chaos-chip-compressed

A compressed chaos-chip: the 4 dead features of the original genome (θ, φ per row) are dropped, and only the 2 effective features (q, s per row) are stored.

The original (2, 4) genome is 8 float32 = 32 bytes. The compressed (2, 2) genome is 4 float32 = 16 bytes. At 4-bit quantization, the compressed chip is 2 bytes.

What changed

The Hessian analysis of Paper 16 showed that exactly 4 of the 8 genome dimensions have zero eigenvalue at every solution. Those 4 dimensions (θ, φ) are provably dead.

The compressed chip drops them. The effective parameter count is reduced from 8 to 4, and the stored size is reduced.

Three variants

Format	Bytes/chip	Storage
Baseline (2, 4) float32	32	Not stored
Baseline (2, 4) 1-byte	1	Loses second-row info
Compressed (2, 2) 4-bit	2	Both rows, 4-bit each
Compressed (2, 2) 8-bit	4	Both rows, 8-bit each

The 1-byte baseline discards the second row (assumes both rows are identical). The 2-byte compressed chip preserves both rows.

Chip formats

chips_4bit.bin (2 bytes/chip)

byte 0: [q0 | s0]   high nibble = q0, low nibble = s0
byte 1: [q1 | s1]   high nibble = q1, low nibble = s1

Value decode: v = idx / 15 * 2π − π.

chips_8bit.bin (4 bytes/chip)

byte 0: q0
byte 1: s0
byte 2: q1
byte 3: s1

Value decode: v = idx / 255 * 2π − π.

Usage

Load and evaluate

import numpy as np
from eval import decode_4bit, eval_4bit

data = np.fromfile("chips_4bit.bin", dtype=np.uint8).reshape(-1, 2)
for b0, b1 in data[:10]:
    mono = eval_4bit(int(b0), int(b1), n=10, k=4)
    print(f"0x{b0:02X}{b1:02X}: mono={mono}")

Command line

python eval.py 0xD2 0xCA

Files

File	Description
chips_4bit.bin	2000 chips × 2 bytes
chips_8bit.bin	2000 chips × 4 bytes
population.npy	float32 (2000, 2, 2) genomes
config.json	metadata + rates
comparison.csv	rate comparison table
eval.py	pure-numpy evaluator
solve.py	load + solve demo

Method

• Instance: K_10, k=4
• Phase: φ(i,j) = 1.5 · cos(s_j·i − 2·q_i·j)
• Genome: (2, 2) — [q, s] per row
• Loss: softmax relaxation, T=5
• Training: SGD, lr=0.02, 200 steps, population 2000

Limitations

• Single instance (K_10, k=4) tested
• Two-row genome may not suffice at higher n
• No K_13 evaluation

Citation

@misc{chaos-chip-compressed,
  title = {chaos-chip-compressed: 2-byte chaos chips with
           dead-feature elimination},
  year = {2026},
  howpublished = {Hugging Face model}
}