# Vision Non-Causal Trapezoidal Mamba: Eliminating Directional Scanning in Vision SSMs with Second-Order Dynamics

arXiv: https://arxiv.org/abs/2607.03589 · HTML: https://mlsanity.com/paper/2607.03589/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Vision Mamba backbones, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 58 of its 67 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Placed in

- State-space sequence models (S4, Mamba) / [Vision Mamba backbones](https://mlsanity.com/ssm/vision-mamba-backbones/)

## Builds on (most cited first, 30 of 58)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [PVT v2: Improved Baselines with Pyramid Vision Transformer](https://mlsanity.com/paper/2106.13797/) (2021)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Neighborhood Attention Transformer](https://mlsanity.com/paper/2204.07143/) (2022)
- [LocalMamba: Visual State Space Model with Windowed Selective Scan](https://mlsanity.com/paper/2403.09338/) (2024)

## Built on by (most cited first, 1 of 1)

- [VisionHOPE: Visual Backbones as Self-Modifying Learning Systems](https://mlsanity.com/paper/2609.33325/) (2026)

## Abstract (arXiv)

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.