相关论文: Label-Aware Neural Tangent Kernel: Toward Better G…

A primary advantage of neural networks lies in their feature learning characteristics, which is challenging to theoretically analyze due to the complexity of their training dynamics. We propose a new paradigm for studying feature learning…

The Neural Tangent Kernel (NTK) is the wide-network limit of a kernel defined using neural networks at initialization, whose embedding is the gradient of the output of the network with respect to its parameters. We study the "after kernel",…

Graph Convolutional Networks (GCNs) have emerged as powerful tools for learning on network structured data. Although empirically successful, GCNs exhibit certain behaviour that has no rigorous explanation -- for instance, the performance of…

In wide neural networks, the Neural Tangent Kernel (NTK) remains approximately constant during training, providing a powerful theoretical tool for studying training dynamics, generalization, and connections to kernel methods. However, this…

The neural tangent kernel (NTK) has garnered significant attention as a theoretical framework for describing the behavior of large-scale neural networks. Kernel methods are theoretically well-understood and as a result enjoy algorithmic…

This paper demonstrates that in classification problems, fully connected neural networks (FCNs) and residual neural networks (ResNets) cannot be approximated by kernel logistic regression based on the Neural Tangent Kernel (NTK) under…

The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key…

The performance of the data-dependent neural tangent kernel (NTK; Jacot et al. (2018)) associated with a trained deep neural network (DNN) often matches or exceeds that of the full network. This implies that DNN training via gradient…

Recent theoretical work has shown that massively overparameterized neural networks are equivalent to kernel regressors that use Neural Tangent Kernels(NTK). Experiments show that these kernel methods perform similarly to real neural…

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a…

In Neural Architecture Search (NAS), reducing the cost of architecture evaluation remains one of the most crucial challenges. Among a plethora of efforts to bypass training of each candidate architecture to convergence for evaluation, the…

There are currently two parameterizations used to derive fixed kernels corresponding to infinite width neural networks, the NTK (Neural Tangent Kernel) parameterization and the naive standard parameterization. However, the extrapolation of…

Neural tangent kernels (NTKs) have been proposed to study the behavior of trained neural networks from the perspective of Gaussian processes. An important result in this body of work is the theorem of equivalence between a trained neural…

Scaling laws offer valuable insights into the relationship between neural network performance and computational cost, yet their underlying mechanisms remain poorly understood. In this work, we empirically analyze how neural networks behave…

The Neural Tangent Kernel (NTK), defined as $\Theta_\theta^f(x_1, x_2) = \left[\partial f(\theta, x_1)\big/\partial \theta\right] \left[\partial f(\theta, x_2)\big/\partial \theta\right]^T$ where $\left[\partial f(\theta,…

Deep neural networks have dramatically transformed machine learning, but their memory and energy demands are substantial. The requirements of real biological neural networks are rather modest in comparison, and one feature that might…

We derive analytical expressions for the generalization performance of kernel regression as a function of the number of training samples using theoretical methods from Gaussian processes and statistical physics. Our expressions apply to…

Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC), a powerful empirical and theoretical framework which…

Quantized neural networks have drawn a lot of attention as they reduce the space and computational complexity during the inference. Moreover, there has been folklore that quantization acts as an implicit regularizer and thus can improve the…

Sequential training from task to task is becoming one of the major objects in deep learning applications such as continual learning and transfer learning. Nevertheless, it remains unclear under what conditions the trained model's…