A transfer parameterization is developed and validated for GNNs trained with SGD, Adam, and AdamW that yields stable feature updates, learning rate transfer, and improved performance as width and depth increase, and provides a practical recipe for scaling GNNs across a variety of learning tasks and training scenarios.
Abstract
The performance of deep learning models crucially depends on the settings of hyperparameters like learning rate, initialization scale, and weight decay. Hyperparameter transfer aims to make near-optimal hyperparameter settings consistent across model scale, so that large models can be optimized by proxy tuning their smaller, cheaper-to-optimize counterparts. While transfer principles are well-studied in the context of dense neural networks in language and vision tasks, they remain comparatively under-explored for graph neural networks (GNNs). We develop and validate a transfer parameterization for GNNs trained with SGD, Adam, and AdamW. Through theoretical scaling analyses and controlled experiments, we show that the proposed parameterization yields stable feature updates, learning rate transfer, and improved performance as width and depth increase. For SGD, we identify graph-dependent first-layer correction factors and show that their use can accelerate early training in graphs with sparse bag-of-words inputs. For Adam, we explore how different message passing normalizations affect early- and late-training transfer behavior, illustrating the importance of message passing normalization and advocating for an associated hyperparameter. For AdamW, we adapt a parameterization that allows for the joint transfer of weight decay and learning rate. Together, these results provide a practical recipe for scaling GNNs across a variety of learning tasks and training scenarios.
Understanding deep neural networks remains a central challenge in machine learning. In particular, the theoretical properties of even two-layer ReLU networks, especially in the presence of weight decay, remain poorly understood. To this end, we derive a sufficient condition on the hyperparameter settings under which the global minima collapse to the zero solution. Interestingly, our experiments reveal that using AdamW as an optimizer prevents the collapse of the learned parameters, whereas using SGD does not, which may help explain the success of AdamW in deep learning training. In addition, when restricting the input dimension to one, we derive an analytical solution for the globally optimal parameter sets of two-layer ReLU networks and show that $\ell_2$-regularization has a width-invariant effect on connectivity, but its dimensionality-reducing effect becomes stronger as the network width increases. These results provide insight into how width-dependent hyperparameters influence the geometry of regularized loss landscapes.
Mixture-of-Experts (MoE) architectures significantly expand model capacity without a proportional increase in computational cost. However, optimizing their hyperparameters---particularly the learning rate---at extreme scales of both model size and token budget via sweeping remains computationally prohibitive. In this paper, we propose a compute-efficient, two-step hyperparameter transfer framework that estimates optimal learning rates for training large MoE models by transferring them across scaling model widths, and subsequently extrapolating to trillion-token horizons. First, we formulate a Maximal Update Parameterization ($\mu$P) adaptation for MoE architectures utilizing Multi-head Latent Attention (MLA) and the Muon optimizer, demonstrating that optimal learning rates transfer consistently across width-scaled models. Second, we extend this transferability along the token dimension by establishing a predictive scaling law. By applying linear regression to the optimal values derived from small proxy models on limited budgets, we successfully extrapolate the ideal learning rate to massive training horizons (e.g., 10 trillion tokens) with high fidelity ($R^2=0.95$). Consequently, this indicates that proxy training on small models is sufficient to determine the optimal learning rate for the extensive training of large-scale MoEs. We apply the proposed methodology to pretrain our foundation model (155B total, 17B active parameters) from scratch, and the stable training and evaluation results validate that optimal configurations for full-scale target models can be accurately predicted with minimal ablation costs.
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