Beyond ZOH: Advanced Discretization Strategies for Vision Mamba

State Space Models (SSMs) have emerged as an alternative to Vision Transformers, yet most vision SSMs inherit directional token scanning from causal sequence modeling. While effective for sequential data, directional scanning introduces spatial bias and orientation-sensitive representations. We present Vision Non-Causal Trapezoidal Mamba (VNCT), a second-order non-causal vision SSM that enables all image tokens to interact in a single pass, eliminating direSctional scanning and achieving low single-image inference latency. VNCT exhibits more orientation-robust representations, showing reduced performance degradation under image rotations and flips, while improving Boundary IoU by up to 3.7 points, leading to more accurate boundary preservation and object localization. Across ImageNet-1K classification, COCO object detection and instance segmentation, and ADE20K semantic segmentation, VNCT consistently outperforms both directional-scanning vision SSMs and first-order non-causal SSMs. These results show that directional scanning is unnecessary for high-performance vision SSMs and that second-order non-causal state-space modeling offers a simple, efficient, and robust alternative for visual recognition.

Vision State Space Models (SSMs) like Vim, VMamba, and SiMBA rely on complex scanning strategies to adapt sequential SSMs to process 2D images, introducing computational overhead and architectural complexity. We propose HAMSA, a scanning-free SSM operating directly in the spectral domain. HAMSA introduces three key innovations: (1) simplified kernel parameterization-a single Gaussian-initialized complex kernel replacing traditional (A, B, C) matrices, eliminating discretization instabilities; (2) SpectralPulseNet (SPN)-an input-dependent frequency gating mechanism enabling adaptive spectral modulation; and (3) Spectral Adaptive Gating Unit (SAGU)-magnitude-based gating for stable gradient flow in the frequency domain. By leveraging FFT-based convolution, HAMSA eliminates sequential scanning while achieving O(L log L) complexity with superior simplicity and efficiency. On ImageNet-1K, HAMSA reaches 85.7% top-1 accuracy (state-of-the-art among SSMs), with 2.2 X faster inference than transformers (4.2ms vs 9.2ms for DeiT-S) and 1.4-1.9X speedup over scanning-based SSMs, while using less memory (2.1GB vs 3.2-4.5GB) and energy (12.5J vs 18-25J). HAMSA demonstrates strong generalization across transfer learning and dense prediction tasks.

State Space Models (SSMs) have emerged as a compelling alternative to attention models for long-range vision tasks, offering input-dependent recurrence with linear complexity. However, most efficient SSM variants reduce computation cost by modifying scan routes, resolutions, or traversal patterns, while largely leaving the recurrent dynamics implicit. Consequently, the model's state-dependent memory behavior is difficult to control, particularly in compact backbones where long scan paths can exceed the effective memory horizon. We propose Token-Conditioned Poles SSM (TCP-SSM), a structured selective SSM framework that improves efficiency while making recurrence dynamics explicit and interpretable through stable poles. TCP-SSM builds each scan operator with 1) real poles that model monotone or sign-alternating decay, and 2) complex-conjugate poles that capture damped oscillatory responses. Using bounded radius and angle modulation, TCP-SSM converts shared base poles into token-dependent poles, allowing each scan step to adapt its memory behavior to the current visual token while preserving pole stability. For practical scalability, we integrate grouped pole sharing with a lightweight low-rank input pathway, yielding an efficient scan operator that preserves linear-time scan complexity. Across image classification, semantic segmentation, and object detection, TCP-SSM reduces SSM computation complexity up to 44% in Vision Mamba-style models while maintaining or surpassing baseline accuracy.