ICLHerd: Herding-Based Data Selection for LLMs with In-Context Learning as a Proxy

As Large Language Model (LLM) datasets scale to trillions of tokens, data selection has emerged as a critical frontier to filter out uninformative noise and construct adaptive learning trajectories. Beyond static heuristic filtering, advanced data selection methods for LLM training largely follow two paradigms, each with fundamental limitations. Influence-based methods provide principled bi-level objectives but require intractable inverse-Hessian computations, while excess-loss methods are computationally efficient but rely on a static reference model that becomes misaligned with the evolving proxy model during training. We propose BLADE (Bi-Level Adaptive Data sElection), a Hessian-free framework for data selection. BLADE reformulates the bi-level optimization problem underlying influence-based methods as a penalized single-level objective via Lagrange multipliers, avoiding inverse-Hessian computation while revealing a principled connection to excess-loss based data selection. The resulting objective recovers an excess-loss form but replaces the static reference model with a dynamic one that stays synchronized with training. Theoretically, we prove that this penalized formulation guarantees first-order convergence. For efficient online batch selection, we instantiate BLADE as a memoryless randomized block-coordinate Frank-Wolfe algorithm. Extensive experiments show that BLADE consistently outperforms state-of-the-art data selection baselines, providing a practical recipe for LLM training.

The In-context learning (ICL) paradigm aids large language models (LLMs) to adapt to new tasks without need for fine-tuning. However, selecting an optimal combination of demonstration examples from a large pool of example subsets is a challenging problem. Existing approaches for selection do not model the complex relationship between ICL samples and downstream LLM performance. They typically perform static task-level selection, choosing subsets once offline, which can fail to generalize to unseen queries. We introduce DearICL (Data Efficient Algorithm for Ranking) ICL samples, a new framework that models demonstration example selection as a subset ranking problem. DearICL employs a non-linear surrogate employing a differentiable sorting objective within a gap-index bandit algorithm. The gap-index based approach enables fine-grained separation of good arms and borderline arms, which is used as an auxiliary objective to train the non-linear surrogate through sufficient sampling of borderline arms, supporting instance-level subset ranking. On exemplar selection benchmarks with open-source LLMs, DearICL achieves 8.08-15.9% accuracy gains over strong linear bandit baselines, with low sample complexity. Code and data: https://github.com/VenkteshV/DearICL.

Data selection methods address a critical challenge in LLM post-training: effectively leveraging scarce, high-fidelity target data alongside abundant but imperfectly aligned general training data. In this work, we move beyond the data-selection framing and introduce Dr. Post-Training (Data-Regularized Post-Training), a novel framework that reconceptualizes general training data as a data-induced regularizer that prevents overfitting to the scarce target objective, rather than serving as a pool for selection. Specifically, our framework proposes that, at each training step, we construct a feasible set of model update directions using the general training data, and project the model update direction specified by the scarce target data onto that feasible set. Standard training and existing data selection methods arise as special cases with different choices of the data-induced regularizer, and these methods correspond to different points on a bias-variance spectrum with different regularization strengths. Building on this view, we propose a family of methods offering a richer design space and more flexible bias-variance tradeoffs. For practical LLM-scale use, we introduce careful system optimizations that realize these methods with minimal overhead. Extensive experiments across SFT, RLHF, and RLVR show that our methods outperform standard training and state-of-the-art data selection baselines, with the largest gains where the general and target data are most misaligned, and system benchmarks confirm their efficiency.