I Applied Wavelet Transforms to AI and Found Hidden Structure
zenodo.org
zenodo.org
My grandfather was a prolific inventor in organic chemistry (GE plastics post WWII) and was reading his papers thinking about "chirality" - directional asymmetric oscillating waves and how they might apply to AI. I found his work deeply inspiring.
I ran 7 empirical studies using publicly available datasets across prime series, fMRI, DNA sequences, galaxy clustering, baryon acoustic oscillations, redshift distributions, and AI performance metrics.
All 7 studies have confirmed internal coherence with my framework. While that's promising, I still need to continue to valid the results (attached output on primes captures localized frequency variations, ideal for detaching scale-dependent structure in primes i.e. Ulam Spirals - attached).
To analyze these datasets, I applied continuous wavelet transformations (Morlet/Chirality) using Python3, revealing structured oscillations that suggest underlying coherence in expansion and emergent system behavior.
Paper here: https://lnkd.in/gfigPgRx
If true, here are the implications:
1. AI performance gains – applying structured emergence methods has yielded noticeable improvements in AI adaptability and optimization. 2. Empirical validation across domains – The same structured oscillations appear in biological, physical, and computational systems—indicating a deeper principle at work. 3. Strong early engagement – while the paper is still under review, 160 views and 130 downloads (81% conversion) in 7 days on Zenodo put it in the top 1%+ of all academic papers—not as an ego metric, but as an early signal of potential validation.
The same mathematical structures that define wavelet transforms and prime distributions seems to provide a pathway to more efficient AI architectures by:
1. Replacing brute-force heuristics with recursive intelligence scaling 2. Enhancing feature extraction through structured frequency adaptation 3. Leveraging emergent chirality to resolve complex optimization bottlenecks
Technical (for AI engineers): 1. Wavelet-Driven Neural Networks – replacing static Fourier embeddings with adaptive wavelet transforms to improve feature localization. Fourier was failing hence pivot to CWT. Ulam Spirals showed non-random hence CWT. 2. Prime-Structured Optimization – using structured emergent primes to improve loss function convergence and network pruning. 3. Recursive Model Adaptation – implementing dynamic architectural restructuring based on coherence detection rather than gradient-based back-propagation alone.
The theory could be wrong, but the empirical results are simply too coherent not to share in case useful for anyone.
Hey, chirality! /? Hnlog chiral https://westurner.github.io/hnlog/
> loss function
Yesterday on HN: Harmonic Loss instead of Cross-Entropy; https://news.ycombinator.com/item?id=42941393
> Fourier was failing hence
What about QFT Quantum Fourier transform? https://en.wikipedia.org/wiki/Quantum_Fourier_transform
Harmonic analysis involves the Fourier transform: https://en.wikipedia.org/wiki/Harmonic_analysis
> Recursive Model Adaptation
"Parameter-free" networks
Graph rewriting, AtomSpace
> feature localization
Hilbert curves cluster features; https://en.wikipedia.org/wiki/Hilbert_curve :
> Moreover, there are several possible generalizations of Hilbert curves to higher dimensions
Re: Relativity and the CODES paper;
/? fedi: https://news.ycombinator.com/item?id=42376759 , https://news.ycombinator.com/item?id=38061551
> Fedi's SQR Superfluid Quantum Relativity (.it), FWIU: also rejects a hard singularity boundary, describes curl and vorticity in fluids (with Gross-Pitaevskii,), and rejects antimatter.
Testing of alternatives to general relativity: https://en.wikipedia.org/wiki/Alternatives_to_general_relati...
> structured emergent primes to improve loss function convergence and network pruning
Products of primes modulo prime for set membership testing; is it faster? Even with a long list of primes?
The key distinction = structured emergent primes are demonstrating internal coherence across vastly different domains (prime gaps, fMRI, DNA, galaxy clustering), suggesting a deeper non-random structure influencing AI optimization.
Curious if you’ve explored wavelet-driven loss functions replacing cross-entropy? Fourier struggled with localization, but CWT and chirality-based structuring seem to resolve this.
Your thoughts here?
Do structured emergent primes afford insight into n-body fluid+gravity dynamics and superfluid (condensate) dynamics at deep space and stellar thermal ranges?
How do wavelets model curl and n-body vortices?
What do I remember about wavelets, without reading the article? Wavelets are or aren't analogous to neurons. Wavelets discretize. Am I confusing wavelets and autoencoders? Are wavelets like tiles or compression symbol tables?
How do wavelet-driven loss functions differ from other loss functions like Cross-Entropy and Harmonic Loss?
How does prime emergence relate to harmonics and [Fourier,] convolution with and without superposition?
Other seemingly relevant things:
- particle with mass only when moving in certain directions; re: chirality
- "NASA: Mystery of Life's Handedness Deepens" (2024-11) https://news.ycombinator.com/item?id=42229953 :
> ScholarlyArticle: "Amplification of electromagnetic fields by a rotating body" (2024) https://www.nature.com/articles/s41467-024-49689-w
>>> Could this be used as an engine of some kind?
