From ee3c172514f235609ee7b1507d83942f7335aa63 Mon Sep 17 00:00:00 2001
From: souzatharsis <souzatharsis@gmail.com>
Date: Mon, 16 Dec 2024 12:11:11 -0300
Subject: [PATCH] fix math blocks

---
 .../_build/.doctrees/environment.pickle       | Bin 4162293 -> 4171337 bytes
 .../_build/.doctrees/markdown/intro.doctree   | Bin 47874 -> 48447 bytes
 .../_build/.doctrees/markdown/preface.doctree | Bin 18511 -> 18547 bytes
 .../_build/.doctrees/markdown/toc.doctree     | Bin 13874 -> 13910 bytes
 .../.doctrees/notebooks/alignment.doctree     | Bin 331125 -> 331298 bytes
 .../_build/.doctrees/notebooks/evals.doctree  | Bin 850743 -> 850779 bytes
 .../notebooks/output_size_limit.doctree       | Bin 90627 -> 90663 bytes
 .../_build/.doctrees/notebooks/safety.doctree | Bin 183787 -> 184709 bytes
 .../notebooks/structured_output.doctree       | Bin 163694 -> 165384 bytes
 .../html/_sources/notebooks/alignment.ipynb   |   4 +-
 tamingllms/_build/html/markdown/intro.html    |   6 +--
 tamingllms/_build/html/markdown/preface.html  |   2 +-
 tamingllms/_build/html/markdown/toc.html      |   2 +-
 .../_build/html/notebooks/alignment.html      |  13 +++---
 tamingllms/_build/html/notebooks/evals.html   |   2 +-
 .../html/notebooks/output_size_limit.html     |   2 +-
 tamingllms/_build/html/notebooks/safety.html  |  10 ++---
 .../html/notebooks/structured_output.html     |  39 ++++++++++--------
 tamingllms/_build/html/searchindex.js         |   2 +-
 .../jupyter_execute/markdown/intro.ipynb      |   2 +-
 .../jupyter_execute/notebooks/alignment.ipynb |   4 +-
 tamingllms/_config.yml                        |   8 ++--
 tamingllms/notebooks/alignment.ipynb          |   4 +-
 23 files changed, 52 insertions(+), 48 deletions(-)

diff --git a/tamingllms/_build/.doctrees/environment.pickle b/tamingllms/_build/.doctrees/environment.pickle
index 8527e3a6cbc97a13427d29adc4bd388786ecaed3..ba61b5768f26d9d309cd36c0e2a1298fdf8e560a 100644
GIT binary patch
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diff --git a/tamingllms/_build/.doctrees/markdown/preface.doctree b/tamingllms/_build/.doctrees/markdown/preface.doctree
index b9d4c1bd3e22efd48bc1aa719a05b9909886cfa8..621f56cdb52d96221cecd98036a02a8cb2f08e42 100644
GIT binary patch
delta 3078
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diff --git a/tamingllms/_build/.doctrees/markdown/toc.doctree b/tamingllms/_build/.doctrees/markdown/toc.doctree
index 78af37b5adf8ad8d76b0a14c9ad04f9166993645..4f4a24086df60421a82a57e640fc62dda543904b 100644
GIT binary patch
delta 151
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delta 85
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diff --git a/tamingllms/_build/.doctrees/notebooks/alignment.doctree b/tamingllms/_build/.doctrees/notebooks/alignment.doctree
index 423fb7aae6b4094f7195d177ed01f57b344a31ba..3f1b2765e98e30147cfa24e958730343c970f1be 100644
GIT binary patch
delta 31274
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diff --git a/tamingllms/_build/.doctrees/notebooks/evals.doctree b/tamingllms/_build/.doctrees/notebooks/evals.doctree
index 7dd38bb0ed29bed1967faffc2553681da220d0ba..87acc5a1158a18f67f646b933f3c9b1ede7f9554 100644
GIT binary patch
delta 3411
zcmZwJe@IhN7{+nWoIlEgsYJ{)$&d(<&~3UI5fKFy6%-MbhACRQtU#<JA`EUJI-)?i
z5fv5@76lp7$_g|hA}T6oMM}63l9bdmQ>ke8sC#tJ{NoDy?(Aisy=>PrYU>=eRck^s
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delta 3396
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diff --git a/tamingllms/_build/.doctrees/notebooks/output_size_limit.doctree b/tamingllms/_build/.doctrees/notebooks/output_size_limit.doctree
index 618cb6055b8d5c4c1b4e69873b3c3239d08b2444..a49406ede417ad5424615c58be99b7592bd4e68f 100644
GIT binary patch
delta 3373
zcmZwJe`w5c9LMp!zjH}uKZv`vA+hWS<+j~!*W$KGBWiRM>DrE6+b!GLOeViu@`sbu
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delta 3355
zcmZwJVQ7s}9LMqf&s;KLo8~TeEM<w&cDLQT-PXEWELK}uBQ34Ww%BG{o83kTEiYu!
