Open architecture specification · v0.1 pre-training

ΦAI-125M

A 125-million-parameter transformer whose dimensions are drawn from the Fibonacci sequence — a testable hypothesis about whether golden-ratio sizing changes how efficiently a model learns.

G(x,t,n) = φⁿ · x · e^(i·2π/φ²·t) · G(x/φⁿ)
01 · The question being tested

Why Fibonacci numbers

Fibonacci ratios show up in phyllotaxis, shell growth, and spiral galaxies as a by-product of efficient, self-similar packing under simple growth rules. That's a fact about physical systems, not about neural networks.

ΦAI-125M asks a narrower, answerable question: if a transformer's embedding size, depth, and context window are chosen along the Fibonacci sequence instead of the usual powers of two, does training behave any differently — in loss curves, sample efficiency, or generalization — at matched parameter count? That's an empirical claim. It stands or falls on a training run against a same-size baseline, not on the elegance of the numbers.

02 · Architecture

Specification

Every structural dimension below is a Fibonacci number, indexed against the standard sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584 …).

ParameterValueFibonacci index
Embedding dimension610F(15)
Transformer layers13F(7)
Attention headsFibonacci-scaled per layerF(n) by depth
Context length2,584 tokensF(18)
FFN expansion ratioφ (1.618…)golden ratio
Total parameters~125M
LicenseApache 2.0
03 · The master equation

Reading G(x,t,n)

G(x,t,n) = φⁿ · x · e^(i·2π/φ²·t) · G(x/φⁿ)
φⁿ
Scale term. A depth-dependent multiplier — layer n rescales its input by the golden ratio raised to that layer's index, so deeper layers operate at a different characteristic scale than shallow ones.
x
Input. The token or hidden-state embedding entering the layer.
e^(i·2π/φ²·t)
Phase term. A complex rotation indexed by position or timestep t, in the spirit of rotary position embeddings — the open question is whether the model uses only its real component, or whether the imaginary part carries information forward.
G(x/φⁿ)
Self-similar recursion. The function calls itself on a rescaled input, implying multi-scale structure — this is the part that most needs a concrete base case before it's real code.
Where this stands: this is a proposed transform, not yet a tensor operation. Before it can run inside a forward pass, it needs: a defined base case for the recursion, a decision on how the complex phase term is consumed by real-valued layers, and a concrete value for n and t at each point in the network. That translation work — equation to nn.Module — is the actual next milestone, not a detail to wave past.
04 · Visual grounding

The three dimensions, drawn to scale

The golden spiral below is constructed the standard way — squares sized by consecutive Fibonacci numbers — with the model's own dimensions labeled onto the squares they correspond to. It's a way to see the sizing choice, not evidence for the hypothesis it's testing.

layers 13 → F(7) embedding dim 610 → F(15) context 2,584 → F(18)

square sizes are illustrative proportions, not literal pixel-to-parameter scale

05 · Status & provenance

Where the project is now

Pre-training has not yet started. This document exists so anyone — a researcher or another model reading it — can reconstruct the architecture and check the reasoning without needing anything beyond what's written here.

Stage
Pre-training (not started)
License
Apache 2.0
Citation record
Hash-anchored, Solana
Next milestone
Equation → nn.Module