Training Data Reconstruction Attacks

Releasing a neural network checkpoint can leak information about its training data, and existing reconstruction results rely on gradient-descent training. We ask whether the choice of optimizer affects the ability to recover the training data. Extending work connecting Karush--Kuhn--Tucker conditions to training-data reconstruction, we show that the implicit biases of popular optimizers (SGD, Adam, Muon) leave very different fingerprints of the training data. We argue that the key distinction is the weight-specificity of these implicit biases, namely how much continuous information about the final weights the optimizer-dependent target of the stationarity conditions encodes. The limiting stationarity conditions for models trained with SGD and Muon retain enough weight-specific information to reconstruct training examples in practice. For Adam in the $\ell_\infty$ implicit-bias regime, the optimizer-dependent part of these conditions encodes only a discrete pattern of maximal coordinates and their signs, and at nondegenerate KKT points the conditions are too few to identify the training set to first order. Experiments on MNIST and CIFAR-10 support these claims: models trained with Muon can yield stronger reconstructions at much lower training cost than models trained with SGD, although this advantage depends on the training regime and architecture, and models trained with Adam appear consistently more resistant to the evaluated attacks.

What can an adversary recover from a model trained with DP-SGD? Its $(\varepsilon,δ)$ guarantee does not answer this question directly. We derive a distortion bound that can be computed before training and applies even to an adversary who observes the parameter trajectory during training, knows every other training record and the population distribution from which the training records are drawn. The analyst may choose the representation in which error is measured, allowing the bound to target the aspects of reconstruction that are privacy-sensitive in a given application. Our information-theoretic framework separates two contributions: the information about a record revealed by training, measured through conditional mutual information, and the uncertainty already present in the data distribution, measured through source entropy. Rate-distortion theory combines them into a lower bound on the expected error of every reconstruction attack. For DP-SGD, the leakage bound depends only on the sampling rates and noise multipliers, while the source entropy is lower-bounded from a sample with finite-sample confidence. An orthogonal block construction keeps the resulting bound informative for high-dimensional images. We instantiate the framework in pixel space and in LPIPS feature space, obtaining, to our knowledge, the first lower bound on reconstruction distortion measured directly by LPIPS. On a range of image datasets the bounds establish non-trivial unavoidable expected reconstruction error within heuristically recommended privacy-budget ranges and beyond. Experiments compare the bounds with strong reconstruction attacks and identify the principal sources of the remaining slack.

In this paper, we show that standard evaluations of high-resolution Model Inversion Attacks (MIAs) significantly underestimate training-data privacy leakage. State-of-the-art privacy defenses, standard training techniques such as MixUp and Adversarial Training, and undefended models all leak training images at rates 1.16 to 6.59 times higher on FaceScrub under simple adaptive changes to the attack, with the largest increases among defenses reporting the strongest privacy. We further show that measured leakage depends on the feature basis of the external classifier used to evaluate reconstructions: for the same reconstructed images, an adversarially trained Inception evaluator identifies the targeted identity at different rates than the standard Inception evaluator. Our results suggest that standard MIA evaluation can mistake optimization and measurement failures for privacy. These underestimated leakage rates also concealed a broader relationship between privacy and adversarial robustness. Once we adapt the attack and vary the evaluator, reconstruction leakage closely tracks adversarial robustness across recent defenses and standard training regimes, suggesting that robustness provides an attack-agnostic proxy for reconstruction vulnerability that applies far more broadly than previously theorized. This raises an open question: can a practical defense reduce training-data reconstruction without paying a corresponding cost in adversarial robustness?

Data reconstruction attacks have empirically been successful in recovering training samples from learned models, raising privacy concerns and motivating defenses with guarantees that remain valid against future threats. While differential privacy (DP) provides formal protection, choosing the privacy budget remains a challenge: small budgets severely reduce utility, but it is hard to quantify how large the budget can be without allowing accurate reconstruction. In this work, we study informed attackers who aim to reconstruct a single $d$-dimensional training sample from a $ρ$-zero-concentrated DP model, knowing all other training data. Our main contribution is to establish a sharp transition at $ρ\asymp d$ for data reconstruction: on the one hand, we derive entropy-based lower bounds for any private mechanism and any attack, characterizing a set of target priors for which reconstruction is information-theoretically impossible for $ρ\ll d$; on the other hand, we analyze a simple attack on private linear regression with output perturbation, showing that reconstruction is practically feasible for $ρ\gg d$. Remarkably, the transition moves to $ρ\asymp s$ for data lying in an $s$-dimensional subspace, demonstrating that the privacy budget guaranteeing adequate protection must be assessed in terms of the effective dimension of the data. We validate our findings via experiments on synthetic data and natural images (CIFAR-10, ImageNet).

