Fast end-to-end learning on protein surfaces

Proteins' biological functions are defined by the geometric and chemical structure of their 3D molecular surfaces. Recent works have shown that geometric deep learning can be used on mesh-based representations of proteins to identify potential functional sites, such as binding targets for potential drugs. Unfortunately though, the use of meshes as the underlying representation for protein structure has multiple drawbacks including the need to pre-compute the input features and mesh connectivities. This becomes a bottle-neck for many important tasks in protein science. In this paper, we present a new framework for deep learning on protein structures that addresses these limitations. Among the key advantages of our method are the computation and sampling of the molecular surface on-the-fly from the underlying atomic point cloud and a novel efficient geometric convolutional layer. As a result, we are able to process large collections of proteins in an end-to-end fashion, taking as the sole input the raw 3D coordinates and chemical types of their atoms, eliminating the need for any hand-crafted pre-computed features. To showcase the performance of our approach, we test it on two tasks in the field of protein structural bioinformatics: the identification of interaction sites and the prediction of protein-protein interactions. On both tasks, we achieve state-of-the-art performance with much faster run times and fewer parameters than previous models. These results will considerably ease the deployment of deep learning methods in protein science and open the door for end-to-end differentiable approaches in protein modeling tasks such as function prediction and design.

Empirical study of the topology and geometry of deep networks

Alhussein Fawzi, Pascal Frossard, Seyed Mohsen Moosavi Dezfooli

The goal of this paper is to analyze the geometric properties of deep neural network image classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical study, we show that state-of-the-art deep nets learn connected classification regions, and that the decision boundary in the vicinity of datapoints is flat along most directions. We further draw an essential connection between two seemingly unrelated properties of deep networks: their sensitivity to additive perturbations of the inputs, and the curvature of their decision boundary. The directions where the decision boundary is curved in fact characterize the directions to which the classifier is the most vulnerable. We finally leverage a fundamental asymmetry in the curvature of the decision boundary of deep nets, and propose a method to discriminate between original images, and images perturbed with small adversarial examples. We show the effectiveness of this purely geometric approach for detecting small adversarial perturbations in images, and for recovering the labels of perturbed images.

2018

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph-structured descriptions. In such settings, it is desirable to design representation learning algorithms that can take into account the information captured by the underlying structure. This thesis focuses on providing new methods to ingrain geometrical information in end-to-end deep learning architectures for graphs through the use of elements from Optimal Transport theory.First, we consider the setting where the data can be described by a fixed graph. In this setting, each datapoint corresponds to a node of the graph and the edges among nodes signify their pairwise relations. We propose an autoencoder architecture that consists of a linear layer in the encoder and a novel Wasserstein barycentric layer at the decoder. Our proposed barycentric layer takes into account the underlying geometry through the diffusion distance of the graph and provides a way to obtain structure-aware, non-linear interpolations, which lead to directly interpretable node embeddings that are stable to perturbations of the graph structure. Further, the embeddings obtained with our proposed autoencoder achieve competitive or superior results compared to state-of-the-art methods in node classification tasks.Second, we consider the setting where the data consist of multiple graphs. In that setting, the graphs can be of varying size and, therefore, a global pooling operation is needed in order to obtain representations of fixed size and enable end-to-end learning with deep networks. We propose a global pooling operation that optimally preserves the statistical properties of the representations. In order to do so, we take into account the geometry of the representation space and introduce a global pooling layer that minimizes the Wasserstein distance between a graph representation and its pooled counterpart, of fixed size. This is achieved by performing a Wasserstein gradient flow with respect to the pooled representation. Our proposed method demonstrates promising results in the task of graph classification.Overall, in this thesis we provide new methods for incorporating geometrical information in end-to-end deep learning architectures for graph structured data. We believe that our proposals will contribute to the development of algorithms that learn meaningful representations and that take fully into account the geometry of the data under consideration.

EPFL2022

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

EPFL2022