Differential Privacy for LLMs

Learning Objectives

• Define (epsilon, delta)-differential privacy and state the DP-SGD recipe.
• Explain the 2024-2025 tension: canary MIA vs training-data extraction give different pictures.
• Describe PMixED and why inference-time private prediction is an alternative to DP training.
• Describe the Differential Privacy Reversal via LLM Feedback attack.

The Problem

LLMs memorize. Carlini et al. 2021 showed production language models reproduce verbatim training text on demand. DP is the formal defense: train so that the output is provably insensitive to any single training example. The 2024-2025 evidence shows DP-SGD is necessary but the deployed ε values may not match the threat model.

The Concept

(ε, δ)-differential privacy

A randomized algorithm $M$ is $(\varepsilon, \delta)$-DP if for any two datasets differing in one example and any event $S$:

P(M(D) \in S) \le e^{\varepsilon} \cdot P(M(D') \in S) + \delta.

Interpretation: the output distribution is close enough (parametrized by ε) that the contribution of any single individual cannot be reliably inferred, except with probability δ.

DP-SGD

Abadi et al. 2016. The standard recipe:

1. Sample a mini-batch.
2. Compute per-example gradients.
3. Clip each per-example gradient to a threshold C.
4. Sum the clipped gradients and add Gaussian noise with std $\sigma \cdot C$.
5. Use the noisy sum to update parameters.

Privacy cost is tracked by an accountant (Moments Accountant, Rényi DP accountant). Reported ε values in the LLM literature vary widely by threat model, data sensitivity, and utility target; there is no universally "safe" default ε. Published examples span roughly ε ≈ 1–10 in some LLM training settings, but these are illustrative — not recommended defaults. Lower ε generally requires more noise and can increase utility loss.

LoRA + DP-SGD

Full DP-SGD of a frontier model is prohibitive. LoRA (Hu et al. 2022) limits gradient updates to a small adapter, reducing per-example gradient storage. LoRA + DP-SGD is the common 2025 configuration. DP guarantees apply to the adapter; the base model is held fixed.

The 2024-2025 tension

Two lines of evidence:

• Canary MIA (Duan et al. 2024). Insert unique canaries into training data, measure whether a membership-inference attacker can identify them. Reports limited success on language models. Suggests MIA is hard.
• Training-data extraction (Carlini 2021, Nasr et al. 2025). Prompt the model with a prefix; measure whether it recovers verbatim text from training. Reports substantial memorization. Suggests MIA is easy in the relevant sense.

March 2025 resolution (arXiv:2503.06808): the two measure different things. MIA asks "is example e in D?" on inserted canaries. Extraction asks "what can I recover of D?" The "most extractable" example is what matters for privacy; canaries under-report this because they are not optimized to be extractable.

New canary designs. Loss-based MIA without shadow models. First nontrivial DP audit of an LLM on real data with realistic DP guarantees.

Alternatives to DP training

• PMixED (arXiv:2403.15638). Private prediction at inference time. Mixture of experts on next-token distributions; each expert sees a shard of training data; aggregation adds noise for DP. Avoids DP training entirely.
• DP synthetic data generation (Google Research 2024). LoRA-fine-tune with DP-SGD, sample synthetic data, train a downstream classifier on the synthetic data.

Both sidestep the utility cost of full DP training at the cost of a different threat model.

Differential Privacy Reversal via LLM Feedback

Emerging 2025 attack. Use a DP-trained model's confidence scores as an oracle to re-identify individuals. Even when outputs do not leak, confidence distributions can.

The defense: do not expose confidences, or truncate/quantize them before exposure. This is an additional requirement beyond (ε, δ)-DP training.

Where this fits in Phase 18

Lessons 20-21 are bias/fairness. Lesson 22 is privacy. Lesson 23 is provenance via watermarking. Lesson 27 covers the regulatory data-provenance layer.

an-dp-clip-noise

Use It

code/main.py simulates DP-SGD on a toy binary-classification dataset. You can sweep the noise multiplier σ and the clipping norm C and track the (ε, δ) budget and the accuracy cost. A "canary attack" inserts a unique training example and measures whether a log-loss test can detect it before and after DP.

Ship It

This lesson produces outputs/skill-dp-audit.md. Given a DP claim on a language model deployment, it audits: the (ε, δ) values, the accountant used, the MIA evaluation protocol, and whether confidence-exposure vectors have been assessed.

Exercises

1. Run code/main.py. Sweep $\sigma \in \lbrace 0.5, 1.0, 2.0 \rbrace$ and report the (ε, δ)-accuracy trade-off. Identify the point at which utility collapses.

2. Implement a canary insertion and a log-loss test. Measure detection rate before and after DP-SGD at $\sigma = 1.0$.

3. Read Nasr et al. 2025 on training-data extraction. Why does extraction success not collapse under moderate ε? What does this imply about MIA-as-evaluation?

4. Design a deployment using PMixED (arXiv:2403.15638) that operates entirely at inference time. What is the threat model that PMixED addresses that DP-SGD does not?

5. Sketch the DP Reversal via LLM Feedback attack. Design a countermeasure that limits confidence-score leakage and estimate its deployment cost.

Key Terms

Further Reading

• Abadi et al. — DP-SGD (arXiv:1607.00133) — the standard DP training algorithm
• Carlini et al. — Extracting Training Data (arXiv:2012.07805) — the canonical extraction paper
• Duan et al. — Canary MIA on LLMs (arXiv:2402.07841, 2024) — limited-success MIA
• Kowalczyk et al. — Auditing DP for LLMs (arXiv:2503.06808, March 2025) — resolution of the tension
• PMixED (arXiv:2403.15638) — inference-time private prediction