This paper presents a phase diagram for two-layer neural networks under different initialization scales.
problem Understanding the behavior of neural networks under varying scales of initialization.
method Analysis of a phase diagram for two-layer neural networks.
result Condensation of weight vectors on isolated orientations during training.
Paper optimizes neural network initialization using SMT solvers.
problem Improving neural network performance through better initialization.
method Reduces initialization to SMT problem solving.
result Proposed method achieves better performance than random initialization.
Neural nets trained with linear discriminant initialization converge faster and more accurately.
problem Training feed-forward neural networks efficiently and accurately.
method Initialize first layer weights with linear discriminants.
result Asymptotic higher accuracy and faster convergence.
A new neural network initialization method is proposed for faster and more accurate training.
problem Efficient initialization for training multi-layer feedforward neural networks.
method Initialization based on Stein's identity, using eigenvectors of cross-moment matrix.
result The SteinGLM method is faster and more accurate than other initialization methods.
New method shows random, diverse initializations are not essential for deep neural networks.
problem The necessity of random, diverse initializations in deep neural networks.
method Constructed a deep convolutional network with identical features by initializing weights to 0, enabling signal propagation and stable gradients.
result Random, diverse initializations are not necessary for training neural networks.
Randomly initialized neural networks can linearly separate arbitrary sets.
problem Mapping two arbitrary sets to linearly separable sets.
method Randomly initialized one-layer neural networks with sufficient width.
result With high probability, these networks can transform two sets into linearly separable sets.
This paper examines the impact of random initialization in neural networks using NTK theory.
problem Understanding the impact of random initialization in neural networks using NTK theory.
method Analyzes the convergence of training dynamics and generalization error of wide neural networks with random initialization.
result The generalization error of wide neural networks trained by gradient descent is \( \Omega(n^{-\frac{3}{d+3}}) \), highlighting the benefits of mirror initialization and suggesting limitations of NTK theory.
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.
The paper studies neural networks' convergence near origin and saddle points.
problem Directional convergence of neural networks near small initializations and saddle points.
method Gradient flow dynamics analysis of two-homogeneous neural networks.
result Neural networks' weights approximately converge in direction to KKT points for small initializations.
New method stabilizes deep neural networks by setting Lyapunov exponent to zero.
problem Stability issues in deep neural networks with low width.
method Lyapunov initialization method to set Lyapunov exponent to zero.
result Lyapunov exponent governs stability of deep networks; standard methods fail for low width.
Proposes a method to optimize neural network initialization using marginal likelihood maximization.
problem Optimizing hyperparameters for neural network initialization.
method Leverages the connection between neural networks and Gaussian processes to infer optimal hyperparameters.
result Marginal likelihood maximization provides near-optimal prediction performance on MNIST classification tasks.
Study challenges the Gaussian pre-activations assumption in neural networks.
problem Challenges the assumption that pre-activations are Gaussian in neural networks.
method Constructs pairs of activation functions and initialization distributions to ensure Gaussian pre-activations.
result Discovered constraints for ensuring Gaussian pre-activations in neural networks.
AutoInit automatically finds good neural network initialization.
problem Finding optimal neural network initialization is crucial but time-consuming.
method Uses Jacobian tuning to automatically adjust network hyperparameters.
result The method finds good initialization for various network architectures.
This work provides an additional step in the theoretical understanding of neural networks. We consider neural networks with one hidden layer and show that when learning symmetric functions, one can choose initial conditions so that standard SGD training efficiently produces generalization guarantees. We empirically ver…
Deep neural networks achieve state-of-the-art performance for a range of classification and inference tasks. However, the use of stochastic gradient descent combined with the nonconvexity of the underlying optimization problems renders parameter learning susceptible to initialization. To address this issue, a variety o…
In this paper, we present a novel approach for initializing deep neural networks, i.e., by turning PCA into neural layers. Usually, the initialization of the weights of a deep neural network is done in one of the three following ways: 1) with random values, 2) layer-wise, usually as Deep Belief Network or as auto-encod…
A new method for neural network initialization using graph degeneracy.
problem Improving neural network performance through better initialization.
method Adapted k-hypercore decomposition for neural network initialization.
result k-hypercore outperforms state-of-the-art initialization methods.
