SOMP: Scalable Gradient Inversion for Large Language Models via Subspace-Guided Orthogonal Matching Pursuit

Given the growing reliance on private data in training Large Language Models (LLMs), Federated Learning (FL) combined with Parameter-Efficient Fine-Tuning (PEFT) has garnered significant attention for enhancing privacy and efficiency. Despite FL's privacy benefits, prior studies have shown that private data can still be extracted from shared gradients. However, these studies, mainly on full-parameter model training, are limited to reconstructing small batches, short input sequences, and specific model architectures, such as encoder-based or decoder-based models. The reconstruction quality becomes even worse when dealing with gradients from PEFT methods. To fully understand the practical attack surface of federated LLMs, this paper proposes FedSpy-LLM, a scalable and generalizable data reconstruction attack designed to reconstruct training data with larger batch sizes and longer sequences while generalizing across diverse model architectures, even when PEFT methods are deployed for training. At the core of FedSpy-LLM is a novel gradient decomposition strategy that exploits the rank deficiency and subspace structure of gradients, enabling efficient token extraction while preserving key signal components at scale. This approach further mitigates the reconstruction challenges introduced by PEFT's substantial null space, ensuring robustness across encoder-based, decoder-based, and encoder-decoder model architectures. Additionally, by iteratively aligning each token's partial-sequence gradient with the full-sequence gradient, FedSpy-LLM ensures accurate token ordering in reconstructed sequences.

Gradient matching attacks (GMAs) in LLM split learning (SL) rely on a critical yet underexplored assumption: the gradient exposed at the split interface is a faithful derivative of the client's full-label training objective. This gradient-objective consistency allows a curious server to recover private labels by searching for a sequence whose induced gradient explains the observation. We propose Gradient Mirage, a defense that breaks this consistency without discarding the optimization utility of the backward signal. Our key idea is to induce the adversary to solve a misspecified inverse problem, in which no plausible label sequence in the sequence space can explain the observed gradients. Concretely, Gradient Mirage achieves this by inducing inconsistency across three dimensions: objective, direction, and scale. Selective Autoregressive Supervision derives the exposed gradient from a masked surrogate loss rather than the full-label objective assumed by the attacker; Scale Blinding then applies randomized multiplicative rescaling, obscuring the gradient's natural magnitude; and Directional Privatization further randomizes the gradient direction while preserving its magnitude through the von Mises-Fisher (vMF) mechanism under a directional metric differential privacy guarantee. Crucially, utility is preserved: the Top segment still learns from all target tokens via Dual-Track Backpropagation, the exposed gradient remains informative since each supervised token retains its complete autoregressive context, and Bottom-Gradient Recovery restores the effective gradient for Bottom-segment optimization. Extensive experiments show that Gradient Mirage provides substantially stronger protection than existing defenses under comparable fine-tuning performance, achieving a better privacy-utility trade-off.

Recent work shows that distinct inputs produce distinct hidden representations in LLMs, so the input can in principle be recovered from them. Yet, no existing method can reliably do so from the model's output text or logits alone. We introduce Sparse One-hot Discrete Adam (SODA), a white-box search-based algorithm that reconstructs textual inputs from partial knowledge of the output. Given output logits, SODA recovers natural sequences of up to 17 tokens with zero false positives and achieves a 4x improvement in exact-match reconstruction over the strongest prior method. We further show that input length and vocabulary size matter more for inversion difficulty than parameter count, with SODA inverting models from 33M to 3B parameters. Finally, we demonstrate proof-of-concept security applications: SODA recovers 6 backdoor triggers from a poisoned LLM in under 1000 iterations, and 139 tokens of personally identifiable information from synthetic user-chatbot interactions. Our code is available at https://github.com/AdrSkapars/inversion_optimisation.