How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions

• URL: http://arxiv.org/abs/2605.29448v1
• Date: Thu, 28 May 2026 06:40:29 GMT
• Title: How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions
• Abstract summary: We show that common neural-scaling-law objectives and the Vendi Score are submodular.<n>Vendi Score is a special case of a broader class of submodular objectives that we call matrix spectral functions.
• Score: 13.381771483955552
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural scaling laws appraise data through dataset size, while the Vendi Score uses quantum entropy to measure dataset value. We show both that common neural-scaling-law objectives and the Vendi Score are submodular. We further show that the Vendi Score is a special case of a broader class of submodular objectives that we call matrix spectral functions. This also includes determinantal (DPP) objectives, as well as many others. We also introduce weakly matrix monotone functions and show how they lead to weakly submodular matrix spectral functions, yielding a broad family of practical objectives for data appraisal. We develop secular-equation-based updates that avoid repeated eigendecompositions during greedy optimization, reducing marginal-gain evaluation for $m$-dimensional embeddings by an $O(m)$ factor relative to oracle queries. This yields an average empirical speedup of about 35,000x, making direct optimization of the Vendi Score feasible on ImageNet-1K-scale datasets. Thus enabled, we compare how well several objectives predict the value of training subsets for held-out test performance under fixed-size, class-balanced, and fixed training-budget regimes, including the Vendi Score, DPPs, facility location, and three new matrix spectral variants. Across multiple datasets, facility location performs the best. Direct optimization also reveals that, while the Vendi Score is predictive over moderate score ranges, pushing the objective to higher values can make it a poor downstream performance proxy. We also find that uniformly at random fixed-size subsets, both unconstrained and class-balanced, are remarkably concentrated in both appraisal scores and held-out performance. Finally, we show that size, class balance, and training budget do not alone determine data value: even when controlling for these factors, performance ranges smoothly from good to bad.

Related papers

• Convex Dataset Valuation for Post-Training [21.22512177964122]
  We propose a scalable convex dataset-level valuation method based on mean matching (KMM) in gradient space.<n>We show that our approach consistently outperforms existing valuation baselines, achieving stronger performance with low overhead.
  arXiv  Detail & Related papers  (2026-05-15T23:35:07Z)
• Talos: Optimizing Top-$K$ Accuracy in Recommender Systems [14.229918568280729]
  We propose Talos, a loss function that is specifically designed to optimize the Talos recommendation accuracy.<n>We develop a sampling-based regression algorithm for efficient and accurate threshold estimation.<n>We incorporate a tailored surrogate function to address discontinuity and enhance robustness against distribution shifts.
  arXiv  Detail & Related papers  (2026-01-27T07:04:09Z)
• Scales++: Compute Efficient Evaluation Subset Selection with Cognitive Scales Embeddings [23.9553588103042]
  We propose a item-centric approach to benchmark subset selection, arguing that selection should be based on the intrinsic properties of the task items themselves.<n>We show Scales++ reduces the upfront selection cost by over 18x while achieving competitive predictive fidelity.<n>We demonstrate that this item-centric approach enables more efficient model evaluation without significant fidelity degradation.
  arXiv  Detail & Related papers  (2025-10-30T11:28:58Z)
• Efficient Data Selection at Scale via Influence Distillation [53.03573620682107]
  This paper introduces Influence Distillation, a mathematicallyjustified framework for data selection.<n>By distilling each sample's influence on a target distribution, our method assigns model-specific weights that are used to select training data.<n>Experiments show that Influence Distillation matches or outperforms state-of-the-art performance while achieving up to $3.5times$ faster selection.
  arXiv  Detail & Related papers  (2025-05-25T09:08:00Z)
• DUPRE: Data Utility Prediction for Efficient Data Valuation [49.60564885180563]
  Cooperative game theory-based data valuation, such as Data Shapley, requires evaluating the data utility and retraining the ML model for multiple data subsets.<n>Our framework, textttDUPRE, takes an alternative yet complementary approach that reduces the cost per subset evaluation by predicting data utilities instead of evaluating them by model retraining.<n>Specifically, given the evaluated data utilities of some data subsets, textttDUPRE fits a emphGaussian process (GP) regression model to predict the utility of every other data subset.
  arXiv  Detail & Related papers  (2025-02-22T08:53:39Z)
• MM-RLHF: The Next Step Forward in Multimodal LLM Alignment [59.536850459059856]
  We introduce MM-RLHF, a dataset containing $mathbf120k$ fine-grained, human-annotated preference comparison pairs.<n>We propose several key innovations to improve the quality of reward models and the efficiency of alignment algorithms.<n>Our approach is rigorously evaluated across $mathbf10$ distinct dimensions and $mathbf27$ benchmarks.
  arXiv  Detail & Related papers  (2025-02-14T18:59:51Z)
• Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning [55.96599486604344]
  We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process. We use Monte Carlo Tree Search (MCTS) to iteratively collect preference data, utilizing its look-ahead ability to break down instance-level rewards into more granular step-level signals. The proposed algorithm employs Direct Preference Optimization (DPO) to update the LLM policy using this newly generated step-level preference data.
  arXiv  Detail & Related papers  (2024-05-01T11:10:24Z)
• Self-Supervised Dataset Distillation for Transfer Learning [77.4714995131992]
  We propose a novel problem of distilling an unlabeled dataset into a set of small synthetic samples for efficient self-supervised learning (SSL) We first prove that a gradient of synthetic samples with respect to a SSL objective in naive bilevel optimization is textitbiased due to randomness originating from data augmentations or masking. We empirically validate the effectiveness of our method on various applications involving transfer learning.
  arXiv  Detail & Related papers  (2023-10-10T10:48:52Z)
• BOtied: Multi-objective Bayesian optimization with tied multivariate ranks [33.414682601242006]
  In this paper, we show a natural connection between non-dominated solutions and the extreme quantile of the joint cumulative distribution function. Motivated by this link, we propose the Pareto-compliant CDF indicator and the associated acquisition function, BOtied. Our experiments on a variety of synthetic and real-world problems demonstrate that BOtied outperforms state-of-the-art MOBO acquisition functions.
  arXiv  Detail & Related papers  (2023-06-01T04:50:06Z)
• SCAI: A Spectral data Classification framework with Adaptive Inference for the IoT platform [0.0]
  We propose a Spectral data Classification framework with Adaptive Inference. Specifically, to allocate different computations for different samples while better exploiting the collaboration among different devices. To the best of our knowledge, this paper is the first attempt to conduct optimization by adaptive inference for spectral detection under the IoT platform.
  arXiv  Detail & Related papers  (2022-06-24T09:22:52Z)
• Pessimistic Minimax Value Iteration: Provably Efficient Equilibrium Learning from Offline Datasets [101.5329678997916]
  We study episodic two-player zero-sum Markov games (MGs) in the offline setting. The goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori.
  arXiv  Detail & Related papers  (2022-02-15T15:39:30Z)
• Efficient Rollout Strategies for Bayesian Optimization [15.050692645517998]
  Most acquisition functions are myopic, meaning that they only consider the impact of the next function evaluation. We show that a combination of quasi-Monte Carlo, common random numbers, and control variables significantly reduce the computational burden of rollout. We then formulate a policy-search based approach that removes the need to optimize the rollout acquisition function.
  arXiv  Detail & Related papers  (2020-02-24T20:54:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.