Foundational models have significantly advanced in natural language processing (NLP) and computer vision (CV), with the Transformer architecture becoming a standard backbone. However, the Transformer's quadratic complexity poses challenges for handling longer sequences and higher resolution images. To address this challenge, State Space Models (SSMs) like Mamba have emerged as efficient alternatives, initially matching Transformer performance in NLP tasks and later surpassing Vision Transformers (ViTs) in various CV tasks. To improve the performance of SSMs, one crucial aspect is effective serialization of image patches. Existing methods, relying on linear scanning curves, often fail to capture complex spatial relationships and produce repetitive patterns, leading to biases. To address these limitations, we propose using fractal scanning curves for patch serialization. Fractal curves maintain high spatial proximity and adapt to different image resolutions, avoiding redundancy and enhancing SSMs' ability to model complex patterns accurately. We validate our method in image classification, detection, and segmentation tasks, and the superior performance validates its effectiveness.

翻译：基础模型在自然语言处理（NLP）和计算机视觉（CV）领域取得了显著进展，其中Transformer架构已成为标准骨干网络。然而，Transformer的二次计算复杂度在处理较长序列和更高分辨率图像时面临挑战。为应对这一挑战，诸如Mamba之类的状态空间模型（SSMs）已成为高效的替代方案，最初在NLP任务中达到与Transformer相当的性能，随后在各种CV任务中超越了视觉Transformer（ViTs）。提升SSMs性能的一个关键方面在于图像块的有效序列化。现有方法依赖线性扫描曲线，往往难以捕捉复杂的空间关系并产生重复模式，从而导致偏差。为克服这些限制，我们提出使用分形扫描曲线进行块序列化。分形曲线保持了较高的空间邻近性，并能适应不同的图像分辨率，避免了冗余并增强了SSMs精确建模复杂模式的能力。我们在图像分类、检测和分割任务中验证了所提方法的有效性，其优越性能证实了该方法的有效性。