arXiv research

This paper examines properties of feedforward graphs to improve neural network performance.

PCGs encompass a broader range of neural networks.

Develops a smooth operator framework for analyzing neural network representations.

A unique challenge in predictive model building for omics data has been the small number of samples $(n)$ versus the large amount of features $(p)$. This "$n\ll p$" property brings difficulties for disease outcome classification using deep learning techniques. Sparse learning by incorporating external gene network info…

We provide a characterization of two types of directed homology for fully-connected, feedforward neural network architectures. These exact characterizations of the directed homology structure of a neural network architecture are the first of their kind. We show that the directed flag homology of deep networks reduces t…

Neural networks' feature geometry evolves like discrete Ricci flow.

Neural networks with DAGs show linearity as width increases.

Computing shortest path distances between nodes lies at the heart of many graph algorithms and applications. Traditional exact methods such as breadth-first-search (BFS) do not scale up to contemporary, rapidly evolving today's massive networks. Therefore, it is required to find approximation methods to enable scalable…

Neural networks extrapolate poorly in simple tasks but succeed in complex ones.

Gene expression data represents a unique challenge in predictive model building, because of the small number of samples $(n)$ compared to the huge amount of features $(p)$. This "$n<<p$" property has hampered application of deep learning techniques for disease outcome classification. Sparse learning by incorporating ex…

In this study, we propose a novel deep neural network and its supervised learning method that uses a feedforward supervisory signal. The method is inspired by the human visual system and performs human-like association-based learning without any backward error propagation. The feedforward supervisory signal that produc…

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and cannot be easily accelerated with parallel computing. To enable parallelization, w…

Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.

The prediction of stock prices is an important task in economics, investment and making financial decisions. This has, for decades, spurred the interest of many researchers to make focused contributions to the design of accurate stock price predictive models; of which some have been utilized to predict the next day ope…

It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely from feedforward processing. We set out to find such codes in the context of one…

TVS-FNNs can approximate any continuous function on expanded input spaces.

Study uses neural networks to improve option pricing accuracy.

We show that there is a simple (approximately radial) function on $\reals^d$, expressible by a small 3-layer feedforward neural networks, which cannot be approximated by any 2-layer network, to more than a certain constant accuracy, unless its width is exponential in the dimension. The result holds for virtually all kn…

We propose a novel learning method for multilayered neural networks which uses feedforward supervisory signal and associates classification of a new input with that of pre-trained input. The proposed method effectively uses rich input information in the earlier layer for robust leaning and revising internal representat…

In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative cont…

New findings show modern neural networks have finite sample complexity in o-minimal structures.

MOTGNN integrates multi-omics data for disease classification with improved accuracy and interpretability.

Optimizes wide low-rank neural networks for reduced parameters and cost.

FNNs can be made more interpretable with statistical methods.

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does …

Model projection transfers convolutional network properties to feedforward networks.

Dense neural networks can't approximate all functions.

Feature networks link ML features via graph structure for enhanced learning.

We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer is a universal approximator of Markov kernels. We show that each possible probabilistic assignment of the states of $n$ output units, given t…

The approximation power of general feedforward neural networks with piecewise linear activation functions is investigated. First, lower bounds on the size of a network are established in terms of the approximation error and network depth and width. These bounds improve upon state-of-the-art bounds for certain classes o…

The paper examines topological features of ReLU networks and their relation to decision boundaries and training loss.

Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. By approximating the tangent subspace, we suggest a sparse representation that enables switching to …

Training feedforward neural networks with standard logistic activations is considered difficult because of the intrinsic properties of these sigmoidal functions. This work aims at showing that these networks can be trained to achieve generalization performance comparable to those based on hyperbolic tangent activations…

Deep RNNs compute American option prices and deltas efficiently.

Graph neural networks improve residential location choice predictions.

Designs an MLP from LDA for multi-Gaussian class classification.

The standard method of generating random weights and biases in feedforward neural networks with random hidden nodes, selects them both from the uniform distribution over the same fixed interval. In this work, we show the drawbacks of this approach and propose a new method of generating random parameters. This method en…

We simplify neural networks to 3D to study their topological changes.

Improved machine learning for reservoir optimization problems.

We prove a negative result for the approximation of functions defined on compact subsets of $\mathbb{R}^d$ (where $d \geq 2$) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to…

Residual neural networks don't help overcome sampling complexity issues.

How to model and encode the semantics of human-written text and select the type of neural network to process it are not settled issues in sentiment analysis. Accuracy and transferability are critical issues in machine learning in general. These properties are closely related to the loss estimates for the trained model.…

Vanilla GANs are connected to Wasserstein distance for better understanding.

Time series anomaly detection is usually formulated as finding outlier data points relative to some usual data, which is also an important problem in industry and academia. To ensure systems working stably, internet companies, banks and other companies need to monitor time series, which is called KPI (Key Performance I…

In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…

A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riema…

Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. Our main idea is to mathematically understand and describe the hierarchical structure of feedforward…

A new algorithm reduces memory usage for deep learning models.