NTK-SAP improves neural network pruning by aligning training dynamics.
problem Improving neural network pruning to reduce training time and memory.
method Prune connections based on the spectrum of the Neural Tangent Kernel (NTK), using multiple random weight realizations and random inputs.
result Empirically, NTK-SAP achieves better performance than all baselines on multiple datasets.
The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting kernel and it stays constant during training. The NTK was also implicit in some…
Study on neural networks with regularisation and its impact on training dynamics.
problem Understanding the dynamics of neural networks with regularization.
method Established explicit dynamics for neural networks with a regularizing term, linearizing around initialisation.
result The regularisation term modifies the standard NTK dynamics, leading to new insights into network training.
Deep learning dynamics and NTK evolution studied through diverse measures.
problem Understanding the training dynamics of deep neural networks and their loss landscapes.
method Phenomenological analysis of training dynamics in multiple architectures and datasets.
result Training dynamics exhibit a chaotic initial transient followed by a stable phase, with the NTK evolving to match full network performance.
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.
The dynamics of DNNs during gradient descent is described by the so-called Neural Tangent Kernel (NTK). In this article, we show that the NTK allows one to gain precise insight into the Hessian of the cost of DNNs. When the NTK is fixed during training, we obtain a full characterization of the asymptotics of the spectr…
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.
GNTK reveals convergence of GNNs on large graphs.
problem Understanding and optimizing GNNs on large graphs.
method Graph Neural Tangent Kernels (GNTK) and graphons.
result GNTKs converge to graphon NTKs on large graphs, enabling task inference.
This paper explains robust overfitting in wide DNNs using adversarial training and NTK theory.
problem Robust overfitting in adversarially trained wide DNNs.
method Theoretical analysis using neural tangent kernel (NTK) theory and adversarial training dynamics.
result Adversarial training can lead to robust overfitting in wide DNNs, which can be mitigated by the proposed Adv-NTK method.
Study shows how neural networks learn eigenfunctions of the NTK in underparameterized settings.
problem Understanding the dynamics of MSE optimization in underparameterized neural networks.
method Analysis of gradient flow dynamics, focusing on eigenfunctions of the NTK.
result Eigenfunctions of the NTK determine the learning dynamics in underparameterized networks.
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.
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 paper analyzes a neural network two-sample test using kernel analysis.
problem Determining if two datasets come from the same distribution.
method Time-analysis on a neural tangent kernel (NTK) two-sample test, extending to realistic neural network dynamics.
result Training times needed to detect deviations are well-separated in null and alternative hypothesis scenarios.
Study on Neural Tangent Kernel of Matrix Product States and their convergence.
problem Understanding the convergence of Neural Tangent Kernel of Matrix Product States.
method Analyzing the Neural Tangent Kernel of Matrix Product States and proving its convergence in the infinite bond dimensional limit.
result The Neural Tangent Kernel of Matrix Product States converges to a constant matrix during training.
The study explains how neural networks align their kernels to target functions during training.
problem Understanding how neural networks align their kernels to target functions during training.
method Theoretical analysis of kernel evolution in toy models and deep networks.
result Kernel alignment naturally emerges during training to accelerate convergence and improve generalization.
PINNs fail to train due to NTK convergence rate discrepancies.
problem Understanding why PINNs fail to train during gradient descent.
method Analyzing PINNs through the Neural Tangent Kernel (NTK) perspective.
result PINNs' NTK converges to a deterministic kernel with constant convergence rate during training.
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.
Frequency bias affects neural network training on non-uniform data.
problem Understanding how frequency bias impacts neural networks trained on non-uniformly distributed data.
method Used the Neural Tangent Kernel (NTK) model to explore the effect of variable density on training dynamics.
result Convergence time for learning a pure harmonic function depends on the local density at a point.
This work analyzes when contrastive models are close to PCA or kernel methods.
problem Understanding when contrastive models are equivalent to kernel methods or PCA.
method Analyzing the training dynamics of two-layer contrastive models with non-linear activation.
result Wide contrastive models with cosine similarity based losses are close to PCA.
3-layer NTK models generalize better than 2-layer models, especially with large input dimensions.
problem Understanding the generalization of overparameterized neural networks.
method Analyzing the 3-layer NTK model's test error and comparing it to 2-layer NTK models.
result 3-layer NTK models have a faster descent in test error with respect to the number of neurons in the second hidden layer.
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.
This paper analyzes deep and wide transformer training dynamics.
problem Understanding the training dynamics of infinitely deep and wide transformers.
method Develops a mean-field framework for gradient-based training of transformers, controlling a neural PDE.
result Establishes a rigorous foundation for gradient-based transformer training, proving convergence to global minima.
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.
The empirical NTK diverges from the NTK in classification problems during overtraining.
problem The divergence of empirical NTK from NTK in classification problems during overtraining.
method Demonstrated strictly positive definiteness of NTKs for FCNs and ResNets. Proved divergence of neural network parameters during training with cross-entropy loss.
result The empirical NTK does not uniformly converge to the NTK across all times on the training samples as the network width increases.
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.
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.
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.
NTK neural networks are robust to adversarial attacks in nonparametric regression.
problem Adversarial robustness of neural networks in nonparametric regression.
method Gradient flow with early stopping for NTK neural networks, proving robustness in Sobolev spaces.
result NTK neural networks achieve optimal adversarial robustness rates in Sobolev spaces.
