图像作为一阶范数+线性自回归：揭示数学不变性
Image as First-Order Norm+Linear Autoregression: Unveiling Mathematical Invariance
AI总结：
本文提出FINOLA性质，将图像表示为潜在空间中的一阶范数+线性自回归过程，并验证其在图像重建与自监督学习中的有效性，仅用三个卷积层即可从单向量重建256x256图像，且预训练表示在分类和检测任务中表现优异。
摘要：
本文提出了一种适用于多种图像的新颖数学性质，称为FINOLA（一阶范数+线性自回归）。FINOLA将潜在空间中的每幅图像表示为一阶自回归过程，其中每个回归步骤仅对相邻像素的归一化值应用一个共享的线性模型。这一引人入胜的性质揭示了一种超越个体图像的数学不变性。从图像网格扩展到连续坐标，我们揭示了两个潜在偏微分方程的存在。我们从两个不同角度验证FINOLA性质：图像重建和自监督学习。首先，我们证明了FINOLA能够仅从放置在中心的一个向量自回归生成高达256x256的特征图（与图像分辨率相同），仅使用三个3x3卷积层作为解码器即可成功重建原始图像。其次，我们利用FINOLA进行自监督学习，采用简单的掩码预测方法。编码单个未掩码象限块，我们自回归预测周围掩码区域。值得注意的是，这种预训练表示在图像分类和目标检测任务中表现出高度有效性，即使集成到轻量级网络中，也无需大量微调。代码将公开提供。
英文摘要：
This paper introduces a novel mathematical property applicable to diverse images, referred to as FINOLA (First-Order Norm+Linear Autoregressive). FINOLA represents each image in the latent space as a first-order autoregressive process, in which each regression step simply applies a shared linear model on the normalized value of its immediate neighbor. This intriguing property reveals a mathematical invariance that transcends individual images. Expanding from image grids to continuous coordinates, we unveil the presence of two underlying partial differential equations. We validate the FINOLA property from two distinct angles: image reconstruction and self-supervised learning. Firstly, we demonstrate the ability of FINOLA to auto-regress up to a 256x256 feature map (the same resolution to the image) from a single vector placed at the center, successfully reconstructing the original image by only using three 3x3 convolution layers as decoder. Secondly, we leverage FINOLA for self-supervised learning by employing a simple masked prediction approach. Encoding a single unmasked quadrant block, we autoregressively predict the surrounding masked region. Remarkably, this pre-trained representation proves highly effective in image classification and object detection tasks, even when integrated into lightweight networks, all without the need for extensive fine-tuning. The code will be made publicly available.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
