Mamba2D: A Natively Multi-Dimensional State-Space Model for Vision Tasks (2412.16146v2)

Abstract: State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

• The paper introduces Mamba2D, a native 2D state-space model that preserves spatial coherence by eliminating arbitrary image flattening.
• It employs an innovative wavefront scan approach that efficiently computes two-dimensional dependencies with enhanced selectivity.
• Experimental results on ImageNet-1K show competitive performance with lower parameter counts, underscoring its practical value.

Overview of "Mamba2D: A Natively Multi-Dimensional State-Space Model for Vision Tasks"

The paper "Mamba2D: A Natively Multi-Dimensional State-Space Model for Vision Tasks" introduces an innovative approach to State-Space Models (SSMs) specifically designed for processing visual data in two-dimensional form. The authors argue that while SSMs have shown potential as efficient alternatives to transformer-based architectures, existing implementations retain certain biases inherited from their application in natural language processing. These biases limit their effectiveness in handling spatial dependencies inherent in visual tasks. The proposed Mamba2D addresses these limitations by formulating a natively multi-dimensional approach, focusing on capturing spatial dependencies more effectively without reshaping data into one-dimensional sequences.

Key Contributions

1. Native 2D State-Space Modelling: The primary contribution of this paper is the introduction of Mamba2D, which redefines the SSM framework to inherently operate in two dimensions. This approach negates the need for arbitrary flattening of images into sequential data, thus preserving spatial coherence and improving the model's ability to capture spatial dependencies.
2. Efficient Wavefront Scanning: Given the computational challenges in extending traditional SSM operations to a two-dimensional paradigm, Mamba2D employs a novel wavefront scan approach. This methodology enables efficient computation across both dimensions simultaneously, which stands in contrast to traditional convolutional or parallel scan processes.
3. Improved Selectivity and Expressibility: Mamba2D retains the selectivity features of prior SSM models, enhancing their ability to dynamically focus on relevant parts of the input data. The model's design is noted for maintaining the full expressibility of its hidden states, which contributes to its efficacy in capturing long-range spatial relations within images.

Experimental Evaluation

The paper reports that the Mamba2D model achieves competitive performance on standard image classification benchmarks, specifically the ImageNet-1K dataset. Results indicate that Mamba2D outperforms many contemporary SSM-based and other established models with similar or lower parameter counts. The construct of Mamba2D allows for notable performance in accuracy while maintaining computational efficiency.

Implications and Future Directions

The implications of this work extend to various practical and theoretical domains. The native 2D processing capability of Mamba2D presents a potential breakthrough in applying SSM frameworks to vision tasks, providing an efficient alternative to transformer and CNN-based architectures. Practically, the model's ability to handle large and complex image data with reduced computational overhead could prove advantageous in applications where resource constraints are a concern.

From a theoretical standpoint, Mamba2D challenges the traditional paradigms by demonstrating the viability of multi-dimensional state-space models outside condensed sequential data formats. This opens avenues for further exploration into state-space formulations that could capture more intricate relationships in multi-dimensional data.

Future work envisioned by the authors includes deploying Mamba2D as a versatile backbone for various vision tasks, potentially scaling up the model sizes and extending hyper-parameter exploration to more comprehensively determine the model's capacities. Additionally, ongoing enhancements to the efficiency of its custom wavefront kernel could further balance the trade-off between computational cost and performance, promoting wider adoption and integration into diverse visual applications.

In conclusion, "Mamba2D: A Natively Multi-Dimensional State-Space Model for Vision Tasks" provides a significant contribution to the field by advancing the application potential of state-space models in vision tasks while challenging entrenched notions about image data processing. Its innovative use of wavefront scanning and inherent 2D operational capability set a foundation for future developments in multi-dimensional machine learning architectures.