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diff --git a/tamingllms/_build/.doctrees/notebooks/safety.doctree b/tamingllms/_build/.doctrees/notebooks/safety.doctree
index d343b784db52df7c77d39e28c2996f3c69324635..b0307184211568ee89ed5d4b91e20ab686036a24 100644
GIT binary patch
delta 4730
zcmZ|RZBSHI9LI6aUr-ppd<qDJ@nL~o5oBRSKrM%2R7lLmN*zkqfxK+u1A-wV4JwlB
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tLeZ*Op=fnLp=i~uP_#O&P_%kaR{WQnE*i>K_U3#>xx{Ys$}i}}{{Y!jiCzEz

delta 4345
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diff --git a/tamingllms/_build/.doctrees/notebooks/structured_output.doctree b/tamingllms/_build/.doctrees/notebooks/structured_output.doctree
index 951501e75246fb67bf16da457fd72099c7c2e461..1d9f1e53727f3fe1e94b6479452d770f5cd0c881 100644
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diff --git a/tamingllms/_build/html/_sources/notebooks/alignment.ipynb b/tamingllms/_build/html/_sources/notebooks/alignment.ipynb
index e88d7fb..2eacf14 100644
--- a/tamingllms/_build/html/_sources/notebooks/alignment.ipynb
+++ b/tamingllms/_build/html/_sources/notebooks/alignment.ipynb
@@ -256,9 +256,9 @@
     "\n",
     "At a high-level DPO maximizes the probability of preferred output and minimize rejected output as defined in the following equation:\n",
     "\n",
-    "\\begin{gather*}\n",
+    "```{math}\n",
     "\\mathcal{L}_{\\text{DPO}}(\\pi_\\theta; \\pi_\\text{ref}) = -\\mathbb{E}_{(x,y_w,y_l) \\sim \\mathcal{D}} \\left[\\log \\sigma \\left(\\beta \\underbrace{\\log \\frac{\\pi_\\theta(y_w | x)}{\\pi_\\text{ref}(y_w | x)}}_{\\color{green}\\text{preferred}} - \\beta \\underbrace{\\log \\frac{\\pi_\\theta(y_l | x)}{\\pi_\\text{ref}(y_l | x)}}_{\\color{red}\\text{rejected}}\\right)\\right]\n",
-    "\\end{gather*}\n",
+    "```\n",
     "\n",
     "This approach is more straightforward than PPO, as it avoids the need for a reward model and instead uses a direct comparison of model outputs against human preferences.\n",
     "\n",
diff --git a/tamingllms/_build/html/markdown/intro.html b/tamingllms/_build/html/markdown/intro.html
index becb25d..b1829c9 100644
--- a/tamingllms/_build/html/markdown/intro.html
+++ b/tamingllms/_build/html/markdown/intro.html
@@ -226,7 +226,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="introduction">
+  <section class="tex2jax_ignore mathjax_ignore" id="introduction">
 <span id="intro"></span><h1><a class="toc-backref" href="#id1" role="doc-backlink"><span class="section-number">2. </span>Introduction</a><a class="headerlink" href="#introduction" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>I am always doing that which I cannot do, in order that I may learn how to do it.</p>
@@ -304,7 +304,7 @@ <h2><a class="toc-backref" href="#id5" role="doc-backlink"><span class="section-
 <li><p>Share their own experiences and solutions with the community</p></li>
 <li><p>Propose new chapters or sections that address emerging challenges</p></li>
 </ul>
-<p>The repository can be found at https://github.com/souzatharsis/tamingllms. Whether you’ve found a typo, have a better solution to share, or want to contribute an entirely new section, your contributions are welcome.</p>
+<p>The repository can be found at <a class="reference external" href="https://github.com/souzatharsis/tamingllms">https://github.com/souzatharsis/tamingllms</a>. Whether you’ve found a typo, have a better solution to share, or want to contribute an entirely new section, your contributions are welcome.</p>
 </section>
 <section id="a-note-on-perspective">
 <h2><a class="toc-backref" href="#id6" role="doc-backlink"><span class="section-number">2.5. </span>A Note on Perspective</a><a class="headerlink" href="#a-note-on-perspective" title="Permalink to this heading">¶</a></h2>
@@ -416,7 +416,7 @@ <h3><a class="toc-backref" href="#id14" role="doc-backlink"><span class="section
 <h2><a class="toc-backref" href="#id15" role="doc-backlink"><span class="section-number">2.10. </span>About the Author(s)</a><a class="headerlink" href="#about-the-author-s" title="Permalink to this heading">¶</a></h2>
 <p>Dr. Tharsis Souza is a computer scientist and product leader specializing in AI-based products. He is a Lecturer at Columbia University’s Master of Science program in Applied Analytics, (<em>incoming</em>) Head of Product, Equities at Citadel, and former Senior VP at Two Sigma Investments. He also enjoys mentoring under-represented students &amp; working professionals to help create a more diverse global AI ecosystem.</p>