Federated learning shares model updates rather than raw data, yet these updates can be inverted to reconstruct the clients' training data. Analytic reconstruction attacks, which invert a gradient in closed form, degrade as the batch grows: prior single-round attacks recover only about half of a batch of size $100$ even when the attacker fully controls the network parameters, and known upper bounds limit what any such method can recover. We establish a connection between gradient inversion and the theory of erasure-correcting codes, and use it to construct attacks that exceed these bounds. Our attacks recover batches exactly, together with every sample's label, from a single FedSGD round, and certify each recovery without ground-truth data. On eight image and tabular benchmarks they outperform prior single-round attacks by a wide margin. Even a passive attacker who only observes an honestly trained network recovers $94$--$100\%$ of ImageNet batches at sizes up to $128$, more than prior single-round attacks achieve even with active manipulation of the model, and in the active setting more than $90\%$ is recovered at batch sizes of several hundred. These results show that the privacy leakage of federated learning has been underestimated.

Federated unlearning aims to remove a client's data from a shared model without retraining from scratch. Some efficient systems make deletion exact by storing compact, additive summaries of the training features and broadcasting an updated linear classifier after every accepted change. We show that these broadcasts can also reveal the hidden summaries. A malicious client can submit known changes, use the returned classifiers to identify the server state, and compare states immediately before and after an isolated deletion. This exposes the deleted sample, class, or client summary and can enable its reinsertion. We characterize exactly when the observations contain enough independent information, give a matching optimal construction for unrestricted probes, and derive a more realistic estimator based on additions formed from the attacker's own data. On MNIST and CIFAR-10, high-precision broadcasts permit exact label recovery for every tested sample deletion with both probe types. Lower-precision broadcasts sharply reduce fine-grained recovery, and insufficiently diverse responses prevent identification altogether. Unrestricted probes are readily detected by their size; most individual attacker-data additions resemble honest batches, although we do not claim that the complete sequence is inconspicuous. The results identify a concrete privacy and integrity risk, its algebraic cause, and practical limits involving broadcast precision, update verification, response rate, and concurrent activity.

Geometric data perturbation enables one-shot representation sharing for privacy-preserving collaborative learning: each participant applies a secret distance-preserving transformation to its private data and uploads the resulting representation to a central analyst. We study analyst-participant collusion, in which a colluding participant discloses its data and transformation to help the analyst reconstruct another participant's data. Independent participant-specific transformations block direct inversion through a disclosed common transformation but leave uploads in incompatible coordinate systems, degrading pooled learning. Data Collaboration analysis restores compatibility by aligning transformed copies of a common anchor matrix withheld from the analyst. We show that, when the centered anchor matrix has full column rank, a colluder who discloses it enables exact recovery of every participant's transformation and inversion of noiseless private representations. Adding noise to private-data representations leaves this transformation-recovery channel intact and reduces leakage at a substantial utility cost. Instead, we perturb the anchor representations: each participant perturbs only its transformed anchor representation, preserving the geometry of its private-data upload while turning known-anchor transformation recovery into a noisy estimation problem. The analyst estimates the alignment using a spectral estimator for a generalized orthogonal Procrustes problem. We analyze recovery attacks against this protocol and compare both noise placements on the CelebA and VGGFace2 facial image datasets. Under the evaluated collusion attacks, noisy-anchor alignment retains higher downstream accuracy at low identity-linkage levels. Participant-count experiments examine the utility gains and limitations of larger collaborations at comparable measured linkage.

In this paper, we challenge the prevailing view that information dependency (including rote memorization) drives training data exposure to image reconstruction attacks. We show that extensive exposure can persist without rote memorization and is instead caused by a tunable connection to adversarial robustness. We begin by presenting three surprising results: (1) recent defenses that inhibit reconstruction by Model Inversion Attacks (MIAs), which evaluate leakage under an idealized attacker, do not reduce standard measures of information dependency (HSIC); (2) models that maximally memorize their training datasets remain robust to MIA reconstruction; and (3) models trained without seeing 97% of the training pixels, where recent information-theoretic bounds give arbitrarily strong privacy guarantees under standard assumptions, can still be devastatingly reconstructed by MIA. To explain these findings, we provide causal evidence that privacy under MIA arises from what the adversarial examples literature calls ``non-robust'' features (generalizable but imperceptible and unstable features). We further show that recent MIA defenses obtain their privacy improvements by unintentionally shifting models toward such features. To establish this causal relationship, we introduce Anti Adversarial Training (AT-AT), a training regime that intentionally learns non-robust features to obtain both superior reconstruction defense and higher accuracy than state-of-the-art defenses. Our results revise the prevailing understanding of training data exposure and reveal a new privacy-robustness tradeoff.

