β-VAE作为有效理论：依赖容忍度的维度
$β$-VAEs as Effective Theories: Tolerance-Dependent Dimension
- Universitat de València（瓦伦西亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对WorldClim上训练的全连接非线性VAEs，探究β-VAE的频谱截断特性，发现非线性相互作用会改变折叠起始点但保留效用排序，且深度存在头尾权衡。
AI中文摘要：
在β-VAE中，增加正则化强度会通过折叠低效用潜在坐标起到频谱截断的作用。在线性高斯VAE中，折叠顺序与重建效用的排名完全匹配，因为两者都由PCA频谱决定。我们探究在WorldClim上训练的全连接非线性VAEs中，这一图景的哪些部分得以保留。我们发现，非线性相互作用会使折叠起始点发生偏移并拓宽，因此阈值不再与效用完全重合。不过，在已解析的排名上，共同的排序得以保留，所以频谱截断仍起到效用截断的作用，有效描述逻辑依然适用。所得的有效维度曲线揭示了一种头尾权衡：增加深度会将效用集中到前几个坐标中，但会恶化尾部保真度。
英文摘要：
In a $β$-VAE, increasing the regularization strength acts as a spectral cutoff by collapsing low-utility latent coordinates. In the linear Gaussian VAE, the collapse order matches the ranking of reconstruction utilities exactly, because both are set by the PCA spectrum. We ask which parts of this picture survive in fully connected nonlinear VAEs trained on WorldClim. We find that nonlinear interactions shift and broaden collapse onsets, so thresholds no longer coincide exactly with utilities. However, the common ordering is preserved over the resolved ranks, so the spectral cutoff still acts as a utility cutoff and the effective-description logic carries through. The resulting effective-dimension curves reveal a head--tail tradeoff: increasing depth concentrates utility into the first few coordinates but worsens tail fidelity.
