Neural Tangents simplifies infinite-width neural networks for research.
problem Training and studying infinite-width neural networks.
method High-level API for specifying complex architectures, analytical or gradient-based training, and automatic distribution.
result Analytical training of infinite-width networks and automatic parallelization.
This study examines the practical equivalence of Laplace and neural tangent kernels.
problem Understanding the practical equivalence of Laplace and neural tangent kernels.
method The study matches the kernels exactly and by matching posteriors of a Gaussian process. It also analyzes the kernels in R^d and experiments with them in regression tasks.
result The Laplace and neural tangent kernels are practically equivalent.
Improved standard parameterization yields well-defined neural tangent kernel.
problem Extrapolation of standard parameterization to infinite width is problematic.
method Proposed an improved extrapolation of the standard parameterization.
result Improved standard parameterization yields similar accuracy to NTK parameterization but with better correspondence to finite width networks.
The study examines Fisher information matrices and neural tangent kernels for simple ReLU networks with random weights.
problem Understanding the relationship between Fisher information matrices and neural tangent kernels for 2-layer ReLU networks.
method Analyzes Fisher information matrices and neural tangent kernels for 2-layer ReLU networks with random hidden weights, focusing on spectral decomposition and eigenfunctions.
result Obtained an approximation formula for functions represented by 2-layer neural networks.
Generalizes neural tangent kernel analysis for two-layer networks with noise and regularization.
problem Limitations of NTK analysis in deep learning practice.
method Generalized NTK analysis for two-layer neural networks with weight decay and gradient noise.
result Noisy gradient descent with weight decay exhibits 'kernel-like' behavior and converges linearly.
The neural tangent kernel equivalence theorem fails in practice.
problem Does the neural tangent kernel (NTK) equivalence theorem hold in practical neural network training?
method Rigorously derived NTK and conducted numerical experiments to evaluate the equivalence theorem.
result Adding a layer to a neural network and the corresponding updated NTK do not yield matching changes in predictor error.
Wide neural networks become linear, with constant tangent kernel, due to Hessian scaling.
problem Understanding the linearity of large non-linear models and the tangent kernel.
method Analyzing the scaling properties of the Hessian matrix of neural networks as their width increases.
result The constancy of the tangent kernel is due to the scaling properties of the Hessian matrix.
A new method approximates tangent spaces to simplify neural networks.
problem Efficiency of hierarchical neural networks is hindered by their complexity and training requirements.
method Approximates tangent subspace to enable sparse representation and switch to shallow networks.
result The method improves and sometimes surpasses the performance of original networks after a few epochs.
Derives a family of hyperparameter scaling strategies for neural networks.
problem Optimizing hyperparameters for wide and deep neural networks.
method Introduces a one-parameter family of hyperparameter scaling strategies.
result Reveals proper scaling of depth with width for large-scale models.
The paper examines the neural tangent kernel for PINNs solving general PDEs and finds convergence conditions.
problem Analyzing the convergence of neural tangent kernel for PINNs solving general PDEs.
method Analysis of NTK initialization and convergence during training for general PDEs using PINNs.
result Homogeneity of differential operators is crucial for NTK convergence.
New method finds sparse networks without labels, improving performance.
problem Sparse connectivity in neural networks to reduce memory and energy demands.
method Neural Tangent Transfer method to find sparse networks without labels.
result Sparse networks achieve higher classification performance and faster convergence.
This work challenges the Neural Tangent Kernel's role in overparameterized neural networks, especially with large width and depth.
problem The Neural Tangent Kernel's behavior in overparameterized neural networks with large width and depth is unclear.
method Experimental and theoretical analysis of ReLU networks with large width and depth.
result The aggregate norm of hidden neuron deviations does not vanish in infinitely-wide ReLU networks, indicating non-trivial behavior.
New framework establishes positivity of DNTK for PINNs.
problem Establishing positivity of NTK for PINNs with multiple differential operators.
method Proposed Differential Neural Tangent Kernel (DNTK) for PINNs.
result Positivity of infinite width DNTK for various activation functions and differential operators.
Paper introduces mcTangent for real-time dynamical systems.
problem Real-time accurate solutions for complex dynamical systems.
method Synergy of tangent slope learning, model-constrained approach, sequential learning, and data randomization.
result Robust and long-time accurate solutions for various equations.
Paper introduces RNTK for recurrent neural networks, improving performance across various datasets.
problem Understanding and optimizing overparametrized recurrent neural networks.
method Developed the Recurrent Neural Tangent Kernel (RNTK) to compare inputs of different lengths.
result RNTK offers significant performance gains over other kernels, including standard NTKs, across multiple datasets.