 <p>With over 15 years of experience delivering technology products across startups and Fortune 500 companies, Dr. Souza is also an author of numerous scholarly publications and is a frequent speaker at academic and business conferences. Grounded on academic background and drawing from practical experience building and scaling up products powered by language models at early-stage startups, major institutions as well as advising non-profit organizations, and contributing to open source projects, he brings a unique perspective on bridging the gap between LLMs promised potential and their practical implementation challenges to enable the next generation of AI-powered products.</p>
-<p>Dr. Tharsis holds a Ph.D. in Computer Science from UCL, University of London following an M.Phil. and M.Sc. in Computer Science and a B.Sc. in Computer Engineering.</p>
+<p>Dr. Tharsis holds a Ph.D. in Computer Science from UCL, University of London following an M.Phil. and <a class="reference external" href="http://M.Sc">M.Sc</a>. in Computer Science and a <a class="reference external" href="http://B.Sc">B.Sc</a>. in Computer Engineering.</p>
 </section>
 </section>
 
diff --git a/tamingllms/_build/html/markdown/preface.html b/tamingllms/_build/html/markdown/preface.html
index beb77f3..d584c01 100644
--- a/tamingllms/_build/html/markdown/preface.html
+++ b/tamingllms/_build/html/markdown/preface.html
@@ -208,7 +208,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="preface">
+  <section class="tex2jax_ignore mathjax_ignore" id="preface">
 <h1><span class="section-number">1. </span>Preface<a class="headerlink" href="#preface" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>Models tell you merely what something is like, not what something is.</p>
diff --git a/tamingllms/_build/html/markdown/toc.html b/tamingllms/_build/html/markdown/toc.html
index 9555fbd..d3e9d48 100644
--- a/tamingllms/_build/html/markdown/toc.html
+++ b/tamingllms/_build/html/markdown/toc.html
@@ -198,7 +198,7 @@
           <div class="content" role="main" v-pre>
             
   <p>Sign-up to receive updates on <a class="reference external" href="https://tamingllm.substack.com/">new Chapters here</a>.</p>
-<section id="taming-llms">
+<section class="tex2jax_ignore mathjax_ignore" id="taming-llms">
 <h1>Taming LLMs<a class="headerlink" href="#taming-llms" title="Permalink to this heading">¶</a></h1>
 <section id="a-practical-guide-to-llm-pitfalls-with-open-source-software">
 <h2><em>A Practical Guide to LLM Pitfalls with Open Source Software</em><a class="headerlink" href="#a-practical-guide-to-llm-pitfalls-with-open-source-software" title="Permalink to this heading">¶</a></h2>
diff --git a/tamingllms/_build/html/notebooks/alignment.html b/tamingllms/_build/html/notebooks/alignment.html
index 8698f18..c23f813 100644
--- a/tamingllms/_build/html/notebooks/alignment.html
+++ b/tamingllms/_build/html/notebooks/alignment.html
@@ -29,7 +29,8 @@
         <script src="../_static/design-tabs.js"></script>
         <script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"; const thebe_selector = ".thebe,.cell"; const thebe_selector_input = "pre"; const thebe_selector_output = ".output, .cell_output"</script>
         <script async="async" src="../_static/sphinx-thebe.js"></script>
-        <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+        <script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+        <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
         <script type="module" src="https://cdn.jsdelivr.net/npm/mermaid@11.2.0/dist/mermaid.esm.min.mjs"></script>
         <script type="module" src="https://cdn.jsdelivr.net/npm/@mermaid-js/layout-elk@0.1.4/dist/mermaid-layout-elk.esm.min.mjs"></script>
         <script type="module">import mermaid from "https://cdn.jsdelivr.net/npm/mermaid@11.2.0/dist/mermaid.esm.min.mjs";import elkLayouts from "https://cdn.jsdelivr.net/npm/@mermaid-js/layout-elk@0.1.4/dist/mermaid-layout-elk.esm.min.mjs";mermaid.registerLayoutLoaders(elkLayouts);mermaid.initialize({startOnLoad:false});</script>
@@ -220,7 +221,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="preference-based-alignment">
+  <section class="tex2jax_ignore mathjax_ignore" id="preference-based-alignment">
 <h1><a class="toc-backref" href="#id159" role="doc-backlink"><span class="section-number">7. </span>Preference-Based Alignment</a><a class="headerlink" href="#preference-based-alignment" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>A people that values its privileges above its principles soon loses both.</p>
@@ -449,10 +450,8 @@ <h4><a class="toc-backref" href="#id165" role="doc-backlink"><span class="sectio
 <li><p>Minimizing the KL divergence between the original and fine-tuned model to preserve general capabilities</p></li>
 </ol>
