deploy: 2b2203c6f7

404.html

@@ -4,4 +4,4 @@
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
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about/index.html

@@ -4,4 +4,4 @@
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
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categories/index.html

@@ -4,4 +4,4 @@
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
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index.html

@@ -4,4 +4,4 @@
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
+<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/2b2203c">[2b2203c]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>

index.xml

@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Eric X. Liu's Personal Page</title><link>/</link><description>Recent content on Eric X. Liu's Personal Page</description><generator>Hugo</generator><language>en</language><lastBuildDate>Tue, 23 Sep 2025 06:14:45 +0000</lastBuildDate><atom:link href="/index.xml" rel="self" type="application/rss+xml"/><item><title>UniFi VLAN Migration to Zone-Based Architecture</title><link>/posts/unifi-vlan-migration-to-zone-based-architecture/</link><pubDate>Mon, 22 Sep 2025 00:00:00 +0000</pubDate><guid>/posts/unifi-vlan-migration-to-zone-based-architecture/</guid><description>&lt;p&gt;Embarking on a network migration to a properly segmented VLAN architecture is a rite of passage for any serious home lab or small business operator. The goal is clear: improve security and organization by separating traffic. However, the path from a flat network to a segmented one is often paved with subtle but critical configuration details that can lead to hours of frustrating troubleshooting.&lt;/p&gt;
+<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Eric X. Liu's Personal Page</title><link>/</link><description>Recent content on Eric X. Liu's Personal Page</description><generator>Hugo</generator><language>en</language><lastBuildDate>Tue, 23 Sep 2025 06:20:36 +0000</lastBuildDate><atom:link href="/index.xml" rel="self" type="application/rss+xml"/><item><title>UniFi VLAN Migration to Zone-Based Architecture</title><link>/posts/unifi-vlan-migration-to-zone-based-architecture/</link><pubDate>Mon, 22 Sep 2025 00:00:00 +0000</pubDate><guid>/posts/unifi-vlan-migration-to-zone-based-architecture/</guid><description>&lt;p&gt;Embarking on a network migration to a properly segmented VLAN architecture is a rite of passage for any serious home lab or small business operator. The goal is clear: improve security and organization by separating traffic. However, the path from a flat network to a segmented one is often paved with subtle but critical configuration details that can lead to hours of frustrating troubleshooting.&lt;/p&gt;
 &lt;p&gt;This article documents that journey. It details the pitfalls encountered, the core networking concepts that were essential to understand, and the best practices that ultimately led to a stable, secure, and logical network design built on a zone-based firewall model.&lt;/p&gt;</description></item><item><title>Quantization in LLMs</title><link>/posts/quantization-in-llms/</link><pubDate>Tue, 19 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/quantization-in-llms/</guid><description>&lt;p&gt;The burgeoning scale of Large Language Models (LLMs) has necessitated a paradigm shift in their deployment, moving beyond full-precision floating-point arithmetic towards lower-precision representations. Quantization, the process of mapping a wide range of continuous values to a smaller, discrete set, has emerged as a critical technique to reduce model size, accelerate inference, and lower energy consumption. This article provides a technical overview of quantization theories, their application in modern LLMs, and highlights the ongoing innovations in this domain.&lt;/p&gt;</description></item><item><title>Breville Barista Pro Maintenance</title><link>/posts/breville-barista-pro-maintenance/</link><pubDate>Sat, 16 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/breville-barista-pro-maintenance/</guid><description>&lt;p&gt;Proper maintenance is critical for the longevity and performance of a Breville Barista Pro espresso machine. Consistent cleaning not only ensures the machine functions correctly but also directly impacts the quality of the espresso produced. This guide provides a detailed, technical breakdown of the essential maintenance routines, from automated cycles to daily upkeep.&lt;/p&gt;
 &lt;h4 id="understanding-the-two-primary-maintenance-cycles"&gt;
  &lt;strong&gt;Understanding the Two Primary Maintenance Cycles&lt;/strong&gt;
@@ -15,7 +15,8 @@
