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.
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.
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.
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 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.
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.
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.
Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the empirical performance of neural networks are observed to exceed their linearized …
New framework connects two neural network theories, improving finite-width approximations.
problem Theoretical guarantees for neural network training in general cases.
method Developed a general framework linking mean-field and constant kernel theories.
result Discrete-time MF limit provides better approximation for finite-width nets.
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.
Recent work by Jacot et al. (2018) has shown that training a neural network using gradient descent in parameter space is related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019) built on this result by establishing that the output of a neural network traine…
This work connects neural network training to convex optimization via the NTK.
problem Understanding and optimizing neural network training via convex programs.
method Interpreting gated ReLU network as MKL, showing NTK equivalence, and improving weights.
result The NTK cannot perform better than the optimal MKL kernel on the training set.
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.
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.
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.
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.
DEQs and explicit networks are nearly equivalent for Gaussian mixtures.
problem Understanding the equivalence between DEQs and explicit neural networks.
method Random matrix theory and analysis of kernel matrices.
result A shallow explicit network can mimic the kernel of a DEQ.
Theoretical framework explains why few epochs are enough for LLM fine-tuning.
problem Understanding why few epochs are sufficient for LLM fine-tuning.
method Combining early stopping theory with attention-based Neural Tangent Kernel (NTK) for LLMs.
result Formalizes convergence rate of attention-based fine-tuning with respect to sample size.
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.
Efficiently applies NTK to large-scale datasets using random features.
problem Computational limitations of kernel methods for large-scale datasets.
method Proposes a sketching-based algorithm combining random features of arc-cosine kernels to construct an efficient feature map of the NTK.
result Achieves comparable error bounds to exact kernel methods but with significantly reduced feature dimensionality.
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…
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.
Lossless compression of deep neural networks using NTK and RMT.
problem Compressing large-scale deep neural networks for low-power devices.
method High-dimensional neural tangent kernel approach.
result Asymptotic spectral equivalence between NTK matrices of wide DNNs enables lossless compression.
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.
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.
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.
One LN layer stabilizes neural network extrapolation.
problem Understanding neural networks' extrapolation behavior.
method Applied NTK theory to infinitely-wide networks.
result Adding one LN layer stabilizes network outputs.
Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An efficient algorithm to c…
Improves understanding of neural network predictions using influence functions.
problem Challenges in understanding neural network predictions.
method Utilized NTK theory to calculate influence functions for over-parameterized neural networks.
result Proved that the approximation error of IF can be arbitrarily small in the over-parameterized regime.
Study on how adversarial training affects neural network kernels and robustness.
problem Understanding and improving adversarial robustness in neural networks.
method Empirical study of the evolution of the empirical Neural Tangent Kernel (NTK) under standard and adversarial training.
result Adversarial training leads to a new kernel that provides robustness, even when non-robust training is performed on top of it.
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…
Wide neural networks on R generalize well with early stopping.
problem Understanding generalization in wide neural networks.
method Analysis of spectral properties of NTK and NNK, convergence of NNK to NTK, minimax rates, and early stopping strategy.
result Wide neural networks trained with early stopping achieve the minimax rate and generalize well.
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide 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.
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.
The fundamental learning theory behind neural networks remains largely open. What classes of functions can neural networks actually learn? Why doesn't the trained network overfit when it is overparameterized? In this work, we prove that overparameterized neural networks can learn some notable concept classes, including…
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 method controls sparse feature updates in deep networks.
problem Understanding sparse feature updates in deep networks during training.
method Iterative linearised training method to control sparse feature updates.
result Iterative linearised training surprisingly performs on par with standard training, requiring less frequent feature learning.
A longstanding goal in the theory of deep learning is to characterize the conditions under which a given neural network architecture will be trainable, and if so, how well it might generalize to unseen data. In this work, we provide such a characterization in the limit of very wide and very deep networks, for which the…
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.
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.
Neural networks outperform NTK on compositional tasks, revealing a complexity gap.
problem Understanding the performance gap between neural networks and NTK on tasks with compositional structure.
method Characterized Fourier and architectural complexities, and analyzed the minimax rates of the architecture class.
result The NTK estimator is exponentially sub-optimal compared to the minimax floor when complexities decouple.
New algorithms use neural networks to minimize regret in contextual bandits.
problem Minimizing regret in sequential decisions with side information.
method Proposes NN-UCB and NTK-UCB algorithms using neural networks.
result Proves sublinear regret bounds for contextual bandits.
New approach to neural networks by incorporating observation noise and arbitrary prior means.
problem Misspecification on noisy data and limitations of NTK-GP equivalence.
method Introducing a regularizer for observation noise and proposing a shifted network for arbitrary prior means.
result Removes key obstacles to practical Gaussian process modeling in neural networks.
Kempe discusses NTK approach to machine learning problems.
problem Generally unsolvable machine learning problems.
method NTK approach focusing on kernel formulations.
result Practical applications like data distillation and adversarial robustness.
New bounds on NTK's smallest eigenvalue for arbitrary data without distributional assumptions.
problem Existing bounds on NTK's smallest eigenvalue require distributional assumptions and high-dimensional data.
method Novel application of the hemisphere transform.
result Bounds on NTK's smallest eigenvalue hold with high probability even for constant input dimension.
We derive finite width and depth corrections for the Neural Tangent Kernel (NTK) of ResNets and DenseNets. Our analysis reveals that finite size residual architectures are initialized much closer to the "kernel regime" than their vanilla counterparts: while in networks that do not use skip connections, convergence to t…