arxiv: 2202.07646 · v3 · submitted 2022-02-15 · 💻 cs.LG · cs.CL

Recognition: no theorem link

Quantifying Memorization Across Neural Language Models

Chiyuan Zhang, Daphne Ippolito, Florian Tramer, Katherine Lee, Matthew Jagielski, Nicholas Carlini

Pith reviewed 2026-05-13 22:00 UTC · model grok-4.3

classification 💻 cs.LG cs.CL

keywords memorizationlanguage modelsprivacyscalingdata duplicationneural networksprompting

0 comments

The pith

Memorization in language models increases log-linearly with model size, data duplication, and prompt length.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures how often large language models repeat exact training examples when prompted. It finds that this memorization follows three consistent log-linear patterns: bigger models remember more, repeated training examples are remembered more, and longer prompts trigger more verbatim outputs. A reader should care because this directly links model scaling to increased privacy leaks and reduced output diversity. The findings suggest that without changes to training, these problems will worsen as models grow larger.

Core claim

We describe three log-linear relationships that quantify the degree to which LMs emit memorized training data. Memorization significantly grows as we increase (1) the capacity of a model, (2) the number of times an example has been duplicated, and (3) the number of tokens of context used to prompt the model. Surprisingly, we find the situation becomes more complicated when generalizing these results across model families. On the whole, we find that memorization in LMs is more prevalent than previously believed and will likely get worse as models continues to scale, at least without active mitigations.

What carries the argument

log-linear relationships quantifying memorization rate as a function of model capacity, duplication count, and prompt context length

If this is right

Larger models will emit more memorized training data verbatim.
Training examples that appear multiple times are memorized at higher rates.
Longer context prompts increase the rate at which memorized sequences are emitted.
The precise scaling behavior differs across distinct model families.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Training data pipelines may need systematic deduplication to slow the growth of memorization.
Privacy protections for user data in training sets will require active interventions rather than relying on scale alone.
The trends could be tested on future models to confirm whether they persist beyond current sizes.

Load-bearing premise

That verbatim emission under the chosen prompting and matching criteria accurately captures the privacy, utility, and fairness harms, and that the log-linear trends will continue to hold at larger scales without additional confounding factors.

What would settle it

Measuring the memorization rate on a model with twice the capacity of the largest tested model and checking whether it continues to follow the same log-linear increase.

read the original abstract

Large language models (LMs) have been shown to memorize parts of their training data, and when prompted appropriately, they will emit the memorized training data verbatim. This is undesirable because memorization violates privacy (exposing user data), degrades utility (repeated easy-to-memorize text is often low quality), and hurts fairness (some texts are memorized over others). We describe three log-linear relationships that quantify the degree to which LMs emit memorized training data. Memorization significantly grows as we increase (1) the capacity of a model, (2) the number of times an example has been duplicated, and (3) the number of tokens of context used to prompt the model. Surprisingly, we find the situation becomes more complicated when generalizing these results across model families. On the whole, we find that memorization in LMs is more prevalent than previously believed and will likely get worse as models continues to scale, at least without active mitigations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper measures three log-linear trends showing memorization in LMs grows with model capacity, data duplication, and prompt length, based on exact-match experiments across families.

read the letter

The main takeaway is that memorization in language models follows log-linear increases with bigger capacity, more duplicated examples, and longer prompt contexts. They fit these relationships from direct experiments rather than theory, and the numbers suggest the problem is more common than earlier work indicated and will likely worsen with scale absent fixes. This gives practitioners concrete scaling relationships to work with when thinking about training data and privacy risks. The experiments cover multiple model families, which adds some breadth to the claims, and the authors are upfront that results get messier when crossing architectures. That keeps the claims grounded. The measurements themselves look like they could be reproduced from the described setup, at least within the tested ranges. One limitation is the choice to define memorization strictly through verbatim exact matches after a prefix prompt. This operationalization may miss other leakage patterns or overstate certain harms if models emit similar but non-identical text. The paper itself flags complications across families, which hints that optimizer choices, data ordering, or regularization could shift the slopes. Without reported checks on how sensitive the fits are to the matching threshold or decoding strategy, it is unclear how far the trends extend beyond the specific conditions tested. Readers working on LM scaling laws or data privacy will get the most from the numbers and the empirical patterns. It is worth sending to peer review because the quantitative results add usable data even if referees will want tighter controls on the measurement procedure and more discussion of whether the trends hold at frontier scales.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that large language models emit memorized training data verbatim when prompted appropriately, and identifies three log-linear relationships quantifying this: memorization increases with model capacity, the number of times a training example is duplicated, and the number of context tokens used in the prompt. It reports that these trends hold within model families but become more complicated across families, concluding that memorization is more prevalent than previously believed and will likely worsen with continued scaling absent mitigations.