 <p>At a high-level DPO maximizes the probability of preferred output and minimize rejected output as defined in the following equation:</p>
-<div class="amsmath math notranslate nohighlight">
-\[\begin{gather*}
-\mathcal{L}_{\text{DPO}}(\pi_\theta; \pi_\text{ref}) = -\mathbb{E}_{(x,y_w,y_l) \sim \mathcal{D}} \left[\log \sigma \left(\beta \underbrace{\log \frac{\pi_\theta(y_w | x)}{\pi_\text{ref}(y_w | x)}}_{\color{green}\text{preferred}} - \beta \underbrace{\log \frac{\pi_\theta(y_l | x)}{\pi_\text{ref}(y_l | x)}}_{\color{red}\text{rejected}}\right)\right]
-\end{gather*}\]</div>
+<div class="math notranslate nohighlight">
+\[\mathcal{L}_{\text{DPO}}(\pi_\theta; \pi_\text{ref}) = -\mathbb{E}_{(x,y_w,y_l) \sim \mathcal{D}} \left[\log \sigma \left(\beta \underbrace{\log \frac{\pi_\theta(y_w | x)}{\pi_\text{ref}(y_w | x)}}_{\color{green}\text{preferred}} - \beta \underbrace{\log \frac{\pi_\theta(y_l | x)}{\pi_\text{ref}(y_l | x)}}_{\color{red}\text{rejected}}\right)\right]\]</div>
 <p>This approach is more straightforward than PPO, as it avoids the need for a reward model and instead uses a direct comparison of model outputs against human preferences.</p>
 <p>Modern libraries such as HuggingFace’s TRL <span id="id21">[<a class="reference internal" href="#id128" title="Hugging Face. Trl. 2024d. TRL. URL: https://huggingface.co/docs/trl/en/index.">Face, 2024d</a>]</span> offer a suite of techniques for fine-tuning language models with reinforcement learning, including PPO, and DPO. It provides a user-friendly interface and a wide range of features for fine-tuning and aligning LLMs, which will be the focus of the next section as we go through a case study.</p>
 </section>
@@ -872,7 +871,7 @@ <h4><a class="toc-backref" href="#id174" role="doc-backlink"><span class="sectio
 </div>
 <p>Recall our base model is <code class="docutils literal notranslate"><span class="pre">HuggingFaceTB/SmolLM2-360M-Instruct</span></code>. Here, we will use the HuggingFace Inference API to generate rejected responses from a cloud endpoint for enhanced performance:</p>
 <ol class="arabic simple">
-<li><p>Visit the HuggingFace Endpoints UI: https://ui.endpoints.huggingface.co/</p></li>
+<li><p>Visit the HuggingFace Endpoints UI: <a class="reference external" href="https://ui.endpoints.huggingface.co/">https://ui.endpoints.huggingface.co/</a></p></li>
 <li><p>Click “New Endpoint” and select the model <code class="docutils literal notranslate"><span class="pre">HuggingFaceTB/SmolLM2-360M-Instruct</span></code></p></li>
 <li><p>Choose the compute resources (e.g., CPU or GPU instance, GPU preferred)</p></li>
 <li><p>Configure the endpoint settings:</p>
diff --git a/tamingllms/_build/html/notebooks/evals.html b/tamingllms/_build/html/notebooks/evals.html
index 33011ee..7ea3c79 100644
--- a/tamingllms/_build/html/notebooks/evals.html
+++ b/tamingllms/_build/html/notebooks/evals.html
@@ -228,7 +228,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="the-evals-gap">
+  <section class="tex2jax_ignore mathjax_ignore" id="the-evals-gap">
 <h1><a class="toc-backref" href="#id153" role="doc-backlink"><span class="section-number">5. </span>The Evals Gap</a><a class="headerlink" href="#the-evals-gap" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>It doesn’t matter how beautiful your theory is, <br>
diff --git a/tamingllms/_build/html/notebooks/output_size_limit.html b/tamingllms/_build/html/notebooks/output_size_limit.html
index bac7fb7..0aa7a05 100644
--- a/tamingllms/_build/html/notebooks/output_size_limit.html
+++ b/tamingllms/_build/html/notebooks/output_size_limit.html
@@ -220,7 +220,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="output-size-limitations">
+  <section class="tex2jax_ignore mathjax_ignore" id="output-size-limitations">
 <h1><a class="toc-backref" href="#id118" role="doc-backlink"><span class="section-number">3. </span>Output Size Limitations</a><a class="headerlink" href="#output-size-limitations" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>Only those who will risk going too far can possibly find out how far one can go.</p>
diff --git a/tamingllms/_build/html/notebooks/safety.html b/tamingllms/_build/html/notebooks/safety.html
index 86c6441..98b8139 100644
--- a/tamingllms/_build/html/notebooks/safety.html
+++ b/tamingllms/_build/html/notebooks/safety.html
@@ -220,7 +220,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="safety">
+  <section class="tex2jax_ignore mathjax_ignore" id="safety">
 <h1><a class="toc-backref" href="#id161" role="doc-backlink"><span class="section-number">6. </span>Safety</a><a class="headerlink" href="#safety" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>Move fast and be responsible.</p>
