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
"Intelligence from Learnable Novelty "
This paper suggests that intelligence is not surprise itself, but the ability to turn surprise into understanding.
Since novelty search gets trapped by noise, and surprise minimization gets trapped by stasis, it splits surprise into learnable and unlearnable parts, then optimizes only the learnable part.
With a cheap differentiable estimator, it finds rule 110, grows solitons, clusters MNIST without labels, and improves RL exploration.
A hopefully significantly clearer, better version of my initial Platonic Space paper (a much modified version of the original 2025 preprint) is here:
https://t.co/QMcAQj9P9k
"Ingressing Minds: Causal Patterns Beyond Genetics and Environment in Natural, Synthetic, and Hybrid Embodiments"
More new papers on this topic coming, but I wanted to update the kickoff manifesto now that we're a year in since I first wrote it. It's submitted to a journal now so there will be a peer-reviewed version available eventually, but the updated preprint is already up.
every city name in California has three ways to pronounce it:
(1) the Spanish way
(2) the way an English speaker would pronounce it if they hadn't heard the name before
(3) the way locals actually pronounce it, which is neither of the previous two. like San Rafell and Beneesha
@anilkseth@ai_sentience Really well articulated, even if just to better understand the differences and why they might matter.
Makes me wonder whether an ASIC has a better chance of embodiment or self-experience than something more reconfigurable…
In this SFI Seminar, Eric Goles of the University of Adolfo Ibáñez explores fungal automata, a cellular automaton model in which information flows only horizontally or vertically. He shows that despite these directional constraints, fungal sandpile automata can simulate arbitrary Boolean circuits and are computationally universal.
Watch Goles’s SFI seminar: https://t.co/4gKoMBJJHt
We are truly standing on the shoulders of Giants today!
@drmichaellevin together with @MillerLabMIT
"Physicalism has been dead since the time of Pythagoras, and probably long before that."
"The basement of all this, I don't think, is math. I think this is behavioral science. I think math is a behavioural science of a certain kind of pattern."
"It's a bioelectric code, because the network instructs the patterns of gene expression and cell behaviour and morphogenesis. If you want the system to make an eye on a tadpole's tail, or a flatworm that has two heads… you have a chance to do that."
Scientists working at the bleeding edge of bioelectricity at very different scales. They agree stuff, they disagree on stuff. Watch now ⬇️
the dichotomy of applied and pure mathematics is often subconsciously conflated with the distinction between mathematics that requires exact alignment to apply and that which can be fired from the hip. i'd like if we had more tools in pure mathematics that can be hip-fired
@drmichaellevin The black regions in these gifs mask the information behind them... the creatures say to themselves "I can't see this, so let me use the remaining information to decide my next move." Behavior emerges from that.
Thank you @drmichaellevin, @BeneHartl, https://t.co/p3IlYdLAlM!
What are the preferences of novel in silico and in vivo agents that aren't directly engineered toward a specific set of behaviors? Here is an example, from the world of Lenia (https://t.co/h1eq78G7H7) - our new #preprint on agnosiophobia (avoidance of the unknown): https://t.co/rrjuRnImEi
@jessescool_