Allocating limited computation among concurrent learning tasks is difficult when each task must reach a target loss before a deadline but its required training effort is unknown. Existing approaches combine online loss prediction with adaptive resource allocation, yet commonly treat computation as continuously divisible throughput. We instead study a practical setting in which tasks arrive over time and computation is provided by discrete nodes. This setting introduces both uncertain demand and constrained sequential decisions. We propose MARA, which predicts future loss trajectories with conditional flow matching and coordinates compute nodes through a cooperative multi-agent autoregressive policy. A potential-based progress reward supplies intermediate training feedback while preserving the undiscounted task-completion objective. Across in-distribution, reinforcement-learning, and vision workloads, flow matching reduces remaining-resource prediction error relative to weighted least squares. At the scheduler's training load, MARA completes 63.46% of tasks on average, 8.54 percentage points above strong baseline Learning with Adaptive Resource Allocation (LARA), and remains ahead under unseen heavier workloads.
Mathurin Videau, Badr Youbi-Idrissi, David Lopez-Paz +1cs.CL
Neural scaling laws are foundational for language model development, yet standard formulations systematically under- and overestimate loss at data-scarce and overtraining extremes. This failure originates in the underlying assumption that model size and training data impact the loss independently. To address this, we introduce the Skaling law, a generalized functional form that couples model capacity and data through a single interaction exponent. This simple extension reduces the Mean Absolute Percentage Error (MAPE) by 1.5-3x across both interpolation and extrapolation regimes. When paired with a sparse grid strategy restricted to low-compute regimes, the Skaling law achieves accurate full-grid extrapolation using approximately 10x less compute than uniform sweeps. By enabling reliable performance prediction from small-scale experiments, the Skaling law provides a more robust and resource-efficient framework for allocating compute budgets in next-generation model training.
Recent research has established empirical scaling laws to predict model performance on multi-domain data mixtures. However, a theoretical understanding of these model loss behaviors remains absent. In this work, we propose a unified framework to explain the underlying mechanics of data mixing. Our approach extends theoretical perspectives originally developed for standard neural scaling laws (e.g., Kaplan and Chinchilla) to the multi-domain setting. Based on the distributional assumption that domains overlap on fundamental skills while diverging on specialized skills, we identify two key factors that govern the domain losses of models trained on different data mixtures: \textit{Capacity Competition}, where the allocation of finite model capacity couples domain losses globally, and \textit{Noise Reduction}, where optimal weights shift toward harder-to-learn domains to minimize overall noise. Empirical evaluations show that our framework outperforms existing baselines by fitting the loss landscape with a lower Mean Relative Error and identifying higher-performing training mixtures. Most importantly, our model successfully extrapolates across scales, predicting highly effective mixtures for large, unseen scales using parameters fitted on smaller ones. In addition, our model achieves these results using significantly fewer parameters compared to previous empirical laws. Our code is available at https://github.com/meiqwq/Explaining-Data-Mixing-Scaling-Laws.