[论文] Neural Networks with Differentiable Belief-Function Layers

论文概要

研究领域: ML
作者: Antonin Sulc
发布时间: 2026-10-24
arXiv: 2610.30173

中文摘要

Yager 1987 年提出的证据组合规则 ⊞ 出于认识论动机：在高冲突下，概率质量应重分配到无知集，而非在类别单形上重归一化。本文指出反向传播恰需要同一规则：Dempster 的归一化因子 (1−κ)⁻¹ 会给梯度引入 (1−κ)⁻² 项，恰在证据源互相矛盾时发散；而 Yager 的 ⊞ 是双线性的，没有这一项。据此构建深度证据流水线：链路上每个质量都是合法的 Dempster–Shafer 质量函数，由 Yager 规则组合；输出落在无知集上的质量 m(Θ) 即网络的「我不知道」信号。网络只用硬标签训练、从未见过标注者分布，m(Θ) 却能在视觉与语言两种模态上对人类分歧排序。Dempster 的对应信号也上升，但归一化子把冲突除了出去：在最具争议的 CIFAR-10H 图像上，Yager 的 vacuity 大 9 倍，无需重校准即可直接读作无知量。OOD 检测上与强单遍基线相当，而得分更高的 clamped Dempster 变体一旦去掉 clamp 就梯度不稳。

原文摘要

Yager's 1987 rule of combination \(\boxplus\) was proposed on epistemic grounds: under high conflict, mass should be redistributed to ignorance rather than renormalised onto the class simplex. We observe that backpropagation needs the same rule: Dempster's normaliser \((1{-}\kappa)^{-1}\), where \(\kappa\) is the conflict mass, puts a \((1{-}\kappa)^{-2}\) term in the gradient that diverges exactly when evidence sources disagree, while Yager's \(\boxplus\) is bilinear and has no such term. Building on this, we construct a deep evidential pipeline in which every mass in the chain from heads to output is a valid Dempster--Shafer mass function, combined by Yager's rule. The output mass on the ignorance set, \(m(\Theta)\), serves as the network's ``I do not know'' signal. The network is fit to hard labels and never sees an annotator distribution, yet \(m(\Theta)\) orders human disagreement in two modalities, visual and linguistic. Dempster's rises too and ranks contested inputs about as well, but its normaliser divides the conflict out: Yager's vacuity is \(9\times\) larger on the most contested CIFAR-10H images, so only Yager's is readable as an amount of ignorance without recalibration. For out-of-distribution detection it is competitive with strong single-pass baselines, while the clamped Dempster variant that scores higher becomes gradient-unstable once the clamp is removed.

自动采集于 2026-10-24

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