stanpony/nca-prepretrain-data

NCA Pre-Pretraining Data

Pre-tokenized Neural Cellular Automata (NCA) trajectory data for transformer pre-pretraining experiments. Based on Lee et al. 2026, "Training Language Models via Neural Cellular Automata".

Files

File	Method	Tokens	Size	Description
nca_data_rule_diverse.bin	Rule-diverse (ours)	100M	191 MB	1 simulation per rule, ~49,653 unique rules
nca_data_paper.bin	Paper baseline (Lee et al.)	100M	191 MB	100 simulations per rule, ~504 rules

Both files are flat binary arrays of uint16 token IDs, ready to be memory-mapped or loaded directly.

How the data is generated

NCA rules

Each NCA rule is a small convolutional network (614 parameters) that defines the update dynamics on a 12×12 grid with 10 cell states. Rules are created deterministically from integer seeds.

Complexity filtering

Not all rules produce interesting dynamics — many converge to fixed points or simple periodic patterns. We filter rules using gzip compression ratio on the tokenized trajectory: only rules with gzip complexity in [0.5, 1.0] are kept (~16% pass rate). This selects for spatiotemporally complex dynamics.

Tokenization

Each grid state is tokenized using 2×2 patches with base-10 positional encoding:

• Patch token = a + 10*b + 100*c + 1000*d for cells [a, b, c, d] → tokens 0–9999
• Grid delimiter tokens: 10000 (start) and 10001 (end)
• Total vocabulary: 10,002 tokens

Each trajectory has 53 recorded grid states (after 10 warmup steps), giving 53 × 38 = 2,014 tokens per trajectory.

Two generation methods

Rule-diverse (nca_data_rule_diverse.bin): Our contribution. One simulation per rule. Each seed determines both the rule weights and the initial grid state. Diversity comes from scanning many different rules (~49,653 unique rules for 100M tokens). The hypothesis is that exposing the model to a wider variety of dynamical systems teaches more general sequential structure.

Paper baseline (nca_data_paper.bin): Reproduction of the method from Lee et al. 2026. Multiple simulations per rule — 504 rules are pre-filtered, then each gets 100 simulations with different random initial grid states. Diversity comes from varying initial conditions within fewer, pre-approved rules. The original paper uses 16,000 rules × 500 sims; we use fewer rules/sims to match the same 100M token budget.

Parameters (matching the paper's actual training script)

Parameter	Value
Grid size	12×12
Cell states	10
Temperature	1e-4
Identity bias	0.0
Warmup steps	10
Patch size	2×2
Gzip threshold	[0.5, 1.0]

Usage

import numpy as np

# Load the data
data = np.fromfile("nca_data.bin", dtype=np.uint16)
print(f"Tokens: {len(data):,}")  # 100,000,000

# Delimiter tokens are the last two in the vocabulary
START_TK = 10000
END_TK = 10001

Loss masking

Grid delimiter tokens (10000, 10001) should have their loss masked during training (target = -100). The model learns to predict only patch tokens, not structural markers.

Reproducibility

Data is fully deterministic given the generation scripts and PyTorch version. Generated with PyTorch on macOS (Apple Silicon).

File	MD5
nca_data_rule_diverse.bin	c857b8397249cd0a5304685fca835553
nca_data_paper.bin	e8b8ad97afb830f41569813af15476ed

Citation

If you use this data, please cite the original NCA pre-pretraining paper:

@article{lee2026nca,
  title={Training Language Models via Neural Cellular Automata},
  author={Lee, Daniel Hyun and others},
  journal={arXiv preprint arXiv:2603.10055},
  year={2026}
}