What the Model Remembers: Extraction, Memorisation, and the Price of a Privacy Guarantee

In 2023 a team of researchers asked ChatGPT to repeat the word "poem" forever. For a while the model complied. Then it stopped behaving like an assistant and began emitting long passages copied verbatim from its pretraining corpus: real email signatures with phone numbers, blocks of source code, bitcoin addresses, paragraphs of copyrighted books. Two hundred dollars of API queries recovered over ten thousand unique memorised training examples, and the authors' extrapolation was that ten times more data was available for more money (Nasr et al., 2023, Scalable Extraction of Training Data from (Production) Language Models, arXiv:2311.17035).

Two cents per memorised training example, against a model that had been through the full alignment pipeline.

The instinct is to file this as a bug that got patched, and the specific prompt was indeed patched. That reading misses the structure. Memorisation is a direct consequence of what maximum-likelihood training on text is, its magnitude grows predictably with model size, data duplication and context length, and the only mitigation with a mathematical guarantee attached currently costs about half a decade of capability. This article is about that trade, and about why the field's most reassuring privacy result, that membership inference barely works on large models, is more fragile than it appears.

Why this matters: Every decision about what goes into a training corpus is a permanent, irreversible disclosure decision, because there is no reliable way to remove a document's influence afterwards. If you fine-tune on customer data, index proprietary documents, or train on scraped text of uncertain provenance, the risk you are taking is quantifiable, and most teams have not quantified it.

TL;DR

• Extraction from a production, RLHF-trained model cost roughly two cents per recovered training example, and the divergence attack raised the rate of training-data emission by about 150x over ordinary prompting.
• Memorisation grows log-linearly in three variables at once: model capacity, the number of times an example is duplicated, and the number of context tokens used to prompt. All three are directions the field is scaling.
• Alignment is not a privacy defence. RLHF changes the policy a model follows, not the knowledge it holds, so any technique that pushes sampling off-distribution restores access to the base-model distribution.
• Membership inference "barely outperforms random guessing" on models from 160M to 12B trained on the Pile, but that is a statement about pretraining-scale conditions, not about fine-tuning, PEFT, or retrieval indexes, where the conditions reverse.
• Much of the earlier evidence that membership inference worked on LLMs was distribution shift in disguise: non-members drawn from a later time period, so the attack detected novelty rather than membership.
• Differential privacy is the only defence bounding attacks not yet invented, and its cost is concrete: VaultGemma, at sequence-level \(\varepsilon \le 2.0\), lands roughly at GPT-2 (1.5B) capability with a 1B-parameter model.
• The reason DP is expensive is dimensional: added noise has norm \(\sigma C \sqrt{d}/B\) while the clipped signal has norm at most \(C\), so at 100M trainable parameters you need batches in the tens of thousands before signal exceeds noise.
• Epsilon values are not comparable across papers unless the unit of privacy matches. Sequence-level \(\varepsilon = 2\) and user-level \(\varepsilon = 8\) are different claims about different things.

At a Glance

flowchart LR
    A["Training corpus"] --> B["Maximum-likelihood<br/>training"]
    B --> C["Model weights"]
    C --> D["Normal prompting<br/>assistant behaviour"]
    C --> E["Off-distribution prompting<br/>base distribution returns"]
    E --> F["Verbatim training text"]
    A --> G["Deduplication<br/>partial, cheap"]
    B --> H["DP-SGD<br/>formal, expensive"]
    G -.-> C
    H -.-> C

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    classDef slate fill:#334155,stroke:#64748b,stroke-width:1px,color:#e2e8f0

    class A blue
    class B,C purple
    class D slate
    class E,F rose
    class G,H emerald

Two intervention points, and they differ in kind. Deduplication reshapes the data and reduces memorisation empirically. DP-SGD changes the optimiser and bounds it provably. Everything else in the diagram happens downstream of both, which is why output filters and refusal training keep failing.

