovered appearance factors correspond to saliency maps that localize concepts of interest, without using any labels. Experiments on a wide range of GAN architectures and datasets show that, in comparison to the state of the art, our method is far more efficient in terms of training time and, most importantly, provides much more accurate localized control. Our code is available at: https://github.com/james-oldfield/PandA.

Building subject-independent deep learning models for EEG decoding faces the challenge of strong covariate-shift across different datasets, subjects and recording sessions. Our approach to address this difficulty is to explicitly align feature distributions at various layers of the deep learning model, using both simple statistical techniques as well as trainable methods with more representational capacity. This follows in a similar vein as covariance-based alignment methods, often used in a Riemannian manifold context. The methodology proposed herein won first place in the 2021 Benchmarks in EEG Transfer Learning (BEETL) competition, hosted at the NeurIPS conference. The first task of the competition consisted of sleep stage classification, which required the transfer of models trained on younger subjects to perform inference on multiple subjects of older age groups without personalized calibration data, requiring subject-independent models. The second task required to transfer models trained on the subjects of one or more source motor imagery datasets to perform inference on two target datasets, providing a small set of personalized calibration data for multiple test subjects.

We propose defensive tensorization, an adversarial defence technique that leverages a latent high-order factorization of the network. The layers of a network are first expressed as factorized tensor layers. Tensor dropout is then applied in the latent subspace, therefore resulting in dense reconstructed weights, without the sparsity or perturbations typically induced by the randomization.Our approach can be readily integrated with any arbitrary neural architecture and combined with techniques like adversarial training. We empirically demonstrate the effectiveness of our approach on standard image classification benchmarks. We validate the versatility of our approach across domains and low-precision architectures by considering an audio classification task and binary networks. In all cases, we demonstrate improved performance compared to prior works.

Deep generative models rely on their inductive bias to facilitate generalization, especially for problems with high dimensional data, like images. However, empirical studies have shown that variational autoencoders (VAE) and generative adversarial networks (GAN) lack the generalization ability that occurs naturally in human perception. For example, humans can visualize a woman smiling after only seeing a smiling man. On the contrary, the standard conditional VAE (cVAE) is unable to generate unseen attribute combinations. To this end, we extend cVAE by introducing a multilinear latent conditioning framework that captures the multiplicative interactions between the attributes. We implement two variants of our model and demonstrate their efficacy on MNIST, Fashion-MNIST and CelebA. Altogether, we design a novel conditioning framework that can be used with any architecture to synthesize unseen attribute combinations.

Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $\Pi$-Nets, a new class of DCNNs. $\Pi$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that $\Pi$-Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $\Pi$-Nets produce state-of-the-art results in three challenging tasks, i.e. image generation, face verification and 3D mesh representation learning.

Generative Adversarial Networks (GANs) have become the gold standard when it comes to learning generative models that can describe intricate, high-dimensional distributions. Since their advent, numerous variations of GANs have been introduced in the literature, primarily focusing on utilization of novel loss functions, optimization/regularization strategies and architectures. In this work, we take an orthogonal approach to the above and turn our attention to the generator. We propose to model the data generator by means of a high-order polynomial using tensorial factors. We design a hierarchical decomposition of the polynomial and demonstrate how it can be efficiently implemented by a neural network. We show, for the first time, that by using our decomposition a GAN generator can approximate the data distribution by only using linear/convolution blocks without using any activation functions. Finally, we highlight that PolyGAN can be easily adapted and used along-side all major GAN architectures. In an extensive series of quantitative and qualitative experiments, PolyGAN improves upon the state-of-the-art by a significant margin.

With the unprecedented success of deep convolutional neural networks came the quest for training always deeper networks. However, while deeper neural networks give better performance when trained appropriately, that depth also translates in memory and computation heavy models, typically with tens of millions of parameters. Several methods have been proposed to leverage redundancies in the network to alleviate this complexity. Either a pretrained network is compressed, e.g. using a low-rank tensor decomposition, or the architecture of the network is directly modified to be more effective. In this paper, we study both approaches in a unified framework, under the lens of tensor decompositions. We show how tensor decomposition applied to the convolutional kernel relates to efficient architectures such as MobileNet. Moreover, we propose a tensor-based method for efficient higher order convolutions, which can be used as a plugin replacement for N-dimensional convolutions. We demonstrate their advantageous properties both theoretically and empirically for image classification, for both 2D and 3D convolutional networks.

Over-parametrization of deep neural networks has recently been shown to be key to their successful training. However, it also renders them prone to overfitting and makes them expensive to store and train. Tensor regression networks significantly reduce the number of effective parameters in deep neural networks while retaining accuracy and the ease of training. They replace the flattening and fully-connected layers with a tensor regression layer, where the regression weights are expressed through the factors of a low-rank tensor decomposition. In this paper, to further improve tensor regression networks, we propose a novel stochastic rank-regularization. It consists of a novel randomized tensor sketching method to approximate the weights of tensor regression layers. We theoretically and empirically establish the link between our proposed stochastic rank-regularization and the dropout on low-rank tensor regression. Extensive experimental results with both synthetic data and real world datasets (i.e., CIFAR-100 and the UK Biobank brain MRI dataset) support that the proposed approach i) improves performance in both classification and regression tasks, ii) decreases overfitting, iii) leads to more stable training and iv) improves robustness to adversarial attacks and random noise.