Architecture: GPT-2 (transformers), trained from scratch.
Parameters: 1,871,056 (non-embedding 1,496,352).
Vocab: 2048 data tokens (uniform random) + BOS = 2049 model vocab.
Sequence length: 64 (paper S=64).
Dataset: 10000 sequences, 640,000 data tokens, dataset entropy 7,040,000 bits (7.040 Mbits).
Trained 7330 steps, AdamW, bfloat16, lr 0.002, batch 512.
Result: train loss 3.7714 bits/tok, held loss 18.0931, memorized 4,626,295 bits = 2.473 bits/parameter.

This is the near-capacity (saturation-boundary) run for this model size. Below- and above-capacity checkpoints for the same architecture are published as state.pt files in the results dataset evalstate/tiny-memorization-results.

Load with:

python

from transformers import GPT2LMHeadModel
model = GPT2LMHeadModel.from_pretrained("evalstate/tiny-gpt-memorization-2m")

Findings are scoped as an exploratory tiny-scale check (three architectures), NOT a universal scaling law.