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.
Paper proves GDL models can approximate any continuous function on non-Euclidean data.
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 output units, given t…
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 …
Study uses neural networks to improve option pricing accuracy.
We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as the visible layer. We show that, within certain parameter domains, deep Boltzmann…
Rank-R FNN handles high-dimensional data efficiently.
Neural networks can approximate functions uniformly across various measures.
Despite the fact that generative models are extremely successful in practice, the theory underlying this phenomenon is only starting to catch up with practice. In this work we address the question of the universality of generative models: is it true that neural networks can approximate any data manifold arbitrarily wel…
In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks represent mappings from a set of inputs to a set of probability distributions o…
Dense neural networks can't approximate all functions.
The paper shows neural networks can approximate functions over non-compact domains with non-polynomial activation.
Complex-valued neural networks can approximate any continuous function.
Neural networks with learned biases can approximate any function.
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…
Transformers can outperform feedforward and recurrent networks due to dynamic sparsity.
Random feature models approximate functions in Banach spaces efficiently.
Model approximates continuous functions in 1-Wasserstein space.
This paper examines properties of feedforward graphs to improve neural network performance.
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…
This paper improves the approximation of machine learning models by transforming them to better fit locally -integrable functions.
Model projection transfers convolutional network properties to feedforward networks.
FNNs can be made more interpretable with statistical methods.
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…
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…
The paper introduces Causal Neural Operators to approximate operators in stochastic analysis.
New findings show modern neural networks have finite sample complexity in o-minimal structures.
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…
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.…
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…
PCGs encompass a broader range of neural networks.
Designs an MLP from LDA for multi-Gaussian class classification.
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…
Optimizes wide low-rank neural networks for reduced parameters and cost.
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…
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.
Residual neural networks don't help overcome sampling complexity issues.
Develops a smooth operator framework for analyzing neural network representations.
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…
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…
Neural networks with random hidden nodes have gained increasing interest from researchers and practical applications. This is due to their unique features such as very fast training and universal approximation property. In these networks the weights and biases of hidden nodes determining the nonlinear feature mapping a…
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…
Token-adaptive FFN design improves LLM expressivity.
We present the Video Ladder Network (VLN) for efficiently generating future video frames. VLN is a neural encoder-decoder model augmented at all layers by both recurrent and feedforward lateral connections. At each layer, these connections form a lateral recurrent residual block, where the feedforward connection repres…
Deep RNNs compute American option prices and deltas efficiently.
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…