@@ -813,7 +813,7 @@ <h4><a class="toc-backref" href="#id189" role="doc-backlink"><span class="sectio
 <p>Anthropic/hh-rlhf</p>
 <ul class="simple">
 <li><p>SALADBench</p></li>
-<li><p>https://huggingface.co/datasets/Anthropic/hh-rlhf</p></li>
+<li><p><a class="reference external" href="https://huggingface.co/datasets/Anthropic/hh-rlhf">https://huggingface.co/datasets/Anthropic/hh-rlhf</a></p></li>
 <li><p>ABC</p></li>
 <li><p>use of synthetic datasets</p></li>
 </ul>
@@ -830,10 +830,10 @@ <h3><a class="toc-backref" href="#id190" role="doc-backlink"><span class="sectio
 <p>LM-Based:</p>
 <ul class="simple">
 <li><p>OpenAI Moderation API</p></li>
-<li><p>IBM Granite Guardian: https://github.com/ibm-granite/granite-guardian</p></li>
+<li><p>IBM Granite Guardian: <a class="reference external" href="https://github.com/ibm-granite/granite-guardian">https://github.com/ibm-granite/granite-guardian</a></p></li>
 <li><p>Llama-Guard</p></li>
-<li><p>NeMo Guardrails: https://github.com/NVIDIA/NeMo-Guardrails</p></li>
-<li><p>Mistral moderation: https://github.com/mistralai/cookbook/blob/main/mistral/moderation/system-level-guardrails.ipynb</p></li>
+<li><p>NeMo Guardrails: <a class="reference external" href="https://github.com/NVIDIA/NeMo-Guardrails">https://github.com/NVIDIA/NeMo-Guardrails</a></p></li>
+<li><p>Mistral moderation: <a class="reference external" href="https://github.com/mistralai/cookbook/blob/main/mistral/moderation/system-level-guardrails.ipynb">https://github.com/mistralai/cookbook/blob/main/mistral/moderation/system-level-guardrails.ipynb</a></p></li>
 </ul>
 <section id="filter-based">
 <h4><a class="toc-backref" href="#id191" role="doc-backlink"><span class="section-number">6.5.2.1. </span>Filter-based</a><a class="headerlink" href="#filter-based" title="Permalink to this heading">¶</a></h4>
diff --git a/tamingllms/_build/html/notebooks/structured_output.html b/tamingllms/_build/html/notebooks/structured_output.html
index 88f4eac..ca8c2fa 100644
--- a/tamingllms/_build/html/notebooks/structured_output.html
+++ b/tamingllms/_build/html/notebooks/structured_output.html
@@ -29,6 +29,8 @@
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         <script async="async" src="../_static/sphinx-thebe.js"></script>
+        <script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
+        <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
 
       
       <!-- bundled in js (rollup iife) -->
@@ -222,7 +224,7 @@
 <hr>
           <div class="content" role="main" v-pre>
             
-  <section id="wrestling-with-structured-output">
+  <section class="tex2jax_ignore mathjax_ignore" id="wrestling-with-structured-output">
 <h1><a class="toc-backref" href="#id128" role="doc-backlink"><span class="section-number">4. </span>Wrestling with Structured Output</a><a class="headerlink" href="#wrestling-with-structured-output" title="Permalink to this heading">¶</a></h1>
 <blockquote class="epigraph">
 <div><p>In limits, there is freedom. Creativity thrives within structure.</p>
@@ -695,30 +697,33 @@ <h3><a class="toc-backref" href="#id139" role="doc-backlink"><span class="sectio
 <p>Outlines <span id="id3">[<a class="reference internal" href="#id15" title="Outlines. Type-safe structured output from llms. https://dottxt-ai.github.io/outlines/latest/, 2024. Accessed: 2024.">Outlines, 2024</a>]</span> is a library specifically focused on structured text generation from LLMs. Under the hood, Outlines works by adjusting the probability distribution of the model’s output logits - the raw scores from the final layer of the neural network that are normally converted into text tokens. By introducing carefully crafted logit biases, Outlines can guide the model to prefer certain tokens over others, effectively constraining its outputs to a predefined set of valid options.</p>
 <p>The authors solve the general guided generation problem <span id="id4">[<a class="reference internal" href="#id60" title="Brandon T. Willard and Rémi Louf. Efficient guided generation for large language models. 2023. URL: https://arxiv.org/abs/2307.09702, arXiv:2307.09702.">Willard and Louf, 2023</a>]</span>, which as a consequence solves the problem of structured output generation, in LLMs by introducing an efficient indexing approach that reformulates neural text generation using finite-state machines (FSMs).</p>
 <p>They define the next token generation as a random variable:</p>
-<p>$$s_{t+1} \sim \text{Categorical}(\alpha) \text{ where } \alpha = \text{LLM}(S_t, \theta)$$</p>
+<div class="math notranslate nohighlight">
+\[s_{t+1} \sim \text{Categorical}(\alpha) \text{ where } \alpha = \text{LLM}(S_t, \theta)\]</div>
