Wide deep neural networks are easy to optimize without constraints.
problem Optimizing wide deep neural networks.
method Analysis of optimization landscapes and empirical-risk minimization.
result Wide neural networks have no confined points, making optimization easier.
Deep and wide networks are shown to be equivalent in terms of their capability.
problem The relationship between the width and depth of neural networks.
method Formulated transforms to map networks, used polynomial representations.
result Deep and wide networks are quasi-equivalent with an arbitrarily small error.
Generalized linear models with nonlinear feature transformations are widely used for large-scale regression and classification problems with sparse inputs. Memorization of feature interactions through a wide set of cross-product feature transformations are effective and interpretable, while generalization requires more…
Single wide layer followed by a pyramidal structure ensures global convergence in deep networks.
problem Ensuring global convergence in deep neural networks with limited width constraints.
method Proves that a single wide layer followed by a pyramidal structure guarantees global convergence for over-parameterized networks.
result Single wide layer of width N suffices for global convergence in deep networks with constant-width remaining layers. Stable processes emerge as limits of deep neural networks with symmetric stable distributions.
problem Understanding the behavior of deep neural networks as they become infinitely wide.
method Analyzing fully connected feed-forward deep neural networks with symmetric stable distributions and showing the limit as a stable process.
result The infinite wide limit of the network is a stable process with multivariate stable distributions.
Wide deep neural networks with Gaussian weights approximate Gaussian processes closely.
problem Understanding the approximation of deep neural networks with Gaussian weights to Gaussian processes.
method Established novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters and Lipschitz activation functions in the wide limit.
result The distance between the network output and the Gaussian approximation scales inversely with the width of the network.
Understanding the loss surface of neural networks is essential for the design of models with predictable performance and their success in applications. Experimental results suggest that sufficiently deep and wide neural networks are not negatively impacted by suboptimal local minima. Despite recent progress, the reason…
Proposes efficient training method for deep thin networks.
problem Deploying deep learning models with accuracy and compactness.
method Three-stage method: widen, warm up, fine tune.
result Deep thin networks trained with method outperform standard deep networks.
The paper examines how deep linear neural networks behave as they become infinitely wide.
problem Understanding the behavior of deep linear neural networks as they approach infinite width.
method Analyzes the infinite-width limit of deep linear neural networks, proving convergence to deterministic models and providing precise laws for random weights.
result The training dynamics of deep linear neural networks converge to those of a deterministic model, and the weights' behavior is precisely described.
Deep networks with a wide layer ensure sublevel set connectivity.
problem Ensuring connectivity of sublevel sets in deep learning.
method Analyzing the connectivity of sublevel sets in deep neural networks with a specific layer width.
result A single wide layer of width N+1 suffices to prove connectivity of sublevel sets. Bayesian inference for wide neural networks using Edgeworth expansion.
problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.
method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.
result Derived non-Gaussian posterior distribution in Bayesian regression tasks.
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward networks with more than one hidden layer and Gaussian processes with a recursive ker…
Study of deep Stable neural networks with various activation functions.
problem Characterizing the infinitely wide limits of deep Stable neural networks.
method Investigation of large-width properties of deep Stable NNs with a generalized central limit theorem for heavy tails.
result Extension of characterization to a broader class of activation functions, including sub-linear, asymptotically linear, and super-linear functions.
Gradient descent proves global convergence for deep networks with a single wide layer.
problem Proving global convergence of gradient descent for deep ReLU networks.
method Simplified proof using a single wide layer, leveraging ReLU's Lipschitz property.
result Gradient descent converges globally for networks with a single wide layer.
Memory split advantage: thinner networks outperform a single wide network.
problem Optimizing deep learning models with limited memory.
method Investigated training a single wide network vs. an ensemble of thinner networks with the same total number of parameters.
result An ensemble of several thinner networks outperforms a single wide network for large memory budgets.
We consider deep linear networks with arbitrary convex differentiable loss. We provide a short and elementary proof of the fact that all local minima are global minima if the hidden layers are either 1) at least as wide as the input layer, or 2) at least as wide as the output layer. This result is the strongest possibl…
Wide neural networks with narrow bottlenecks behave like deep Gaussian processes.
problem Understanding the behavior of neural networks with narrow layers in the wide limit.
method Analyzing the wide limit of BNNs with narrow bottlenecks, showing they behave like a composition of GPs.
result Wide neural networks with narrow bottlenecks form a composition of GPs, termed a bottleneck NNGP.
