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。

核化归一化流

Kernelised Normalising Flows

Optical aberrations of optical systems cause significant degradation of
imaging quality. Aberration correction by sophisticated lens designs and
special glass materials generally incurs high cost of manufacturing and the
increase in the weight of optical systems, thus recent work has shifted to
aberration correction with deep learning-based post-processing. Though
real-world optical aberrations vary in degree, existing methods cannot
eliminate variable-degree aberrations well, especially for the severe degrees
of degradation. Also, previous methods use a single feed-forward neural network
and suffer from information loss in the output. To address the issues, we
propose a novel aberration correction method with an invertible architecture by
leveraging its information-lossless property. Within the architecture, we
develop conditional invertible blocks to allow the processing of aberrations
with variable degrees. Our method is evaluated on both a synthetic dataset from
physics-based imaging simulation and a real captured dataset. Quantitative and
qualitative experimental results demonstrate that our method outperforms
compared methods in correcting variable-degree optical aberrations.

采用可逆结构的新型畸变校正方法，通过条件可逆块处理可变程度的畸变，实验证明性能优于现有方法。