 <p>Where:</p>
 <ul class="simple">
-<li><p>$s_{t+1}$ is the next token to be generated</p></li>
-<li><p>$S_t = (s_1…s_t)$ represents a sequence of t tokens with $s_t \in V$</p></li>
-<li><p>$V$ is the vocabulary with size $|V| = N$ (typically around $10^4$ or larger)</p></li>
-<li><p>$\alpha \in \mathbb{R}^N$ is the output logits/probabilities over the vocabulary</p></li>
-<li><p>$\theta$ is the set of trained parameters of the LLM</p></li>
-<li><p>$\text{LLM}$ refers to a deep neural network trained on next-token-completion tasks</p></li>
-<li><p>$\text{Categorical}(\alpha)$ represents sampling from a categorical distribution with probabilities $\alpha$</p></li>
+<li><p><span class="math notranslate nohighlight">\(s_{t+1}\)</span> is the next token to be generated</p></li>
+<li><p><span class="math notranslate nohighlight">\(S_t = (s_1...s_t)\)</span> represents a sequence of t tokens with <span class="math notranslate nohighlight">\(s_t \in V\)</span></p></li>
+<li><p><span class="math notranslate nohighlight">\(V\)</span> is the vocabulary with size <span class="math notranslate nohighlight">\(|V| = N\)</span> (typically around <span class="math notranslate nohighlight">\(10^4\)</span> or larger)</p></li>
+<li><p><span class="math notranslate nohighlight">\(\alpha \in \mathbb{R}^N\)</span> is the output logits/probabilities over the vocabulary</p></li>
+<li><p><span class="math notranslate nohighlight">\(\theta\)</span> is the set of trained parameters of the LLM</p></li>
+<li><p><span class="math notranslate nohighlight">\(\text{LLM}\)</span> refers to a deep neural network trained on next-token-completion tasks</p></li>
+<li><p><span class="math notranslate nohighlight">\(\text{Categorical}(\alpha)\)</span> represents sampling from a categorical distribution with probabilities <span class="math notranslate nohighlight">\(\alpha\)</span></p></li>
 </ul>
 <p>When applying masking for guided generation, this becomes:</p>
-<p>$$
+<div class="math notranslate nohighlight">
+\[
 \tilde{\alpha} = m(S_t) \odot \alpha
-$$</p>
-<p>$$
+\]</div>
+<div class="math notranslate nohighlight">
+\[
 \tilde{s}_{t+1} \sim \text{Categorical}(\tilde{\alpha})
-$$</p>
+\]</div>
 <p>Where:</p>
 <ul class="simple">
-<li><p>$m: P(V) \rightarrow {0,1}^N$ is a boolean mask function</p></li>
-<li><p>$\odot$ represents element-wise multiplication</p></li>
-<li><p>$\tilde{\alpha}$ is the masked (constrained) probability distribution</p></li>
-<li><p>$\tilde{s}_{t+1}$ is the next token sampled under constraints</p></li>
+<li><p><span class="math notranslate nohighlight">\(m: P(V) \rightarrow {0,1}^N\)</span> is a boolean mask function</p></li>
+<li><p><span class="math notranslate nohighlight">\(\odot\)</span> represents element-wise multiplication</p></li>
+<li><p><span class="math notranslate nohighlight">\(\tilde{\alpha}\)</span> is the masked (constrained) probability distribution</p></li>
+<li><p><span class="math notranslate nohighlight">\(\tilde{s}_{t+1}\)</span> is the next token sampled under constraints</p></li>
 </ul>
 <p>This formulation allows the masking operation to guide the generation process by zeroing out probabilities of invalid tokens according to the finite state machine states. But instead of checking the entire vocabulary (size N) at each generation step (O(N) complexity) to enforce output constraints, they convert constraints (regex/grammar) into FSM states and build an index mapping FSM states to valid vocabulary tokens. This achieves O(1) average complexity for token generation.</p>
 <p>In summary, there are two stages in the Outlines framework <span id="id5">[<a class="reference internal" href="#id59" title="Vivien Tran-Thien. Fast, high-fidelity llm decoding with regex constraints. 2024. URL: https://vivien000.github.io/blog/journal/llm-decoding-with-regex-constraints.html.">Tran-Thien, 2024</a>]</span>:</p>
diff --git a/tamingllms/_build/html/searchindex.js b/tamingllms/_build/html/searchindex.js
index b0187e8..b1650d1 100644
--- a/tamingllms/_build/html/searchindex.js
+++ b/tamingllms/_build/html/searchindex.js
