arXiv:2605.29448v1 Announce Type: new 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,
This paper offers a novel theoretical framework to quantify dataset value in AI, bridging existing empirical scaling laws with new mathematical approaches, which is timely given the increasing importance of data in AI development.
A strategic reader should care because improved methods for dataset valuation can optimize resource allocation, enhance model performance, and clarify the economic implications of data ownership and quality in AI.
The ability to quantitatively assess the value of training datasets will shift AI development from empirical guesswork to more principled, efficient data curation and acquisition strategies.
- · AI data providers
- · AI research institutions
- · Companies with proprietary datasets
- · Machine learning engineers
- · AI developers relying on arbitrary dataset selection
- · Companies with low-quality or redundant data
- · Inefficient AI data labeling services
More precise methods for dataset valuation will emerge, improving the efficiency of AI model training and development.
This efficiency gain could lead to a 'data arms race' where the ability to curate and leverage high-value datasets becomes a key competitive differentiator in AI.
The economic value of data could become better understood and even financialized, potentially leading to new markets for quantified datasets.
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Read at arXiv cs.LG