GEM: Geometric Entropy Mixing for Optimal LLM Data Curation
This paper proposes GEM (Geometric Entropy Mixing), a framework that reformulates data curation as a variational problem on the hypersphere with a mixing-balance regularizer. It overcomes cluster collapse to discover balanced semantic structures invisible to Euclidean heuristics. Using teacher-student distillation for scalability and introducing the Geometric Influence Score (GIS) for interpretable taxonomy generation, GEM integrated into mixing strategies like DoReMi and RegMix improves average downstream accuracy by up to 1.2% on 1.1B-parameter models.
Article intelligence
Key points
- GEM reformulates data curation as a variational problem on the hypersphere with a mixing-balance regularizer to overcome cluster collapse.
- It employs teacher-student distillation for scaling and introduces GIS for interpretable taxonomy generation.
- Integrated into DoReMi and RegMix, GEM improves average downstream accuracy by up to 1.2% on 1.1B-parameter models.
Why it matters
This matters because GEM reformulates data curation as a variational problem on the hypersphere with a mixing-balance regularizer to overcome cluster collapse.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.26121] GEM: Geometric Entropy Mixing for Optimal LLM Data Curation
[Submitted on 27 Apr 2026]
Title:GEM: Geometric Entropy Mixing for Optimal LLM Data Curation
View a PDF of the paper titled GEM: Geometric Entropy Mixing for Optimal LLM Data Curation, by Yue Min and 3 other authors
View PDF HTML (experimental)
Abstract:LLM pre-training efficacy increasingly depends on data composition rather than sheer volume. Yet, optimal mixing is hindered by categorization flaws: human taxonomies suffer from ontological misalignment, and Euclidean clustering fails to address embedding anisotropy. We introduce GEM (Geometric Entropy Mixing), a framework reformulating data curation as a variational problem on the hypersphere augmented with a mixing-balance regularizer. By decoupling the generative prior and optimizing the objective via a provable MM (Minorize-Maximize) algorithm, GEM effectively counteracts the cluster collapse to discover balanced semantic structures invisible to Euclidean heuristics. We employ teacher-student distillation to scale this geometric fidelity to web-scale corpora and introduce the Geometric Influence Score (GIS) for interpretable taxonomy generation. Experiments with 1.1B-parameter models demonstrate that GEM establishes a new state-of-the-art when integrated into mixing strategies like DoReMi and RegMix, improving average downstream accuracy by up to 1.2% and offering a robust coordinate system for predictable data mixing.
Comments: Submitted to ICML 2026
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2605.26121 [cs.LG]
(or arXiv:2605.26121v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.26121
arXiv-issued DOI via DataCite
Submission history
From: Yue Min [view email] [v1] Mon, 27 Apr 2026 06:42:28 UTC (1,462 KB)
Full-text links:
Access Paper:
View a PDF of the paper titled GEM: Geometric Entropy Mixing for Optimal LLM Data Curation, by Yue Min and 3 other authors
View PDF
HTML (experimental)
TeX Source
view license
Current browse context:
cs.LG
new | recent | 2026-05
Change to browse by:
cs cs.AI
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?)