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[4, 5, 7], "conclus": [4, 5, 7], "what": 5, "ar": 5, "token": 5, "across": 5, "chunk": 5, "contextu": 5, "link": 5, "long": 5, "form": 5, "step": 5, "write": 5, "templat": 5, "construct": 5, "dynam": 5, "paramet": 5, "report": 5, "exampl": 5, "usag": 5, "implic": 5, "futur": 5, "risk": 6, "ai": 6, "amplifi": 6, "exist": 6, "harm": 6, "novel": 6, "associ": 6, "autonom": 6, "exacerb": 6, "specif": [6, 7], "integr": 6, "bia": 6, "privaci": 6, "secur": 6, "guidanc": 6, "govern": 6, "organ": 6, "privat": 6, "sector": 6, "openai": 6, "anthrop": 6, "googl": 6, "rubric": 6, "mlcommon": 6, "centr": 6, "porquoi": 6, "red": 6, "team": 6, "constitut": 6, "explain": 6, "xai": 6, "reinforc": 6, "learn": 6, "feedback": 6, "rlhf": 6, "technic": 6, "implement": 6, "compon": 6, "salad": 6, "bench": 6, "hh": 6, "filter": 6, "make": 6, "mistral": 6, "7b": 6, "harmless": 6, "need": 7, "solut": 7, "strategi": 7, "techniqu": 7, "One": 7, "shot": 7, "json": 7, "mode": 7, "langchain": 7, "outlin": 7, "ollama": 7, "compar": 7, "framework": 7, "best": 7, "research": 7, "ongo": 7, "debat": 7, "acknowledg": 7}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinxcontrib.bibtex": 9, "sphinx": 57}, "alltitles": {"Introduction": [[0, "introduction"], [3, "introduction"], [3, "id22"], [4, "introduction"], [6, "introduction"], [7, "introduction"]], "Contents": [[0, "contents"], [3, "contents"], [4, "contents"], [5, "contents"], [6, "contents"], [7, "contents"]], "Core Challenges We\u2019ll Address": [[0, "core-challenges-we-ll-address"]], "A Practical Approach": [[0, "a-practical-approach"]], "An Open Source Approach": [[0, "an-open-source-approach"]], "Open Source Book": [[0, "open-source-book"]], "A Note on Perspective": [[0, "a-note-on-perspective"]], "Who This Book Is For": [[0, "who-this-book-is-for"]], "Outcomes": [[0, "outcomes"]], "Prerequisites": [[0, "prerequisites"]], "Setting Up Your Environment": [[0, "setting-up-your-environment"]], "Code Repository": [[0, "code-repository"]], "Python Environment Setup": [[0, "python-environment-setup"]], "API Keys Configuration": [[0, "api-keys-configuration"]], "Troubleshooting Common Issues": [[0, "troubleshooting-common-issues"]], "About the Author(s)": [[0, "about-the-author-s"]], "Preface": [[1, "preface"], [2, "preface"]], "References": [[1, "references"], [3, "references"], [4, "references"], [5, "references"], [6, "references"], [7, "references"]], "Taming LLMs": [[2, "taming-llms"]], "A Practical Guide to LLM Pitfalls with Open Source Software": [[2, "a-practical-guide-to-llm-pitfalls-with-open-source-software"]], "Chapter 1: Introduction": [[2, "chapter-1-introduction"]], "Chapter 2: Wrestling with Structured Output": [[2, "chapter-2-wrestling-with-structured-output"]], "Chapter 3: Input Data Challenge": [[2, "chapter-3-input-data-challenge"]], "Chapter 4: Output Size and Length Limitations": [[2, "chapter-4-output-size-and-length-limitations"]], "Chapter 5: The Evals Gap": [[2, "chapter-5-the-evals-gap"]], "Chapter 6: Safety Concerns": [[2, "chapter-6-safety-concerns"]], "Chapter 7: Preference-based Alignment": [[2, "chapter-7-preference-based-alignment"]], "Chapter 8: Breaking Free from Cloud Providers": [[2, "chapter-8-breaking-free-from-cloud-providers"]], "Chapter 9: The Cost Factor": [[2, "chapter-9-the-cost-factor"]], "Chapter 10: Frontiers": [[2, "chapter-10-frontiers"]], "Appendix A: Tools and Resources": [[2, "appendix-a-tools-and-resources"]], "Citation": [[2, "citation"], [3, "citation"]], "Preference-Based Alignment": [[3, "preference-based-alignment"]], "From Raw Capabilities to Preference Alignment": [[3, "from-raw-capabilities-to-preference-alignment"]], "On the Misalignment of Language Models": [[3, "on-the-misalignment-of-language-models"]], "Aligning Language Models with Human Preferences": [[3, "aligning-language-models-with-human-preferences"]], "Supervised Fine-Tuning (SFT) for Model Alignment": [[3, "supervised-fine-tuning-sft-for-model-alignment"]], "Augmenting SFT with Human Preferences": [[3, "augmenting-sft-with-human-preferences"]], "Case Study: Aligning a Language Model to a Policy": [[3, "case-study-aligning-a-language-model-to-a-policy"]], "Experimental Setup": [[3, "experimental-setup"]], "Deliverables": [[3, "deliverables"]], "A Note on smolLM2 Models": [[3, "a-note-on-smollm2-models"]], "Policy": [[3, "policy"]], "Preference Dataset - Synthetic Dataset Generation": [[3, "preference-dataset-synthetic-dataset-generation"]], "User Prompts": [[3, "user-prompts"]], "Rejected Responses": [[3, "rejected-responses"]], "Chosen Responses": [[3, "chosen-responses"]], "Generate DPO Dataset": [[3, "generate-dpo-dataset"]], "DPO-Based Optimization": [[3, "dpo-based-optimization"]], "Data Preparation": [[3, "data-preparation"]], "Fine-Tuning": [[3, "fine-tuning"]], "Vibe Check": [[3, "vibe-check"]], "Alignment Evaluation": [[3, "alignment-evaluation"]], "Discussion": [[3, "discussion"], [5, "discussion"], [7, "discussion"]], "The Evals Gap": [[4, "the-evals-gap"]], "Non-Deterministic Generative Machines": [[4, "non-deterministic-generative-machines"]], "Emerging Properties": [[4, "emerging-properties"]], "Problem Statement": [[4, "problem-statement"], [5, "problem-statement"], [7, "problem-statement"]], "Evals