用傅里叶嵌入解决角度表示难题，支持灵活的核函数设计。
On periodic distributed representations using Fourier embeddings
- 采用高维周期性嵌入表示角度，避免传统方式的歧义问题。
- 通过傅里叶嵌入实现可调控的点积相似性，构建多种核形状。
- 基于空间语义指针框架，具神经可解释性，适合感知建模任务。
周期信号在表征物理与感知现象中至关重要。传统的标量实数角度（如弧度、度数）在处理邻近角度时存在困难，尤其当绝对差值超过π时。我们可通过高维空间中的实值周期嵌入规避此问题。这类表示还能控制点积相似性的性质，从而构建多种不同的核函数形式。本文旨在阐明此类表示的构造方法，并重点形式化使用神经可解释的时空语义指针方案实现的Dirichlet与周期高斯核。
原文摘要 · Abstract (English)
Periodic signals are critical for representing physical and perceptual phenomena. Scalar, real angular measures, e.g., radians and degrees, result in difficulty processing and distinguishing nearby angles, especially when their absolute difference exceeds pi. We can avoid this problem by using real-valued, periodic embeddings in high-dimensional space. These representations also allow us to control the nature of their dot product similarities, allowing us to construct a variety of different kernel shapes. In this work, we aim of highlight how these representations can be constructed and focus on the formalization of Dirichlet and periodic Gaussian kernels using the neurally-plausible representation scheme of Spatial Semantic Pointers.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。