Instruction tuning improves the ability of large language models (LLMs) to follow diverse human instructions, but achieving strong performance on specific target tasks remains challenging. A critical bottleneck is selecting the most relevant data to maximize task-specific performance. Existing data selection approaches include unstable influence-based methods and more stable distribution alignment methods, the latter of which critically rely on the underlying sample representation. In practice, most distribution alignment methods, from shallow features (e.g., BM25) to neural embeddings (e.g., BGE, LLM2Vec), may fail to capture how the model internally processes samples. To bridge this gap, we adopt a model-centric strategy in which each sample is represented by its neuronal activation pattern in the model, directly reflecting internal computation. However, directly using raw neuron activations leads to spurious similarity between unrelated samples due to neuron polysemanticity, where a single neuron may respond to multiple, unrelated concepts. To address this, we employ sparse autoencoders to disentangle polysemantic activations into sparse, monosemantic representations, and introduce a dedicated similarity metric for this space to better identify task-relevant data. Comprehensive experiments across multiple instruction datasets, models, tasks, and selection ratios show that our approach consistently outperforms existing data selection baselines in both stability and task-specific performance2.

Instruction tuning is essential for Large Language Models (LLMs) to effectively follow user instructions. To improve training efficiency and reduce data redundancy, recent works use LLM-based scoring functions, e.g., Instruction-Following Difficulty (IFD), to select high-quality instruction-tuning data with scores above a threshold. While these data selection methods often lead to models that can match or even exceed the performance of models trained on the full datasets, we identify two key limitations: (i) they assess quality at the sample level, ignoring token-level informativeness; and (ii) they overlook the robustness of the scoring method, often selecting a sample due to superficial lexical features instead of its true quality. In this work, we propose Token-Selective HIeRarchical Data Selection for Instruction Tuning (T-SHIRT), a novel data selection framework that introduces a new scoring method to include only informative tokens in quality evaluation and also promotes robust and reliable samples whose neighbors also show high quality with less local inconsistencies. We demonstrate that models instruction-tuned on a curated dataset (only 5% of the original size) using T-SHIRT can outperform those trained on the entire large-scale dataset by up to 5.48 points on average across eight benchmarks. Across various LLMs and training set scales, our method consistently surpasses existing state-of-the-art data selection techniques, while also remaining both costeffective and highly efficient. For instance, by using GPT-2 for score computation, we are able to process a dataset of 52k samples in 40 minutes on a single GPU.

Fine-tuning large language models (LLMs) using diverse datasets is crucial for enhancing their overall performance across various domains. In practical scenarios, existing methods based on modeling the mixture proportions of data composition often struggle with data whose domain labels are missing, imprecise or nonnormalized, while methods based on data selection usually encounter difficulties in balancing multi-domain performance. To address these challenges, in this work, we investigate the role of data diversity in enhancing the overall abilities of LLMs by empirically constructing contrastive data pools and theoretically deriving explanations. Building upon the insights gained, we propose a new method that gives the LLM a dual identity: an output model to cognitively probe and select data based on diversity reward, as well as an input model to be tuned with the selected data. Extensive experiments show that the proposed method notably boosts performance across domain-undetermined data and a series of foundational downstream tasks when applied to various advanced LLMs. We release our code and hope this study can shed light on the understanding of data diversity and advance feedback-driven data-model co-design for LLMs.

Process Reward Models (PRMs) have recently emerged as a powerful framework for supervising intermediate reasoning steps in large language models (LLMs). Previous PRMs are primarily trained on model final output responses and struggle to evaluate intermediate thinking trajectories robustly, especially in the emerging setting of trajectory-response outputs generated by frontier reasoning models like Deepseek-R1. In this work, we introduce ReasonFlux-PRM, a novel trajectory-aware PRM explicitly designed to evaluate the trajectory-response type of reasoning traces. ReasonFlux-PRM incorporates both step-level and trajectorylevel supervision, enabling fine-grained reward assignment aligned with structured chain-of-thought data. We adapt ReasonFlux-PRM to support reward supervision under both offline and online settings, including (i) selecting high-quality model distillation data for downstream supervised fine-tuning of smaller models, (ii) providing dense process-level rewards for policy optimization during reinforcement learning, and (iii) enabling reward-guided Best-of-N test-time scaling. Empirical results on challenging downstream benchmarks such as AIME, MATH500, and GPQA-Diamond demonstrate that ReasonFlux-PRM-7B selects higher quality data than strong PRMs (e.g., Qwen2.5-Math-PRM-72B) and human-curated baselines.

Data selection improves computational efficiency by choosing informative subsets of training samples. However, existing methods ignore the compute budget, treating data selection and importance evaluation independently of compute budget constraints. Yet empirical studies show no algorithm can consistently outperform others (or even random selection) across varying budgets. We therefore argue that compute budget must be integral to data-selection strategies, since different budgets impose distinct requirements on data quantity, quality, and distribution for effective training. To this end, we propose a novel Computational budget-Aware Data Selection (CADS) method and naturally formulate it into a bilevel optimization framework, where the inner loop trains the model within the constraints of the computational budget on some selected subset of training data, while the outer loop optimizes data selection based on model evaluation.

