GRACE:Gradient-guided Coreset Selection for LLM Unlearning

Machine Unlearning methods for Large Language Models typically assume pre-specified forget and retain sets. In realistic settings, however, requests may provide only a few examples of undesired behavior, requiring forget and retain sets to be inferred from heterogeneous corpora. We study this data-selection problem and propose GRACE , a gradient-guided coreset selection method that constructs both forget and retain sets for LLM unlearning. GRACE first computes a forget direction from seed examples that elicit the undesired behavior, then selects a compact forget coreset whose gradients approximate this direction using non-negative orthogonal matching pursuit. To preserve model utility, it selects retain examples after projecting out the forget direction and applying clustered orthogonal matching pursuit in the remaining gradient space. Across two target domains, two model families, and four unlearning algorithms, GRACE improves model utility while maintaining comparable forget quality, with particularly consistent gains over prior gradient-based selection methods.

GLOBE: Trajectory-Aligned Gradient Matching with Structured SparseOptimization for Coreset Selection

On-device training of deep neural networks is fundamentally constrained by the computational and memory costs of large-scale datasets. Coreset selection offers a practical solution by retaining only a compact subset of real training samples. However, existing gradient-based methods commonly rely on gradients computed at a single model snapshot and employ greedy or pursuit-based selection procedures, limiting their ability to capture evolving optimization dynamics and handle strongly correlated samples. We propose GLOBE (Gradient Local-Balanced Extraction), a trajectory-aligned coreset selection framework that formulates sample selection as a globally optimized sparse weighting problem. GLOBE represents each sample by a gradient trajectory constructed across multiple training checkpoints, thereby capturing its influence throughout different stages of optimization. To preserve the training behavior of the full dataset, we introduce a multi-order matching objective that jointly aligns the first-order mean and projected uncentered second-order moments of gradient trajectories. GLOBE further combines Group LASSO, Elastic Net regularization, and nonnegative budget constraints to induce group- and sample-level sparsity while stabilizing the weights of correlated trajectories. Finally, class-balanced Top-K selection maintains adequate category coverage under limited sampling budgets. Experiments across six benchmarks and five evaluation architectures demonstrate that GLOBE consistently outperforms existing coreset selection methods in downstream test accuracy, particularly at low retention ratios. These results highlight the effectiveness of combining dynamic gradient information, multi-order distribution matching, and structured sparsity for data-efficient learning.

Minibatch Selection for Language Models via Partition Matroid Constrained Gradient Matching

Training large language models (LLMs) on heterogeneous data requires selecting minibatches that balance convergence speed with coverage across domains. Existing methods either select samples independently within each domain or rely on computationally expensive proxy models to learn continuous domain weights. We propose PartitionSel, a cross-domain minibatch selection approach that maximizes a validation-guided gradient-matching utility under per-domain budgets encoded as a partition-matroid constraint. By coupling the per-domain budgets through a single utility, PartitionSel is designed to reduce redundancy in selections across domains. The proposed objective is weakly submodular and admits an orthogonal matching pursuit algorithm with provable approximation guarantees. Empirically, we evaluate PartitionSel for minibatch selection during the fine-tuning of Qwen2.5 and Llama-3 on MetaMathQA and Mol-Instructions. PartitionSel achieves robust gains over per-domain and domain-agnostic baselines on both benchmarks. It also reduces the number of conflicting gradient pairs within each batch, indicating that the cross-domain coupling translates into more compatible training updates.