Gradient descent benefits from tangent kernel advantages under specific conditions.
problem Comparing gradient descent with tangent kernel methods in learning.
method Analysis of gradient descent and tangent kernel methods under different conditions.
result Gradient descent can achieve small error only if tangent kernel methods have a non-trivial advantage, but this advantage can be very small.
Paper studies ResNet dynamics using NTH, reducing width requirement.
problem Understanding ResNet dynamics and improving training efficiency.
method Uses Neural Tangent Hierarchy (NTH) to analyze ResNet dynamics.
result Reduces width requirement from quartic to cubic for ResNet.
New method for neural network uncertainty quantification using empirical Neural Tangent Kernel.
problem Accurately quantify uncertainty in neural network predictions.
method Post-hoc, sampling-based approach using gradient-descent on linearized networks.
result Method effectively approximates Gaussian process posterior and outperforms existing methods in efficiency and accuracy.
Quantum neural tangent kernels help understand variational quantum circuits in machine learning.
problem Designing and predicting performance of variational quantum circuits.
method Using quantum neural tangent kernels and dynamical equations for loss functions.
result Analytical solutions for training dynamics in variational quantum circuits.
A new method uses neural tangent kernel to efficiently compute MMD statistic.
problem Efficiently computing Maximum Mean Discrepancy (MMD) statistic with low memory and computational complexity.
method Identifies a connection between neural tangent kernel (NTK) and MMD to develop a computationally and memory-efficient approach.
result The proposed NTK-MMD statistic is validated through numerical experiments on synthetic and real-world datasets.
Novel algorithms improve efficiency of finite width NTK computation.
problem Efficiency of computing finite width Neural Tangent Kernel (NTK).
method Leveraging neural network structure, propose two novel algorithms.
result Significantly improved efficiency in compute and memory requirements.
Deep neural kernels and Laplace kernel have equivalent RKHS on spheres.
problem Comparing RKHS of deep neural tangent and Laplace kernels.
method Proof of RKHS equivalence using sphere restrictions and kernel properties.
result RKHS of deep neural tangent kernel and Laplace kernel are the same on Sd−1. Regularization effect found in neural feature alignment.
problem Implicit regularization in deep learning models.
method Geometrical viewpoint and analysis of Rademacher complexity.
result Neural features align along task-relevant directions, leading to regularization.
In this paper, we theoretically prove that the deep ReLU neural networks do not lie in spurious local minima in the loss landscape under the Neural Tangent Kernel (NTK) regime, that is, in the gradient descent training dynamics of the deep ReLU neural networks whose parameters are initialized by a normal distribution i…
This work introduces the concept of tangent space regularization for neural-network models of dynamical systems. The tangent space to the dynamics function of many physical systems of interest in control applications exhibits useful properties, e.g., smoothness, motivating regularization of the model Jacobian along sys…
We analyze GANs using neural tangent kernels, revealing flaws and advancing understanding.
problem Flaws in previous GAN analysis models.
method Neural Tangent Kernel framework for infinite-width discriminator.
result New insights into GAN convergence and generated distribution.
This paper analyzes convergence of FL for neural networks using NTK.
problem Theoretical guarantees of FL for neural networks with explicit forms and multi-step updates are unexplored.
method FL-NTK framework for federated learning of ReLU neural networks trained by gradient descent.
result FL-NTK converges to a global-optimal solution at a linear rate with proper learning parameters.
Measures neural network complexity using tangent space diversity.
problem Estimating the true complexity of neural networks.
method Entropy-based measure of tangent spaces from different inputs.
result Captures effective complexity, not just theoretical capacity.
This paper improves neural tangent kernels for better generalization and local elasticity.
problem Performance gap between neural tangent kernels and real-world neural networks.
method Introduces label-aware kernels using Hoeffding decomposition.
result Models trained with proposed kernels simulate NNs better in terms of generalization and local elasticity.
Empirical study shows standard CNNs deviate from NTK predictions.
problem Understanding how standard finite-width CNNs behave compared to their infinite-width NTK counterparts.
method Empirical analysis of AlexNet and LeNet architectures.
result Standard CNNs deviate significantly from their NTK counterparts, but deviation decreases with wider networks.
Paper explains spectral bias in neural networks and its relation to neural tangent kernel.
problem Understanding the spectral bias of deep learning models.
method Decomposes neural network training into eigenfunctions of the neural tangent kernel, proving convergence rates.
result Neural networks learn functions with lower complexity faster, explained by eigenvalues of the neural tangent kernel.