Two Decades of Trying to Bound What a Model Knows

The privacy literature and the language-model literature ran in parallel for a long time and only collided recently. The collision is what makes the current moment interesting.

timeline
    title From Statistical Databases to Extractable Chatbots
    2006 : Dwork and colleagues formalise differential privacy for statistical databases
         : Privacy becomes a property of an algorithm rather than of a released dataset
    2016 : Abadi et al. publish DP-SGD, making deep networks trainable under a privacy budget
         : Per-example clipping plus Gaussian noise plus a moments accountant
    2017 : Shokri et al. formalise membership inference with shadow models
         : The canonical empirical privacy attack on machine learning
    2020 : Carlini et al. extract hundreds of verbatim sequences from GPT-2
         : Extraction moves from theoretical concern to demonstrated attack
    2021 : Carlini et al. reframe attack evaluation around TPR at low FPR with LiRA
         : Li et al. show pretrained models are strong DP learners with the right hyperparameters
    2022 : Carlini et al. quantify memorisation as log-linear in capacity, duplication and context
         : Memorisation becomes a scaling law rather than an anecdote
    2023 : Nasr et al. extract over ten thousand examples from ChatGPT for two hundred dollars
         : Alignment shown to be no barrier to extraction
    2024 : Duan et al. find membership inference near chance on LLMs and identify distribution shift as a confound
    2025 : VaultGemma trains a 1B model from scratch at sequence-level epsilon under two
         : The capability cost of a real guarantee becomes measurable

The 2022 result is the hinge. Before it, memorisation was a collection of striking examples; after it, it was a predictable function of quantities engineers control. That reframing is what makes memorisation a design parameter rather than a surprise.

Why Models Memorise

The objective does not distinguish

Pretraining minimises negative log-likelihood over a corpus. There is nothing in that objective that separates "learn the general structure of English" from "reproduce this specific paragraph." A sequence that appears in the training data is, by construction, a sequence the model is rewarded for assigning high probability. Generalisation and memorisation are the same operation viewed at different frequencies.

What varies is how much probability mass a particular sequence earns, and that is where structure appears. Carlini et al. (2022, Quantifying Memorization Across Neural Language Models, arXiv:2202.07646) established three log-linear relationships:

1. Capacity. Larger models memorise more of the same corpus.
2. Duplication. A sequence appearing \(n\) times is far more likely to be emitted than one appearing once, and the relationship is log-linear in \(n\).
3. Context. The more of the true prefix you supply, the more reliably the true suffix follows.

Read those three together and the conclusion is uncomfortable. Model scaling increases the first. Web-scale corpora, which are heavily internally duplicated, feed the second. Long-context training increases the third. Absent deliberate mitigation, memorisation gets worse along every axis the field is currently pushing on.

[IMAGE: Three small log-log panels sharing a y-axis labelled "fraction of examples memorised". Panel one plots against model parameters, panel two against duplication count in the corpus, panel three against prompt context length. All three show an approximately straight rising line. Caption: "Three log-linear laws. Every x-axis is a quantity the field is actively increasing."]

The authors' own conclusion is unambiguous: memorisation "is more prevalent than previously believed and will likely get worse as models continue to scale, at least without active mitigations."

Discoverable is not extractable

The distinction that organises the whole literature, and the one most often blurred in discussion.

Discoverable memorisation: you hold the training document, prompt the model with its true prefix, and check whether the true suffix follows. Requires training-set access. This is the auditor's measurement, and it upper-bounds what is stored.

Extractable memorisation: an adversary with no knowledge of the training set constructs some prompt that makes the model emit a training example. This is the attacker's measurement, and the one that determines disclosure risk.

Extractable is a subset of discoverable. For years the gap between them was treated as a safety margin: yes, the model contains the data, but nobody can get it without already having it.

The divergence attack collapsed that argument for a class of models. It did not increase what was memorised; it increased what was reachable, by a factor of about 150.

[IMAGE: Two nested set diagrams. The outer set, "training corpus", contains a smaller shaded region "discoverably memorised", which contains a much smaller region "extractable with ordinary prompting". An arrow labelled "divergence attack, 150x" shows the inner region expanding to fill most of the middle one. Caption: "The attack did not change what the model stored. It changed what an outsider could reach."]

