## 2 Related Works  
### Downsampling in Neural Networks  
To reduce model complexity, researchers have developed various downsampling methods that are tailored to specific tasks and architectures, including pooling-based [17; 19], subsampling-based [16; 30], patch-based [31; 32], and learnable pooling [19; 33] methods. In the early stages of neural network development, Maximum Pooling or Average Poolingwere commonly adopted to achieve downsampling by taking the maximum or average value within a local window. These methods are fast and memory-efficient, yet t room for improvement remains in terms of information retention [11]. Some methods that combine Max and Average Pooling, such as Mixed Pooling [34], exhibit better performance compared to a single method. Unlike Maximum Pooling, Average Pooling, and their variants, SoftPool exponentially weights the activations using Softmax (normalized exponential function) kernels to retain feature information [12]. [PERSON] et al. [35] proposed pyramid pooling for the transformer architecture; pyramid pooling which applies different scales of average pooling layers to generate pyramid feature maps, thus capturing powerful contextual features. There are also pooling methods that are designed to enhance the generalization of a model. For example, Fractional Pooling [36], S3 Pool [13], and Stochastic Pooling [30] can prevent overfitting by taking random samples in the pooling region. However, most pooling-based methods are hand-crafted nonlinear mappings which usually employ fixed, unlearnable prior knowledge [37]. Nonlinear mapping can also be generated by overlaying complex convolutional layers and activation functions in a deep neural network (DNN) [16]. When the network is shallow, pooling has some advantages. When the network goes deeper, multi-layer stacked convolution can learn better nonlinearity than pooling. It can also achieve better results [38]. Therefore, Strided Convolution, which reduces spatial dimensionality by adjusting the stride to skip some pixels in the feature map, is generally used for downsampling in convolutional neural networks at present [16]. Pooling and Stride Convolution have the advantage of extracting stronger semantic features, although at the cost of losing some detailed information [39]. In contrast, the features extracted via passthrough downsampling [40] have less semantic information but retain more detailed information. In transformer-based networks, patch-based downsampling is generally adopted [31; 32]. Patch merging is a method of reducing the number of tokens in transformer architectures which concatenates the features of each group of 2 \(\times\) 2 neighboring patches and extracts the features with a linear layer [32]. Patch-based methods perform poorly at capturing fine spatial structures and details, like edges and texture [41]. [PERSON] et al. [42] stacked the results of the Discrete Wavelet Transform in the channel dimension instead of directly stacking patches to prevent spatial domain distortion. Moreover, [PERSON] et al. [43] proposed a Robust Feature Downsampling Module by combining various techniques such as slice, Max Pooling, and group convolution, achieving satisfactory results in remote sensing visual tasks. In recent years, learnable weights were gradually introduced into some advanced downsampling methods. [PERSON] et al. [19] proposed Detail Preserving Pooling methods that use learnable weights to emphasize spatial changes and preserve edges and texture details. [PERSON] et al. [33] proposed Local Importance-Based Pooling to retain important features based on weights learned by a local attention mechanism. [PERSON] and [PERSON] et al. [44] proposed spatial attention pooling to learn feature weights and refine local features. [PERSON] et al. [45] introduced a Content-Adaptive Downsampling method that downsamples only the non-critical regions learned by a network, effectively preserving detailed information in the regions of interest.