Federated learning allows multiple clients to jointly train a shared model by sending gradient updates to a central server while keeping raw inputs local. However, prior gradient inversion attacks show that these updates can reveal enough information to reconstruct client inputs. Existing attacks on transformers either optimize dummy inputs to match the true client updates, which is costly and unstable for modern models, or exploit the low rank of attention gradients to identify a subspace containing the true layer embeddings, followed by a discrete membership test for candidate tokens. However, this token test is brittle under numerical noise, i.e., from quantization or Differential Privacy (DP), and scales poorly for encoder models with non-causal attention. We introduce TIGER, a continuous gradient inversion attack that turns this subspace signal into a differentiable objective. Instead of searching over tokens or matching full gradients, TIGER directly optimizes token embeddings to minimize their distance to the subspace. Our experiments demonstrate that on encoder-only models, TIGER substantially improves both reconstruction quality and runtime over existing attacks, while on decoder models, TIGER is more robust than prior subspace-based attacks, enabling the first successful reconstructions in DP-defended federated learning settings.

Split learning provides a practical paradigm for resource-constrained users to train Large Language Models (LLMs) by offloading computation-intensive layers to a server while keeping raw data local. However, existing privacy-preserving split learning methods still face a difficult trade-off among utility, privacy, efficiency, and stability. Specifically, these methods often suffer from substantial utility degradation, remain vulnerable to advanced data reconstruction attacks, incur prohibitive computational and communication overhead, or exhibit unstable performance across different tasks. In this paper, we propose MIXGUARD, a novel mixup-based privacy-preserving split learning framework for LLMs. MIXGUARD introduces token-level obfuscation, representation-level obfuscation, and adaptive gradient perturbation mechanisms, which operate jointly to preserve useful learning signals while preventing privacy leakage to the server. Technically, MIXGUARD first constructs a lightweight calibration model on a public dataset to refine the approximated target representation, and then applies this model during privacy-preserving fine-tuning on private data. We conduct extensive experiments on four classification tasks and four text generation tasks across multiple LLM families, model sizes, architectures, and fine-tuning strategies. The results show that MIXGUARD preserves model utility comparable to non-split training baselines, consistently achieves stronger privacy protection than existing split learning defense methods against state-of-the-art data reconstruction attacks, and remains robust under adaptive attack settings.

We here study whether training biases can make hidden neurons specialize in minimal one-hidden-layer MLPs, and whether such specialization improves prototype-based reconstruction of the training dataset from the learned weights. We consider Gaussianactivation MLPs of width equal to dataset size and compare three structural losses that respectively encourage coverage of the training samples, separation between neuron-induced prototypes, and low overlap of hidden responses, against the standard fitting baseline. Experiments on uniformly sampled one-dimensional datasets show a stable pattern from N = 3 to N = 100 across 480 controlled runs. Coverage regularization gives the lowest mean reconstruction error at every tested size and raises the prototype-usage specialization ratio relative to the standard baseline, while separation has mixed effects and overlap penalties are systematically harmful. We show that the harm is not an optimization failure: overlap-active approaches fit the data as well as overlap-free ones but route the optimizer to a degenerate equilibrium in which prototype centers are pushed outside the convex hull of the training inputs. Coverage cannot reward this expulsion and acts as an attractor: separation admits it only at large temperature and overlap admits it at the nominal hyperparameter choice. A direct τ-sweep on the separation-only mask and a prototype-position visualization at N = 100 confirm the mechanism. The findings yield a simple design principle for prototype-recoverability-aware training: every repulsive structural loss must be compensated by a compatible attractor, or it will collapse the latent geometry it was meant to refine.

Data reconstruction attacks on trained neural networks aim to recover the data on which the network has been trained and pose a significant threat to privacy, especially if the training dataset contains sensitive information. Here, we propose a unified optimization formulation of the data reconstruction problem based on initial and trained parameter values, incorporating state-of-the-art proposals. We show that in the random feature model, this formulation provably leads to training data reconstruction with high probability, provided the network width is sufficiently large; this unprecedented finite-width result uses PAC-style bounds. Furthermore, when the data lies in a low-dimensional subspace, we show that the network width requirement for successful reconstruction can be relaxed, with bounds depending on the subspace dimension rather than the ambient dimension. For general neural network models and unknown data orientations, we propose an efficient reconstruction algorithm that approximates the low-dimensional data subspace through the change in the first-layer weights during training and uses only the last-layer weights for reconstruction, thus reducing the search space dimension and the required network width for high-quality reconstructions. Our numerical experiments on synthetic datasets and CIFAR-10 confirm that our subspace-aware reconstruction approach outperforms standard full-space techniques.

