具有显式时间间隔动力学的波函数反向传播
Wave Function Backpropagation with Explicit Temporal-Interval Dynamics
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中文总结 AI 辅助
本文提出波函数反向传播（WFB），将其实例化为前馈轨迹预测器，实验显示其在平均位移误差（ADE）上优于基线FFN，证明WFB是可行的结构化前馈学习公式。
中文摘要 AI 辅助
传统神经网络主要通过仿射变换后接非线性激活函数进行学习，而经过的时间通常被视为辅助特征或假设为均匀采样。本文提出了波函数反向传播（WFB），一种以波参数化的学习公式，其中神经响应由可学习的振幅、波数、角频率和相位表示。该公式通过可微时空波的相位，将观测状态与其时间间隔Δt相关联。我们推导了标准WFB梯度以及基于波响应拉普拉斯的空间曲率校正。WFB被实例化为一个刻意的前馈轨迹预测器，以提供受控的概念验证；序列学习不在本评估范围内。在运动特征下，使用真实间隔的STD-WFB相对于原始FFN基线将平均位移误差（ADE）降低了20.4%。在一项新的仅位置评估中，通过预计算的速度和加速度消除了时间泄漏，使用真实间隔的WFB相对于原始FFN将ADE降低了10.4%，并且与参数匹配的ReLU对照相比仍具有竞争力，比带有显式Δt的匹配FFN的平均ADE低2.1%。打乱间隔的WFB获得了最低的平均ADE，表明当前证据支持波表示的有效性，但不将增益归因于间隔对齐。这些结果确立了WFB作为一种可行的结构化前馈学习公式，并为后续的架构研究奠定了明确的基础。
英文摘要
Conventional neural networks learn predominantly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniformly sampled. This paper introduces Wave Function Backpropagation (WFB), a wave-parameterized learning formulation in which neural responses are represented by learnable amplitude, wavenumber, angular frequency, and phase. The formulation associates an observed state with its temporal interval Delta t through the phase of a differentiable spatiotemporal wave. We derive standard WFB gradients and a spatial-curvature correction based on the Laplacian of the wave response. WFB is instantiated in a deliberately feed-forward trajectory predictor to provide a controlled proof of concept; sequence learning is outside the scope of the present evaluation. With motion features, STD-WFB using real intervals reduces average displacement error (ADE) by 20.4% relative to the original FFN baseline. In a new position-only evaluation that removes temporal leakage through precomputed velocity and acceleration, real-interval WFB reduces ADE by 10.4% relative to the original FFN and remains competitive with parameter-matched ReLU controls, obtaining 2.1% lower mean ADE than the matched FFN with explicit Delta t. Shuffled-interval WFB attains the lowest mean ADE, indicating that the present evidence supports the effectiveness of the wave representation but does not attribute the gain to interval alignment. These results establish WFB as a viable structured feed-forward learning formulation and define a clear basis for subsequent architectural studies.
发表机构
- University of the District of Columbia（哥伦比亚特区大学）
机构由 AI 辅助整理，请以论文原文为准。