 &lt;p&gt;That message is the tell: Secure Boot is enabled and the kernel refuses to load modules not signed by a trusted key.&lt;/p&gt;</description></item><item><title>Beyond Words: How RVQ Teaches LLMs to See and Hear</title><link>/posts/how-rvq-teaches-llms-to-see-and-hear/</link><pubDate>Thu, 07 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/how-rvq-teaches-llms-to-see-and-hear/</guid><description>&lt;p&gt;Large Language Models (LLMs) are masters of text, but the world is not made of text alone. It’s a symphony of sights, sounds, and experiences. The ultimate goal for AI is to understand this rich, multi-modal world as we do. But how do you teach a model that thinks in words to understand a picture of a sunset or the melody of a song?&lt;/p&gt;
 &lt;p&gt;The answer lies in creating a universal language—a bridge between the continuous, messy world of pixels and audio waves and the discrete, structured world of language tokens. One of the most elegant and powerful tools for building this bridge is &lt;strong&gt;Residual Vector Quantization (RVQ)&lt;/strong&gt;.&lt;/p&gt;</description></item><item><title>Supabase Deep Dive: It's Not Magic, It's Just Postgres</title><link>/posts/supabase-deep-dive/</link><pubDate>Sun, 03 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/supabase-deep-dive/</guid><description>&lt;p&gt;In the world of Backend-as-a-Service (BaaS), platforms are often treated as magic boxes. You push data in, you get data out, and you hope the magic inside scales. While this simplicity is powerful, it can obscure the underlying mechanics, leaving developers wondering what&amp;rsquo;s really going on.&lt;/p&gt;
 &lt;p&gt;Supabase enters this space with a radically different philosophy: &lt;strong&gt;transparency&lt;/strong&gt;. It provides the convenience of a BaaS, but it’s built on the world&amp;rsquo;s most trusted relational database: PostgreSQL. The &amp;ldquo;magic&amp;rdquo; isn&amp;rsquo;t a proprietary black box; it&amp;rsquo;s a carefully assembled suite of open-source tools that enhance Postgres, not hide it.&lt;/p&gt;</description></item><item><title>A Deep Dive into PPO for Language Models</title><link>/posts/ppo-for-language-models/</link><pubDate>Sat, 02 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/ppo-for-language-models/</guid><description>&lt;p&gt;Large Language Models (LLMs) have demonstrated astonishing capabilities, but out-of-the-box, they are simply powerful text predictors. They don&amp;rsquo;t inherently understand what makes a response helpful, harmless, or aligned with human values. The technique that has proven most effective at bridging this gap is Reinforcement Learning from Human Feedback (RLHF), and at its heart lies a powerful algorithm: Proximal Policy Optimization (PPO).&lt;/p&gt;
-&lt;p&gt;You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.&lt;/p&gt;</description></item><item><title>Mixture-of-Experts (MoE) Models Challenges &amp; Solutions in Practice</title><link>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</link><pubDate>Wed, 02 Jul 2025 00:00:00 +0000</pubDate><guid>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</guid><description>&lt;p&gt;Mixture-of-Experts (MoEs) are neural network architectures that allow different parts of the model (called &amp;ldquo;experts&amp;rdquo;) to specialize in different types of inputs. A &amp;ldquo;gating network&amp;rdquo; or &amp;ldquo;router&amp;rdquo; learns to dispatch each input (or &amp;ldquo;token&amp;rdquo;) to a subset of these experts. While powerful for scaling models, MoEs introduce several practical challenges.&lt;/p&gt;
+&lt;p&gt;You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.
+&lt;img src="/images/ppo-for-language-models/7713bd3ecf27442e939b9190fa08165d.png" alt="S3 File"&gt;&lt;/p&gt;</description></item><item><title>Mixture-of-Experts (MoE) Models Challenges &amp; Solutions in Practice</title><link>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</link><pubDate>Wed, 02 Jul 2025 00:00:00 +0000</pubDate><guid>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</guid><description>&lt;p&gt;Mixture-of-Experts (MoEs) are neural network architectures that allow different parts of the model (called &amp;ldquo;experts&amp;rdquo;) to specialize in different types of inputs. A &amp;ldquo;gating network&amp;rdquo; or &amp;ldquo;router&amp;rdquo; learns to dispatch each input (or &amp;ldquo;token&amp;rdquo;) to a subset of these experts. While powerful for scaling models, MoEs introduce several practical challenges.&lt;/p&gt;
 &lt;h3 id="1-challenge-non-differentiability-of-routing-functions"&gt;
  1. Challenge: Non-Differentiability of Routing Functions
  &lt;a class="heading-link" href="#1-challenge-non-differentiability-of-routing-functions"&gt;

