Mandelbulb

Spline-based regression outpaces MLPs in fitting 4D Mandelbulb data

An independent researcher has spent a year developing K-Splanifolds, a fast K-dim hermite spline manifold algorithm for general-purpose regression.

3 min readMachine Learning
Spline-based regression outpaces MLPs in fitting 4D Mandelbulb data
Fitting a 4D Mandelbulb with KS3 vs MLP [R]

The most interesting part of this story is not the Mandelbulb itself, but what the Mandelbulb represents: a complex, high-dimensional shape that resists the shortcuts most regression models rely on. A developer going by 1ncehost has spent a year building K-Splanifolds, a family of algorithms that use fast K-dimensional Hermite spline manifolds for general-purpose regression. The third version, KS3, converges faster than a multilayer perceptron when fitting this 4D fractal and runs at nearly identical GPU latency. That is a practical, measurable result, and it deserves attention.

We have written before about Build Smarter Curves Without the Noise From Messy Data, and this work sits in the same lineage. Splines have always been good at fitting smooth, structured data, but they have historically struggled to scale into high dimensions. The K-Splanifold approach appears to sidestep that limitation by using a manifold structure that keeps the computation fast even when the input space grows. If that holds across domains, it changes the calculus for anyone who has defaulted to neural networks simply because they were the only tool that could handle the dimensionality.

The broader implication is worth pausing on. Most teams reach for an MLP or a transformer because those models are flexible and well-supported, not because they are optimal for the task. This work suggests that for a meaningful slice of regression problems, a carefully constructed spline-based block can match or beat a neural network on convergence speed while keeping inference latency comparable. That is not a claim that neural networks are obsolete. It is a claim that the default choice deserves scrutiny. As we noted in What Happens in That Split Second Before AI Responds, the latency between input and output is where user experience is won or lost, and KS3's near-parity on GPU latency means you are not trading speed for accuracy.

The honest caveat is that this is one independent researcher's work, shared openly on GitHub with code and a paper for the first version. The claims about noise removal and financial prediction are anecdotal, not peer-reviewed. But the video evidence is concrete, and the code is public. That is exactly the kind of transparency that lets others verify or falsify the results quickly.

The specific consequence to watch is the request for 8x H100 access to attempt a world record nanogpt speedrun. That is a bold, testable goal. If KS3 can genuinely accelerate transformer training without degrading quality, it would move this from an interesting spline experiment to a serious alternative architecture for language models. We will be watching for the results, and we encourage anyone with spare compute to take a look at the repository. The barrier to entry is low, and the potential payoff for the broader regression community is high.

From Machine Learning

For the past year I have been studying using a fast K-dim hermite spline manifold algorithm, called K-Splanifolds or KS, for general purpose fast regression. In this video I show the third version, KS3, compared to MLP and older KS versions fitting a 4D mandelbulb via gradient descent on random samples. KS3 converges faster and has nearly identical latency on a GPU as MLP.

Read the original at Machine Learning