The mechanism behind the divergence attack

sequenceDiagram
    participant U as Attacker
    participant P as Alignment policy
    participant B as Base distribution
    participant O as Output

    U->>P: Ordinary question
    P->>B: Sample within assistant region
    B-->>O: Fluent, non-verbatim answer
    Note over U,O: Extraction rate: baseline

    U->>P: "Repeat the word poem forever"
    P->>B: Degenerate repetition, low entropy
    Note over P: Sampling leaves the region alignment shaped
    B-->>O: Base-model continuation, memorised spans included
    Note over U,O: Extraction rate: roughly 150x baseline

RLHF fits a policy over a narrow region of the base model's output distribution. Nothing removes the rest of the distribution; the policy simply avoids it. A prompt that drives the sampler into a degenerate state, unbounded repetition being the simplest, exits that region, and the model resumes doing what it was pretrained to do.

This generalises well past one prompt. Any defence implemented on the conversational surface is defeated by any technique that moves generation off-distribution. Refusal training, system-prompt instructions, style constraints: all of them operate in the region where the policy is defined. Defences on the weights or on the data are categorically different, which is the argument for machine unlearning and, more strongly, for differential privacy.

The Guarantee, and Why It Costs

A randomised training algorithm \(\mathcal{A}\) is \((\varepsilon, \delta)\)-differentially private if for any two datasets \(D\), \(D'\) differing in one record and any output set \(S\):

It is a bound on distinguishability. Because membership inference is exactly the task of distinguishing these two cases, a DP bound caps the success of every membership attack, including attacks nobody has designed yet. That property, and only that property, is what you are paying for.

DP-SGD, step by step

flowchart TB
    A["Poisson-sample batch<br/>each record with prob q"] --> B["Per-example gradients<br/>one per record, not one per batch"]
    B --> C["Clip each to L2 norm C<br/>bounds single-record influence"]
    C --> D["Sum clipped gradients"]
    D --> E["Add Gaussian noise<br/>sigma times C, per coordinate"]
    E --> F["Divide by batch size"]
    F --> G["Optimiser step"]
    G --> H["Privacy accountant<br/>updates cumulative epsilon"]
    H --> A

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    class A blue
    class B,C purple
    class D,E,F amber
    class G,H emerald

Three details in that loop are where implementations go wrong.

Poisson sampling, not shuffling. The privacy accounting relies on amplification by subsampling, which assumes each record is included independently with probability \(q\). A standard fixed-size shuffled dataloader does not satisfy that assumption, and code that shuffles while quoting subsampled accounting reports an \(\varepsilon\) it has not earned. This is common and almost never visible in a results table.

Per-example gradients, not batch gradients. Naively this multiplies activation memory by the batch size. For linear layers, clipping can be performed without ever materialising the per-example gradients (Li et al., 2021, Large Language Models Can Be Strong Differentially Private Learners, arXiv:2110.05679), which is what made DP fine-tuning of transformers practical.

Clipping is not rescaling. It truncates. Examples whose gradients exceed \(C\) have their direction preserved and their magnitude discarded, which biases the update away from atypical data. More on that below, because it is the least-discussed cost of DP.

[IMAGE: Annotated code-style diagram of one DP-SGD step, with the standard SGD step shown greyed out beside it and the three inserted operations highlighted: per-example gradient computation, per-example norm clipping, and Gaussian noise addition. Arrows point from each to a cost annotation: memory, bias against atypical examples, and signal-to-noise. Caption: "Three lines of difference from SGD, and each one buys a distinct part of the guarantee at a distinct cost."]

The dimensional argument for why DP is expensive

Consider one DP-SGD step. Batch size \(B\), clipping norm \(C\), noise multiplier \(\sigma\), and \(d\) trainable parameters. The averaged update is

The signal term has norm at most \(C\), since each clipped gradient has norm at most \(C\) and the average of vectors of norm \(\le C\) has norm \(\le C\). The noise term is a \(d\)-dimensional Gaussian with per-coordinate standard deviation \(\sigma C / B\), so its expected norm is approximately

Set the two equal and solve for the batch size at which signal and noise are comparable:

That is the whole story of DP's cost, in one expression. Noise grows with the square root of the parameter count; signal does not grow at all. The only lever is batch size.