posts/breville-barista-pro-maintenance/index.html

@@ -25,4 +25,4 @@ Understanding the Two Primary Maintenance Cycles Link to heading The Breville Ba
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
+<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/2b2203c">[2b2203c]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>

posts/espresso-theory-application-a-guide-for-the-breville-barista-pro/index.html

@@ -20,4 +20,4 @@ Our overarching philosophy is simple: isolate and change only one variable at a
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
+<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/2b2203c">[2b2203c]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>

posts/how-rvq-teaches-llms-to-see-and-hear/index.html

@@ -18,4 +18,4 @@ The answer lies in creating a universal language—a bridge between the continuo
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
+<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/2b2203c">[2b2203c]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>

posts/index.html

@@ -14,4 +14,4 @@
 2016 -
 2025
 Eric X. Liu
-<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/7cd5bd6">[7cd5bd6]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>
+<a href="https://git.ericxliu.me/eric/ericxliu-me/commit/2b2203c">[2b2203c]</a></section></footer></main><script src=/js/coder.min.6ae284be93d2d19dad1f02b0039508d9aab3180a12a06dcc71b0b0ef7825a317.js integrity="sha256-auKEvpPS0Z2tHwKwA5UI2aqzGAoSoG3McbCw73gloxc="></script><script defer src=https://static.cloudflareinsights.com/beacon.min.js data-cf-beacon='{"token": "987638e636ce4dbb932d038af74c17d1"}'></script></body></html>

