# CliffordNet: All You Need is Geometric Algebra

arXiv: https://arxiv.org/abs/2601.06793 · HTML: https://mlsanity.com/paper/2601.06793/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 17 references that are in the map.
- First posted on arXiv 11 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [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)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [RiemannFormer: A Framework for Attention in Curved Spaces](https://mlsanity.com/paper/2506.07405/) (2025)
- [The Curved Spacetime of Transformer Architectures](https://mlsanity.com/paper/2511.03060/) (2025)

## Built on by (most cited first, 7 of 7)

- [Metriplector: From Field Theory to Neural Architecture](https://mlsanity.com/paper/2603.29496/) (2026)
- [Ananke: Contractive Torus Attractor Networks](https://mlsanity.com/paper/2609.24737/) (2026)
- [Minkowski Attractor Networks: Closed-Form Hyperbolic Flows for Visual Representations](https://mlsanity.com/paper/2609.37817/) (2026)
- [Less is More in Semantic Space: Intrinsic Decoupling via Clifford-M for Fundus Image Classification](https://mlsanity.com/paper/2603.20806/) (2026)
- [UHD Low-Light Image Enhancement via Real-Time Enhancement Methods with Clifford Information Fusion](https://mlsanity.com/paper/2604.09321/) (2026)
- [Toward a Functional Geometric Algebra for Natural Language Semantics](https://mlsanity.com/paper/2604.25902/) (2026)
- [QSV: Quat-Sphere-Vision for Coupled Quaternion Attention on Spherical Lattices](https://mlsanity.com/paper/2609.30592/) (2026)

## Abstract (arXiv)

Modern computer vision architectures, from CNNs to Transformers, predominantly rely on the stacking of heuristic modules: spatial mixers (Attention/Conv) followed by channel mixers (FFNs). In this work, we challenge this paradigm by returning to mathematical first principles. We propose the Clifford Algebra Network (CAN), also referred to as CliffordNet, a vision backbone grounded purely in Geometric Algebra. Instead of engineering separate modules for mixing and memory, we derive a unified interaction mechanism based on the Clifford Geometric Product (uv = u · v + u wedge v). This operation ensures algebraic completeness regarding the Geometric Product by simultaneously capturing feature coherence (via the generalized inner product) and structural variation (via the exterior wedge product). Implemented via an efficient sparse rolling mechanism with strict linear complexity O(N), our model reveals a surprising emergent property: the geometric interaction is so representationally dense that standard Feed-Forward Networks (FFNs) become redundant. Empirically, CliffordNet establishes a new Pareto frontier: our Nano variant achieves 77.82% accuracy on CIFAR-100 with only 1.4M parameters, effectively matching the heavy-weight ResNet-18 (11.2M) with 8× fewer parameters, while our Lite variant (2.6M) sets a new SOTA for tiny models at 79.05%. Our results suggest that global understanding can emerge solely from rigorous, algebraically complete local interactions, potentially signaling a shift where geometry is all you need. Code is available at https://github.com/ParaMind2025/CAN.