Plug in numbers. For a fine-tune with \(d = 10^{8}\) trainable parameters and \(\sigma = 1.1\):

And that is the optimistic case, assuming perfectly aligned per-example gradients so the signal actually reaches norm \(C\). In practice gradients partially cancel and the signal is smaller, so the required batch is larger still.

This is why the conventional wisdom held that DP could not train high-dimensional models: the noise scales with dimension and the model is enormous. The empirical surprise in Li et al. was that DP fine-tuning of pretrained models does not suffer the dimension-dependent degradation the argument predicts. The most likely explanation connects to the intrinsic dimension hypothesis: the useful fine-tuning update lives in a subspace of far lower dimension than \(d\), so the effective \(\sqrt{d}\) in the analysis overstates the noise the update direction actually has to fight.

That is a hypothesis with supporting evidence, not a proof, and it is one of the more interesting open threads in the area.

By the Numbers

Sources: Carlini et al., 2020 (arXiv:2012.07805); Carlini et al., 2021 (arXiv:2112.03570); Carlini et al., 2022 (arXiv:2202.07646); Nasr et al., 2023 (arXiv:2311.17035); Duan et al., 2024 (arXiv:2402.07841); Google Research, 2025, VaultGemma. The LiRA figure is from the classifier setting and does not transfer directly to language models; the "five years of capability" framing is Google's own characterisation, not an independent benchmark.

A Concrete Example

Take a realistic decision. You have 50,000 customer support transcripts and want a fine-tuned assistant. Some transcripts contain names, account numbers and addresses. What does each option actually cost?

Option A: ordinary fine-tuning, three epochs.

Duplication is the dominant memorisation axis, and three epochs multiplies every record's effective duplication count by three. Worse, support transcripts are formulaic: the same product names, the same boilerplate, the same phrasings recur across thousands of records, so distinctive strings (a specific account number in a specific context) sit in an otherwise highly predictable surround, which is exactly the condition under which a model completes a prefix confidently.

The membership-inference literature says the risk here is real, not theoretical. Duan et al.'s negative result applies to pretraining conditions: one epoch, hundreds of billions of tokens, negligible per-example influence. Every one of those conditions is inverted in this fine-tune. Small dataset, multiple epochs, high per-example influence.

Option B: DP-SGD, LoRA adapter, epsilon budget.

Take a LoRA configuration with \(d = 20\) million trainable parameters, \(\sigma = 1.0\), \(C = 1.0\).

So batches of roughly 4,500 examples before the update direction is signal-dominated in the optimistic case. Against 50,000 examples, that is about 11 optimiser steps per epoch. Gradient accumulation gets you there without the memory, but the number of useful optimiser steps is now small, and DP fine-tuning is correspondingly slower to converge in steps even when each step is cheap.

Notice what the arithmetic tells you: DP pushed you toward PEFT for a reason unrelated to memory. Reducing \(d\) from 7 billion to 20 million reduces \(B^{*}\) by a factor of roughly \(\sqrt{350} \approx 19\). Parameter-efficient fine-tuning is a privacy technique as much as an efficiency one.

[IMAGE: Bar chart of required batch size B* on a log y-axis against trainable parameter count d on a log x-axis, with points marked for a 20M-parameter LoRA adapter, a 100M-parameter partial fine-tune, and a 7B full fine-tune, at sigma = 1.0. A dashed reference line marks a typical non-private batch size of 512. Caption: "The square-root law is why parameter-efficient fine-tuning is a privacy decision as well as a memory one."]

Option C: do not train on it at all.

Put the transcripts in a retrieval index and keep them out of the weights. The privacy properties change completely: the data is now in a system with access control, deletion semantics, and audit logs, none of which model weights have. Deleting a record from an index is a DELETE; removing its influence from weights is an open research problem.

The cost is that retrieval is a different capability, not the same one delivered differently, and the index is now an attack surface of its own.