Deep networks can classify data on smooth curves with high probability.
problem Classifying data from two disjoint smooth curves on the unit sphere.
method Gradient descent on a deep neural network, proving convergence and generalization via NTK dynamics.
result Randomly-initialized gradient descent learns to classify all points on the two curves with high probability when the network is sufficiently deep.
Generalizes NTK for surrogate gradient learning in neural networks.
problem Lack of theoretical foundation for surrogate gradient learning.
method Generalizes neural tangent kernel (NTK) for surrogate gradient learning (SGL).
result Surrogate gradient NTK provides a good characterization of SGL.
Paper calculates eigenvalue decay rates for neural network kernels on general domains.
problem Determining eigenvalue decay rates for neural network kernels on arbitrary domains.
method Proved dynamics of wide neural networks approximates NTK on general domains, used minimax optimality and interpolation spaces.
result Provided strategy to calculate eigenvalue decay rates for neural network kernels.
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.
Linearized attention fails to converge to NTK limit even at large widths.
problem Understanding the convergence of attention mechanisms to the kernel regime.
method Analyzes linearized attention and its relationship to the NTK limit, considering practical widths and conditions.
result Linearized attention does not converge to its NTK limit at any practical width, revealing a fundamental trade-off.
This paper improves neural network learning by escaping the NTK regime and efficiently learning sparse polynomials.
problem Learning sparse polynomials efficiently using neural networks.
method Spectral analysis of NTK, identifying 'good' directions, and constructing a regularizer.
result Gradient descent on a two-layer neural network can learn sparse polynomials efficiently, improving over the NTK and QuadNTK.
This paper studies nonlinear representation learning dynamics beyond the NTK regime.
problem Efficient reasoning and inference in raw sensory data representations.
method Identifies common model structure assumption and data-architecture alignment condition for global convergence and optimality.
result Theoretical framework explains network size effects and provides practical model structure guidelines.
This work analyzes PINNs for advection-diffusion equations using NTK theory.
problem Understanding and resolving the training difficulties of PINNs for advection-diffusion equations.
method Neural Tangent Kernel (NTK) analysis of PINNs for the linear advection-diffusion equation (LAD).
result PINNs struggle due to spectral bias and convergence rate disparity, especially in advection-dominated and diffusion-dominated regimes.
Infinitely wide neural nets perform well on small datasets.
problem Performing well on small datasets with limited training samples.
method Using Neural Tangent Kernels (NTKs) for kernel regression.
result NTK SVM outperforms Random Forests and Convolutional NTK on CIFAR-10 with 10-640 training samples.
The study examines spectral dynamics in deep neural networks, predicting how outliers evolve during training.
problem Understanding spectral evolution in deep neural networks during training.
method Developed a two-level dynamical mean-field theory (DMFT) to track spectral dynamics.
result The theory predicts how outliers evolve with training time, width, output scale, and initialization variance.
Early neural networks can be simplified to linear models, revealing surprising simplicity.
problem Complexity of neural network learning dynamics.
method Formal proof and empirical verification of early-time learning dynamics of neural networks.
result Early learning dynamics of neural networks can be approximated by simple linear models.
This paper studies large-width asymptotics for ReLU neural networks with α-Stable initializations.
problem Characterizing the large-width behavior of ReLU neural networks with α-Stable initializations.
method Analysis of the large-width distributions and training dynamics of ReLU neural networks initialized with α-Stable distributions.
result For ReLU neural networks with α-Stable initializations, the large-width training dynamics achieve zero training error at a linear rate, characterized by a random kernel.
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.
Ensembles of neural networks improve training dynamics and performance.
problem Improving neural network performance through model size increase.
method Defining collegial ensembles (CE) as multiple independent models trained as a single model, and using theoretical results on NTK to optimize architecture search.
result CE dynamics simplify and scale favorably, resembling wide models, and can be efficiently implemented using group convolutions and block diagonal layers.
This paper explains GCNs using NTKs and improves their performance.
problem GCNs' performance degrades with depth, and skip connections marginally improve it.
method Derive NTKs for GCNs, validate with simulations, propose NTK as a surrogate model.
result Suitable normalisation can prevent drastic performance drop with depth.
New limits found for training deep learning models efficiently.
problem Optimizing the training speed of deep learning models without sacrificing accuracy.
method Applied stochastic thermodynamics to set speed limits for neural network training.
result Training neural networks is optimal within certain scaling assumptions.
NTK theory fails to predict practical behavior of large-width neural networks.
problem Theoretical limits of NTK do not match practical neural network architectures.
method Empirical investigation of NTK's applicability to large-width architectures.
result Practically relevant behavior of large-width architectures differs from NTK theory.
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.
New NTK bounds show deep networks with minimum over-parameterization can still memorize and optimize.
problem Understanding memorization and optimization in sub-linear over-parameterized deep networks.
method Lower bound on NTK eigenvalues for deep networks with minimum over-parameterization.
result Deep networks with minimum over-parameterization can still be powerful memorizers and optimizers.
ResNets and DenseNets converge to NTK with depth and width, offering advantages for kernel regression.
problem Understanding convergence of ResNets and DenseNets to Neural Tangent Kernel (NTK).
method Analysis of finite width and depth corrections for NTK of ResNets and DenseNets.
result ResNets and DenseNets can converge to NTK with depth and width, unlike vanilla networks.