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.
TVS-FNNs can approximate any continuous function on expanded input spaces.
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…
Study uses neural networks to improve option pricing accuracy.
This paper examines properties of feedforward graphs to improve neural network performance.
PCGs encompass a broader range of neural networks.
We show that there is a simple (approximately radial) function on , 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…
Residual neural networks don't help overcome sampling complexity issues.
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…
Optimizes wide low-rank neural networks for reduced parameters and cost.
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…
We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among other things, we deduce that feedforward ReLU neural networks with one hidden laye…
New findings show modern neural networks have finite sample complexity in o-minimal structures.
FNNs can be made more interpretable with statistical methods.
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 …
We prove a negative result for the approximation of functions defined on compact subsets of (where ) 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…
Improved machine learning for reservoir optimization problems.
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…
Deep RNNs compute American option prices and deltas efficiently.
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 …
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…
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…
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…
Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.
We simplify neural networks to 3D to study their topological changes.
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the network output with respect to the space variables which is needed to approxima…
A new faster neural network training method using backprojection.
Neural networks can separate non-separable data using feature maps.
This paper improves deep neural network approximation for fully connected networks, achieving optimal convergence rates.
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.…
Proves existence of optimal shallow neural networks with ReLU activation.
Recent years, many researches attempt to open the black box of deep neural networks and propose a various of theories to understand it. Among them, Information Bottleneck (IB) theory claims that there are two distinct phases consisting of fitting phase and compression phase in the course of training. This statement att…
A new neural network initialization method is proposed for faster and more accurate training.
Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled. We introduce a novel recurrent architecture based on the conceptual separation b…
Improved sampling for Bayesian neural networks reduces vanishing acceptance rates and increases predictive accuracy.
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…
Extends branch and bound for probabilistic neural network verification.
Math theory explains how neural networks learn abstract representations.
Model projection transfers convolutional network properties to feedforward networks.
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…
Develops a smooth operator framework for analyzing neural network representations.
Review of neural network expressivity and architectures.
LCW reduces activation shift in neural networks, improving training efficiency and generalization.
Recurrent Neural Networks (RNNs) are powerful models for sequential data that have the potential to learn long-term dependencies. However, they are computationally expensive to train and difficult to parallelize. Recent work has shown that normalizing intermediate representations of neural networks can significantly im…
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…
Functional dimension varies in ReLU networks, with implications for symmetry and connectivity.
Neural networks can approximate functions uniformly across various measures.