posts/index.xml

@@ -1,4 +1,4 @@
-<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Posts on Eric X. Liu's Personal Page</title><link>/posts/</link><description>Recent content in Posts on Eric X. Liu's Personal Page</description><generator>Hugo</generator><language>en</language><lastBuildDate>Tue, 23 Sep 2025 06:14:45 +0000</lastBuildDate><atom:link href="/posts/index.xml" rel="self" type="application/rss+xml"/><item><title>UniFi VLAN Migration to Zone-Based Architecture</title><link>/posts/unifi-vlan-migration-to-zone-based-architecture/</link><pubDate>Mon, 22 Sep 2025 00:00:00 +0000</pubDate><guid>/posts/unifi-vlan-migration-to-zone-based-architecture/</guid><description>&lt;p&gt;Embarking on a network migration to a properly segmented VLAN architecture is a rite of passage for any serious home lab or small business operator. The goal is clear: improve security and organization by separating traffic. However, the path from a flat network to a segmented one is often paved with subtle but critical configuration details that can lead to hours of frustrating troubleshooting.&lt;/p&gt;
+<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Posts on Eric X. Liu's Personal Page</title><link>/posts/</link><description>Recent content in Posts on Eric X. Liu's Personal Page</description><generator>Hugo</generator><language>en</language><lastBuildDate>Tue, 23 Sep 2025 06:20:36 +0000</lastBuildDate><atom:link href="/posts/index.xml" rel="self" type="application/rss+xml"/><item><title>UniFi VLAN Migration to Zone-Based Architecture</title><link>/posts/unifi-vlan-migration-to-zone-based-architecture/</link><pubDate>Mon, 22 Sep 2025 00:00:00 +0000</pubDate><guid>/posts/unifi-vlan-migration-to-zone-based-architecture/</guid><description>&lt;p&gt;Embarking on a network migration to a properly segmented VLAN architecture is a rite of passage for any serious home lab or small business operator. The goal is clear: improve security and organization by separating traffic. However, the path from a flat network to a segmented one is often paved with subtle but critical configuration details that can lead to hours of frustrating troubleshooting.&lt;/p&gt;
 &lt;p&gt;This article documents that journey. It details the pitfalls encountered, the core networking concepts that were essential to understand, and the best practices that ultimately led to a stable, secure, and logical network design built on a zone-based firewall model.&lt;/p&gt;</description></item><item><title>Quantization in LLMs</title><link>/posts/quantization-in-llms/</link><pubDate>Tue, 19 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/quantization-in-llms/</guid><description>&lt;p&gt;The burgeoning scale of Large Language Models (LLMs) has necessitated a paradigm shift in their deployment, moving beyond full-precision floating-point arithmetic towards lower-precision representations. Quantization, the process of mapping a wide range of continuous values to a smaller, discrete set, has emerged as a critical technique to reduce model size, accelerate inference, and lower energy consumption. This article provides a technical overview of quantization theories, their application in modern LLMs, and highlights the ongoing innovations in this domain.&lt;/p&gt;</description></item><item><title>Breville Barista Pro Maintenance</title><link>/posts/breville-barista-pro-maintenance/</link><pubDate>Sat, 16 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/breville-barista-pro-maintenance/</guid><description>&lt;p&gt;Proper maintenance is critical for the longevity and performance of a Breville Barista Pro espresso machine. Consistent cleaning not only ensures the machine functions correctly but also directly impacts the quality of the espresso produced. This guide provides a detailed, technical breakdown of the essential maintenance routines, from automated cycles to daily upkeep.&lt;/p&gt;
 &lt;h4 id="understanding-the-two-primary-maintenance-cycles"&gt;
  &lt;strong&gt;Understanding the Two Primary Maintenance Cycles&lt;/strong&gt;
@@ -15,7 +15,8 @@
 &lt;p&gt;That message is the tell: Secure Boot is enabled and the kernel refuses to load modules not signed by a trusted key.&lt;/p&gt;</description></item><item><title>Beyond Words: How RVQ Teaches LLMs to See and Hear</title><link>/posts/how-rvq-teaches-llms-to-see-and-hear/</link><pubDate>Thu, 07 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/how-rvq-teaches-llms-to-see-and-hear/</guid><description>&lt;p&gt;Large Language Models (LLMs) are masters of text, but the world is not made of text alone. It’s a symphony of sights, sounds, and experiences. The ultimate goal for AI is to understand this rich, multi-modal world as we do. But how do you teach a model that thinks in words to understand a picture of a sunset or the melody of a song?&lt;/p&gt;
 &lt;p&gt;The answer lies in creating a universal language—a bridge between the continuous, messy world of pixels and audio waves and the discrete, structured world of language tokens. One of the most elegant and powerful tools for building this bridge is &lt;strong&gt;Residual Vector Quantization (RVQ)&lt;/strong&gt;.&lt;/p&gt;</description></item><item><title>Supabase Deep Dive: It's Not Magic, It's Just Postgres</title><link>/posts/supabase-deep-dive/</link><pubDate>Sun, 03 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/supabase-deep-dive/</guid><description>&lt;p&gt;In the world of Backend-as-a-Service (BaaS), platforms are often treated as magic boxes. You push data in, you get data out, and you hope the magic inside scales. While this simplicity is powerful, it can obscure the underlying mechanics, leaving developers wondering what&amp;rsquo;s really going on.&lt;/p&gt;
 &lt;p&gt;Supabase enters this space with a radically different philosophy: &lt;strong&gt;transparency&lt;/strong&gt;. It provides the convenience of a BaaS, but it’s built on the world&amp;rsquo;s most trusted relational database: PostgreSQL. The &amp;ldquo;magic&amp;rdquo; isn&amp;rsquo;t a proprietary black box; it&amp;rsquo;s a carefully assembled suite of open-source tools that enhance Postgres, not hide it.&lt;/p&gt;</description></item><item><title>A Deep Dive into PPO for Language Models</title><link>/posts/ppo-for-language-models/</link><pubDate>Sat, 02 Aug 2025 00:00:00 +0000</pubDate><guid>/posts/ppo-for-language-models/</guid><description>&lt;p&gt;Large Language Models (LLMs) have demonstrated astonishing capabilities, but out-of-the-box, they are simply powerful text predictors. They don&amp;rsquo;t inherently understand what makes a response helpful, harmless, or aligned with human values. The technique that has proven most effective at bridging this gap is Reinforcement Learning from Human Feedback (RLHF), and at its heart lies a powerful algorithm: Proximal Policy Optimization (PPO).&lt;/p&gt;
-&lt;p&gt;You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.&lt;/p&gt;</description></item><item><title>Mixture-of-Experts (MoE) Models Challenges &amp; Solutions in Practice</title><link>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</link><pubDate>Wed, 02 Jul 2025 00:00:00 +0000</pubDate><guid>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</guid><description>&lt;p&gt;Mixture-of-Experts (MoEs) are neural network architectures that allow different parts of the model (called &amp;ldquo;experts&amp;rdquo;) to specialize in different types of inputs. A &amp;ldquo;gating network&amp;rdquo; or &amp;ldquo;router&amp;rdquo; learns to dispatch each input (or &amp;ldquo;token&amp;rdquo;) to a subset of these experts. While powerful for scaling models, MoEs introduce several practical challenges.&lt;/p&gt;
+&lt;p&gt;You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.
+&lt;img src="/images/ppo-for-language-models/7713bd3ecf27442e939b9190fa08165d.png" alt="S3 File"&gt;&lt;/p&gt;</description></item><item><title>Mixture-of-Experts (MoE) Models Challenges &amp; Solutions in Practice</title><link>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</link><pubDate>Wed, 02 Jul 2025 00:00:00 +0000</pubDate><guid>/posts/mixture-of-experts-moe-models-challenges-solutions-in-practice/</guid><description>&lt;p&gt;Mixture-of-Experts (MoEs) are neural network architectures that allow different parts of the model (called &amp;ldquo;experts&amp;rdquo;) to specialize in different types of inputs. A &amp;ldquo;gating network&amp;rdquo; or &amp;ldquo;router&amp;rdquo; learns to dispatch each input (or &amp;ldquo;token&amp;rdquo;) to a subset of these experts. While powerful for scaling models, MoEs introduce several practical challenges.&lt;/p&gt;
 &lt;h3 id="1-challenge-non-differentiability-of-routing-functions"&gt;
  1. Challenge: Non-Differentiability of Routing Functions
  &lt;a class="heading-link" href="#1-challenge-non-differentiability-of-routing-functions"&gt;