Selecting a compact subset of visual instruction-following data has emerged as an effective way to align large multimodal models with human intentions while avoiding the high cost of full-dataset training. Yet we observe that both full-data training and existing state-of-the-art data selection methods tend to inherit underlying dataset biases such as position bias and spurious correlations, leading to biased model behaviors. To address this issue, we introduce ARDS, a robustness-aware targeted visual instruction-selection framework that explicitly mitigates these weaknesses, sidestepping the need for access to downstream data or time-consuming gradient computation. Specifically, we first identify the worst-case evaluation subgroups through visual and textual task-specific perturbations. The robust training mixture is then constructed by prioritizing samples that are semantically closer to these subgroups in a rich multimodal embedding space. Extensive experiments demonstrate that ARDS substantially boosts both robustness and data efficiency for visual instruction tuning. We also showcase that the robust mixtures produced with a smaller model transfer effectively to larger architectures. Our code and selected datasets that have been demonstrated transferable across models are available at https://github.com/xyang583/ARDS.

Effective data selection is critical for efficient training of modern Large Language Models (LLMs). This paper introduces Influence Distillation, a novel, mathematically-justified framework for data selection that employs second-order information to optimally weight training samples. By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data for LLM fine-tuning, guiding it toward strong performance on the target domain. We derive these optimal weights for both Gradient Descent and Adam optimizers. To ensure scalability and reduce computational cost, we propose a $\textit{landmark-based approximation}$: influence is precisely computed for a small subset of landmark samples and then efficiently propagated to all other samples to determine their weights.

Instruction tuning is essential for Large Language Models (LLMs) to effectively follow user instructions. To improve training efficiency and reduce data redundancy, recent works use LLM-based scoring functions, e.g., Instruction-Following Difficulty (IFD), to select high-quality instruction-tuning data with scores above a threshold. While these data selection methods often lead to models that can match or even exceed the performance of models trained on the full datasets, we identify two key limitations: (i) they assess quality at the sample level, ignoring token-level informativeness; and (ii) they overlook the robustness of the scoring method, often selecting a sample due to superficial lexical features instead of its true quality. In this work, we propose Token-Selective HIeRarchical Data Selection for Instruction Tuning (T-SHIRT), a novel data selection framework that introduces a new scoring method to include only informative tokens in quality evaluation and also promote robust and reliable samples whose neighbors also show high quality with less local inconsistencies. We demonstrate that models instruction-tuned on a curated dataset (only 5% of the original size) using T-SHIRT can outperform those trained on the entire large-scale dataset by up to 5.48 points on average across eight benchmarks. Across various LLMs and training set scales, our method consistently surpasses existing state-of-the-art data selection techniques, while also remaining both cost-effective and highly efficient. For instance, by using GPT-2 for score computation, we are able to process a dataset of 52k samples in 40 minutes on a single GPU.

This study identifies that visual-related functional decoding is distributed across different decoder layers in Multimodal Large Language Models (MLLMs). Typically, each function, such as counting, grounding, or OCR recognition, narrows down to two or three layers, which we define as Vision Function Layers (VFL). Additionally, the depth and its order of different VFLs exhibits a consistent pattern across different MLLMs, which is well-aligned with human behaviors (e.g., recognition occurs first, followed by counting, and then grounding). These findings are derived from Visual Token Swapping, our novel analytical framework that modifies targeted KV cache entries to precisely elucidate layer-specific functions during decoding. Furthermore, these insights offer substantial utility in tailoring MLLMs for real-world downstream applications. For instance, when LoRA training is selectively applied to VFLs whose functions align with the training data, VFL-LoRA not only outperform full-LoRA but also prevent out-of-domain function forgetting. Moreover, by analyzing the performance differential on training data when particular VFLs are ablated, VFL-select automatically classifies data by function, enabling highly efficient data selection to directly bolster corresponding capabilities. Consequently, VFL-select surpasses human experts in data selection, and achieves 98% of full-data performance with only 20% of the original dataset. This study delivers deeper comprehension of MLLM visual processing, fostering the creation of more efficient, interpretable, and robust models.

Data selection improves computational efficiency by choosing informative subsets of training samples. However, existing methods ignore the compute budget, treating data selection and importance evaluation independently of compute budget constraints. Yet empirical studies show no algorithm can consistently outperform others (or even random selection) across varying budgets. We therefore argue that compute budget must be integral to data-selection strategies, since different budgets impose distinct requirements on data quantity, quality, and distribution for effective training. To this end, we propose a novel Computational budget-Aware Data Selection (CADS) method and naturally formulate it into a bilevel optimization framework, where the inner loop trains the model within the constraints of the computational budget on some selected subset of training data, while the outer loop optimizes data selection based on model evaluation.