用隐式微分加速集合函数学习，提升训练效率。
Learning Set Functions with Implicit Differentiation
- 采用隐式微分避免显式计算大雅可比矩阵，降低计算开销。
- 在合成与真实数据上验证，训练速度显著提升且精度保持稳定。
- 适用于推荐系统、异常检测等集合选择任务，尤其适合大规模场景。
Ou 等人（2022）提出了从最优子集预言机生成的数据中学习集合函数的问题。其方法使用能量模型近似潜在效用函数，并通过均场变分推断估计参数。该过程退化为固定点迭代；然而，随着迭代次数增加，自动微分因反向传播中堆叠的雅可比矩阵过大而变得计算成本极高。本文通过隐式微分解决此问题，并分析了固定点迭代的收敛条件。我们在合成数据和真实世界子集选择任务（包括产品推荐、集合异常检测和化合物选择）上实证表明，该方法具有更高的效率。
原文摘要 · Abstract (English)
Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are estimated via mean-field variational inference. Ou et al. (2022) show this reduces to fixed point iterations; however, as the number of iterations increases, automatic differentiation quickly becomes computationally prohibitive due to the size of the Jacobians that are stacked during backpropagation. We address this challenge with implicit differentiation and examine the convergence conditions for the fixed-point iterations. We empirically demonstrate the efficiency of our method on synthetic and real-world subset selection applications including product recommendation, set anomaly detection and compound selection tasks.
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