Laplace kernel and Neural Tangent Kernels are shown to be nearly identical for normalized data.
problem Understanding the similarity between Laplace and Neural Tangent Kernels.
method Theoretical analysis and experiments on normalized data.
result Laplace kernel and Neural Tangent Kernels have nearly identical eigenfunctions and RKHS for normalized data.
New method uses neural tangent kernel for efficient active learning.
problem Efficiently approximating deep learning's look-ahead selection criteria.
method Approximates retraining with neural tangent kernel for active learning.
result Approximation works asymptotically and enables sequential active learning.
TKIL improves class-balanced performance in incremental learning.
problem Catastrophic forgetting in sequential learning tasks.
method Introduces Tangent Kernel for Incremental Learning (TKIL) based on Neural Tangent Kernel (NTK).
result TKIL achieves better overall accuracy and variance across classes.
This paper explains why ResNets generalize better than FFNets using neural tangent kernels.
problem Understanding why deep ResNets generalize better than deep FFNets.
method Using neural tangent kernels to compare the learnability of functions induced by the kernels of ResNets and FFNets.
result The kernel of ResNets does not exhibit degeneracy as depth increases, unlike FFNets.
Generalizes leverage score sampling for neural networks, accelerating kernel methods and deep learning.
problem Accelerating kernel methods and deep learning training.
method Generalizes leverage score sampling to neural networks and proves equivalence to neural tangent kernel ridge regression.
result Equivalence between regularized neural network and neural tangent kernel ridge regression under leverage score sampling initialization.
OGD proves robustness to Catastrophic Forgetting in Continual Learning.
problem Catastrophic Forgetting in Continual Learning with deep neural networks.
method Theoretical framework based on Neural Tangent Kernel for OGD.
result First generalization bound for SGD and OGD in Continual Learning.
Tensor programs prove neural network limits for any architecture.
problem Understanding the limits of neural networks of any architecture.
method Prove convergence of neural network's Tangent Kernel (NTK) to a deterministic limit as network widths increase.
result Identify conditions for correct NTK limit calculation based on gradient independence assumption.
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.
New framework for understanding infinite-width neural networks.
problem Understanding the infinite-width limit behavior of neural networks.
method General framework to study limit behavior of neural models based on hyperparameter scaling.
result Derives scaling for existing mean-field and neural tangent kernel limits and introduces new dynamically stable limits.
Neural networks with DAGs show linearity as width increases.
problem Understanding linearity in neural networks with arbitrary DAG structures.
method Analyzing the transition to linearity in networks with arbitrary DAGs, characterizing width by minimum in-degree.
result General neural networks with DAGs exhibit linearity as width approaches infinity.
The paper examines stability of ReLU networks in tangent space and activation regions.
problem Stability and sensitivity of ReLU networks to small changes.
method Tangent sensitivity measure for ReLU networks, focusing on stability induced by individual examples.
result Tangent sensitivity correlates with the distribution of activation regions and generalization gap.
Study of deep neural networks' NTK evolution during training.
problem Understanding the performance gap between deep neural networks and kernel regression.
method Derive an infinite hierarchy of ordinary differential equations (NTH) to capture gradient descent dynamics of deep neural networks.
result Truncated NTH approximates the dynamic of the NTK up to arbitrary precision under certain conditions.
New insights into how overfitting affects neural networks' performance.
problem Understanding the generalization of overfitted two-layer neural networks.
method Analyzing the NTK model with ReLU activation, focusing on min ℓ2-norm solutions. result Generalization error of overfitted NTK models approaches a small limiting value, even with infinite neurons and samples.
DNNs improve SIMP method but not spatially invariant, study shows.
problem Improving SIMP method with DNNs but maintaining spatial invariance.
method Use of DNNs for density field generation, study of NTK filter properties.
result DNNs lead to a non-spatially invariant filter, requiring embeddings for spatial invariance.
Averaged SGD achieves optimal convergence rate for neural networks in the NTK regime.
problem Convergence analysis of averaged stochastic gradient descent for neural networks.
method Analyzed convergence of averaged stochastic gradient descent for overparameterized two-layer neural networks.
result Achieved minimax optimal convergence rate with global convergence guarantee.
Paper establishes rates of universal approximation for neural tangent kernels using transport mappings.
problem Universal approximation for neural tangent kernels with microscopic weight changes.
method Generic scheme to approximate functions with NTK using transport mappings, constructed via Fourier transforms.
result Approximation of continuous functions with roughly 1 / δ^(10d) nodes, where δ depends on function continuity.
Paper analyzes sample complexity of polynomial neural networks.
problem Understanding the sample complexity of polynomial neural networks.
method Extends previous literature to polynomial neural networks and analyzes sample complexity.
result Obtains novel results on sample complexity of polynomial neural networks.