From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity — mentioned by fc417fc802

Fri, 09 Jan 2026 15:10:58 GMT

Note that I'm not great at math so it's possible I've entirely misunderstood you. Here's an example of directly leveraging a transform to optimize the training process. ( https://arxiv.org/abs/2410.21265 ) And here are two examples that apply geometry to neural nets more generally. ( https://arxiv.org/abs/2506.13018 ) ( https://arxiv.org/abs/2309.16512 )

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From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity — mentioned by pizza

Tue, 06 Jan 2026 03:05:34 GMT

Yes to this. Furthermore: - you can solve neural networks in analytic form with a hodge star approach* [0] - if you use a picture to set your initial weights for your nn, you can see visually how close or far your choice of optimizer is actually moving the weights - eg non-dualized optimizers look like they barely change things whereas dualized Muon changes the weights much more to the point you cannot recognize the originals [1] *unfortunately, this is exponential in memory [0] M. Pilanci — From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's…

Paper and discussion history. A mention is not an endorsement.

From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity · HackerPapers discussions

From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity — mentioned by fc417fc802

From Complexity to Clarity: Analytical Expressions of Deep Neural Network Weights via Clifford's Geometric Algebra and Convexity — mentioned by pizza