通过相对几何分析，揭示神经网络如何在潜空间中对齐动态结构。
Relative Geometry of Neural Forecasters: Linking Accuracy and Alignment in Learned Latent Geometry
- 提出无旋转缩放的相对嵌入方法，消除潜空间歧义。
- 发现多层感知机与循环网络各自内部对齐更强，而变换器等仍能高精度预测。
- 适用于研究模型家族如何内化动态系统结构，适合机器学习可解释性研究者。
神经网络能够精确预测复杂动力系统，但其内部如何表征潜在几何结构仍不明确。本文从表示对齐视角出发，引入基于锚点的、与几何无关的相对嵌入，消除了潜空间中的旋转和缩放歧义。在七个典型动力系统（涵盖周期到混沌）上应用该框架，揭示出可复现的家族级结构：多层感知机与多层感知机对齐，循环网络与循环网络对齐；而变换器和回声状态网络虽对齐较弱，却仍实现强预测性能。对齐程度通常与预测准确性相关，但高精度可与低对齐共存。相对几何为比较不同模型家族如何内化和表征动力结构提供了简洁且可复现的基础。
原文摘要 · Abstract (English)
Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecasters through the lens of representational alignment, introducing anchor-based, geometry-agnostic relative embeddings that remove rotational and scaling ambiguities in latent spaces. Applying this framework across seven canonical dynamical systems - ranging from periodic to chaotic - we reveal reproducible family-level structure: multilayer perceptrons align with other MLPs, recurrent networks with RNNs, while transformers and echo-state networks achieve strong forecasts despite weaker alignment. Alignment generally correlates with forecasting accuracy, yet high accuracy can coexist with low alignment. Relative geometry thus provides a simple, reproducible foundation for comparing how model families internalize and represent dynamical structure.
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