its okay to not have your own fully developed opinion about every opinion expressed in the legacy media and you shouldn't feel pressure to form one under those constraints, its a real problem🙂
FRACTALS IN NEURAL NETWORKS
Hyperparameter tuning feels like navigating a coastline. Turns out that's literally true: the boundary between learning rates that train and ones that diverge is a fractal.
Why? Gradient descent is an iterated map, θ → θ − η∇L(θ), exactly like z → z² + c, the law that draws the Mandelbrot set. Iterate a nonlinear function, ask "does it stay bounded?", and you get a fractal.
So I made it interactive: drag to zoom, and each dive recomputes 65,536 full training runs on the GPU in ~1s. New inlets and peninsulas surface at every depth. The coast never resolves.
Same story with real data (MNIST-1D), the fractal survives. The best learning rates live right up against this shore. That's part of why tuning is so hard.
The fun part: I built this like a story pairing with Claude Code inside the running notebook via marimo-pair. It ran code in the same GPU kernel I did, read live state, and edited cells while the fractal recomputed in front of us.
Molab link below 👇
An interactive, story-driven notebook — built with @marimo_io + JAX + marimo-pair + Claude Code in molab. All credit to Jascha Sohl-Dickstein's paper "The boundary of neural network trainability is fractal"
#MachineLearning #JAX #DeepLearning #builtWithMarimo
Solid mathematical ideas almost always outperform contrived engineering tricks.
For years deep learning has been dominated by increasingly complex architectural hacks: CNN blocks, attention layers, channel mixers, residual pathways, normalization stacks.
Every few years a new architecture is announced as if it were a revolution.
One of the most famous examples was Kaiming He and Residual Networks (ResNet). At the time he was paraded around the AI world like a celebrity because residual connections supposedly “solved” deep learning.
But these were largely engineering patches.
Now something much more interesting appeared.
A new architecture called CliffordNet returns to mathematics — specifically Clifford Algebra, developed in the 19th century by William Kingdon Clifford.
Instead of stacking arbitrary modules, the model is built around the geometric product
uv = u·v + u∧v
A single algebraic operation that simultaneously captures inner product structure and geometric interactions.
In other words: the math already contains the interaction mechanism.
No attention blocks.
No mixer layers.
No architectural spaghetti.
The result:
• 77.82% accuracy on CIFAR-100 with only 1.4M parameters
• roughly 8× fewer parameters than ResNet-18
And with strict O(N) complexity.
The paper even suggests that once geometric interactions are modeled correctly, feed-forward networks become largely redundant.
A good reminder for the AI community.
Engineering tricks can dominate for years.
But eventually mathematics shows up and deletes half the architecture.
Paper:
https://t.co/9rQuZYvZ0o
19th century geometry just walked into computer vision.
Vladimir Levenshtein won the IEEE Hamming Medal for his work on edit distance. This is now a leetcode medium problem companies expect you to solve in 45 minutes. Either you are a Hamming Medal-level intellect who can derive the solution under interview pressure or you grinded a bunch of practice problems on this subtopic like the desperate job supplicant you are.
Central Washington is ethnically, ecologically, climatically more like norteño counties than it is like western Washington. It’s probably one of the poorest understood regions in the country.
i lived through a brief historical moment in the early 00’s when texting someone that you were there to pick them up was considered rude, where knocking on their door to signal your presence was preferred 🙂
@RagingBitcoin i didn’t say remove the permitting process, just relax local zoning policy to allow for a greater supply of housing, which would have an outsized effect on stabilizing housing prices relative to onerous property taxes, ref: dallas, tx circa 08-09
@RagingBitcoin .. where as density bonuses, relaxed parking restrictions and setbacks, plus other development incentives to increase housing supply would have a much greater impact to your desired outcome
@RagingBitcoin discouraging housing purchases beyond your primary residence would have such a marginal impact to stabilizing prices - maybe 5% roughly speaking
@RagingBitcoin but second and third homes do not absorb enough housing stock to meaningfully increase housing prices the same way that restrictive local zoning laws do