This paper presents the results of analysing and modelling a set of 8 ``master key filters'', which have been extracted by applying a clustering approach to the receptive fields learned in depthwise-separable deep networks based on the ConvNeXt architecture. For this purpose, we first compute spatial spread measures in terms of weighted mean values and weighted variances of the absolute values of the learned filters, which support the working hypotheses that: (i) the learned filters can be modelled by separable filtering operations over the spatial domain, and that (ii) the spatial offsets of the those learned filters that are non-centered are rather close to half a grid unit. Then, we model the clustered ``master key filters'' in terms of difference operators applied to a spatial smoothing operation in terms of the discrete analogue of the Gaussian kernel, and demonstrate that the resulting idealized models of the receptive fields show good qualitative similarity to the learned filters. This modelling is performed in two different ways: (i) using possibly different values of the scale parameters in the coordinate directions for each filter, and (ii) using the same value of the scale parameter in both coordinate directions. Then, we perform the actual model fitting by either (i) requiring spatial spread measures in terms of spatial variances of the absolute values of the receptive fields to be equal, or (ii) minimizing the discrete $l_1$- or $l_2$-norms between the idealized receptive field models and the learned filters. Complementary experimental results then demonstrate the idealized models of receptive fields have good predictive properties for replacing the learned filters by idealized filters in depthwise-separable deep networks, thus showing that the learned filters in depthwise-separable deep networks can be well approximated by discrete scale-space filters.

翻译：本文呈现了对一组8个“主密钥滤波器”进行分析和建模的结果，这些滤波器是通过对基于ConvNeXt架构的深度可分离深度网络中所学感受野应用聚类方法提取得到的。为此，我们首先计算了所学滤波器绝对值在加权平均值和加权方差意义上的空间展布度量，这些度量支持以下工作假设：(i) 所学滤波器可以通过空间域上的可分离滤波操作进行建模，以及(ii) 那些非中心化所学滤波器的空间偏移相当接近半个网格单位。接着，我们基于应用于离散高斯核模拟的空间平滑操作的差分算子，对聚类得到的“主密钥滤波器”进行建模，并证明所得感受野的理想化模型与所学滤波器在定性上表现出良好的相似性。该建模通过两种不同方式实现：(i) 对每个滤波器在坐标方向上使用可能不同的尺度参数值，以及(ii) 在两个坐标方向上使用相同的尺度参数值。随后，我们通过以下两种方式进行实际模型拟合：(i) 要求感受野绝对值在空间方差意义上的空间展布度量相等，或(ii) 最小化理想化感受野模型与所学滤波器之间的离散$l_1$-范数或$l_2$-范数。补充实验结果表明，理想化感受野模型在深度可分离深度网络中用理想化滤波器替换所学滤波器时具有良好的预测特性，从而证明深度可分离深度网络中的所学滤波器可以很好地用离散尺度空间滤波器来近似。