Normalising Flows are generative models characterised by their invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve satisfactory outcomes. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in the low-data regime, enabling flexible non-parametric density estimation in applications with sparse data availability.

翻译：正则化流是一类以可逆架构为特征的生成模型。然而，可逆性要求对其表达能力施加了约束，需要大量参数和创新的架构设计才能取得令人满意的结果。尽管基于流的模型主要依赖神经网络变换来实现表达性设计，但其他变换方法受到的关注有限。本文提出Ferumal流——一种将核方法融入正则化流框架的新型核化正则化流范式。结果表明，核化流在保持参数效率的同时，能够取得与基于神经网络的流相竞争甚至更优的结果。核化流在低数据场景中尤其表现出色，能够在数据稀缺的应用中实现灵活的非参数密度估计。