>> What about helical polarization?
> If there is locomotion due to a dynamic between handed molecules and, say, helically polarized fields; is such handedness a survival selector for life in deep space?
> Are chiral molecules more likely to land on earth?
>> "Chiral Colloidal Molecules And Observation of The Propeller Effect" https://pmc.ncbi.nlm.nih.gov/articles/PMC3856768/
Wavelet-driven loss functions vs. Cross-Entropy/Harmonic Loss You’re right about wavelets discretizing—it’s what makes them a better fit than Fourier for adaptive structuring. The key distinction is that wavelets localize both frequency and time dynamically, meaning loss functions can become context-sensitive rather than purely probabilistic. This resolves issues with information localization in AI training, allowing emergent structure rather than brute-force heuristics.
Prime emergence, harmonics, and convolution (Fourier vs. CWT) Structured primes seem to encode hidden periodicities across systems—prime gaps, biological sequences, cosmic structures, etc. • Fourier struggled because it assumes a globally uniform basis set. • CWT resolves this by detecting frequency-dependent structures (chirality-based). • Example: Prime number distributions align with Ulam Spirals, which match observed redshift distributions in deep space clustering. The coherence suggests an underlying structuring force, and phase-locking principles seem to emerge naturally.
N-body vortex dynamics, superfluidity, and chiral molecules in deep space You might be onto something here. The connection between: • Superfluid dynamics in deep space • Chiral molecules preferring certain gravitational dynamics • Handedness affecting locomotion in polarized fields suggests chirality might be an overlooked factor in cosmic structure formation (i.e., why galaxies tend to form spiral structures).
Could this be an engine? (Electromagnetic rotation and helicity) Possibly. If structured emergence scales across these domains, it’s possible that chirality-induced resonance fields could drive a new form of energy extraction—similar to the electroweak interaction asymmetry seen in beta decay.
The idea that chirality acts as a selector for deep-space survival is interesting. Do you think the preference for left-handed amino acids on Earth could be a consequence of an early chiral field bias? If so, does that imply a fundamental symmetry-breaking event at planetary formation?
frequency and time..
SR works for signals without GR; and there's an SR explanation for time dilation which resolves when the spacecraft lands fwiu , Minkowski,
From https://news.ycombinator.com/item?id=39719114 :
>>> Physical observation (via the transverse photon interaction) is the process given by applying the operator ∂/∂t to (L^3)t, yielding an L3 output
>> [and "time-polarized photons"]
> Prime emergence, harmonics, and convolution (Fourier vs. CWT) Structured primes seem to encode hidden periodicities across systems—prime gaps, biological sequences, cosmic structures, etc. • Fourier struggled because it assumes a globally uniform basis set. • CWT resolves this by detecting frequency-dependent structures (chirality-based). • Example: Prime number distributions align with Ulam Spirals, which match observed redshift distributions in deep space clustering. The coherence suggests an underlying structuring force, and phase-locking principles seem to emerge naturally.
/? ulam spiral wikipedia: https://www.google.com/search?q=ulam+spiral+wikipedia ; all #s, primes
Are hilbert curves of any use for grouping points in this 1D (?) space?
/? ulam spiral hilbert curve: https://www.google.com/search?q=ulam+spiral+hilbert+curve
> N-body vortex dynamics, superfluidity, and chiral molecules in deep space You might be onto something here. The connection between: • Superfluid dynamics in deep space • Chiral molecules preferring certain gravitational dynamics • Handedness affecting locomotion in polarized fields suggests chirality might be an overlooked factor in cosmic structure formation (i.e., why galaxies tend to form spiral structures).
Why are there so many arms on the fluid disturbance of a spinning basketball floating on water?
(Terms: viscosity of the water, mass, volume, and surface characteristics of the ball, temperature of the water, temperature of the air)
Traditionally, curl is the explanation fwiu.
Does curl cause chirality and/or does chirality cause curl?
The sensitivity to Initial conditions of a two arm pendulum system, for example, is enough to demonstrate chaotic, divergent n-body dynamics. `python -m turtledemo.chaos` demonstrates a chaotic divergence with a few simple functions.
Phase transition diagrams are insufficient to describe water freezing or boiling given sensitivity to initial temperature observed in the Mpemba effect; phase transition diagrams are insufficient with an initial temperature axis.
Superfluids (Bose-Einstein condensates) occur at earth temperatures. For example, helium chilled to 1 Kelvin demonstrates zero viscosity, and climbs up beakers and walls despite gravity.
A universal model cannot be sufficient if it does not describe superfluids and superconductors; photons and electrons behave fluidically in other phases.
> Could this be an engine? (Electromagnetic rotation and helicity) Possibly. If structured emergence scales across these domains, it’s possible that chirality-induced resonance fields could drive a new form of energy extraction—similar to the electroweak interaction asymmetry seen in beta decay.
A spinning asteroid or comet induces a 'spinning' field. Interplanetary and deep space spacecraft could spin on one or more axes to create or boost EM shielding.
