Mamba-ND: Multi-Dimensional Data Modeling with State Space Models

Core Concepts

Mamba-ND extends state space models to multi-dimensional data efficiently.

Abstract

The content discusses Mamba-ND, a model that extends state space models to multi-dimensional data. It compares Mamba-ND with other alternatives like Bi-directional LSTMs and S4ND. The design of Mamba-ND involves unraveling input data across different dimensions in row-major orderings. Extensive comparisons show competitive performance on various benchmarks like ImageNet-1K classification, action recognition, weather forecasting, and 3D segmentation.
Directory:

Introduction

Transformers vs. State Space Models like Mamba.

ImageNet-1K Comparison

Mamba-ND outperforms ViT with fewer parameters.

Video Action Recognition

Extension of Mamba-2D to Mamba-3D for video tasks.

Global Weather Forecasting

Performance comparison with Cli-ViT using ERA5 data.

3D Medical Image Segmentation

Evaluation on BTCV dataset against UNETR and Swin-UNETR.

Meta Architectures Study

Ablation studies on layer designs and scan factorization techniques.

Effective Receptive Field Analysis

Visualization of ERF for different model designs.

Depths versus Widths Discussion

Importance of depth over width in model performance.

Stats

Mamba demonstrates +3.8 accuracy improvement compared to ViT-B on ImageNet-1K while reducing parameter count by 20.7%.

Quotes

"Unlike convolution or self-attention operations, which can be computed in parallel across the ND input data, Mamba requires a specific ordering of the data."
"In this work, we conducted an extensive study on these possible design choices."
"Mamba consistently outperforms transformers with fewer parameters."

Key Insights Distilled From

Mamba-ND

by Shufan Li,Ha... at arxiv.org 03-14-2024

https://arxiv.org/pdf/2402.05892.pdf

Deeper Inquiries

How does the alternating-directional design impact the overall performance compared to more complex multi-directional designs

交互方向性设计对整体性能的影响是非常显著的。研究表明，尽管存在更复杂的多方向设计选择，但简单的交替方向设计在各种任务中仍然表现出色。这种简单而有效的设计不仅提高了模型性能，还减少了参数数量。相比之下，其他更复杂的多方向设计可能会增加计算图深度，并导致性能下降。

What are the implications of the effective receptive field analysis on model architecture design

有效感受野分析对模型架构设计有重要意义。通过可视化有效感受野（ERF），我们可以评估模型在输入数据上学习到信息的范围和敏感度。从结果中可以看出，在考虑垂直结构时，多方向模型展示出更均匀且全局性强大的敏感度图案，这解释了它们优于其他基线模型的原因。因此，在进行模型架构设计时应该考虑如何最大程度地扩展有效感受野以捕获全局信息并保持平衡。

How can the findings from this study be applied to other domains beyond image classification and video tasks

这项研究结果可以应用于除图像分类和视频任务之外的其他领域。例如，在自然语言处理领域中，可以探索将Mamba-ND框架应用于文本序列建模或情绪识别等任务中。此外，在生物医学领域，该框架也可用于医学影像分割或疾病诊断等问题上。通过调整输入数据形式和层级结构组织方式，可以将这些发现推广到各种不同领域，并取得类似优异成果。