Related papers: Barcodes as Summary of Loss Function Topology

We study the loss surface of a feed-forward neural network with ReLU non-linearities, regularized with weight decay. We show that the regularized loss function is piecewise strongly convex on an important open set which contains, under some…

We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…

We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…

In this paper, we propose a cascaded non-local neural network for point cloud segmentation. The proposed network aims to build the long-range dependencies of point clouds for the accurate segmentation. Specifically, we develop a novel…

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating…

Evaluating the performance of generative models in image synthesis is a challenging task. Although the Fr\'echet Inception Distance is a widely accepted evaluation metric, it integrates different aspects (e.g., fidelity and diversity) of…

Marking tumors and organs is a challenging task suffering from both inter- and intra-observer variability. The literature quantifies observer variability by generating consensus among multiple experts when they mark the same image.…

We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…

Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…

Recent research shows that sublevel sets of the loss surfaces of overparameterized networks are connected, exactly or approximately. We describe and compare experimentally a panel of methods used to connect two low-loss points by a low-loss…

Neuroscientific data analysis has classically involved methods for statistical signal and image processing, drawing on linear algebra and stochastic process theory. However, digitized neuroanatomical data sets containing labelled neurons,…

Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original…

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

Neural network minima are often connected by curves along which train and test loss remain nearly constant, a phenomenon known as mode connectivity. While this property has enabled applications such as model merging and fine-tuning, its…

Image Segmentation has been an active field of research as it has a wide range of applications, ranging from automated disease detection to self-driving cars. In the past five years, various papers came up with different objective loss…

The decoding of error syndromes of surface codes with classical algorithms may slow down quantum computation. To overcome this problem it is possible to implement decoding algorithms based on artificial neural networks. This work reports a…

Neuroscientific data analysis has traditionally relied on linear algebra and stochastic process theory. However, the tree-like shapes of neurons cannot be described easily as points in a vector space (the subtraction of two neuronal shapes…

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving…

Neural network algorithms simulated on standard computing platforms typically make use of high resolution weights, with floating-point notation. However, for dedicated hardware implementations of such algorithms, fixed-point synaptic…