Existing disentanglement methods for deep generative models rely on hand-picked priors and complex encoder-based architectures. In this paper, we propose the Hessian Penalty, a simple regularization term that encourages the Hessian of a generative model with respect to its input to be diagonal. We introduce a model-agnostic, unbiased stochastic approximation of this term based on Hutchinson's estimator to compute it efficiently during training. Our method can be applied to a wide range of deep generators with just a few lines of code. We show that training with the Hessian Penalty often causes axis-aligned disentanglement to emerge in latent space when applied to ProGAN on several datasets. Additionally, we use our regularization term to identify interpretable directions in BigGAN's latent space in an unsupervised fashion. Finally, we provide empirical evidence that the Hessian Penalty encourages substantial shrinkage when applied to over-parameterized latent spaces.

通过引入Hessian Penalty正则化项并应用于多个数据集的ProGAN来训练，我们证明基于Hessian Penalty的方法在潜空间中产生平行于轴的解缠缚现象。并且在BigGAN的潜空间中无需监督地识别可解释方向。我们还提供了实证证据表明，当应用于超参数化的潜空间时，Hessian Penalty鼓励显著的收缩。

Hessian Penalty: 无监督分离的弱先验