Scaling laws are well studied for language models and first-stage retrieval, but not for reranking. We present the first systematic study of scaling laws for cross-encoder rerankers across pointwise, pairwise, and listwise objectives. Across model size and training exposure, ranking quality follows predictable power laws, enabling larger rerankers to be forecast from smaller runs. Using models up to 150M parameters, we forecast 400M and 1B rerankers on MSMARCO-dev and TREC DL. Beyond forecasting, we derive compute-allocation rules from the fitted joint scaling law and compare them with equal-compute checkpoints, showing that retrieval metrics often favor data-heavy scaling, though the recommendation depends on the training objective. The forecasts are accurate and typically conservative, making them useful for planning expensive large-model training. These results provide practical scaling principles for industrial reranking systems, and we will release code and evaluation protocols.

翻译：规模定律在语言模型和第一阶段检索中已得到充分研究，但在重排序领域尚属空白。我们首次针对逐点、逐对和列表式目标函数下的交叉编码器重排序器开展了系统性规模定律研究。在模型规模和训练曝光度维度上，排序质量遵循可预测的幂律关系，使得通过小规模运行结果预测更大规模重排序器成为可能。基于参数规模达1.5亿的模型，我们在MSMARCO-dev和TREC DL数据集上预测了4亿和10亿参数规模的重排序器性能。除预测外，我们还从拟合的联合规模定律中推导出计算资源分配规则，并将其与等量计算资源的检查点进行比较，结果表明检索指标通常偏向数据密集型的规模扩展策略，但具体建议取决于训练目标函数。该预测方法准确且通常趋于保守，因此对规划昂贵的大规模模型训练具有实用价值。这些研究成果为工业级重排序系统提供了可操作的规模扩展原则，我们将公开相关代码与评估协议。