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…
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48 results for “rectifier units”
Paper proposes a new activation function to reduce overfitting and large weight update issues.
problem Overfitting and large weight update problems in neural networks.
method Introduces a new activation function called Thresholded Exponential Rectified Linear Units (TERELU).
result TERELU shows better performance in reducing overfitting and large weight update issues compared to other activation functions.
CRITS improves time series classification with interpretable local explanations.
problem Lack of detailed explanations in time series classification models.
method CRITS uses convolutional kernels, max-pooling, and rectified linear units to extract feature weights.
result CRITS provides intrinsically interpretable local explanations without requiring gradients or random perturbations.
Dropout training improves neural networks' performance.
problem Improving neural network convergence and generalization.
method Two-layer neural networks with ReLU activations, overparametrization, and positive margin assumption.
result Dropout training achieves ε-suboptimality in test error in O(1/ε) iterations.
In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We characterize rectifying curves in the -dimensional Euclidean space in different ways…
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…
The paper characterizes rectifying curves on smooth surfaces using isometries and Darboux frames.
problem Characterizing rectifying curves on smooth surfaces under isometries.
method Using Darboux frames and isometries to investigate rectifying curves.
result Find deviations of rectifying curves under isometries and analyze their properties.
In this article, we show that, for any compact 3-manifold, there is a volume-minimizing one-dimensional foliation. More generally, we show the existence of mass-minimizing rectifiable sections of sphere bundles without isolated "pole points" in the base manifold. This same analysis is used to show that the exam…
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…
AReLU uses attention-based rectification to improve neural network performance.
problem Improving neural network performance through better activation functions.
method Integrates attention mechanism with rectified linear unit (ReLU) to learn and scale feature maps.
result AReLU significantly boosts performance of most network architectures with minimal changes.
A neural network with a single hidden layer can't represent certain multivariable functions.
problem Representing certain multivariable functions with a neural network having only one hidden layer.
method Developed a continuum version of a one-hidden-layer neural network with ReLU activation, and proved constraints on its parameters and second derivative.
result Existence of a smooth binary function that cannot be precisely represented by any such neural network.
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…
Convex relaxations improve CNNs with fixed weights.
problem Improving CNNs with fixed weights.
method Convex relaxations for CNNs with fixed weights using second order cone programs.
result The relaxation recovers the global minimum under a planted model assumption.
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 …
Improved activation function NLReLU boosts neural network performance.
problem Performance issues with ReLU activation function.
method NLReLU uses parametric natural logarithmic transform to improve ReLU.
result NLReLU provides higher accuracy than ReLU in various neural networks.
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
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…
Feed-forward nets fail to learn equality relations, but adding DR units helps.
problem Feed-forward neural networks struggle to learn equality relations reliably.
method Introduced differential rectifier (DR) units to create an inductive bias.
result DR units enable feed-forward nets to learn equality relations reliably.
Convexifying Sparse Interpolation with Infinitely Wide Neural Networks: An Atomic Norm Approachcs.LG
This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.
problem Exact data interpolation using sparse, infinitely wide neural networks.
method Atomic norm framework to derive convex hulls and equivalent convex formulations.
result Simple characterizations of convex hulls for different constraints on network weights and biases.
Study of spatial curves in generalized Minkowski spaces.
problem Characterizing and invariants of spatial curves in non-Euclidean spaces.
method Derive Frenet-type results and invariants for spatial curves in generalized Minkowski spaces.
result Characterization of cylindrical helices and rectifying curves in generalized Minkowski spaces.
The paper analyzes deep neural networks using rectified linear units.
problem Understanding the individual affine linear representations of deep neural networks.
method Signal processing perspective, atomic decompositions, Lipschitz regularity estimation.
result Conditions for stabilizing learning in deep neural networks without network depth constraints.
Multivariate splines linked to infinitely-wide neural networks with improved numerical performance.
problem Understanding the relationship between multivariate splines and neural networks.
method Showed multivariate splines can be represented as random features in infinitely-wide neural networks with a homogeneous activation function.
result The function space of multivariate splines is a Sobolev space on a Euclidean ball with explicit norm bounds on derivatives.
Study approximates nonlinear functionals using deep ReLU networks.
problem Approximating nonlinear continuous functionals with neural networks.
method Constructs continuous piecewise linear interpolation under simple triangulation, analyzes rates of approximation.
result Established rates of approximation for functional deep ReLU networks.
Theoretical analysis shows RNNs with various nonlinearities benefit from depth efficiency.
problem Theoretical understanding of RNNs' efficiency is limited.
method Extended analysis to RNNs with Rectified Linear Unit (ReLU) and other nonlinearities.
result Various nonlinear RNNs also benefit from depth efficiency.
We present a probabilistic variant of the recently introduced maxout unit. The success of deep neural networks utilizing maxout can partly be attributed to favorable performance under dropout, when compared to rectified linear units. It however also depends on the fact that each maxout unit performs a pooling operation…
What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theorystat.ML
New framework explains deep neural networks using variational spline theory.
problem Understanding functions learned by deep neural networks.
method Developed a variational framework and function space.
result Deep ReLU networks are solutions to regularized data fitting problems over the proposed function space.
New algorithm reveals piecewise affine structure of neural networks.
problem Lack of strong guarantees on deep neural networks' behavior in safety-critical applications.
method Developed a novel algorithm to compute the piecewise affine form of neural networks.
result Computed piecewise affine representations of neural networks with rectified linear unit activations.
