memcap-results — learning curves & capacity estimates

All measurements from a tiny-scale reproduction of How much do language models memorize? (Morris et al.). GPT-2 models of 0.54M / 1.86M / 8.44M parameters trained from scratch on uniformly random tokens (pngwn/memcap-random-data; vocab 2048, seq len 64, entropy = 63 × log₂(2048) = 693 bits/sequence).

memorized bits = dataset entropy − model NLL on the training data (bits)

Contents

• runs/*.json — one file per training cell (18 cells): final metrics + full learning curve (probe memorization every 250 steps). Naming: {size}_n{N}_s{seed}_{precision}.
• runs/archive_v2_*.json — superseded v2-script versions of three cells, kept as evidence of optimization-budget effects (see REPORT.md).
• analysis/summary.csv / summary.json — all cells, one row each.
• analysis/model_size_vs_memorized_bits.png — the headline plot: measured capacity vs the 3.6 bits/param prediction.
• analysis/memorized_bits_vs_N.png — memorization vs dataset size per model size, with entropy ceiling.
• analysis/near_capacity_seeds_bf16.png — seed & precision spread for the 8.44M model at N=43,000.
• analysis/bits_per_param_vs_relative_N.png — bits/param vs dataset entropy relative to predicted capacity.
• train_memcap.py — the exact training script (pinned deps in PEP 723 header).
• REPORT.md — the full reproduction report.

Headline numbers

model	params	capacity (bits/param)	paper fp32
s	538,464	3.14	~3.83
m	1,856,768	3.50	~3.83
l	8,438,784	2.64 (lower bound — optimization-limited)	~3.83

Checkpoints: all 18 cells on branches of pngwn/memcap-runs; the three most informative as dedicated repos: memcap-l-below-capacity, memcap-m-near-capacity, memcap-l-above-capacity.