A Multi-Power Law for Loss Curve Prediction Across Learning Rate Schedules

Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how the pretraining loss of large language models evolves under different learning rate schedules, such as constant, cosine, and step decay schedules. Our proposed law takes a multi-power form, combining a power law based on the sum of learning rates and additional power laws to account for a loss reduction effect induced by learning rate decay. We extensively validate this law on various model sizes and architectures, and demonstrate that after fitting on a few learning rate schedules, the law accurately predicts the loss curves for unseen schedules of different shapes and horizons. Moreover, by minimizing the predicted final pretraining loss across learning rate schedules, we are able to find a schedule that outperforms the widely used cosine learning rate schedule. Interestingly, this automatically discovered schedule bears some resemblance to the recently proposed Warmup-Stable-Decay (WSD) schedule (Hu et al, 2024) but achieves a slightly lower final loss. We believe these results could offer valuable insights for understanding the dynamics of pretraining and designing learning rate schedules to improve efficiency.

Exploring the Robustness of In-Context Learning with Noisy Labels

Recently, the mysterious In-Context Learning (ICL) ability exhibited by Transformer architectures, especially in large language models (LLMs), has sparked significant research interest. However, the resilience of Transformers' in-context learning capabilities in the presence of noisy samples, prevalent in both training corpora and prompt demonstrations, remains underexplored. In this paper, inspired by prior research that studies ICL ability using simple function classes, we take a closer look at this problem by investigating the robustness of Transformers against noisy labels. Specifically, we first conduct a thorough evaluation and analysis of the robustness of Transformers against noisy labels during in-context learning and show that they exhibit notable resilience against diverse types of noise in demonstration labels. Furthermore, we delve deeper into this problem by exploring whether introducing noise into the training set, akin to a form of data augmentation, enhances such robustness during inference, and find that such noise can indeed improve the robustness of ICL. Overall, our fruitful analysis and findings provide a comprehensive understanding of the resilience of Transformer models against label noises during ICL and provide valuable insights into the research on Transformers in natural language processing. Our code is available at https://github.com/InezYu0928/in-context-learning.

Rethinking the Graph Polynomial Filter via Positive and Negative Coupling Analysis

Recently, the optimization of polynomial filters within Spectral Graph Neural Networks (GNNs) has emerged as a prominent research focus. Existing spectral GNNs mainly emphasize polynomial properties in filter design, introducing computational overhead and neglecting the integration of crucial graph structure information. We argue that incorporating graph information into basis construction can enhance understanding of polynomial basis, and further facilitate simplified polynomial filter design. Motivated by this, we first propose a Positive and Negative Coupling Analysis (PNCA) framework, where the concepts of positive and negative activation are defined and their respective and mixed effects are analysed. Then, we explore PNCA from the message propagation perspective, revealing the subtle information hidden in the activation process. Subsequently, PNCA is used to analyze the mainstream polynomial filters, and a novel simple basis that decouples the positive and negative activation and fully utilizes graph structure information is designed. Finally, a simple GNN (called GSCNet) is proposed based on the new basis. Experimental results on the benchmark datasets for node classification verify that our GSCNet obtains better or comparable results compared with existing state-of-the-art GNNs while demanding relatively less computational time.