A mathematical theory of balancing relational generalization and memorization
A new mathematical theory explores how learning systems balance relational generalization and memorization of exceptions. The authors introduce a task called transitive inference with exceptions to investigate this balance. Their findings suggest that while models can achieve this balance, successful generalization is sensitive to the representational geometry used.
- ▪The study addresses the challenge of balancing general rules and exceptions in learning systems.
- ▪A novel task, transitive inference with exceptions, is introduced to test relational generalization.
- ▪The research finds that neural network models can balance generalization and memorization, but with specific representational constraints.
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Record
| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.22972 |
| Publication time | Mon, 25 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-25T04:07:35.648Z |
| Last seen | 2026-05-25T04:07:35.648Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | DAhnY0_SRRP2 |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Computer Science > Machine Learning arXiv:2605.22972 (cs) [Submitted on 21 May 2026] Title:A mathematical theory of balancing relational generalization and memorization Authors:Luke Cheng, Samuel Lippl View a PDF of the paper titled A mathematical theory of balancing relational generalization and memorization, by Luke Cheng and 1 other authors View PDF HTML (experimental) Abstract:Humans, animals, and modern machine learning models exhibit impressive abilities to learn complex behaviors and generalize these behaviors to unseen situations. This ability requires us to learn rules and regularities that allow for such generalizations. At the same time, in most complex environments, any rule will have its exceptions.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at arXiv cs.AI.
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