Dataset distillation compresses a large real dataset into a small synthetic one, enabling models trained on the synthetic data to achieve performance comparable to those trained on the real data. Although synthetic datasets are assumed to be privacy-preserving, we show that existing distillation methods can cause severe privacy leakage because synthetic datasets implicitly encode the weight trajectories of the distilled model, they become over-informative and exploitable by adversaries. To expose this risk, we introduce the Information Revelation Attack (IRA) against state-of-the-art distillation techniques. Experiments show that IRA accurately predicts both the distillation algorithm and model architecture, and can successfully infer membership and recover sensitive samples from the real dataset.

Detecting LLM training data is generally framed as a membership inference attack (MIA) problem. However, conventional MIAs operate passively on fixed model weights, using log-likelihoods or text generations. In this work, we introduce Active Data Reconstruction Attack (ADRA), a family of MIA that actively induces a model to reconstruct a given text through training. We hypothesize that training data are more reconstructible than non-members, and the difference in their reconstructibility can be exploited for membership inference. Motivated by findings that reinforcement learning (RL) sharpens behaviors already encoded in weights, we leverage on-policy RL to actively elicit data reconstruction by finetuning a policy initialized from the target model. To effectively use RL for MIA, we design reconstruction metrics and contrastive rewards. The resulting algorithms, ADRA and its adaptive variant ADRA+, improve both reconstruction and detection given a pool of candidate data. Experiments show that our methods consistently outperform existing MIAs in detecting pre-training, post-training, and distillation data, with an average improvement of 10.7% over the previous runner-up. In particular, \MethodPlus~improves over Min-K%++ by 18.8% on BookMIA for pre-training detection and by 7.6% on AIME for post-training detection.

Big data scenarios, where massive, heterogeneous datasets are distributed across clients, demand scalable, privacy-preserving learning methods. Federated learning (FL) enables decentralized training of machine learning (ML) models across clients without data centralization. Decentralized training, however, introduces a computational burden on client devices. U-shaped federated split learning (UFSL) offloads a fraction of the client computation to the server while keeping both data and labels on the clients' side. However, the intermediate representations (i.e., smashed data) shared by clients with the server are prone to exposing clients' private data. To reduce exposure of client data through intermediate data representations, this work proposes k-anonymous differentially private UFSL (KD-UFSL), which leverages privacy-enhancing techniques such as microaggregation and differential privacy to minimize data leakage from the smashed data transferred to the server. We first demonstrate that an adversary can access private client data from intermediate representations via a data-reconstruction attack, and then present a privacy-enhancing solution, KD-UFSL, to mitigate this risk. Our experiments indicate that, alongside increasing the mean squared error between the actual and reconstructed images by up to 50% in some cases, KD-UFSL also decreases the structural similarity between them by up to 40% on four benchmarking datasets. More importantly, KD-UFSL improves privacy while preserving the utility of the global model. This highlights its suitability for large-scale big data applications where privacy and utility must be balanced.

Machine unlearning aims to remove specific data points from a trained model, often striving to emulate "perfect retraining", i.e., producing the model that would have been obtained had the deleted data never been included. We demonstrate that this approach, and security definitions that enable it, carry significant privacy risks for the remaining (undeleted) data points. We present a reconstruction attack showing that for certain tasks, which can be computed securely without deletions, a mechanism adhering to perfect retraining allows an adversary controlling merely $ω(1)$ data points to reconstruct almost the entire dataset merely by issuing deletion requests. We survey existing definitions for machine unlearning, showing they are either susceptible to such attacks or too restrictive to support basic functionalities like exact summation. To address this problem, we propose a new security definition that specifically safeguards undeleted data against leakage caused by the deletion of other points. We show that our definition permits several essential functionalities, such as bulletin boards, summations, and statistical learning.

Privacy attacks, particularly data reconstruction attacks, pose significant challenges to federated learning despite its promise in privacy-preserving collaborative training. This paper presents a comprehensive theoretical analysis of privacy leakage in federated learning through dual perspectives: linear algebra and optimization theory. By analyzing the client-update Jacobian, we identify conditions under which distinct data batches produce the same model update and derive a sufficient batch-size criterion for non-unique reconstruction. Through optimization theory, we establish a novel upper bound for privacy leakage that incorporates batch size, distortion extent, and other critical parameters. These theoretical insights elucidate the fundamental relationships between system parameters and privacy vulnerability, laying the groundwork for developing more robust privacy-preserving federated learning frameworks.