用球坐标压缩高维潜在空间，提升VAE生成效果
Improving the Generation of VAEs with High Dimensional Latent Spaces by the use of Hyperspherical Coordinates
- 用球坐标参数化潜在变量，聚焦分布于超球面的局部区域
- 显著降低潜在空间稀疏性，生成样本更真实有效
- 方法轻量易实现，适合高维潜在变量的生成任务
变分自编码器（VAE）将数据编码为低维潜在向量后解码回数据。训练完成后，从先验中随机采样潜在向量通常无法生成有意义的数据，尤其当潜在空间维度超过十几维时。本文借鉴高维统计学观点：标准VAE的潜在向量在高维下天然均匀分布在超球面上。为此，我们提出使用球坐标参数化潜在空间，使潜在向量集中于超球面的一个局部区域，从而减少潜在空间稀疏性，并验证该方法能显著提升VAE的生成能力。所提方法仅引入少量计算开销，且可灵活应用于各类模型。
原文摘要 · Abstract (English)
Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, decoding a random latent vector from the prior usually does not produce meaningful data, at least when the latent space has more than a dozen dimensions. In this paper, we investigate this issue by drawing insight from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are by construction distributed uniformly on a hypersphere. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards an island on the hypersphere, thereby reducing the latent sparsity and we show that this improves the generation ability of the VAE. We propose a new parameterization of the latent space with limited computational overhead.
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