Now we return to the second part of (9). This illustrates how tight the upper bound is. We use a GeForce RTX 2080 Ti GPU for all experiments. Instead, we always carve out a validation set from our training set. Figure 1 The batch size is set to 128, and 1000 fixed images are used for the validation data. Here we provide the raw hypergradients corresponding to the outer optimization shown in Appendices: Figure 1.

We appreciate the reviewers' time and suggestions! We address them all and report new experimental results below. Although DIH can be helpful to identify noisy data in noisy-label setting (ref.Middle plot in Figure 1), DIHCL still achieves 90.34% test-set accuracy under 40% symmetric label noise on CIFAR10 (ref.Top plot in Figure 1). The statement may be revised that "updating in-6 Is the method specific to cyclic learning rate... DI-23 HCL is applicable to other learning rate schedules. We report the result of DIHCL with a piecewise exponential decay learning rate in Figure 1.

Now we return to the second part of (9). This illustrates how tight the upper bound is. We use a GeForce RTX 2080 Ti GPU for all experiments. Instead, we always carve out a validation set from our training set. Figure 1 The batch size is set to 128, and 1000 fixed images are used for the validation data. Here we provide the raw hypergradients corresponding to the outer optimization shown in Appendices: Figure 1.

Lemma A.5 of [ 19 ] we have By substituting ( A.5) into ( A.1) we have, All experiments are conducted on a single NVIDIA V100. It runs on the GNU Linux Debian 4.9 operating The experiment is implemented via PyTorch 1.6.0. This makes the learning problem of CIFAR100 much harder. To demonstrate the fact that the over-fitting problem all comes from perturbation stability in Section 3.2(3), we We found this schedule is the most effective one when only training on the original CIFAR10. In this part, we provide a complete visualization for the two parts in Eqn. We test WideResNet-34 on CIFAR10 and CIFAR10.

In this work, we introduce a novel approach for optimizing LLM training by adjusting learning rates across weights of different components in Transformer models. Traditional methods often apply a uniform learning rate across all network layers, potentially overlooking the unique dynamics of each part. Remarkably, our introduced relative learning rates, RLRS, method accelerates the training process by up to $23\%$, particularly in complex models such as Mixture of Experts (MoE). Hyperparameters of RLRS can be efficiently tuned on smaller models and then effectively reused on models up to $27\times$ larger. This simple and effective method results in a substantial reduction in training time and computational resources, offering a practical and scalable solution for optimizing large-scale neural networks.