A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete unde…
This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.
problem Analyzing the function space of finite neural networks and providing error bounds.
method Applying sampling theory to finite neural networks with non-expansive activation functions, considering both deterministic and random sampling.
result Novel error bounds for univariate neural networks under band-limited input assumption, highlighting the advantage of deterministic uniform sampling.
The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network's own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of th…
Link prediction in networks is typically accomplished by estimating or ranking the probabilities of edges for all pairs of nodes. In practice, especially for social networks, the data are often collected by egocentric sampling, which means selecting a subset of nodes and recording all of their edges. This sampling mech…
We introduce the adversarially learned inference (ALI) model, which jointly learns a generation network and an inference network using an adversarial process. The generation network maps samples from stochastic latent variables to the data space while the inference network maps training examples in data space to the sp…
The paper proposes a neural network architecture inspired by Langevin Monte Carlo for sampling from target distributions.
problem Sampling from complex target distributions efficiently.
method A neural network architecture inspired by Langevin Monte Carlo is proposed to map samples from a simple reference distribution to samples from the target.
result The proposed neural network architecture achieves approximation rates in the Wasserstein-2 distance for smooth, log-concave target distributions.
Infrastructure monitoring is critical for safe operations and sustainability. Water distribution networks (WDNs) are large-scale networked critical systems with complex cascade dynamics which are difficult to predict. Ubiquitous monitoring is expensive and a key challenge is to infer the contaminant dynamics from parti…
The robustness and integrity of IP networks require efficient tools for traffic monitoring and analysis, which scale well with traffic volume and network size. We address the problem of optimal large-scale flow monitoring of computer networks under resource constraints. We propose a stochastic optimization framework wh…
Deep Neural Networks for image classification have been found to be vulnerable to adversarial samples, which consist of sub-perceptual noise added to a benign image that can easily fool trained neural networks, posing a significant risk to their commercial deployment. In this work, we analyze adversarial samples throug…
We consider training a deep neural network to generate samples from an unknown distribution given i.i.d. data. We frame learning as an optimization minimizing a two-sample test statistic---informally speaking, a good generator network produces samples that cause a two-sample test to fail to reject the null hypothesis. …
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the …
Training deep neural networks is known to require a large number of training samples. However, in many applications only few training samples are available. In this work, we tackle the issue of training neural networks for classification task when few training samples are available. We attempt to solve this issue by pr…
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that the algorithm scales to large samples. This paper proposes a two-sample statistic …
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the friendship networks on Facebook and LinkedIn. The practical approach to such prob…
Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.
problem Understanding when and why Transformers outperform other neural network architectures.
method Analyzing a sequence-to-sequence data generating model with dynamic sparsity, proving sample complexity differences between feedforward, recurrent, and Transformers.
result Transformers can learn dynamic sparsity models with lower sample complexity than feedforward and recurrent networks.