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.
New method grows deep networks efficiently by dynamically pruning and growing layers.
It is well-known that neural networks are universal approximators, but that deeper networks tend in practice to be more powerful than shallower ones. We shed light on this by proving that the total number of neurons required to approximate natural classes of multivariate polynomials of variables grows only line…
New causal models for growing networks avoid node deletion constraints.
Depth is a key component of Deep Neural Networks (DNNs), however, designing depth is heuristic and requires many human efforts. We propose AutoGrow to automate depth discovery in DNNs: starting from a shallow seed architecture, AutoGrow grows new layers if the growth improves the accuracy; otherwise, stops growing and …
We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size …
Study on neural networks' performance under different normalizations as N grows.
Large deviation principle for deep neural networks with ReLU activation.
We propose a new method for learning deep neural network models that is based on a greedy learning approach: we add one basis function at a time, and a new basis function is generated as a non-linear activation function applied to a linear combination of the previous basis functions. Such a method (growing deep neural …
Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisi…
We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with a variant of the popular SIR model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term \textbf{rumor centrality…
ReLU networks don't exponentially distort curve lengths as previously thought.
We develop a progressive training approach for neural networks which adaptively grows the network structure by splitting existing neurons to multiple off-springs. By leveraging a functional steepest descent idea, we derive a simple criterion for deciding the best subset of neurons to split and a splitting gradient for …
Wide Bayesian neural networks have a simpler weight posterior, leading to faster MCMC sampling.
We introduce a novel generative autoencoder network model that learns to encode and reconstruct images with high quality and resolution, and supports smooth random sampling from the latent space of the encoder. Generative adversarial networks (GANs) are known for their ability to simulate random high-quality images, bu…
Recent research on Bitcoin Transaction Networks reveals a growing, sparse, and core-periphery structure.
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationa…
StreamBP optimally detects communities in growing networks.
Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representation and graph generation, most of them can not handle isolated new nod…
Study on optimal ReLU networks with weight decay for interpolation.
Study on critical points in random neural networks, revealing three regimes based on activation function.
Time series data constitutes a distinct and growing problem in machine learning. As the corpus of time series data grows larger, deep models that simultaneously learn features and classify with these features can be intractable or suboptimal. In this paper, we present feature learning via long short term memory (LSTM) …
Over the past decade, Deep Convolutional Neural Networks (DCNNs) have shown remarkable performance in most computer vision tasks. These tasks traditionally use a fixed dataset, and the model, once trained, is deployed as is. Adding new information to such a model presents a challenge due to complex training issues, suc…
Augmenting a neural network with memory that can grow without growing the number of trained parameters is a recent powerful concept with many exciting applications. We propose a design of memory augmented neural networks (MANNs) called Labeled Memory Networks (LMNs) suited for tasks requiring online adaptation in class…
Two-layer CNNs can overfit well if initialized correctly.
Study finds root vertex in large networks with high probability.
We consider the problem of accelerating distributed optimization in multi-agent networks by sequentially adding edges. Specifically, we extend the distributed dual averaging (DDA) subgradient algorithm to evolving networks of growing connectivity and analyze the corresponding improvement in convergence rate. It is know…
Two-layer neural networks can overfit without increasing risk when data is noisy.
Deep neural networks approximate option prices in high-dimensional Lévy models efficiently.
It is well-known that the expressivity of a neural network depends on its architecture, with deeper networks expressing more complex functions. In the case of networks that compute piecewise linear functions, such as those with ReLU activation, the number of distinct linear regions is a natural measure of expressivity.…
New findings connect shaped and unshaped neural networks using differential equations.
Deep networks with orthogonal weights show stable fluctuations, improving generalization and training speed.
Gradient descent with growing learning rate enables learning non-linear features in neural networks.
Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models also increases. We introduce a technique to train deep neural networks using hal…
We consider the problem of inferring the input and hidden variables of a stochastic multi-layer neural network from an observation of the output. The hidden variables in each layer are represented as matrices. This problem applies to signal recovery via deep generative prior models, multi-task and mixed regression and …
Develops a new method to create object models from medical images.
Training very deep networks is an important open problem in machine learning. One of many difficulties is that the norm of the back-propagated error gradient can grow or decay exponentially. Here we show that training very deep feed-forward networks (FFNs) is not as difficult as previously thought. Unlike when back-pro…
Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially…
Researchers develop a neural network that learns like humans, overcoming forgetting and structure issues.
Differentiable NAS frameworks grow networks wider and deeper, revealing biases in wiring evolution.
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual network datasets continue to grow in size, it is necessary to develop models tha…
A plethora of networks is being collected in a growing number of fields, including disease transmission, international relations, social interactions, and others. As data streams continue to grow, the complexity associated with these highly multidimensional connectivity data presents novel challenges. In this paper, we…
Sharp representation theorems show depth benefits for ReLU networks.
GCNs converge and remain stable on large random graphs, revealing geometric insights.
In recent years, there is a growing interest in learning Bayesian networks with continuous variables. Learning the structure of such networks is a computationally expensive procedure, which limits most applications to parameter learning. This problem is even more acute when learning networks with hidden variables. We p…
Study reveals how Fisher information changes with network depth, finding it grows linearly.
Deep learning speeds up gravitational wave analysis.
New method reduces clustering time and improves accuracy.
Mathematical methods characterize RNNs' asymptotics as hidden units and data grow.