Related papers: Symmetry meets AI
Image denoising methods must effectively model, implicitly or explicitly, the vast diversity of patterns and textures that occur in natural images. This is challenging, even for modern methods that leverage deep neural networks trained to…
Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this…
It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what…
Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather…
This paper proposes a new deep convolutional neural network (DCNN) architecture that learns pixel embeddings, such that pairwise distances between the embeddings can be used to infer whether or not the pixels lie on the same region. That…
Harmony in visual compositions is a concept that cannot be defined or easily expressed mathematically, even by humans. The goal of the research described in this paper was to find a numerical representation of artistic compositions with…
Artificial Intelligence significantly enhances the visual art industry by analyzing, identifying and generating digitized artistic images. This review highlights the substantial benefits of integrating geometric data into AI models,…
We define a new measure of network symmetry that is capable of capturing approximate global symmetries of networks. We apply this measure to different networks sampled from several classic network models, as well as several real-world…
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
Humans perceive and interact with hundreds of objects every day. In doing so, they need to employ mental models of these objects and often exploit symmetries in the object's shape and appearance in order to learn generalizable and…
Learning methods for relative camera pose estimation have been developed largely in isolation from classical geometric approaches. The question of how to integrate predictions from deep neural networks (DNNs) and solutions from geometric…
Motivated by the Gestalt pattern theory, and the Winograd Challenge for language understanding, we design synthetic experiments to investigate a deep learning algorithm's ability to infer simple (at least for human) visual concepts, such as…
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…
Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
Understanding the inner workings of deep neural networks (DNNs) is essential to provide trustworthy artificial intelligence techniques for practical applications. Existing studies typically involve linking semantic concepts to units or…
The attribution of artworks in general and of paintings in particular has always been an issue in art. The advent of powerful artificial intelligence models that can generate and analyze images creates new challenges for painting…
In this paper, we consider the problem of formation of a series of geometric patterns [4] by a network of oblivious mobile robots that communicate only through vision. So far, the problem has been studied in models where robots are either…
In the past few years, convolutional neural nets (CNN) have shown incredible promise for learning visual representations. In this paper, we use CNNs for the task of predicting surface normals from a single image. But what is the right…