Working the numbers on Option A's exposure. Suppose 200 of the 50,000 transcripts contain a distinctive customer identifier, and each is seen three times. The memorisation literature does not give you a probability for a specific string, but it does give you the shape: risk rises log-linearly in duplication, so three epochs is materially worse than one, and rises with model capacity, so a 70B fine-tune is worse than a 7B one at equal data. Both of those are decisions you control and both are usually made for unrelated reasons.

The auditable version of this is a canary: insert a small number of synthetic records containing high-entropy strings that appear nowhere else, at known duplication counts, then after training measure whether the model completes their prefixes. This gives you a direct, quantitative, per-run measurement of discoverable memorisation at each duplication level, on your data and your architecture. It costs almost nothing and remarkably few teams do it.

[IMAGE: Line chart with duplication count on a log x-axis from 1 to 1,000 and canary extraction rate on the y-axis, showing three curves for a 1B, 7B and 70B fine-tune. All three rise roughly linearly on the log axis, with the larger models shifted upward. Caption: "A canary experiment turns memorisation from a worry into a number you can put in a risk register."]

Where It Breaks

Verbatim matching under-counts, badly

Nearly all extraction measurement uses exact substring matching against a reference corpus. A model that reproduces a paragraph with one word changed scores as clean. For privacy and copyright alike, approximate reproduction is squarely within the harm, and it is essentially unmeasured because it is much harder to measure. Every extraction number in this article is therefore a lower bound of unknown tightness.

"No detectable memorisation" is a statement about a test

VaultGemma's result is real and was obtained by a specific procedure: prompt with 50-token prefixes from training documents and check for suffix completion. Change the prefix length, the suffix length, the sampling temperature, the number of samples per prefix, or the corpus searched, and you have a different test. This is not a criticism of that work, which is unusually transparent. It is a caution about the sentence when it appears in a model card with no procedure attached.

The negative result on membership inference is routinely over-read

Duan et al. showed attacks near chance across Pythia 160M to 12B on the Pile, and identified the three reasons: near-single-epoch training, enormous corpora, and blurred member/non-member boundaries caused by web-text redundancy. All three are properties of pretraining.

The regimes practitioners control invert all three. Fine-tuning on a private corpus, PEFT adapters shared more freely than checkpoints would be, small RLHF preference sets optimised against repeatedly, and retrieval indexes that store documents outright rather than inferring them. Citing the pretraining negative result as evidence that a fine-tune is private is a category error.

The paper's finding about distribution shift is the more transferable lesson: much of the earlier apparent success came from evaluations where non-members were drawn from a later time period, so the attack detected temporal novelty. Any membership evaluation whose members and non-members differ in topic, date or style is measuring that difference.

Epsilon is not a comparable number

Two claims, \(\varepsilon = 2\) and \(\varepsilon = 8\), tell you nothing until you know the unit of privacy and the accounting method. Sequence-level DP over 1,024-token windows protects a window. If one person contributed twenty documents, roughly twenty times the budget is spent against them, and their personal guarantee is far weaker than the headline. User-level DP is stronger and requires a data-to-person mapping that web corpora do not have. VaultGemma is explicit that its unit is the sequence, precisely because that mapping was unavailable.

Clipping has a distributional cost that no epsilon captures

Clipping preserves direction and discards magnitude above \(C\). Atypical examples produce large gradients. Rare dialects, minority languages, unusual domains and long-tail facts are systematically the examples whose contribution gets truncated hardest.

So the privacy guarantee is uniform across records while the utility damage is concentrated on the least-represented ones. A DP model can hold aggregate benchmark performance and get measurably worse for exactly the populations that most need representation. This is a property of the mechanism, not of the data collection, and it deserves more attention than it gets.

Unlearning is not a substitute

The appeal of machine unlearning is obvious: train normally, remove influence on request. The difficulty is that verifying removal is close to as hard as the original privacy problem. A model that no longer completes a canary's prefix may have had the influence removed or may have learned to suppress a behaviour while retaining the knowledge, and the sleeper-agent literature shows those are genuinely different states that look identical from outside.

Alternative Designs

The last row is the cheapest item on the list and the most consistently skipped. It does not reduce risk; it makes risk observable, which is a precondition for the rest of the table being anything other than guesswork.

