Foundation models are increasingly trained on sequences of user actions in recommendation, payments, fraud, and commerce, but these models still lack the kind of compute calibration that scaling laws provide for language models. We study a common two-part behavioral-model architecture: a feature-based event embedder maps each multi-modal item to a vector, and a decoder-only transformer predicts the next event from the resulting sequence. Across roughly 600 runs on real interaction data, spanning $10^{15}$-$10^{19}$ training FLOPs, we jointly vary four deployment-relevant axes: the two-part parameter split, critical batch size, model/data allocation, and the number of sampled negatives used after freezing the embedder. A small embedder ($s^{\star}\!\approx\!2\%$ of parameters) is compute-optimal at every budget we test because embedder parameters are both more expensive per step and exposed to far more repeated items than contextualizer parameters. Compute-optimal training is data-heavy relative to text at low compute, but its $D/N$ ratio moves toward the Chinchilla heuristic as compute increases. The sampled training objective and deployed ranking metrics disagree in ways that themselves scale: critical batch size, optimal negative count after freezing, and the agreement between loss and ranking quality all shift with compute and with the chosen evaluation metric. For negative sampling, larger budgets increasingly prefer more negatives; by $10^{19}$ FLOPs the active constraint is candidate-axis memory rather than FLOPs. In behavioral foundation models, the evaluation metric is therefore part of the scaling law: changing it can change the compute-optimal recipe.

翻译：基础模型越来越多地基于推荐、支付、欺诈检测和电商领域的用户行为序列进行训练，但这些模型仍缺乏语言模型缩放定律所提供的计算校准能力。我们研究了一种常见的两部件行为模型架构：基于特征的序列嵌入器将每个多模态项目映射为向量，解码器型Transformer从生成的序列中预测下一个事件。在真实交互数据上约600次运行中，跨越$10^{15}$-$10^{19}$次训练FLOPs，我们联合调整四个与部署相关的维度：两部件参数分配、关键批量大小、模型/数据分配，以及冻结嵌入器后使用的负采样数量。小型嵌入器（参数占比$s^{\star}\!\approx\!2\%$）在测试的每个计算预算下都是计算最优的，因为嵌入器参数每步成本更高，且比上下文器参数接触到更多重复项目。在低计算量下，计算最优训练比文本任务更偏向数据密集型，但随着计算量增加，其$D/N$比率趋向于Chinchilla启发式方法。训练目标与部署排序指标之间存在可缩放的差异：关键批量大小、冻结后的最优负样本数量，以及损失与排序质量之间的一致性，均随计算量和所选评估指标而变化。对于负采样，更大的预算倾向于使用更多负样本；当达到$10^{19}$次FLOPs时，活跃约束变为候选轴内存而非FLOPs。在行为基础模型中，评估指标因此成为缩放定律的一部分：改变它可能改变计算最优的方案。