发表机构
Neryva（内里瓦）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多任务学习中损失尺度不匹配导致同方差加权性能下降的问题，提出BPGS方法，经实验验证其在合成测试和三个真实基准上均表现出良好的尺度鲁棒性与性能。
AI 中文摘要
多任务学习通常会结合跨度达数个数量级的损失，这会导致同方差不确定性加权方法的性能严重下降。我们提出了有界精度几何缩放（Bounded Precision-Geometry Scaling，BPGS），该方法通过锚定到分离的批次损失统计量的有界sigmoid参数化，映射每个任务的对数方差，并将网络优化与不确定性优化解耦。其归一化任务权重在非退化损失尺度下可证明对均匀重缩放具有不变性。我们在合成压力测试和三个真实世界基准上评估BPGS：NYUv2密集预测、Yeast多标签分类和RF1多目标回归。在从×1到×1000的纯损失重缩放下，其宏分数从0.777变为0.778，而Kendall加权则从0.780降至0.637；对Kendall权重进行ℓ₁归一化并未缩小差距。在NYUv2上，BPGS记录了所有对比方法（包括Nash-MTL）中最低的深度绝对相对误差（0.223）、深度RMSE（0.790）和总损失（1.891）。对批次大小和校准的敏感性研究显示，在测试范围内变化很小，相对于Kendall的运行时开销低于1%。BPGS获得了最高的Yeast微F1（0.616），并在RF1上具有竞争力，尽管PCGrad在该数据集上的RMSE和MAE领先。这些发现确立了BPGS作为同方差不确定性加权的尺度鲁棒替代方案，在损失尺度差异主导多任务优化时尤为有效。
英文摘要
Multi-task learning often combines losses that span several orders of magnitude, causing homoscedastic uncertainty weighting to degrade severely. We propose Bounded Precision-Geometry Scaling (BPGS), a method that maps each task's log-variance through a bounded sigmoid parameterisation anchored to detached batch loss statistics, and decouples network optimisation from uncertainty optimisation. Its normalised task weights are provably invariant to uniform rescaling under non-degenerate loss scales. We evaluate BPGS on synthetic stress tests and three real-world benchmarks: NYUv2 dense prediction, Yeast multi-label classification, and RF1 multi-target regression. Under pure loss rescaling from $\times 1$ to $\times 1000$, its macro score changes from 0.777 to 0.778, whereas Kendall weighting drops from 0.780 to 0.637; $\ell_1$-normalising Kendall's weights does not close the gap. On NYUv2, BPGS records the lowest depth absolute relative error (0.223), depth RMSE (0.790), and total loss (1.891) among all compared methods, including Nash-MTL. Sensitivity studies on batch size and calibration show small variation across the tested ranges, and runtime overhead relative to Kendall is under 1%. BPGS posts the highest Yeast micro-F1 (0.616) and is competitive on RF1, though PCGrad leads RMSE and MAE there. These findings establish BPGS as a scale-robust alternative to homoscedastic uncertainty weighting, notably effective when loss-scale disparities dominate multi-task optimisation.
