memcap-random-data

Uniformly random token datasets for measuring the memorization capacity of small language models, reproducing the protocol of "How much do language models memorize?" (Sec. 3.2) at tiny scale.

Because the data has no structure, generalization is impossible: every bit of likelihood gain over the uniform distribution is pure memorization.

Generation

• Each token is sampled i.i.d. uniform over a vocabulary of V = 2048.
• Sequence length S = 64 tokens. No tokenizer; tokens are integer ids directly.
• Generator: numpy.random.Generator(numpy.random.PCG64(seed)), rng.integers(0, 2048, size=(N, 64), dtype=int32).
• Within each config, datasets are nested: the first N rows are the subset used for a sweep point with dataset size N.

Exact entropy calculations

Each token carries exactly log2(2048) = 11 bits of entropy.

• Raw dataset entropy: H(X) = N × 64 × 11 = 704·N bits.
• Teacher-forced predictable entropy (what an autoregressive model can score, 63 of 64 positions): H_pred(X) = N × 63 × 11 = 693·N bits. This is the reference used for the memorization measurements in the companion results repo.

Config	N	Data seed	H(X) = 704·N (bits)	H_pred = 693·N (bits)
small	44,000	100	30,976,000	30,492,000
medium	152,000	200	107,008,000	105,336,000
large	640,000	300	450,560,000	443,520,000
large_n43000_s1	43,000	301	30,272,000	29,799,000
large_n43000_s2	43,000	302	30,272,000	29,799,000

large_n43000_s1/s2 are independent redraws of the near-capacity dataset for the ~8M-parameter model (predicted saturation at N ≈ P/195 ≈ 43,000), used for seed replicates.

Schema

Single column input_ids: sequence of int32, length 64, values in [0, 2048).

Reproduce

import numpy as np
rng = np.random.default_rng(np.random.PCG64(300))  # seed per config table
data = rng.integers(0, 2048, size=(640000, 64), dtype=np.int32)

Companion repos: results/metrics at pngwn/memcap-results, trained checkpoints at pngwn/memcap-runs.