Related papers: Barcodes as Summary of Loss Function Topology

The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…

Boolean network tomography is a powerful tool to infer the state (working/failed) of individual nodes from path-level measurements obtained by egde-nodes. We consider the problem of optimizing the capability of identifying network failures…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…

We study sublevel set and superlevel set persistent homology on discrete functions through the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains. Finite ordered sets also serve as the codomain of our…

Designing proper loss functions is essential in training deep networks. Especially in the field of semantic segmentation, various evaluation metrics have been proposed for diverse scenarios. Despite the success of the widely adopted…

The loss landscape of neural networks is a critical aspect of their training, and understanding its properties is essential for improving their performance. In this paper, we investigate how the loss surface changes when the sample size…

The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…

Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural…

A linear error correcting code is a subspace of a finite-dimensional space over a finite field with a fixed coordinate system. Such a code is said to be locally recoverable with locality $r$ if, for every coordinate, its value at a codeword…

Loss functions are error metrics that quantify the difference between a prediction and its corresponding ground truth. Fundamentally, they define a functional landscape for traversal by gradient descent. Although numerous loss functions…

Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…

We investigate the topics of sensitivity and robustness in feedforward and convolutional neural networks. Combining energy landscape techniques developed in computational chemistry with tools drawn from formal methods, we produce empirical…

Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…

State-of-the-art methods for quantifying wear in cylinder liners of large internal combustion engines require disassembly and cutting of the liner. This is followed by laboratory-based high-resolution microscopic surface depth measurement…

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

Quantum Neural Networks (QNNs), or the so-called variational quantum circuits, are important quantum applications both because of their similar promises as classical neural networks and because of the feasibility of their implementation on…

We look at the internal structure of neural networks which is usually treated as a black box. The easiest and the most comprehensible thing to do is to look at a binary classification and try to understand the approach a neural network…