Properties of the geometry of solutions and capacity of multi-layer neural networks with Rectified Linear Units activationscond-mat.dis-nn
Analyzes how ReLU affects neural network capacity and solution space geometry.
problem Understanding the effects of ReLU on neural network capacity and solution space.
method Analytical and numerical studies of two-layer neural networks with ReLU activations.
result The capacity of ReLU networks remains finite as the number of hidden neurons increases, unlike for threshold units.
We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and Riesz--Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptio…
PHP connects to ReLU neural networks for scalable Bayesian inference.
problem Scalability and Bayesian inference in two-layer ReLU neural networks.
method PHP with Gaussian prior, decomposition propositions, annealed sequential Monte Carlo.
result PHP provides an alternative scalable representation for two-layer ReLU neural networks.
Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraintscs.LG
MVRSM optimizes expensive functions with mixed variables, outperforming state-of-the-art methods.
problem Minimizing expensive functions with mixed continuous and integer variables.
method Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) using rectified linear units.
result MVRSM outperforms state-of-the-art methods on synthetic and real-life benchmarks.
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 investigates how target normalization and momentum affect dying ReLUs in neural networks.
problem Understanding and mitigating the dying ReLU problem in neural networks.
method Empirical analysis and theoretical modeling of a discrete-time linear autonomous system.
result Target variance plays a crucial role in the dying ReLU phenomenon, and momentum exacerbates this issue.
The study evaluates the performance of ANNs in financial forecasting.
problem Mixed evidence on the predictive performance of ANNs for financial time-series data.
method Proposes a flexible nonparametric model and compares its performance to other estimators.
result The proposed model shows better performance than basic benchmarks in estimating Value-at-Risk.
A new method prunes neural network channels based on operation characteristics.
problem Compressing deep neural networks efficiently and maintaining accuracy.
method Differentiable masks for channel pruning considering BN and ReLU.
result Outstanding performance in accuracy with less resources compared to state-of-the-art methods.
The paper provides theoretical guarantees for neural network-based anomaly detection.
problem Theoretical guarantees for unsupervised neural network-based anomaly detection.
method Casting anomaly detection as a binary classification problem, establishing non-asymptotic upper bounds and convergence rates.
result The convergence rate on the excess risk matches the minimax optimal rate.
Deep neural networks enforce non-crossing quantile regression curves.
problem Estimating quantile regression curves without crossing.
method Penalized deep ReQU neural networks with a non-crossing penalty.
result Established non-asymptotic risk and error bounds for the estimated QRP.
ReLU units can 'die' in neural networks, causing slower convergence.
problem ReLU units sometimes produce near-zero outputs during training.
method Simulation and statistical analysis of a simplified ReLU unit model.
result Activation probability decreases as training progresses, leading to slower convergence.
The paper calculates bounds on the local Lipschitz constants of neural network layers.
problem Understanding the Lipschitz constants of neural network layers for robustness analysis.
method Analytical approach to determine upper bounds on local Lipschitz constants of affine-ReLU functions.
result The method produces tighter bounds than the standard conservative bound, especially for small perturbations.
DEUs learn nonlinear activation functions from data, reducing network size.
problem Fixed activation functions in neural networks limit performance.
method Differential equation units (DEUs) learn nonlinear activation functions from data.
result DEUs enable neurons to change their activation functions during training.
Deep learning method for semiparametric regression of spatial data.
problem Estimating relationships between response and covariates in spatially dependent data.
method A sparsely connected deep neural network with ReLU activation function.
result The method is consistent and can handle large datasets.
ADMM algorithm solves nonlinear matrix decompositions efficiently.
problem Nonlinear matrix decompositions for various applications.
method Alternating Direction Method of Multipliers (ADMM) for nonlinear matrix factorization.
result The method efficiently solves diverse nonlinear matrix decompositions.
We introduce and study co-dimension one area-minimizing locally rectifiable currents with tangentially immersed boundary: is locally a finite sum of orientable co-dimension two submanifolds which only intersect tangentially with equal orientation. We show that any such is supported in a s…
We present a novel neural network algorithm, the Tensor Switching (TS) network, which generalizes the Rectified Linear Unit (ReLU) nonlinearity to tensor-valued hidden units. The TS network copies its entire input vector to different locations in an expanded representation, with the location determined by its hidden un…
We give a parametrization to the asymptotic Teichmuller space of the open unit disk through equivalent classes of shear functions induced by quasisymmetric homeomorphisms on the Farey tesselation of the unit disk. Then using the parametrization, we define a new metric on the asymptotic Teichmuller space. Two other rela…
Perpendicularity and Locality for Codimension-One Varifolds with Bounded Anisotropic Mean Curvaturemath.AP
This paper extends Euclidean theorems to anisotropic settings for varifolds.
problem Anisotropic mean curvature of codimension-one varifolds.
method Proves perpendicularity and locality of mean curvature for bounded anisotropic mean curvature varifolds.
result Anisotropic mean curvature agrees with the approximate mean curvature on the rectifiable part of the varifold.
Algorithm removes units and layers of neural networks without losing accuracy.
problem Deploying large neural networks under limited resources.
method Mixed-Integer Linear Programming (MILP) and L1 regularization.
result Lossless compression of neural networks is achieved.
For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit sphere, as opposed to the entire space, and the threshold can be trained in a boun…