Reconstructing MRI from highly undersampled measurements is crucial for accelerating medical imaging, but is challenging due to the ill-posedness of the inverse problem. While supervised deep learning approaches have shown remarkable success, they rely on fully-sampled ground truth data, which is often impractical or impossible to obtain. Recently, numerous self-supervised methods have emerged that do not require ground truth, however, the lack of systematic comparison and standard experimental setups have hindered research. We present the first comprehensive review of loss functions from all feedforward self-supervised methods and the first benchmark on accelerated MRI reconstruction without ground truth, showing that there is a wide range in performance across methods. In addition, we propose Multi-Operator Equivariant Imaging (MO-EI), a novel framework that builds on the imaging model considered in existing methods to outperform all state-of-the-art and approaches supervised performance. Finally, to facilitate reproducible benchmarking, we provide implementations of all methods in the DeepInverse library (https://deepinv.github.io) and easy-to-use demo code at https://andrewwango.github.io/deepinv-selfsup-fastmri.

Hyperspectral imaging (HSI) is a key technology for earth observation, surveillance, medical imaging and diagnostics, astronomy and space exploration. The conventional technology for HSI in remote sensing applications is based on the push-broom scanning approach in which the camera records the spectral image of a stripe of the scene at a time, while the image is generated by the aggregation of measurements through time. In real-world airborne and spaceborne HSI instruments, some empty stripes would appear at certain locations, because platforms do not always maintain a constant programmed attitude, or have access to accurate digital elevation maps (DEM), and the travelling track is not necessarily aligned with the hyperspectral cameras at all times. This makes the enhancement of the acquired HS images from incomplete or corrupted observations an essential task. We introduce a novel HSI inpainting algorithm here, called Hyperspectral Equivariant Imaging (Hyper-EI). Hyper-EI is a self-supervised learning-based method which does not require training on extensive datasets or access to a pre-trained model. Experimental results show that the proposed method achieves state-of-the-art inpainting performance compared to the existing methods.

The field of neuromorphic computing holds great promise in terms of advancing computing efficiency and capabilities by following brain-inspired principles. However, the rich diversity of techniques employed in neuromorphic research has resulted in a lack of clear standards for benchmarking, hindering effective evaluation of the advantages and strengths of neuromorphic methods compared to traditional deep-learning-based methods. This paper presents a collaborative effort, bringing together members from academia and the industry, to define benchmarks for neuromorphic computing: NeuroBench. The goals of NeuroBench are to be a collaborative, fair, and representative benchmark suite developed by the community, for the community. In this paper, we discuss the challenges associated with benchmarking neuromorphic solutions, and outline the key features of NeuroBench. We believe that NeuroBench will be a significant step towards defining standards that can unify the goals of neuromorphic computing and drive its technological progress. Please visit neurobench.ai for the latest updates on the benchmark tasks and metrics.

In many real-world settings, only incomplete measurement data are available which can pose a problem for learning. Unsupervised learning of the signal model using a fixed incomplete measurement process is impossible in general, as there is no information in the nullspace of the measurement operator. This limitation can be overcome by using measurements from multiple operators. While this idea has been successfully applied in various applications, a precise characterization of the conditions for learning is still lacking. In this paper, we fill this gap by presenting necessary and sufficient conditions for learning the signal model which indicate the interplay between the number of distinct measurement operators $G$, the number of measurements per operator $m$, the dimension of the model $k$ and the dimension of the signals $n$. In particular, we show that generically unsupervised learning is possible if each operator obtains at least $m>k+n/G$ measurements. Our results are agnostic of the learning algorithm and have implications in a wide range of practical algorithms, from low-rank matrix recovery to deep neural networks.

This article reviews recent progress in the development of the computing framework Vector Symbolic Architectures (also known as Hyperdimensional Computing). This framework is well suited for implementation in stochastic, nanoscale hardware and it naturally expresses the types of cognitive operations required for Artificial Intelligence (AI). We demonstrate in this article that the ring-like algebraic structure of Vector Symbolic Architectures offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant in modern computing. In addition, we illustrate the distinguishing feature of Vector Symbolic Architectures, "computing in superposition," which sets it apart from conventional computing. This latter property opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. Vector Symbolic Architectures are Turing complete, as we show, and we see them acting as a framework for computing with distributed representations in myriad AI settings. This paper serves as a reference for computer architects by illustrating techniques and philosophy of VSAs for distributed computing and relevance to emerging computing hardware, such as neuromorphic computing.

Deep convolutional neural networks have been shown to be able to fit a labeling over random data while still being able to generalize well on normal datasets. Describing deep convolutional neural network capacity through the measure of spectral complexity has been recently proposed to tackle this apparent paradox. Spectral complexity correlates with GE and can distinguish networks trained on normal and random labels. We propose the first GE bound based on spectral complexity for deep convolutional neural networks and provide tighter bounds by orders of magnitude from the previous estimate. We then investigate theoretically and empirically the insensitivity of spectral complexity to invariances of modern deep convolutional neural networks, and show several limitations of spectral complexity that occur as a result.

The most common method for DNN pruning is hard thresholding of network weights, followed by retraining to recover any lost accuracy. Recently developed smart pruning algorithms use the DNN response over the training set for a variety of cost functions to determine redundant network weights, leading to less accuracy degradation and possibly less retraining time. For experiments on the total pruning time (pruning time + retraining time) we show that hard thresholding followed by retraining remains the most efficient way of reducing the number of network parameters. However smart pruning algorithms still have advantages when retraining is not possible. In this context we propose a novel smart pruning algorithm based on difference of convex functions optimisation and show that it is often orders of magnitude faster than competing approaches while achieving the lowest classification accuracy degradation. Furthermore we investigate theoretically the effect of hard thresholding on DNN accuracy. We show that accuracy degradation increases with remaining network depth from the pruned layer. We also discover a link between the latent dimensionality of the training data manifold and network robustness to hard thresholding.

Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers, often with little or no drop in classification accuracy. However, most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. We start by proposing a cheap pruning algorithm for fully connected DNN layers based on difference of convex functions (DC) optimisation, that requires little or no retraining. We then provide a theoretical analysis for the growth in the Generalization Error (GE) of a DNN for the case of bounded perturbations to the hidden layers, of which weight pruning is a special case. Our pruning method is orders of magnitude faster than competing approaches, while our theoretical analysis sheds light to previously observed problems in DNN pruning. Experiments on commnon feedforward neural networks validate our results.

Recently the generalisation error of deep neural networks has been analysed through the PAC-Bayesian framework, for the case of fully connected layers. We adapt this approach to the convolutional setting.

Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in scenarios where computational power is restricted. We consider in this paper a simple yet efficient alternative to sparse coding for feature extraction. We study a classification scheme that applies the soft-thresholding nonlinear mapping in a dictionary, followed by a linear classifier. A novel supervised dictionary learning algorithm tailored for this low complexity classification architecture is proposed. The dictionary learning problem, which jointly learns the dictionary and linear classifier, is cast as a difference of convex (DC) program and solved efficiently with an iterative DC solver. We conduct experiments on several datasets, and show that our learning algorithm that leverages the structure of the classification problem outperforms generic learning procedures. Our simple classifier based on soft-thresholding also competes with the recent sparse coding classifiers, when the dictionary is learned appropriately. The adopted classification scheme further requires less computational time at the testing stage, compared to other classifiers. The proposed scheme shows the potential of the adequately trained soft-thresholding mapping for classification and paves the way towards the development of very efficient classification methods for vision problems.