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 <!doctype html><html lang=en><head><title>A Deep Dive into PPO for Language Models · Eric X. Liu's Personal Page</title><meta charset=utf-8><meta name=viewport content="width=device-width,initial-scale=1"><meta name=color-scheme content="light dark"><meta name=author content="Eric X. Liu"><meta name=description content="Large Language Models (LLMs) have demonstrated astonishing capabilities, but out-of-the-box, they are simply powerful text predictors. They don&rsquo;t inherently understand what makes a response helpful, harmless, or aligned with human values. The technique that has proven most effective at bridging this gap is Reinforcement Learning from Human Feedback (RLHF), and at its heart lies a powerful algorithm: Proximal Policy Optimization (PPO).
-You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows."><meta name=keywords content="software engineer,performance engineering,Google engineer,tech blog,software development,performance optimization,Eric Liu,engineering blog,mountain biking,Jeep enthusiast,overlanding,camping,outdoor adventures"><meta name=twitter:card content="summary"><meta name=twitter:title content="A Deep Dive into PPO for Language Models"><meta name=twitter:description content="Large Language Models (LLMs) have demonstrated astonishing capabilities, but out-of-the-box, they are simply powerful text predictors. They don’t inherently understand what makes a response helpful, harmless, or aligned with human values. The technique that has proven most effective at bridging this gap is Reinforcement Learning from Human Feedback (RLHF), and at its heart lies a powerful algorithm: Proximal Policy Optimization (PPO).
+You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.
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-You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows."><meta property="og:locale" content="en"><meta property="og:type" content="article"><meta property="article:section" content="posts"><meta property="article:published_time" content="2025-08-02T00:00:00+00:00"><meta property="article:modified_time" content="2025-08-20T06:04:36+00:00"><link rel=canonical href=/posts/ppo-for-language-models/><link rel=preload href=/fonts/fa-brands-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-regular-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-solid-900.woff2 as=font type=font/woff2 crossorigin><link rel=stylesheet href=/css/coder.min.c8e4eea149ae1dc7c61ba9b0781793711a4e657f7e07a4413f9abc46d52dffc4.css integrity="sha256-yOTuoUmuHcfGG6mweBeTcRpOZX9+B6RBP5q8RtUt/8Q=" crossorigin=anonymous media=screen><link rel=stylesheet href=/css/coder-dark.min.a00e6364bacbc8266ad1cc81230774a1397198f8cfb7bcba29b7d6fcb54ce57f.css integrity="sha256-oA5jZLrLyCZq0cyBIwd0oTlxmPjPt7y6KbfW/LVM5X8=" crossorigin=anonymous media=screen><link rel=icon type=image/svg+xml href=/images/favicon.svg sizes=any><link rel=icon type=image/png href=/images/favicon-32x32.png sizes=32x32><link rel=icon type=image/png href=/images/favicon-16x16.png sizes=16x16><link rel=apple-touch-icon href=/images/apple-touch-icon.png><link rel=apple-touch-icon sizes=180x180 href=/images/apple-touch-icon.png><link rel=manifest href=/site.webmanifest><link rel=mask-icon href=/images/safari-pinned-tab.svg color=#5bbad5></head><body class="preload-transitions colorscheme-auto"><div class=float-container><a id=dark-mode-toggle class=colorscheme-toggle><i class="fa-solid fa-adjust fa-fw" aria-hidden=true></i></a></div><main class=wrapper><nav class=navigation><section class=container><a class=navigation-title href=/>Eric X. Liu's Personal Page
+You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows."><meta property="og:locale" content="en"><meta property="og:type" content="article"><meta property="article:section" content="posts"><meta property="article:published_time" content="2025-08-02T00:00:00+00:00"><meta property="article:modified_time" content="2025-09-23T06:20:36+00:00"><link rel=canonical href=/posts/ppo-for-language-models/><link rel=preload href=/fonts/fa-brands-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-regular-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-solid-900.woff2 as=font type=font/woff2 crossorigin><link rel=stylesheet href=/css/coder.min.c8e4eea149ae1dc7c61ba9b0781793711a4e657f7e07a4413f9abc46d52dffc4.css integrity="sha256-yOTuoUmuHcfGG6mweBeTcRpOZX9+B6RBP5q8RtUt/8Q=" crossorigin=anonymous media=screen><link rel=stylesheet href=/css/coder-dark.min.a00e6364bacbc8266ad1cc81230774a1397198f8cfb7bcba29b7d6fcb54ce57f.css integrity="sha256-oA5jZLrLyCZq0cyBIwd0oTlxmPjPt7y6KbfW/LVM5X8=" crossorigin=anonymous media=screen><link rel=icon type=image/svg+xml href=/images/favicon.svg sizes=any><link rel=icon type=image/png href=/images/favicon-32x32.png sizes=32x32><link rel=icon type=image/png href=/images/favicon-16x16.png sizes=16x16><link rel=apple-touch-icon href=/images/apple-touch-icon.png><link rel=apple-touch-icon sizes=180x180 href=/images/apple-touch-icon.png><link rel=manifest href=/site.webmanifest><link rel=mask-icon href=/images/safari-pinned-tab.svg color=#5bbad5></head><body class="preload-transitions colorscheme-auto"><div class=float-container><a id=dark-mode-toggle class=colorscheme-toggle><i class="fa-solid fa-adjust fa-fw" aria-hidden=true></i></a></div><main class=wrapper><nav class=navigation><section class=container><a class=navigation-title href=/>Eric X. Liu's Personal Page