[IMAGE: Two-axis positioning chart with "strength of guarantee" on the y-axis (from empirical to formal) and "capability cost" on the x-axis. Deduplication and output filtering sit low-left, canary auditing sits at zero on both with a note "measurement, not mitigation", DP fine-tuning sits mid-right, DP pretraining sits top-right, unlearning sits low-middle with a wide uncertainty bar. Caption: "The only quadrant with a proof attached is also the expensive one."]

How It Is Used in Practice

Frontier pretraining treats deduplication as standard and DP as out of reach at scale. That is a defensible engineering position given the current capability gap, but it should be stated as a trade rather than assumed. The practical mitigations in use are corpus-level: aggressive dedup, PII detection and removal, licensing and provenance filtering, and post-hoc memorisation testing before release.

Enterprise fine-tuning is where the risk is highest and the attention is lowest. Small datasets, multiple epochs, real personal data, and adapters shared across teams. The three highest-value interventions are unglamorous: deduplicate the fine-tuning set (which teams routinely skip because it is small), run one epoch rather than three unless there is measured benefit, and add canaries so you have a number rather than an opinion.

Regulated deployments are where DP starts to be worth its cost, because the guarantee is a compliance artefact and not just a technical property. VaultGemma's significance is less its benchmark score than its existence as a reference point: a real model, real epsilon, real published unit of privacy, real memorisation test. It gives a procurement conversation something to point at.

Retrieval-first architectures deserve more credit than they get as a privacy design. Moving sensitive data out of the weights and into an access-controlled index converts an unsolved research problem (removing influence from weights) into a solved engineering one (deleting a row). The trade is real, since the index becomes an attack surface and retrieval is a different capability, but for data with deletion or residency requirements it is frequently the correct answer.

[IMAGE: Decision-tree figure starting from "Does the data need to be in the weights?" branching to a retrieval-index path (access control, deletion, audit) and a training path, which branches again on "Is a formal guarantee required?" into DP-SGD with PEFT versus deduplicate-plus-single-epoch-plus-canaries. Each leaf annotated with its residual risk in one line. Caption: "Most of the value is in the first branch, which is the one least often asked."]

Insights Worth Remembering

1. Memorisation is a scaling law, not an anecdote. Log-linear in capacity, duplication and context length. That reframing, from surprising examples to a predictable function, is what makes it a design parameter you can budget for.

2. Alignment relocates behaviour; it does not remove knowledge. RLHF fits a policy on a narrow region of the base distribution. Any technique that leaves that region restores access to what the base model learned, which is why surface-level defences keep falling to prompts nobody anticipated.

3. Extraction is priced, and the price is low. Roughly two cents per recovered training example against a production aligned model. Once an attack is that cheap, the relevant question is who cares enough to run it, not whether it is feasible.

4. DP's cost is dimensional, and PEFT is therefore a privacy technique. With noise norm scaling as \(\sigma C \sqrt{d}/B\) against a signal bounded by \(C\), cutting trainable parameters by a factor of 350 cuts the required batch size by roughly 19. Nobody chooses LoRA for this reason and everybody benefits from it.

5. Epsilon without a unit of privacy is a number, not a claim. Sequence-level, record-level and user-level guarantees differ by more than the epsilon value typically does. Compare units before comparing epsilons.

6. The privacy guarantee is uniform; the utility damage is not. Gradient clipping truncates atypical examples hardest, so DP training degrades long-tail performance more than aggregate benchmarks reveal. This is a fairness consequence of the mechanism itself.

7. A negative attack result has a shelf life; a bound does not. "No current attack succeeds" covers the attacks tried, with the compute available, on the models tested. Differential privacy bounds attacks that do not yet exist. That difference in kind is the entire argument for paying its cost.

8. The cheapest thing you are not doing is canaries. Inserting known high-entropy strings at known duplication counts turns memorisation from an argument into a per-run measurement. It costs almost nothing and it is what makes every other decision on this list evidence-based.

