数据合并可能让神经网络做出相反决策,研究如何避免这种错误。
More Data, Worse Decisions? Preference Reversals in Neural Networks under Gram Incompatibility

- 通过分析特征几何结构,发现合并数据会改变权重分配导致偏好反转。
- 实验显示在负载、医疗和金融场景中,约10%~30%的决策出现有害反转。
- 提出几何正则化与三阶段审计,适合需高可靠性的决策系统开发者。
神经网络越来越多地融合跨群体、跨时段和不同工况的数据以提升泛化能力,但这引发可靠性问题:模型在合并数据上重新训练后,是否仍保持各来源支持的决策顺序?基于案例决策理论(CBDT)的组合公理要求源数据支持的偏好在合并后仍应成立。本文研究固定表示神经网络搭配普通最小二乘(OLS)输出头时该性质的成立条件。首先,证明合并重训会改变用于加权源证据的逆-格拉姆几何,可能导致共享偏好的反转,并推导出精确与近似保留条件。其次,提出一种尺度不变的格拉姆不匹配度量以优先筛选候选数据池,并设计面向几何结构的正则化方法,在训练中调控源数据几何。最后,构建三阶段审计流程,追踪严格成对反转的决策变化至任务定义的效用损失。在负载竞价代理、医疗与金融决策代理上的实验揭示了稳定与易反转的合并模式:负载审计识别出在代理效用下存在可观测的非零比例有害共识性决策;跨域审计显示相似不匹配可能对应截然不同的保留率。面向几何的目标占据不同的描述准确率-一致性-几何-危害权衡点。整体框架使组合可靠性可测量、可操作,通过筛选、分析认证、几何导向训练与决策后果审计实现。
原文摘要 · Abstract (English)
Neural networks increasingly combine data across populations, time periods, and operating conditions to improve generalization. This raises a reliability question: whether a model refitted on pooled data preserves an action ordering supported by both sources. Case-Based Decision Theory (CBDT) formalizes this requirement through its composition axiom, which requires source-supported preferences to survive their union. We study when this property holds for fixed-representation neural networks with ordinary least squares (OLS) output heads. First, we show that pooled refitting recomputes the inverse-Gram geometry used to weight source evidence, which can reverse shared preferences, and derive exact and approximate preservation conditions. Next, we introduce a scale-invariant Gram mismatch measure for prioritizing candidate pools and geometry-oriented regularization for shaping source geometry during training. Finally, we develop a three-stage audit that traces strict pairwise reversals through decision changes to task-defined utility loss. Experiments spanning a load-based bidding proxy and medical and financial decision proxies reveal stable and reversal-prone pooling regimes: the load audit identifies a measurable nonzero class of source-consensus-relative harmful decisions under the proxy utility, while cross-domain audits show that comparable mismatch can correspond to sharply different preservation rates. Geometry-oriented objectives occupy distinct descriptive accuracy-consistency-geometry-harm operating points. Together, the framework makes compositional reliability measurable and operational through screening, analytic certification, geometry-oriented training, and decision-consequence auditing.
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