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.
Neural networks can approximate rectifiable measures with small error.
In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …
In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evalu…
Paper proposes a new activation function to reduce overfitting and large weight update issues.
CRITS improves time series classification with interpretable local explanations.
This paper provides a theoretical justification of the superior classification performance of deep rectifier networks over shallow rectifier networks from the geometrical perspective of piecewise linear (PWL) classifier boundaries. We show that, for a given threshold on the approximation error, the required number of b…
Methods from convex optimization are widely used as building blocks for deep learning algorithms. However, the reasons for their empirical success are unclear, since modern convolutional networks (convnets), incorporating rectifier units and max-pooling, are neither smooth nor convex. Standard guarantees therefore do n…
Dropout training improves neural networks' performance.
Rectified flows achieve optimal sample complexity for generating data.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
We consider a neural network architecture with randomized features, a sign-splitter, followed by rectified linear units (ReLU). We prove that our architecture exhibits robustness to the input perturbation: the output feature of the neural network exhibits a Lipschitz continuity in terms of the input perturbation. We fu…
AReLU uses attention-based rectification to improve neural network performance.
Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely used as building blocks for deep learning algorithms. This paper provides the fi…
New framework explains deep neural networks using variational spline theory.
A neural network with a single hidden layer can't represent certain multivariable functions.
New method trains deep vanilla networks as fast as ResNets without shortcut connections.
Scattering networks maximize separation on low-dimensional data.
We introduce a new neural network model, together with a tractable and monotone online learning algorithm. Our model describes feed-forward networks for classification, with one output node for each class. The only nonlinear operation is rectification using a ReLU function with a bias. However, there is a rectifier on …
Study rectifying curves in 3D multiplicative Euclidean space.
Investigates Darboux rectifying curves on smooth surfaces.
A space curve in a Euclidean 3-space is called a rectifying curve if its position vector field always lies in its rectifying plane. This notion of rectifying curves was introduced by the author in [Amer. Math. Monthly {\bf 110} (2003), no. 2, 147-152]. In this present article, we introduce and study the n…
Study characterizes -rectifiable sets in homogeneous groups.
Recalls and refines the concept of algebraically rectifiable curves.
Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on ReLU have been proposed, but each carry performance drawbacks. In this paper, w…
This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.
Harmonic maps to Euclidean buildings have rectifiable singular strata.
A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of mo…
We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite mass and finite size is rectifiable. It also leads to a simple necessary and su…
We present QuickNet, a fast and accurate network architecture that is both faster and significantly more accurate than other fast deep architectures like SqueezeNet. Furthermore, it uses less parameters than previous networks, making it more memory efficient. We do this by making two major modifications to the referenc…
New methods for solving hydrodynamic-type equations using quasi-rectifiable Lie algebras.
Rectifies singular set of harmonic maps into complex.
The paper generalizes rectifying and normal curves in Lorentzian n-space.
We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable, showing the equivalence of this notion of rectifiability with that of Franchi, Serra Cassano and Serapioni for such surfaces.
Study approximates nonlinear functionals using deep ReLU networks.
The notion of rectifying curve in the Euclidean space is introduced by Chen as a curve whose position vector always lies in its rectifying plane spanned by the tangent and the binormal vector field t and n_2 of the curve. In this study, we have obtained some characterizations of semi-real spatial quaternionic rectifyin…
PHP connects to ReLU neural networks for scalable Bayesian inference.
Multivariate splines linked to infinitely-wide neural networks with improved numerical performance.
We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the m…
In Heisenberg groups, rectifiability is studied for subsets using -regular surfaces.
The paper characterizes rectifying curves on smooth surfaces using isometries and Darboux frames.
Neural networks with rectified linear unit activations are essentially multivariate linear splines. As such, one of many ways to measure the "complexity" or "expressivity" of a neural network is to count the number of knots in the spline model. We study the number of knots in fully-connected feedforward neural networks…
The paper proves smoothness of stationary varifolds.
In this paper, we introduce a new class of curves αcalled a f-rectifying curves, which its f-position vector defined by α_{f}(s)=\int f(s)T(s)ds always lie in the rectifying plane of α, where f is an integrable function and T is the speed curve of α. In particular case, when the function f=0 or constant, the class of f…
The paper explores rectified flows and their relation to optimal transport.
The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass models and mean-field approximations, but at the expense of strongly simplifying th…
We extend rectified flow to infinite-dimensional Hilbert space.
The rectified flow method is analyzed for its statistical properties.
Improves AI-prior reliability for Bayesian inference.