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 <time datetime=2025-08-02T00:00:00Z>August 2, 2025
 </time></span><span class=reading-time><i class="fa-solid fa-clock" aria-hidden=true></i>
-7-minute read</span></div></div></header><div class=post-content><p>Large Language Models (LLMs) have demonstrated astonishing capabilities, but out-of-the-box, they are simply powerful text predictors. They don&rsquo;t inherently understand what makes a response helpful, harmless, or aligned with human values. The technique that has proven most effective at bridging this gap is Reinforcement Learning from Human Feedback (RLHF), and at its heart lies a powerful algorithm: Proximal Policy Optimization (PPO).</p><p>You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.</p><p><img src=/images/ppo-for-language-models/.png alt></p><p>This post will decode that diagram, piece by piece. We&rsquo;ll explore the &ldquo;why&rdquo; behind each component, moving from high-level concepts to the deep technical reasoning that makes this process work.</p><h3 id=translating-rl-to-a-conversation>Translating RL to a Conversation
+7-minute read</span></div></div></header><div class=post-content><p>Large Language Models (LLMs) have demonstrated astonishing capabilities, but out-of-the-box, they are simply powerful text predictors. They don&rsquo;t inherently understand what makes a response helpful, harmless, or aligned with human values. The technique that has proven most effective at bridging this gap is Reinforcement Learning from Human Feedback (RLHF), and at its heart lies a powerful algorithm: Proximal Policy Optimization (PPO).</p><p>You may have seen diagrams like the one below, which outlines the RLHF training process. It can look intimidating, with a web of interconnected models, losses, and data flows.
+<img src=/images/ppo-for-language-models/7713bd3ecf27442e939b9190fa08165d.png alt="S3 File"></p><p>This post will decode that diagram, piece by piece. We&rsquo;ll explore the &ldquo;why&rdquo; behind each component, moving from high-level concepts to the deep technical reasoning that makes this process work.</p><h3 id=translating-rl-to-a-conversation>Translating RL to a Conversation
 <a class=heading-link href=#translating-rl-to-a-conversation><i class="fa-solid fa-link" aria-hidden=true title="Link to heading"></i>
 <span class=sr-only>Link to heading</span></a></h3><p>The first step is to understand how the traditional language of reinforcement learning maps to the world of text generation.</p><ul><li><strong>State (<code>s_t</code>)</strong>: In a chat setting, the &ldquo;state&rdquo; is the context of the conversation so far. It&rsquo;s the initial prompt (<code>x</code>) plus all the text the model has generated up to the current moment (<code>y₁, ..., y_{t-1}</code>).</li><li><strong>Action (<code>a_t</code>)</strong>: The &ldquo;action&rdquo; is the model&rsquo;s decision at each step. For an LLM, this means generating the very next token (<code>y_t</code>). A full response is a sequence of these actions.blob:https://aistudio.google.com/872e746f-88c1-40ec-8e45-fa0efce97299</li><li><strong>Reward (<code>r</code>)</strong>: The &ldquo;reward&rdquo; is a numeric score that tells the model how good its full response (<code>y</code>) was. This score comes from a separate <strong>Reward Model</strong>, which has been trained on a large dataset of human preference comparisons (e.g., humans rating which of two responses is better). This reward is often only awarded at the end of the entire generated sequence.</li></ul><p>Let&rsquo;s make this concrete. If a user provides the prompt <strong>(x)</strong>: <em>&ldquo;The best thing about AI is&rdquo;</em>, and the model generates the response <strong>(y)</strong>: <em>&ldquo;its potential to solve problems.&rdquo;</em>, here is how it&rsquo;s broken down for training:</p><ul><li><strong>State 1</strong>: &ldquo;The best thing about AI is&rdquo;<ul><li><strong>Action 1</strong>: &ldquo;its&rdquo;</li></ul></li><li><strong>State 2</strong>: &ldquo;The best thing about AI is its&rdquo;<ul><li><strong>Action 2</strong>: " potential"</li></ul></li><li><strong>State 3</strong>: &ldquo;The best thing about AI is its potential&rdquo;<ul><li><strong>Action 3</strong>: " to"</li></ul></li><li>&mldr;and so on for every generated token.</li></ul><p>This breakdown transforms a single prompt-response pair into a rich trajectory of state-action pairs, which becomes the raw data for our learning algorithm.</p><h3 id=the-cast-of-models-an-actor-critic-ensemble>The Cast of Models: An Actor-Critic Ensemble
 <a class=heading-link href=#the-cast-of-models-an-actor-critic-ensemble><i class="fa-solid fa-link" aria-hidden=true title="Link to heading"></i>
@@ -23,4 +25,4 @@ where <code>δ_t = r_t + γV(s_{t+1}) - V(s_t)</code></p><ul><li><strong>γ (gam
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@@ -30,4 +30,4 @@ But to truly understand the field, we must look at the pivotal models that explo
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posts/transformer-s-core-mechanics/index.html

