How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
arXiv:2605.29448 (cs)
[Submitted on 28 May 2026]
Title:How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions
View a PDF of the paper titled How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions, by Jeff A. Bilmes and Gantavya Bhatt and Arnav M. Das
View PDF
HTML (experimental)
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.
| Comments: | 75 pages |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Information Theory (cs.IT) |
| Cite as: | arXiv:2605.29448 [cs.LG] |
| (or arXiv:2605.29448v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.29448
arXiv-issued DOI via DataCite (pending registration)
|
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled How Much Is a Dataset Worth? Scaling Laws, the Vendi Score, and Matrix Spectral Functions, by Jeff A. Bilmes and Gantavya Bhatt and Arnav M. Das
Current browse context:
cs.LG
References & Citations
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
One Mask to Rule Them All: On Hidden Facts after Editing and How to Find Them
May 29
-
Representation Signatures and Risk-Feedback Alignment in LLM Trading Agents
May 29
-
Mechanistic origins of catastrophic forgetting: why RL preserves circuits better than SFT?
May 29
-
Molecular Lead Optimization via Agentic Tool Planning
May 29
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.