背景梯度塑造流匹配中的记忆化
Background Gradients Shape Memorization in Flow Matching
AI总结：
本研究通过配对轨迹框架揭示背景梯度响应是类条件流匹配中同类别图像影响目标记忆化与复制的关键机制，实验显示替换重复图像使提取率从80.7%降至18.0%。
AI中文摘要：
重复与生成模型中的记忆化密切相关，但其他训练图像如何影响目标的保留和复制仍不清楚。我们在类条件流匹配中研究此问题，其中目标集之外的图像构成背景。在固定目标重复次数和同类别背景行数的情况下，将重复的同类别图像替换为不同图像，目标提取率从80.7%降至18.0%。为解释此效应，我们开发了一个配对轨迹框架，隔离目标引起的参数位移及背景梯度对此的响应。该响应具有精确的路径积分曲率表示，将背景损失几何与目标学习联系起来。重复背景与不同背景之间的互惠响应传递双向改变目标的保留和复制，确立了响应的因果作用。目标移除后，平行于目标引起位移的响应校正保留了完整响应传递复制效应的约90%。直接缩放位移也能在不进一步训练的情况下改变复制。互惠传递的移除后复制效应在多个数据集和架构上得到复现。综上，这些结果确定了背景梯度响应是一种机制，通过该机制，同类别训练数据塑造目标学习的保留和目标图像的复制。
英文摘要：
Repetition is closely associated with memorization in generative models, but how other training images affect the retention and copying of targets remains unclear. We study this question in class-conditioned flow matching, where images outside the target set form the background. At fixed target repetition and same-class background row count, replacing repeated same-class images with distinct images reduces the target extraction rate from 80.7% to 18.0%. To explain this effect, we develop a paired-trajectory framework that isolates target-induced parameter displacement and the background gradient response to it. This response has an exact path-integrated curvature representation, connecting background loss geometry to target learning. Reciprocal response transfer between repeated and distinct backgrounds changes target retention and copying in both directions, establishing the response's causal role. After target removal, the response correction parallel to the target-induced displacement preserves approximately 90% of the copying effects of full response transfer. Directly scaling the displacement also changes copying without further training. The post-removal copying effects of reciprocal transfer are reproduced across datasets and architectures. Together, these results identify the background gradient response as a mechanism through which same-class training data shape the retention of target learning and the reproduction of target images.
