生成常微分方程中积分误差的空间传输
Spatial Transport of Integration Error in Generative ODEs
- Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究生成常微分方程中积分误差的空间传输问题，通过带符号的源和传输计算，利用单步截断残差和结构破坏零值等方法分析误差，还发现训练惩罚注入变化可降误差，模型可据此训练改变。
AI中文摘要：
训练好的流或扩散模型通常仅用少量求解器步骤运行，留下的积分误差在图像上分布不均。我们研究误差注入位置及其如何到达终点，通过对一阶的几步积分误差进行带符号的源和传输计算来回答。在256^2分辨率下对五个模型的扰动实验表明，学习到的动力学广泛传播局部干扰。带符号的单步截断残差通过模型自身的线性化动力学传播，能重建大部分终点误差方向和区域结构。结构破坏零值定位携带计算的因素，训练惩罚注入变化可降低几步误差。
英文摘要：
A trained flow or diffusion model is usually run with only a handful of solver steps, and the integration error this leaves behind is unevenly distributed across the image. We ask where that error is injected and how it reaches the endpoint, and answer with a signed source-and-transport accounting of few-step integration error, tested to first order. A perturbation experiment on five models at 256^2 resolution shows the learned dynamics spread local disturbances widely: near the start of sampling, under 10% of the summed endpoint response remains at the source. Signed one-step truncation residuals, propagated through the model's own linearized dynamics, reconstruct much of the endpoint error's direction and regional structure (cosine 0.81-0.87), and a region's error owes more to what arrives from elsewhere than to its own injection. Structure-destroying nulls, with protocols frozen before evaluation, locate what carries the account: randomizing contribution signs halves it, and reassigning which region receives each contribution, with content, norms, and signs intact, destroys it entirely. Where the injections land is readable from the model itself. The variation of its velocity or prediction field along the trajectory, a structure that emerges during training, predicts the final per-region gap (within-image rho of 0.57-0.70 on fine trajectories, weaker from the cheap solve alone). The prediction is partial because endpoint error depends not only on injected magnitude but on its sign, timing, and transport through the learned dynamics. A training penalty on the injected variation lowers few-step error, so the structure is one a model can be trained to change.
