Position: Don't Just "Fix it in Post": A Science of AI Must Study Training Dynamics

A new position paper argues that artificial intelligence research must shift its focus from analyzing finished models to studying the training dynamics that produce them, contending that treating models as static artifacts obscures the origins of their capabilities and failures [1]. The paper, posted to arXiv on June 3, 2026, asserts that models are not fixed objects but snapshots of time-evolving processes shaped by data, objectives, architectures, and optimization dynamics [1]. The authors call for a science of AI that supports predicting outcomes from early training signals, intervening when trajectories go wrong, and designing training procedures that more reliably produce desired properties [1]. Scaling laws have made prediction routine for loss, but extending this success to capabilities, biases, robustness, and safety-relevant behaviors remains the central challenge [1]. The work grounds its requirements in the history and philosophy of science and examines progress in mechanistic interpretability, fairness, memorization, and simplicity bias [1]. Understanding training dynamics is not merely a conceptual exercise; it carries direct consequences for the stability of post-training methods now widely used on large language models. Reinforcement learning from human feedback and related techniques often operate off-policy due to training-inference mismatch and policy staleness, making trust-region control essential for stable optimization [2]. Mainstream methods such as PPO and GRPO approximate this control with ratio-clipping, but the importance ratio can be a poor proxy for distributional shift in long-tailed vocabularies [2]. Recent work has replaced ratio-based clipping with divergence-based masks, yet those approaches still discard gradients once a token crosses a trust-region boundary rather than correcting them [2]. A newly proposed method, Divergence Regularized Policy Optimization, replaces the hard mask with a smooth advantage-weighted quadratic regularizer that attenuates diverging updates and provides corrective signals beyond the boundary, improving stability and efficiency across model scales, architectures, and precision settings [2]. Parallel efforts to impose structure on learning processes are emerging in other domains. Topological Neural Operators, introduced in a separate preprint, lift neural operators from functions on points or edges to cell complexes, using Discrete Exterior Calculus to model interactions through gradient-, curl-, and divergence-type operators [6]. The framework decouples where information flows, governed by fixed topological operators, from how it is transformed, which is learned, yielding models that respect the geometric support of physical quantities and expose conservation and compatibility structure [6]. Hierarchical variants incorporate learned coarse complexes to propagate long-range and topology-dependent information, and controlled studies isolate the benefits of native higher-rank and topological structure across irregular-geometry flow problems [6]. These developments illustrate the broader point that the dynamics of learning—whether in the optimization of language models or the operator learning on physical domains—determine the properties of the resulting systems. The position paper argues that without theories that connect early training signals to eventual behaviors, the field will remain reliant on post-hoc fixes rather than principled design [1].