Add constant 80 (Ising perceptron capacity threshold)#47
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Robertboy18 wants to merge 2 commits intoteorth:mainfrom
Open
Add constant 80 (Ising perceptron capacity threshold)#47Robertboy18 wants to merge 2 commits intoteorth:mainfrom
Robertboy18 wants to merge 2 commits intoteorth:mainfrom
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Pull request overview
Adds a new constants entry documenting the Ising (binary) perceptron zero-margin storage-capacity threshold and links it from the main constants table in the README.
Changes:
- Added
constants/80a.mddescribing the constant, bounds, and references for the Ising perceptron capacity threshold. - Updated
README.mdto include the new constant in the constants index table.
Reviewed changes
Copilot reviewed 2 out of 2 changed files in this pull request and generated 6 comments.
| File | Description |
|---|---|
constants/80a.md |
New constant entry defining the threshold and summarizing known bounds and references. |
README.md |
Adds the row linking to constant 80 and summarizing current bounds. |
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Addressed all the Copilot reviews!! |
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So, I added constants/80a.md for the Ising perceptron capacity threshold, which I think is a really exciting problem at the boundary of probability, combinatorics, and theoretical machine learning.
Informally, this constant measures how many random constraints a binary perceptron can satisfy before solutions disappear. In other words, it is a sharp “capacity limit” for a simple neural-network-style model with binary weights.
This PR includes some of the older upper-bound history, the Krauth Mézard prediction which I thought is cool, and the more recent rigorous progress, while trying to clearly separate unconditional results from conditional bounds. I also added the corresponding row to README.md.
Let me know if anything else is needed or changes! I did use GPT5.4 Pro for help with a deeper literature study.