Orthogonal initialization does not speed up training in ultra-wide neural networks.
problem Exploring the effect of orthogonal initialization on training speed in deep neural networks.
method Study of neural tangent kernel dynamics in FCNs and CNNs with orthogonal initialization.
result The NTK of orthogonally-initialized networks remains constant during training, suggesting no speedup in the NTK regime.
This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal control, in which neural networks are represented as discretizations of time-de…
We develop a general duality between neural networks and compositional kernels, striving towards a better understanding of deep learning. We show that initial representations generated by common random initializations are sufficiently rich to express all functions in the dual kernel space. Hence, though the training ob…
Residual Network (ResNet) is the state-of-the-art architecture that realizes successful training of really deep neural network. It is also known that good weight initialization of neural network avoids problem of vanishing/exploding gradients. In this paper, simplified models of ResNets are analyzed. We argue that good…
Initializing the weights and the biases is a key part of the training process of a neural network. Unlike the subsequent optimization phase, however, the initialization phase has gained only limited attention in the literature. In this paper we discuss some consequences of commonly used initialization strategies for va…
Improved portfolio optimization reduces sensitivity to neural network initialization.
problem High sensitivity to neural network initialization in portfolio optimization.
method Robust end-to-end framework for risk budgeting portfolios.
result Enhanced stability in portfolio optimization without compromising performance.
Study on adversarial robustness in neural networks across initialization and training phases.
problem Understanding adversarial robustness in neural networks during different learning stages.
method Analyzes adversarial robustness in various scenarios of over-parameterized networks with quadratic targets and infinite samples.
result Robustness can worsen when test error improves, and vice versa, revealing new tradeoffs.
We explore how neural networks train to zero loss, focusing on initial scale.
problem Understanding neural network training dynamics and zero loss.
method Macroscopic limits analysis of gradient descent dynamics.
result Gradient descent can drive deep neural networks to zero loss regardless of initialization.
Early training of deep neural networks leads to small, directionally converging weights.
problem Training dynamics of deep homogeneous neural networks with small initializations.
method Gradient flow analysis and study of KKT points for neural correlation function.
result Weights converge in direction to KKT points during early training stages.
Our study analyzes how neural network initialization affects privacy and utility in overparameterized models.
problem Privacy and utility trade-off in overparameterized neural networks.
method Analytical proof of KL divergence privacy bound, focusing on initialization, width, and depth.
result Privacy bound improvement with increasing depth under certain initializations, degradation under others.
Single neural network predicts ImageNet model parameters for faster training.
problem Training diverse ImageNet models requires significant resources and time.
method Trained a neural network to predict ImageNet model parameters and used them for initialization.
result Models initialized with predicted parameters converge faster and achieve competitive performance.
ReLU neural networks define piecewise linear functions of their inputs. However, initializing and training a neural network is very different from fitting a linear spline. In this paper, we expand empirically upon previous theoretical work to demonstrate features of trained neural networks. Standard network initializat…
New method for initializing low-rank neural networks improves performance.
problem Training low-rank neural networks efficiently and accurately.
method Inspired by function approximation, proposes a novel low-rank initialization framework.
result Demonstrates significant gap between spectral and low-rank initialization approaches.
Graph neural networks benefit from a new initialization method that improves node learning.
problem Poor initialization in GNNs leads to slower convergence and increased training instability.
method Integrates a statistically grounded one-hot graph encoder embedding (GEE) into standard GNNs.
result GG framework provides consistent and substantial performance gains in node classification.
Untrained neural networks can unfairly assign predictions to the same class.
problem Biasing effects in neural networks during initial training phases.
method Theoretical analysis of deep neural networks, focusing on Initial Guessing Bias (IGB).
result Model structure and preprocessing methods influence IGB.
SGD fails to converge for deep ReLU networks with limited random initializations.
problem SGD convergence in deep neural networks with limited random initializations.
method Analysis of four discretization parameters: network architecture, training data, gradient steps, and random initializations.
result SGD fails to converge for ReLU networks with depth much larger than width.
Proposes a new method to initialize neural networks by estimating global curvature of weights.
problem Improving the initialization of neural networks for better training and convergence.
method Estimates the global curvature of weights across layers using the Hessian matrix norm.
result The proposed method helps in more rigorously initializing weights, leading to better performance.
