[2601.06793] CliffordNet: All You Need is Geometric Algebra

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Computer Science > Computer Vision and Pattern Recognition

arXiv:2601.06793 (cs)

[Submitted on 11 Jan 2026 (v1), last revised 15 Feb 2026 (this version, v2)]

Title:CliffordNet: All You Need is Geometric Algebra

Authors:Zhongping Ji<br>View a PDF of the paper titled CliffordNet: All You Need is Geometric Algebra, by Zhongping Ji

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Abstract: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 ($uv = u \cdot v + u \wedge v$). 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 $8\times$ 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 this https URL.

Comments:<br>16 pages

Subjects:

Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)

Cite as:<br>arXiv:2601.06793 [cs.CV]

(or<br>arXiv:2601.06793v2 [cs.CV] for this version)

https://doi.org/10.48550/arXiv.2601.06793

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arXiv-issued DOI via DataCite

Submission history<br>From: Zhongping Ji [view email]<br>[v1]<br>Sun, 11 Jan 2026 07:26:02 UTC (138 KB)

[v2]<br>Sun, 15 Feb 2026 07:59:31 UTC (140 KB)

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