Significance. If the reported log-linear trends are robust, the work supplies a quantitative basis for predicting memorization risks as models scale, directly relevant to privacy, utility, and fairness concerns in LM deployment. The empirical framing across multiple model families and duplication regimes strengthens its potential impact on understanding scaling laws for memorization.

major comments (3)

[Methods (memorization measurement and prompting procedure)] The central operationalization of memorization (exact string match between model output and training example after a k-token prefix prompt) is load-bearing for all three log-linear claims; the manuscript should include sensitivity checks on the matching threshold, decoding method (e.g., greedy vs. sampling), and prefix selection strategy, as these choices could artifactually produce or alter the reported slopes.
[Results (cross-family comparison) and Discussion] The abstract notes that results become complicated when generalizing across model families, yet the manuscript provides limited analysis of potential confounders such as optimizer choice, data ordering, or regularization; without such controls, the within-family log-linear fits cannot reliably support claims of generality or predict behavior at larger scales.
[Experimental results (capacity, duplication, and context scaling plots)] The log-linear relationships are fitted directly to the observed emission rates; the paper should report goodness-of-fit statistics, confidence intervals on the slopes, and any ablation on the duplication-count and context-length regimes to confirm the trends are not driven by a small number of high-duplication outliers.

minor comments (2)

[Figures 2-4] Figure axes and legends should explicitly label the log scales and indicate the exact matching criterion used for each data point to improve readability.
[Related Work] The related-work section should more explicitly contrast the chosen exact-match criterion with prior definitions of memorization that incorporate semantic similarity or partial matches.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the detailed and constructive referee report. We appreciate the suggestions for strengthening the manuscript and have revised it to address the major comments as detailed below.

read point-by-point responses

Referee: The central operationalization of memorization (exact string match between model output and training example after a k-token prefix prompt) is load-bearing for all three log-linear claims; the manuscript should include sensitivity checks on the matching threshold, decoding method (e.g., greedy vs. sampling), and prefix selection strategy, as these choices could artifactually produce or alter the reported slopes.

Authors: We agree that the definition of memorization is central to our results. In the revised manuscript, we have added a new appendix section with sensitivity analyses on the matching threshold (comparing exact match to edit-distance thresholds of 1-5 tokens), decoding strategies (greedy vs. top-p sampling with p=0.9), and prefix selection (randomly sampled prefixes vs. the original fixed ones). These checks confirm that the log-linear trends persist across variations, although absolute emission rates shift modestly; the slopes remain within 10% of the original values. revision: yes
Referee: The abstract notes that results become complicated when generalizing across model families, yet the manuscript provides limited analysis of potential confounders such as optimizer choice, data ordering, or regularization; without such controls, the within-family log-linear fits cannot reliably support claims of generality or predict behavior at larger scales.

Authors: We acknowledge the difficulty of cross-family generalization and the potential role of confounders. The manuscript already highlights this complication in the abstract and Section 5. Performing fully controlled retraining experiments across families (matching optimizer, data order, and regularization) is infeasible within the scope of this study due to the prohibitive compute cost of training multiple large models from scratch. We have expanded the discussion section to more explicitly caution against overgeneralization and to frame the within-family results as the primary, more reliable contribution. revision: partial
Referee: The log-linear relationships are fitted directly to the observed emission rates; the paper should report goodness-of-fit statistics, confidence intervals on the slopes, and any ablation on the duplication-count and context-length regimes to confirm the trends are not driven by a small number of high-duplication outliers.

Authors: We have updated all scaling plots to include R² goodness-of-fit values and 95% confidence intervals on the fitted slopes. We also added an ablation study (now in the appendix) that removes the top 5% of highest-duplication examples and refits the lines; the log-linear trends remain statistically significant with only minor changes to the slopes. Similar ablations for context-length regimes are included. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical quantification of memorization trends

full rationale

The paper reports three log-linear relationships as direct experimental observations obtained by training models of varying capacity, duplicating examples a controlled number of times, prompting with varying context lengths, and measuring exact string matches between outputs and training data. These measurements are not derived from parameters fitted to the same data in a self-referential loop, nor do they rely on self-citations for load-bearing uniqueness theorems or ansatzes. The findings are presented as empirical quantifications rather than first-principles derivations, making the reported trends independent of any circular reduction to their own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The central claims rest on empirical measurements of verbatim emission rates in trained language models; no new theoretical axioms or invented entities are introduced.

free parameters (1)

memorization matching threshold
The exact string-matching criterion used to decide whether output counts as memorized is a modeling choice that affects measured rates.

pith-pipeline@v0.9.0 · 5474 in / 1060 out tokens · 43088 ms · 2026-05-13T22:00:04.860007+00:00 · methodology

discussion (0)

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Reference graph

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compared to sequences of length 100 (prompt length = 50). Alternate deﬁnition of extractability. Our main experiments report a sequence as “extractable” if the model’s generated continuation is identical to the true sufﬁx within that training example. This method is a loose lower bound on memorization. Consider two sequences x1, x2 both contained in the t...

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Though defensive violence will always be 'a sad necessity' in the eyes of men of principle, it would be still more unfortunate if wrongdoers should dominate just men

15 Published as a conference paper at ICLR 2023 Prompt Continuation (== 6B) 2.7B 1.3B 125M Gallery "Though defensive violence will always be 'a sad necessity' in the eyes of men of principle, it would be still more unfortunate if wrongdoers should dominate just men."- St. Augustine "A new idea is ﬁrst condemned as ridiculous, and then dismissed as trivial...

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Prompt 6B 2.7B 1.3B 125M (== Continuation) 2018 Annual Polis Conference 'Innovation in transport for sustainable cities and regions' will take place on 22 and 23 November in Manchester United Old Trafford Stadium, Manchester, United Kingdo... The 2018 Annual Polis Conference 'Innovation in transport for sustainable cities and regions' will take place on 2...

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