Wide neural networks converge to Gaussian processes, improving generalization.
problem Understanding the generalization of wide neural networks, especially deep equilibrium models.
method Investigation of deep equilibrium models (DEQs) with infinite-depth layers, focusing on their convergence to Gaussian processes as width and depth approach infinity.
result Wide DEQs converge to Gaussian processes, maintaining generalization performance.
GCNIII combines Wide & Deep for better node classification.
problem Issues with graph convolutional networks in node classification tasks.
method Proposes GCNIII framework integrating Wide & Deep architecture and three techniques.
result Demonstrates improved performance in various node classification tasks.
Wide and Deep GNN learns from distributed graphs and retrain online.
problem Decentralized graph support changes over time, causing mismatch between training and testing graphs.
method Wide and Deep GNN architecture with distributed online learning.
result Convergence guarantees for online retraining of the wide part of the GNN.
We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has more neurons than the number of training samples. This condition holds e.g. for the…
Wide neural networks' last hidden layers split into groups of redundant neurons.
problem Understanding why wide neural networks generalize well despite overfitting.
method Analyzed the last hidden layer representations of various convolutional neural networks.
result Wide hidden layers split into groups of redundant neurons, which help generalize.
Paper proposes knockoff-based methods to simplify deep neural networks by controlling false discovery rates.
problem High-dimensional deep neural networks with many irrelevant parameters and inputs.
method Knockoff methods combined with regularized neural networks for variable screening.
result Proposed algorithms show satisfactory performance in controlling false discovery rates.
We prove that for an L-layer fully-connected linear neural network, if the width of every hidden layer is Ω~(L⋅r⋅dout⋅κ3), where r and κ are the rank and the condition number of the input data, and dout is the output dimension, then gradient descent with Gaussi…
Deep Gaussian Processes are reinterpreted as deep trigonometric networks for tractable inference.
problem Challenging inference in DGPs due to intractable marginalization in latent function space.
method Viewing DGPs as deep trigonometric networks with Bochner's theorem, and using the wide limit with a bottleneck to translate DGPs into deep trigonometric networks.
result The weight space view yields the same effective covariance functions as obtained in function space, and varying prior distributions over network parameters is equivalent to employing different kernels.
The paper proves neural networks' consistency and optimal convergence rates for various function classes.
problem Proving neural networks' consistency and optimal convergence rates for diverse function classes.
method Analyzes wide and deep ReLU neural networks trained on logistic loss and Kolmogorov-Donoho optimal function classes.
result Proves universal consistency and minimax optimal convergence rates for neural networks.
We prove the precise scaling, at finite depth and width, for the mean and variance of the neural tangent kernel (NTK) in a randomly initialized ReLU network. The standard deviation is exponential in the ratio of network depth to width. Thus, even in the limit of infinite overparameterization, the NTK is not determinist…
The study characterizes conditions for trainability and generalization in deep neural networks.
problem Understanding the conditions for deep neural networks to be trainable and generalize well.
method Analysis of Neural Tangent Kernel (NTK) for wide and deep networks.
result Large regions of hyperparameter space exist where networks can memorize training data but fail to generalize.
The paper examines when NTK theory applies to real finite-width neural networks.
problem Understanding when NTK theory accurately predicts the behavior of finite-width neural networks.
method Empirical study of fully-connected ReLU and sigmoid DNNs with various hyperparameters and depths.
result NTK theory does not always apply to sufficiently deep networks with exploding gradients, and the kernel changes significantly during training.
Deep linear ResNets converge globally with certain transformations.
problem Global convergence of training deep linear ResNets.
method Gradient descent and stochastic gradient descent for training L-hidden-layer linear ResNets. result GD and SGD can converge to global minimum for deep linear ResNets with specific transformations.
Study of infinitely deep but narrow neural networks using NTK theory.
problem Analyzing the role of depth in deep learning with overparameterized networks.
method Infinite-depth limit analysis of MLP and CNN using Neural Tangent Kernel (NTK) theory.
result Established trainability guarantee for infinitely deep but narrow neural networks.
Deep learning algorithms have achieved excellent performance lately in a wide range of fields (e.g., computer version). However, a severe challenge faced by deep learning is the high dependency on hyper-parameters. The algorithm results may fluctuate dramatically under the different configuration of hyper-parameters. A…
WideBNet learns inverse scattering from wide-band data efficiently and stably.
problem Learning the inverse scattering map from wide-band scattering data.
method Combines butterfly factorization, FFT, and deep learning.
result WideBNet requires fewer training points and has stable training dynamics.