The paper establishes principles for initializing and designing GNNs with ReLU activations to avoid oversmoothing and correlation collapse.
problem Oversmoothing and correlation collapse in deep ReLU GNNs.
method The paper derives and validates three principles for initialization and architecture selection in finite width graph neural networks with ReLU activations.
result Correct initialization, residual aggregation operators, and residual connections significantly improve early training dynamics in deep ReLU GNNs.
Standard practice in training neural networks involves initializing the weights in an independent fashion. The results of recent work suggest that feature "diversity" at initialization plays an important role in training the network. However, other initialization schemes with reduced feature diversity have also been sh…
Optimizes deep neural network initialization variance for better performance.
problem Improving deep neural network performance through optimal initialization variance.
method Using SGD dynamics and Fokker-Planck equations, we study the relationship between initialization and expected loss function.
result An optimal condition for initialization variance that leads to lower training loss and higher test accuracy.
Bayesian method improves neural net convergence for character recognition.
problem Improving convergence rate of neural network training algorithms.
method Customization of Kalman filter into Bayesian statistics for initialization of weights.
result Improved convergence rate for backpropagation training algorithm.
We propose \emph{Taylorized training} as an initiative towards better understanding neural network training at finite width. Taylorized training involves training the k-th order Taylor expansion of the neural network at initialization, and is a principled extension of linearized training---a recently proposed theory …
New method trains shallow neural networks with subquadratic width scaling.
problem Training shallow neural networks with optimal width scaling.
method Polyak-Lojasiewicz condition, smoothness, standard data assumptions, random matrix theory.
result Subquadratic scaling on network width with standard initialization strategies.
New method solves PDEs for any initial condition without retraining.
problem Solving PDEs for different initial conditions requires retraining neural solvers.
method Formulate solution as conditional probability distribution.
result Approximates PDE solution for arbitrary initial conditions.
New sample complexity bounds for linear predictors and neural networks, focusing on initialization.
problem Understanding sample complexity for vector-valued linear predictors and neural networks, especially under initialization-dependent conditions.
method Size-independent bounds on Frobenius norm distance from a fixed reference matrix, applying to vector-valued predictors and neural networks.
result Established new sample complexity bounds for feed-forward neural networks, resolving open questions and introducing a new learnable problem.
Improved neural network training by coupled initialization reduces neuron count.
problem Training neural networks efficiently with fewer neurons.
method Coupled initialization of weights into pairs of identical Gaussian vectors.
result Significantly reduced number of neurons required for network convergence.
Theory proposes neural networks can be initialized for optimal information transmission.
problem Optimizing neural networks for optimal information transmission and representation.
method Developed a corrected mean-field framework to study neural networks as information channels, proving mutual information maximization at dynamic isometry.
result Mutual information maximization is realized between inputs and propagated signals when neural networks are initialized at dynamic isometry.
Neural IVP solves IVPs with neural networks, overcoming scaling and conditioning issues.
problem Solving initial value PDEs with neural networks is challenging due to numerical errors and limited scalability.
method Developed an ODE-based approach to solve IVPs with neural networks, preventing ill-conditioning and scaling issues.
result Neural IVP solves challenging PDEs with neural networks efficiently and accurately.
This paper extends the Gaussian process interpretation of deep networks to more varied weight distributions.
problem Understanding the impact of different weight initialization schemes on deep learning dynamics.
method Extending the Gaussian process interpretation to PSEUDO-IID weight distributions, including sparse and low-rank networks.
result PSEUDO-IID initialized networks are effectively equivalent up to variance, enabling tractable posterior distributions.
We explore the loss landscape of fully-connected and convolutional neural networks using random, low-dimensional hyperplanes and hyperspheres. Evaluating the Hessian, H, of the loss function on these hypersurfaces, we observe 1) an unusual excess of the number of positive eigenvalues of H, and 2) a large value of $…
Recurrent Neural Networks (RNNs) can be seriously impacted by the initial parameters assignment, which may result in poor generalization performances on new unseen data. With the objective to tackle this crucial issue, in the context of RNN based classification, we propose a new supervised layer-wise pretraining strate…