相关论文: How deep learning works --The geometry of deep lea…

This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…

Deep neural network algorithms are difficult to analyze because they lack structure allowing to understand the properties of underlying transforms and invariants. Multiscale hierarchical convolutional networks are structured deep…

In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…

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 Learning is a state-of-the-art technique to make inference on extensive or complex data. As a black box model due to their multilayer nonlinear structure, Deep Neural Networks are often criticized to be non-transparent and their…

Deep learning models are yielding increasingly better performances thanks to multiple factors. To be successful, model may have large number of parameters or complex architectures and be trained on large dataset. This leads to large…

Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

Deep neural networks have achieved remarkable success, yet our understanding of how they learn remains limited. These models can learn high-dimensional tasks, which is generally statistically intractable due to the curse of dimensionality.…

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

In many contexts, simpler models are preferable to more complex models and the control of this model complexity is the goal for many methods in machine learning such as regularization, hyperparameter tuning and architecture design. In deep…

Recently, there has been a surge of interest in combining deep learning models with reasoning in order to handle more sophisticated learning tasks. In many cases, a reasoning task can be solved by an iterative algorithm. This algorithm is…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We…

We propose DeepV2D, an end-to-end deep learning architecture for predicting depth from video. DeepV2D combines the representation ability of neural networks with the geometric principles governing image formation. We compose a collection of…

We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps.…