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 In deep learning, a &ldquo;channel&rdquo; can be thought of as a feature dimension. While this term is common in Convolutional Neural Networks for images (e.g., Red, Green, Blue channels), in LLMs, the analogous concept is the model&rsquo;s primary embedding dimension, commonly referred to as d_model."><meta name=keywords content="software engineer,performance engineering,Google engineer,tech blog,software development,performance optimization,Eric Liu,engineering blog,mountain biking,Jeep enthusiast,overlanding,camping,outdoor adventures"><meta name=twitter:card content="summary"><meta name=twitter:title content="Transformer's Core Mechanics"><meta name=twitter:description content="The Transformer architecture is the bedrock of modern Large Language Models (LLMs). While its high-level success is widely known, a deeper understanding requires dissecting its core components. This article provides a detailed, technical breakdown of the fundamental concepts within a Transformer block, from the notion of “channels” to the intricate workings of the attention mechanism and its relationship with other advanced architectures like Mixture of Experts.
 1. The “Channel”: A Foundational View of d_model Link to heading In deep learning, a “channel” can be thought of as a feature dimension. While this term is common in Convolutional Neural Networks for images (e.g., Red, Green, Blue channels), in LLMs, the analogous concept is the model’s primary embedding dimension, commonly referred to as d_model."><meta property="og:url" content="/posts/transformer-s-core-mechanics/"><meta property="og:site_name" content="Eric X. Liu's Personal Page"><meta property="og:title" content="Transformer's Core Mechanics"><meta property="og:description" content="The Transformer architecture is the bedrock of modern Large Language Models (LLMs). While its high-level success is widely known, a deeper understanding requires dissecting its core components. This article provides a detailed, technical breakdown of the fundamental concepts within a Transformer block, from the notion of “channels” to the intricate workings of the attention mechanism and its relationship with other advanced architectures like Mixture of Experts.
-1. The “Channel”: A Foundational View of d_model Link to heading In deep learning, a “channel” can be thought of as a feature dimension. While this term is common in Convolutional Neural Networks for images (e.g., Red, Green, Blue channels), in LLMs, the analogous concept is the model’s primary embedding dimension, commonly referred to as d_model."><meta property="og:locale" content="en"><meta property="og:type" content="article"><meta property="article:section" content="posts"><meta property="article:published_time" content="2025-04-01T00:00:00+00:00"><meta property="article:modified_time" content="2025-08-20T06:28:39+00:00"><link rel=canonical href=/posts/transformer-s-core-mechanics/><link rel=preload href=/fonts/fa-brands-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-regular-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-solid-900.woff2 as=font type=font/woff2 crossorigin><link rel=stylesheet href=/css/coder.min.c8e4eea149ae1dc7c61ba9b0781793711a4e657f7e07a4413f9abc46d52dffc4.css integrity="sha256-yOTuoUmuHcfGG6mweBeTcRpOZX9+B6RBP5q8RtUt/8Q=" crossorigin=anonymous media=screen><link rel=stylesheet href=/css/coder-dark.min.a00e6364bacbc8266ad1cc81230774a1397198f8cfb7bcba29b7d6fcb54ce57f.css integrity="sha256-oA5jZLrLyCZq0cyBIwd0oTlxmPjPt7y6KbfW/LVM5X8=" crossorigin=anonymous media=screen><link rel=icon type=image/svg+xml href=/images/favicon.svg sizes=any><link rel=icon type=image/png href=/images/favicon-32x32.png sizes=32x32><link rel=icon type=image/png href=/images/favicon-16x16.png sizes=16x16><link rel=apple-touch-icon href=/images/apple-touch-icon.png><link rel=apple-touch-icon sizes=180x180 href=/images/apple-touch-icon.png><link rel=manifest href=/site.webmanifest><link rel=mask-icon href=/images/safari-pinned-tab.svg color=#5bbad5></head><body class="preload-transitions colorscheme-auto"><div class=float-container><a id=dark-mode-toggle class=colorscheme-toggle><i class="fa-solid fa-adjust fa-fw" aria-hidden=true></i></a></div><main class=wrapper><nav class=navigation><section class=container><a class=navigation-title href=/>Eric X. Liu's Personal Page
+1. The “Channel”: A Foundational View of d_model Link to heading In deep learning, a “channel” can be thought of as a feature dimension. While this term is common in Convolutional Neural Networks for images (e.g., Red, Green, Blue channels), in LLMs, the analogous concept is the model’s primary embedding dimension, commonly referred to as d_model."><meta property="og:locale" content="en"><meta property="og:type" content="article"><meta property="article:section" content="posts"><meta property="article:published_time" content="2025-04-01T00:00:00+00:00"><meta property="article:modified_time" content="2025-09-23T06:20:36+00:00"><link rel=canonical href=/posts/transformer-s-core-mechanics/><link rel=preload href=/fonts/fa-brands-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-regular-400.woff2 as=font type=font/woff2 crossorigin><link rel=preload href=/fonts/fa-solid-900.woff2 as=font type=font/woff2 crossorigin><link rel=stylesheet href=/css/coder.min.c8e4eea149ae1dc7c61ba9b0781793711a4e657f7e07a4413f9abc46d52dffc4.css integrity="sha256-yOTuoUmuHcfGG6mweBeTcRpOZX9+B6RBP5q8RtUt/8Q=" crossorigin=anonymous media=screen><link rel=stylesheet href=/css/coder-dark.min.a00e6364bacbc8266ad1cc81230774a1397198f8cfb7bcba29b7d6fcb54ce57f.css integrity="sha256-oA5jZLrLyCZq0cyBIwd0oTlxmPjPt7y6KbfW/LVM5X8=" crossorigin=anonymous media=screen><link rel=icon type=image/svg+xml href=/images/favicon.svg sizes=any><link rel=icon type=image/png href=/images/favicon-32x32.png sizes=32x32><link rel=icon type=image/png href=/images/favicon-16x16.png sizes=16x16><link rel=apple-touch-icon href=/images/apple-touch-icon.png><link rel=apple-touch-icon sizes=180x180 href=/images/apple-touch-icon.png><link rel=manifest href=/site.webmanifest><link rel=mask-icon href=/images/safari-pinned-tab.svg color=#5bbad5></head><body class="preload-transitions colorscheme-auto"><div class=float-container><a id=dark-mode-toggle class=colorscheme-toggle><i class="fa-solid fa-adjust fa-fw" aria-hidden=true></i></a></div><main class=wrapper><nav class=navigation><section class=container><a class=navigation-title href=/>Eric X. Liu's Personal Page
