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Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different…
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel…
In recent years, deep neural networks have revolutionized many application domains of machine learning and are key components of many critical decision or predictive processes. Therefore, it is crucial that domain specialists can understand…
Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
A network supporting deep unsupervised learning is presented. The network is an autoencoder with lateral shortcut connections from the encoder to decoder at each level of the hierarchy. The lateral shortcut connections allow the higher…
Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…
In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling-based deep network…
Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…
Deep representation learning is a crucial procedure in multimedia analysis and attracts increasing attention. Most of the popular techniques rely on convolutional neural network and require a large amount of labeled data in the training…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
Contours or closed planar curves are common in many domains. For example, they appear as object boundaries in computer vision, isolines in meteorology, and the orbits of rotating machinery. In many cases when learning from contour data,…
The deep neural networks (DNNs) have achieved great success in learning complex patterns with strong predictive power, but they are often thought of as "black box" models without a sufficient level of transparency and interpretability. It…
In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarises relevant work, much of it from the previous…
Deep neural networks have seen enormous success in various real-world applications. Beyond their predictions as point estimates, increasing attention has been focused on quantifying the uncertainty of their predictions. In this review, we…
Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use…
Graph neural networks (GNNs) have become a core paradigm for learning on relational data. In materials science, equivariant GNNs (EGNNs) have emerged as a compelling backbone for crystalline-structure prediction, owing to their ability to…
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized.…
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…