Open Questions

Why does DP fine-tuning escape dimension-dependent degradation? Measured: Li et al. found DP fine-tuning of pretrained models does not degrade with dimension the way the noise analysis predicts. Likely but unproven: the useful update occupies a low-dimensional subspace, so the effective dimensionality fighting the noise is far below the parameter count. A rigorous account would sharpen DP-SGD's analysis considerably.

Can approximate memorisation be measured at scale? Every number in the literature relies on exact matching, so paraphrased reproduction is invisible. Measuring semantic reproduction requires a similarity judgement over a corpus of billions of documents, and no scalable method exists. Until one does, all extraction results are lower bounds of unknown tightness.

Does the memorisation scaling law bend? The log-linear relationships were established over the model sizes available in 2022. Whether they continue, saturate, or change slope at frontier scale is unmeasured, and the answer determines whether memorisation is a manageable cost or a growing one.

Is verified unlearning possible at all? Known: current methods reduce measurable extraction of the target. Unknown: whether that reflects removal or suppression. Given that adversarial training has been shown elsewhere to conceal behaviours rather than remove them, the burden of proof should sit with the claim of removal.

What is the right privacy unit for a web corpus? User-level DP is the meaningful guarantee for a person and requires a data-to-person mapping scraped corpora do not have. Sequence-level DP is achievable and protects something narrower than people usually assume it does. Bridging that gap, either technically or by changing how corpora are assembled, is arguably the most consequential open problem here.

Sources and Further Reading

1. Carlini, N., Tramèr, F., Wallace, E., Jagielski, M., Herbert-Voss, A., Lee, K., Roberts, A., Brown, T., Song, D., Erlingsson, Ú., Oprea, A., & Raffel, C. (2020). "Extracting Training Data from Large Language Models." USENIX Security 2021. arXiv:2012.07805

2. Carlini, N., Ippolito, D., Jagielski, M., Lee, K., Tramèr, F., & Zhang, C. (2022). "Quantifying Memorization Across Neural Language Models." ICLR 2023. arXiv:2202.07646

3. Nasr, M., Carlini, N., Hayase, J., Jagielski, M., Cooper, A. F., Ippolito, D., Choquette-Choo, C. A., Wallace, E., Tramèr, F., & Lee, K. (2023). "Scalable Extraction of Training Data from (Production) Language Models." arXiv:2311.17035

4. Abadi, M., Chu, A., Goodfellow, I., McMahan, H. B., Mironov, I., Talwar, K., & Zhang, L. (2016). "Deep Learning with Differential Privacy." ACM CCS 2016, 308-318. arXiv:1607.00133

5. Li, X., Tramèr, F., Liang, P., & Hashimoto, T. (2021). "Large Language Models Can Be Strong Differentially Private Learners." ICLR 2022. arXiv:2110.05679

6. Shokri, R., Stronati, M., Song, C., & Shmatikov, V. (2017). "Membership Inference Attacks Against Machine Learning Models." IEEE S&P 2017. arXiv:1610.05820

7. Carlini, N., Chien, S., Nasr, M., Song, S., Terzis, A., & Tramèr, F. (2021). "Membership Inference Attacks From First Principles." IEEE S&P 2022. arXiv:2112.03570

8. Duan, M., Suri, A., Mireshghallah, N., Min, S., Shi, W., Zettlemoyer, L., Tsvetkov, Y., Choi, Y., Evans, D., & Hajishirzi, H. (2024). "Do Membership Inference Attacks Work on Large Language Models?" arXiv:2402.07841

9. Google Research (2025). "VaultGemma: The world's most capable differentially private LLM." Research blog

10. Dwork, C., McSherry, F., Nissim, K., & Smith, A. (2006). "Calibrating Noise to Sensitivity in Private Data Analysis." Theory of Cryptography (TCC 2006), LNCS 3876, 265-284. DOI:10.1007/11681878_14

11. Hubinger, E., Denison, C., Mu, J., et al. (2024). "Sleeper Agents: Training Deceptive LLMs that Persist Through Safety Training." arXiv:2401.05566 (context for why suppression and removal are hard to tell apart)

12. Related concepts on this site: training data memorisation and extraction, membership inference on language models, differential privacy for language models, deduplication and memorisation, machine unlearning for LLMs, PII detection and removal.

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