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.

本研究提出了 Ferumal 流，一种新型的基于核的归一化流范式，将核函数与框架结合。结果表明，与基于神经网络的流相比，基于核的流可以在保持参数效率的同时产生竞争性或更好的结果。基于核的流在数据稀缺情况下表现出色，可在应用中进行灵活的非参数密度估计。