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Hopfield Networks

Description

This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.

Below is a brief overview of the key files:

  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.

For more details, see the individual files.

Installation

Installing Lean can be done by following the leanprover community website. Our project uses Lean version 4.18.0.

This repository can then be cloned by following the instructions on this page.

License

See LICENSE.md

About

No description, website, or topics provided.

Resources

Readme
MIT license
Activity

Stars

8 stars

Watchers

2 watching

Forks

1 fork
Report repository

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

Skip to content
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Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

Skip to content
BranchesTags
Repository files navigation
Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
BranchesTags
Repository files navigation
Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Repository files navigation
Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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Hopfield Networks
Description
This repository contains Lean formalizations related to Hopfield Networks written in the Lean theorem prover language.
Below is a brief overview of the key files:
  • HN.Core.lean – Formalization of general neural networks.
  • HN.Asym.lean – Formalization of asymmetric Hopfield networks.
  • HN.lean – Formalization of symmetric Hopfield networks.
  • Stochastic.lean – Formalization of stochastic algorithms.
  • HN.aux.lean – Auxiliary lemmas.
  • HN.test.lean – Computations and implementation of the Hebbian learning algorithm.
  • DetailedBalance.lean – Formalization of the detailed balance property for Hopfield networks.
  • HN.aux.lean – Markov Chain Framework.
  • BM.Core.lean – Formalization of Boltzmann Machines (BMs).
  • BM.Markov.lean – Formalization of probability distributions for Boltzmann Machines.
For more details, see the individual files.
Installation
Installing Lean can be done by following the leanprover community website.
Our project uses Lean version 4.18.0.
This repository can then be cloned by following the instructions on this page.
License
See LICENSE.md
About
No description, website, or topics provided.
Resources
Readme
MIT license
Activity
Stars
8 stars
Watchers
2 watching
Forks
1 fork
Report repository
Releases
Packages
Used by
Contributors
Languages