11–20 of 39 posts
My understanding after scanning the code examples is the technique expands the dimensionality of each data point with a set consisting of the quadratic coefficients of its existing dimensions. I thought it sounded like kernel PCA.
Anisotropy and the cone ideas may explain why PCA underperforms, but it does not uniquely justify this particular quadratic decoder. The geometric story is not doing explanatory work beyond “data is nonlinear,” and the real substance is simply that second-order reconstruction empirically helps.
Author here — questions and pushback both welcome.
I came here from a discussion about CS students who should not be bothered to set up email filters. How can they ever expect to be able to digest just the first paragraph in that article?
None of this stuff is as difficult to understand as people claim it is once you work with it.
By representing data as multivectors, translational and rotational symmetries are encoded natively which allows them to handle geometric hierarchies with massive efficiency gains (reports of up to 78x speedups and 200x parameter reductions) compared to standard Transformers.
> A novel sequence architecture is introduced, Versor, which uses Conformal Geometric Algebra (CGA) in place of traditional linear operations to achieve structural generalization and significant performance improvements on a variety of tasks, while offering improved interpretability and efficiency. By embedding states in the manifold and evolving them via geometric transformations (rotors), Versor natively represents -equivariant relationships without requiring explicit structural encoding. Versor is validated on chaotic N-body dynamics, topological reasoning, and standard multimodal benchmarks (CIFAR-10, WikiText-103), consistently outperforming Transformers, Graph Networks, and geometric baselines (GATr, EGNN).
Author here — questions and pushback both welcome.
Cool idea. But it only works when the data never changes. could you make a streaming/incremental version? One that updates the math cheaply when new data arrives, instead of recomputing everything, or does the math fundamentally prevent it?
Author here — questions and pushback both welcome.
Author here — questions and pushback both welcome.
I came here from a discussion about CS students who should not be bothered to set up email filters. How can they ever expect to be able to digest just the first paragraph in that article?