Scaling Vision Mamba Across Resolutions via Fractal Traversal (2505.14062v1)

Abstract: Vision Mamba has recently emerged as a promising alternative to Transformer-based architectures, offering linear complexity in sequence length while maintaining strong modeling capacity. However, its adaptation to visual inputs is hindered by challenges in 2D-to-1D patch serialization and weak scalability across input resolutions. Existing serialization strategies such as raster scanning disrupt local spatial continuity and limit the model's ability to generalize across scales. In this paper, we propose FractalMamba++, a robust vision backbone that leverages fractal-based patch serialization via Hilbert curves to preserve spatial locality and enable seamless resolution adaptability. To address long-range dependency fading in high-resolution inputs, we further introduce a Cross-State Routing (CSR) mechanism that enhances global context propagation through selective state reuse. Additionally, we propose a Positional-Relation Capture (PRC) module to recover local adjacency disrupted by curve inflection points. Extensive experiments on image classification, semantic segmentation, object detection, and change detection demonstrate that FractalMamba++ consistently outperforms previous Mamba-based backbones, particularly under high-resolution settings.