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 <label class="menu-button float-right" for=menu-toggle><i class="fa-solid fa-bars fa-fw" aria-hidden=true></i></label><ul class=navigation-list><li class=navigation-item><a class=navigation-link href=/posts/>Posts</a></li><li class=navigation-item><a class=navigation-link href=https://chat.ericxliu.me>Chat</a></li><li class=navigation-item><a class=navigation-link href=https://git.ericxliu.me/user/oauth2/Authenitk>Git</a></li><li class=navigation-item><a class=navigation-link href=https://coder.ericxliu.me/api/v2/users/oidc/callback>Coder</a></li><li class=navigation-item><a class=navigation-link href=/>|</a></li><li class=navigation-item><a class=navigation-link href=https://sso.ericxliu.me>Sign in</a></li></ul></section></nav><div class=content><section class="container post"><article><header><div class=post-title><h1 class=title><a class=title-link href=/posts/transformer-s-core-mechanics/>Transformer's Core Mechanics</a></h1></div><div class=post-meta><div class=date><span class=posted-on><i class="fa-solid fa-calendar" aria-hidden=true></i>
 <time datetime=2025-04-01T00:00:00Z>April 1, 2025
@@ -20,7 +20,7 @@ In deep learning, a &ldquo;channel&rdquo; can be thought of as a feature dimensi
 <span class=sr-only>Link to heading</span></a></h3><p>A Transformer layer is primarily composed of two sub-layers: a Multi-Head Attention block and a position-wise Feed-Forward Network (FFN). The parameters for these are stored in several key weight matrices. Understanding their dimensions is crucial.</p><p>Let&rsquo;s define our variables:</p><ul><li><code>d_model</code>: The core embedding dimension.</li><li><code>d_ff</code>: The inner dimension of the FFN, typically <code>4 * d_model</code>.</li><li><code>h</code>: The number of attention heads.</li><li><code>d_head</code>: The dimension of each attention head, where <code>d_model = h * d_head</code>.</li></ul><p>The dimensions of the weight matrices are as follows:</p><table><thead><tr><th>Layer</th><th>Weight Matrix</th><th>Input Vector Shape</th><th>Output Vector Shape</th><th><strong>Weight Matrix Dimension</strong></th></tr></thead><tbody><tr><td><strong>Attention Projections</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Query</td><td><code>W_Q</code></td><td><code>d_model</code></td><td><code>d_model</code></td><td><strong><code>[d_model, d_model]</code></strong></td></tr><tr><td>Key</td><td><code>W_K</code></td><td><code>d_model</code></td><td><code>d_model</code></td><td><strong><code>[d_model, d_model]</code></strong></td></tr><tr><td>Value</td><td><code>W_V</code></td><td><code>d_model</code></td><td><code>d_model</code></td><td><strong><code>[d_model, d_model]</code></strong></td></tr><tr><td>Output</td><td><code>W_O</code></td><td><code>d_model</code></td><td><code>d_model</code></td><td><strong><code>[d_model, d_model]</code></strong></td></tr><tr><td><strong>Feed-Forward Network</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Layer 1 (Up-projection)</td><td><code>W_ff1</code></td><td><code>d_model</code></td><td><code>d_ff</code></td><td><strong><code>[d_model, d_ff]</code></strong></td></tr><tr><td>Layer 2 (Down-projection)</td><td><code>W_ff2</code></td><td><code>d_ff</code></td><td><code>d_model</code></td><td><strong><code>[d_ff, d_model]</code></strong></td></tr></tbody></table><h3 id=3-deconstructing-multi-head-attention-mha>3. Deconstructing Multi-Head Attention (MHA)
 <a class=heading-link href=#3-deconstructing-multi-head-attention-mha><i class="fa-solid fa-link" aria-hidden=true title="Link to heading"></i>
 <span class=sr-only>Link to heading</span></a></h3><p>The core innovation of the Transformer is Multi-Head Attention. It allows the model to weigh the importance of different tokens in the sequence from multiple perspectives simultaneously.
-<img src=/images/transformer-s-core-mechanics/.png alt></p><h4 id=31-the-why-beyond-a-single-attention>3.1. The &ldquo;Why&rdquo;: Beyond a Single Attention
+<img src=/images/transformer-s-core-mechanics/c7fe4af2633840cfbc81d7c4e3e42d0c.png alt="S3 File"></p><h4 id=31-the-why-beyond-a-single-attention>3.1. The &ldquo;Why&rdquo;: Beyond a Single Attention
 <a class=heading-link href=#31-the-why-beyond-a-single-attention><i class="fa-solid fa-link" aria-hidden=true title="Link to heading"></i>
 <span class=sr-only>Link to heading</span></a></h4><p>A single attention mechanism would force the model to average all types of linguistic relationships into one pattern. MHA avoids this by creating <code>h</code> parallel subspaces. Each &ldquo;head&rdquo; can specialize, with one head learning syntactic dependencies, another tracking semantic similarity, and so on. This creates a much richer representation.</p><h4 id=32-an-encodingdecoding-analogy>3.2. An Encoding/Decoding Analogy
 <a class=heading-link href=#32-an-encodingdecoding-analogy><i class="fa-solid fa-link" aria-hidden=true title="Link to heading"></i>
@@ -36,4 +36,4 @@ In deep learning, a &ldquo;channel&rdquo; can be thought of as a feature dimensi
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posts/unifi-vlan-migration-to-zone-based-architecture/index.html

@@ -28,4 +28,4 @@ This article documents that journey. It details the pitfalls encountered, the co
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posts/useful/index.html

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