The Evaluation Blind Spot: A Stereological Theory of Benchmark Coverage for Large Language Models
A new paper proposes a stereological theory for evaluating LLM benchmark coverage, revealing that effective dimensionality of benchmark suites leads to large blind spots that dwarf score differences, and suggests minimal benchmark sets and resolves Gardner's problem.
[2606.05169] The Evaluation Blind Spot: A Stereological Theory of Benchmark Coverage for Large Language Models
[Submitted on 15 Apr 2026]
Title:The Evaluation Blind Spot: A Stereological Theory of Benchmark Coverage for Large Language Models
View a PDF of the paper titled The Evaluation Blind Spot: A Stereological Theory of Benchmark Coverage for Large Language Models, by Jason Z Wang
View PDF HTML (experimental)
Abstract:We give a stereological theory of LLM benchmark coverage. For any suite with effective dimensionality d_eff, the visible Hausdorff distance between two convex capability profiles consistent with the same scores is bounded by epsilon + C R m^(-1/(d_eff-1)), with matching Lipschitz lower bound. Empirically, three independent leaderboards (Open LLM v2, an extended 12-benchmark suite, LiveBench) all have d_eff in [2.86, 4.80] on their competitive frontier; the structural blind spot exceeds the observed runner-up score gap by two orders of magnitude and dominates statistical noise by 52-127x. Under a chi-squared projection model, the isotropic prior is the optimistic case; across six hidden-capability priors and four ambient dimensions the simulated half-split swap rate of the top two models stays in [0.38, 0.49], and a 500-trial random visible/held-out split shows that 92% of trials swap the top-1 ranking with on average 2.83 of 5 top-5 models changing. A submodular greedy algorithm with the Nemhauser (1 - 1/e) guarantee finds a stable core of 4 benchmarks; 7 of 12 suffice for 90% coverage, and the trained subset transfers across temporal quarters with 93-97% retention. A counterfactual validation across 12 internal benchmarks and 27 Chatbot Arena categories confirms that the eigenstructure predicts which evaluations are irreplaceable (rho = -0.69, p = 0.013 for removal disruption) and which external evaluations bring new information (rho = +0.38). As a second, independent theoretical contribution, we resolve Gardner's Problem 1.5 (1995) for C^2 support functions, establishing the minimax rate Theta(R/(kappa m^(2/(D-1)))) in general dimension via optimal recovery theory on S^(D-1).
Comments: 55 pages, 3 figures, 3 tables, extensive appendix with proofs
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2606.05169 [cs.LG]
(or arXiv:2606.05169v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.05169
arXiv-issued DOI via DataCite
Submission history
From: Jason Z Wang [view email] [v1] Wed, 15 Apr 2026 08:56:58 UTC (131 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled The Evaluation Blind Spot: A Stereological Theory of Benchmark Coverage for Large Language Models, by Jason Z Wang
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-06
Change to browse by:
cs
References & Citations
NASA ADS
Google Scholar
Semantic Scholar
Loading...
Data provided by:
Bibliographic Tools
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, Media
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
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Related Papers
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?)
Author
Venue
Institution
Topic
About arXivLabs
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.
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)