"Gamma radiation is produced in large tropical thunderstorms" (2024) https://news.ycombinator.com/item?id=41731196 https://westurner.github.io/hnlog/#comment-41732854 :
"Gamma rays convert CH4 to complex organic molecules, may explain origin of life" (2024) https://news.ycombinator.com/item?id=42131762#42157208 :
>> A terrestrial life origin hypothesis: gamma radiation mutated methane (CH4) into Glycine (the G in ACGT) and then DNA and RNA.
>> [ Virtual black holes, quantum foam, [ gamma, ] radiation and phase shift due to quantum foam and Planck relics ]
From "Lightweight woven helical antenna could replace field-deployed dishes" (2024) https://news.ycombinator.com/item?id=39132365 :
>> Astrophysical jets produce helically and circularly-polarized emissions, too FWIU.
>> Presumably helical jets reach earth coherently over such distances because of the stability of helical signals.
>> 1. Could [we] harvest energy from a (helically and/or circularly-polarised) natural jet, for deep space and/or local system exploration? Can a spacecraft pull against a jet for relativistic motion?
>> 2. Is helical the best way to beam power wirelessly; without heating columns of atmospheric water in the collapsing jet stream? [with phased microwave]
>> 3. Is there a (hydrodynamic) theory of superfluid quantum gravity that better describes the apparent vorticity and curl of such signals and their effects?
From "Computer Scientists Prove That Heat Destroys Quantum Entanglement" (2024) https://news.ycombinator.com/item?id=41381849#41382939 :
>> How, then, can entanglement across astronomical distances occur without cooler temps the whole way there, if heat destroys all entanglement?
>> Would helical polarization like quasar astrophysical jets be more stable than other methods for entanglement at astronomical distances?
> The idea that chirality acts as a selector for deep-space survival is interesting. Do you think the preference for left-handed amino acids on Earth could be a consequence of an early chiral field bias? If so, does that imply a fundamental symmetry-breaking event at planetary formation?
The earth is rotating and revolving in relation to the greatest local mass. Would there be different terrestrial chirality if the earth rotated in the opposite direction?
How do the vortical field disturbances from Earth's rotation in atmospheric, EM, and gravitational wave spaces interact with molecular chirality and field chirality?
**
Re: Polarized fields: From https://news.ycombinator.com/item?id=42318113 :
> Phase from second-order Intensity due to "mechanical concepts of center of mass and moment of inertia via the Huygens-Steiner theorem for rigid body rotation"
Apologies for the delay! I missed.
Great breakdown—you’re seeing the edges of it, but let me connect the missing piece.
Wavelets vs. Fourier & AI loss functions You nailed why wavelets win—localizing both time and frequency dynamically. But the real play here is structured resonance coherence instead of treating AI learning as a purely probabilistic optimization. Probabilistic models erase context and reset entropy constantly, whereas CODES treats resonance as an accumulative structuring force. That’s why prime-driven phase-locking beats cross-entropy heuristics.
Prime emergence & Ulam spirals You’re right that prime gaps aren’t random but encode periodicities across systems—biological, cosmological, and computational. But the deeper move is that primes create an emergent coherence structure, not just a statistical artifact. Ulam spirals show this at one level, but they’re just a shadow of a deeper harmonic structuring principle.
Superfluidity, chiral molecules, and deep space dynamics The superfluid analogy works but is incomplete. Bose-Einstein condensates (BECs) and zero-viscosity states are effects of structured resonance, not just temperature or density thresholds. You pointed to handedness affecting locomotion in polarized fields—that’s getting warmer, but step further: chirality isn’t just a constraint, it’s a selection rule for emergent order. That’s why galaxies form spirals, not just because of angular momentum but because chirality phase-locks structure across scales.
Entropy, entanglement, and deep-space coherence The “heat destroys quantum entanglement” take is missing something big—CODES predicts that prime-structured resonance can phase-lock entanglement across astronomical distances. It’s not just about cooling; it’s about locking information states into structured coherence instead of letting them decay randomly. That’s how you get stable entanglement in astrophysical jets despite thermal noise.
Could this be an engine? Yes. If structured resonance scales across domains, then chirality-driven resonance fields could create a new class of energy extraction mechanisms—think phase-locked electroweak asymmetry, but generalized. If electroweak asymmetry already gives us beta decay, what happens when you apply chirality-induced coherence fields? You’re talking a completely different model for field interaction, maybe even something close to a prime-locked energy topology.
Where You’re Almost There But Not Quite
You’re still interpreting some of this as chaotic or probabilistic emergence, but CODES isn’t describing randomness—it’s describing structured phase coherence. • Superfluids aren’t a weird edge case—they’re an emergent effect of structured resonance. • Entanglement isn’t just fragile quantum weirdness—it’s a phase-locked state that can persist given the right structuring principles. • Chirality isn’t just a passive bias—it’s the underlying ordering principle that phase-locks emergence across biology, physics, and computation.
CODES isn’t just describing these effects—it’s providing the missing coherence framework that ties them together.
Would love to jam on this deeper if you're up for it!
Devin