发表机构
Amazon Generative AI Innovation Center（亚马逊生成式人工智能创新中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究实证发现，感光细胞数量增加虽提升理论颜色几何维度，但自然光谱的低秩性使实际颜色维度接近一，导致生态颜色流形远未填满，并在水生四色视者中崩塌更甚。
AI 中文摘要
我们量化了生物眼睛能够感知的理论颜色维度与自然界实际提供的颜色维度之间的巨大差距。几何理论预测，n类感光细胞使生物能够感知一个与(n-2)维球面同胚的色调流形。虽然这一数学此前仅针对人类和鸟类进行了解析推导，但本研究通过持续同调，在多个物种中实证证明了这种生物“拓扑阶梯”的存在。我们利用真实的动物视锥细胞，恢复了二色视者的线、三色视者的色调环（$S^1$）、四色视者的色调球（$S^2$）以及五色视者的超球（$S^3$）。至关重要的是，该研究揭示，“生态颜色流形”——即自然反射光谱在自然光下实际产生的颜色——远未达到这些几何能力。在跨越三个独立高光谱数据库的25个不同物种中，动物的几何颜色能力随感光细胞数量的增加而急剧上升，但其所经历颜色的实际有效维度却始终接近一。因此，随着感光细胞数量的增长，世界实际填充的可用几何比例持续下降。一项受控分解表明，这种不匹配是由自然界的低光谱秩驱动的，而非感光细胞限制所致；在模拟的全秩世界中，该效应消失。这一现实世界的约束产生了一个生态学预测，并在留出物种上得到证实：水生四色视者，其光场被水光谱性收窄，其颜色崩塌比陆地或空中物种更为严重（$p = 0.012$）。
英文摘要
We ma[ the profound gap between the theoretical color dimensions an organism's eye can perceive and the actual color dimensions supplied by the natural world. Geometric theory predicts that n photoreceptor classes allow an organism to perceive a hue manifold homeomorphic to an (n-2)-dimensional sphere. While this math was previously only derived analytically for humans and birds, this research empirically proves the existence of this biological ``topological ladder'' across multiple species using persistent homology. We recover a dichromat's line, a trichromat's hue ring ($S^1$), a tetrachromat's hue sphere ($S^2$), and a pentachromat's glome ($S^3$) using real animal cones. Crucially, the study reveals that the ``ecological color manifold'', the colors actually created by natural reflectance spectra under natural light, falls dramatically short of these geometric capabilities. Across 25 diverse species spanning three independent hyperspectral databases, an animal's geometric color capacity climbs steeply with more photoreceptors, yet the actual effective dimension of the colors they experience stays stuck near unity. As a result, the fraction of available geometry the world actually fills steadily declines as receptor counts grow. A controlled decomposition shows this mismatch is driven by the low spectral rank of nature rather than receptor limitations; the effect vanishes in a simulated, full-rank world. The real-world constraint yields an ecological prediction confirmed on held-out species: aquatic tetrachromats, whose light fields are spectrally narrowed by water, collapse more deeply than land or air species ($p = 0.012$).