Improved bounds on neural network expressivity.
problem Understanding neural network expressivity and approximation capabilities.
method Improved bounds on the maximal number of linear regions of ReLU-networks.
result New insights into the expressivity of neural networks.
Study on infinitely-wide CNNs and their adaptability to function spatial scales.
problem Understanding how CNNs efficiently learn high-dimensional functions and their adaptability to function spatial scales.
method Study infinitely-wide deep CNNs in the kernel regime, characterizing their spectrum and using generalisation bounds to prove adaptability.
result Deep CNNs adapt to the spatial scale of the target function, with error decay controlled by the effective dimensionality of function subsets.
This paper provides a mathematical foundation for deep neural networks solving PDEs.
problem Mathematical foundation for deep neural networks solving high-dimensional PDEs.
method Decomposed generalization error into approximation and training errors; derived gradient flow in the wide network limit.
result Generalization error tends to zero as the number of neurons and training time tend to infinity.
Wide networks with polynomial activations have proven asymptotic behavior.
problem Understanding the behavior of neural networks in the large width limit.
method Proving a conjecture for deep networks with polynomial activation functions.
result Tight bounds on the behavior of wide networks during stochastic gradient descent and derivation of their finite-width dynamics.
Deep, wide ConvResNets can approximate functions and their smoothness.
problem Function approximation and smoothness in deep networks.
method Analyzing ConvResNets, proving their ability to approximate functions and their smoothness.
result Large ConvResNets can approximate functions and exhibit sufficient first-order smoothness.
Deep neural networks (DNNs) have been widely used in the fields such as natural language processing, computer vision and image recognition. But several studies have been shown that deep neural networks can be easily fooled by artificial examples with some perturbations, which are widely known as adversarial examples. A…
Deep neural networks are widely used in various domains. However, the nature of computations at each layer of the deep networks is far from being well understood. Increasing the interpretability of deep neural networks is thus important. Here, we construct a mean-field framework to understand how compact representation…
This paper investigates the impact of normalization on deep neural networks for click-through rate prediction.
problem The effect of normalization on deep neural network models for CTR estimation.
method Systematic study of various normalization approaches applied to feature embedding and MLP part of DNN models.
result Correct normalization significantly enhances model performance, as demonstrated by extensive experiments on real-world datasets.
New model explains deep learning performance at large learning rates.
problem Understanding deep learning performance at different learning rates.
method Developed neural networks with solvable training dynamics.
result Large learning rates lead to convergence to flatter minima.
Bounds neural network output distribution to Gaussian for random initialization.
problem Quantifying the distribution of randomly initialized deep neural networks.
method Quantitative Gaussian approximation using quadratic Wasserstein distance.
result Explicit inequalities show how network sizes affect Gaussian behavior.
Study on MC dropout in wide neural networks and its convergence to Gaussian processes.
problem Understanding the behavior of Monte Carlo dropout in wide neural networks.
method Rigorously studied the limiting distribution of wide untrained NNs under dropout, proving convergence to Gaussian processes. Investigated correlations and non-Gaussian behavior in finite width NNs.
result Wide untrained neural networks under dropout converge to Gaussian processes for fixed sets of weights and biases.
Improved DNN calibration without sacrificing accuracy.
problem Poor calibration of over-parametrized DNNs in safety-critical applications.
method Decoupling feature extraction and classification layers, and applying Gaussian priors.
result Significant improvement in model calibration with minimal training cost.
Infinite CNNs lose spatial correlations, but can be restored by correlated weights.
problem Infinite CNNs lose spatial correlations, which are crucial for their performance.
method Introduced correlated weights to restore spatial correlations in infinite CNNs.
result Optimal performance is achieved with a moderate level of weight correlation.
Study proves deep narrow RNNs can approximate any function, with minimum width independent of data length.
problem Proving universality of deep narrow RNNs with bounded widths.
method Analyzing RNNs as dynamical systems, proving universality for deep narrow structures with specific widths.
result Minimum width for universality of deep narrow RNNs is independent of data length.
We introduce a wide and deep neural network for prediction of progression from patients with mild cognitive impairment to Alzheimer's disease. Information from anatomical shape and tabular clinical data (demographics, biomarkers) are fused in a single neural network. The network is invariant to shape transformations an…