Morris et al. (2025) — ARXIV-2505.24832
Key takeaways
- The methodological move is the contribution. Memorization has been measured by extraction (can the model be made to emit the string?) and by membership inference (can train be told from test?). The paper argues neither is necessary or sufficient — a model can be coerced into emitting almost anything, and a model that correctly adds two numbers it never saw has not memorized them. Instead: define memorization as compression rate in bits against the model, and split it into unintended memorization (information about this dataset) and generalization (information about the process that produced it).
- Eliminate generalization by making it impossible. Train on uniformly sampled random bitstrings, where the Shannon information is exactly computable and there is nothing general to learn. Whatever the model then holds is capacity.
- The number is ~3.6 bits per parameter for GPT-style transformers, and the measurements cluster tightly (3.61–3.68) across widths and depths.
- Precision barely matters. bfloat16 to float32 doubles the bits in the weights and moves capacity from 3.51 to 3.83 — so nearly all the extra bits are not used for storage. That is a fact about what parameters are for, and it is the most quietly surprising line in the paper.
- Capacity is linear in parameter count, smoothly, across models from ~500K to 1.5B parameters. The authors note this is measured by gradient descent and so is a lower bound on what the architecture could hold.
- Double descent gets a mechanism. On both synthetic bitstrings and text, the test loss turns over exactly where the dataset’s information content exceeds the model’s capacity in bits — the first time the crossing point has been located with both quantities measured rather than proxied. The proposed reading: once the model can no longer store datapoints separately it is forced to share representation between them, and sharing is generalization.
- A scaling law for membership inference follows, sigmoidal in dataset-to-capacity ratio, and it predicts that modern models are trained on far too much data for reliable membership inference on an average point.
- What gets memorized most, in text, is the documents with the rarest words.
Standing in the anthology
The record has argued about data repetition for months in a vocabulary it
could not ground. SOTA-124 turns on a memorization window — roughly
100–500 GT for a 7B model, “scaling linearly”, which its own source calls an
early understanding and which its promote_when: asks somebody to measure at
a second scale. This is the closest thing published to that measurement, and
it is worth being precise about how close.
What it does settle: the linear-in-parameters assumption. Capacity here scales smoothly and linearly with parameter count over more than three orders of magnitude, measured rather than conjectured. SOTA-124 was relying on one figure for that shape.
What it does not settle: the window itself. Falcon’s quantity is a token
count — how much unique data must sit between repeats before repetition stops
being memorized. Morris’s is a bit count — how much a model can hold at all.
The two are related through the information content of the tokens, and that
conversion is exactly what nobody has done. SOTA-124 stays Proposed, with
its conjecture now half-checked rather than unchecked.
The more useful transfer is to SOTA-171 and SOTA-173, which disagree about whether repetition overfits. This supplies the quantity that would make the disagreement decidable: overfitting on repeated data ought to begin when the corpus’s information content stops exceeding the model’s capacity, which is a prediction with two measurable sides. Nobody has tested it in the multi-epoch setting those practices describe — the double-descent result here is at fixed epochs and varying dataset size.