Beyond ZOH: Advanced Discretization Strategies for Vision Mamba

2026-04-22

AI Summary

This work addresses the limitations of the default zero-order hold (ZOH) discretization in Vision Mamba, which assumes constant inputs over sampling intervals and struggles to capture temporal dynamics in visual scenes. For the first time in vision state space models, the study systematically evaluates six discretization strategies—ZOH, first-order hold (FOH), bilinear transform (BIL), polynomial interpolation (POL), higher-order hold (HOH), and fourth-order Runge–Kutta (RK4)—across image classification, semantic segmentation, and object detection tasks. Experimental results reveal that while POL and HOH substantially improve accuracy, they incur significant computational overhead. In contrast, the bilinear transform (BIL) consistently outperforms ZOH with minimal additional cost, offering an optimal trade-off between accuracy and efficiency, and is thus established as the new default discretization method for Vision Mamba.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Vision Mamba, as a state space model (SSM), employs a zero-order hold (ZOH) discretization, which assumes that input signals remain constant between sampling instants. This assumption degrades temporal fidelity in dynamic visual environments and constrains the attainable accuracy of modern SSM-based vision models. In this paper, we present a systematic and controlled comparison of six discretization schemes instantiated within the Vision Mamba framework: ZOH, first-order hold (FOH), bilinear/Tustin transform (BIL), polynomial interpolation (POL), higher-order hold (HOH), and the fourth-order Runge-Kutta method (RK4). We evaluate each method on standard visual benchmarks to quantify its influence in image classification, semantic segmentation, and object detection. Our results demonstrate that POL and HOH yield the largest gains in accuracy at the cost of higher training-time computation. In contrast, the BIL provides consistent improvements over ZOH with modest additional overhead, offering the most favorable trade-off between precision and efficiency. These findings elucidate the pivotal role of discretization in SSM-based vision architectures and furnish empirically grounded justification for adopting BIL as the default discretization baseline for state-of-the-art SSM models.

Problem

• discretization
• state space model
• Vision Mamba
• temporal fidelity
• zero-order hold

Innovation

• discretization
• Vision Mamba
• state space model
• bilinear transform
• temporal fidelity