of Traditional Software vs LLMs": [[4, "evals-table"]], "Evals Design": [[4, "evals-design"]], "LLM Application Testing Requirements Matrix": [[4, "validation-requirements"]], "Conceptual Overview": [[4, "conceptual-overview"]], "Design Considerations": [[4, "design-considerations"]], "Metrics": [[4, "metrics"]], "Key Metrics for Evaluating Generative Tasks": [[4, "key-metrics"]], "Evaluators": [[4, "evaluators"]], "Model-Based Evaluation": [[4, "model-based-evaluation"]], "Evaluating Evaluators": [[4, "evaluating-evaluators"]], "Benchmarks and Leaderboards": [[4, "benchmarks-and-leaderboards"]], "Tools": [[4, "tools"], [6, "tools"]], "LightEval": [[4, "lighteval"]], "MMLU Econometrics Task Dataset sample": [[4, "mmlu-econometrics"]], "Model Families Evaluated Using LightEval": [[4, "model-families"]], "LangSmith": [[4, "langsmith"]], "PromptFoo": [[4, "promptfoo"]], "Comparison": [[4, "comparison"]], "Comparison of Lighteval, LangSmith, and Promptfoo": [[4, "tool-comparison"]], "Conclusion": [[4, "conclusion"], [5, "conclusion"], [7, "conclusion"]], "Output Size Limitations": [[5, "output-size-limitations"]], "What are Token Limits?": [[5, "what-are-token-limits"]], "Token Cost and Length Limitation Comparison Across Key Models": [[5, "token-cost-table"]], "Content Chunking with Contextual Linking": [[5, "content-chunking-with-contextual-linking"]], "Generating long-form content": [[5, "generating-long-form-content"]], "Step 1: Chunking the Content": [[5, "step-1-chunking-the-content"]], "Step 2: Writing the Base Prompt Template": [[5, "step-2-writing-the-base-prompt-template"]], "Step 3: Constructing Dynamic Prompt Parameters": [[5, "step-3-constructing-dynamic-prompt-parameters"]], "Step 4: Generating the Report": [[5, "step-4-generating-the-report"]], "Example Usage": [[5, "example-usage"]], "Implications": [[5, "implications"]], "Future Considerations": [[5, "future-considerations"]], "Safety": [[6, "safety"]], "Safety Risks": [[6, "safety-risks"]], "General AI Safety Risks": [[6, "general-ai-safety-risks"]], "Amplified Existing Harms and Novel Risks": [[6, "amplified-existing-harms-and-novel-risks"]], "Risks Associated with Autonomous AI": [[6, "risks-associated-with-autonomous-ai"]], "Exacerbating Factors": [[6, "exacerbating-factors"]], "LLMs Specific Safety Risks": [[6, "llms-specific-safety-risks"]], "Data Integrity and Bias": [[6, "data-integrity-and-bias"]], "Privacy and Security": [[6, "privacy-and-security"]], "Guidance": [[6, "guidance"]], "Governments & Organizations": [[6, "governments-organizations"]], "Private Sector": [[6, "private-sector"]], "OpenAI": [[6, "openai"]], "Anthropic": [[6, "anthropic"]], "Google": [[6, "google"]], "Rubrics": [[6, "rubrics"]], "MLCommons AI Safety Benchmark": [[6, "mlcommons-ai-safety-benchmark"]], "Centre for the Governance of AI Rubric": [[6, "centre-for-the-governance-of-ai-rubric"]], "Porquoi": [[6, "porquoi"]], "Approaches": [[6, "approaches"]], "Red Teaming": [[6, "red-teaming"]], "Constitutional AI": [[6, "constitutional-ai"]], "Explainable AI (XAI)": [[6, "explainable-ai-xai"]], "Reinforcement Learning from Human Feedback (RLHF)": [[6, "reinforcement-learning-from-human-feedback-rlhf"]], "Technical Implementation Components": [[6, "technical-implementation-components"]], "Benchmarks & Datasets": [[6, "benchmarks-datasets"]], "SALAD-Bench": [[6, "salad-bench"]], "Anthropic/hh-rlhf": [[6, "anthropic-hh-rlhf"]], "Filter-based": [[6, "filter-based"]], "LLM-based": [[6, "llm-based"]], "Benchmarks": [[6, "benchmarks"]], "Case Study: Making Mistral 7B Harmless": [[6, "case-study-making-mistral-7b-harmless"]], "Wrestling with Structured Output": [[7, "wrestling-with-structured-output"]], "User Needs": [[7, "user-needs"]], "Solutions": [[7, "solutions"]], "Strategies": [[7, "strategies"]], "Techniques and Tools": [[7, "techniques-and-tools"]], "One-Shot Prompts": [[7, "one-shot-prompts"]], "Structured Output with Provider-Specific APIs": [[7, "structured-output-with-provider-specific-apis"]], "JSON Mode": [[7, "json-mode"]], "LangChain": [[7, "langchain"]], "Outlines": [[7, "outlines"]], "Ollama": [[7, "ollama"]], "Comparing Solutions": [[7, "comparing-solutions"]], "Structured Output Frameworks Comparison": [[7, "structured-output-frameworks"]], "Best Practices": [[7, "best-practices"]], "Research and Ongoing Debate": [[7, "research-and-ongoing-debate"]], "Acknowledgements": [[7, "acknowledgements"]]}, "indexentries": {}})
\ No newline at end of file
diff --git a/tamingllms/_build/jupyter_execute/markdown/intro.ipynb b/tamingllms/_build/jupyter_execute/markdown/intro.ipynb
index 8b5f457..4e957c8 100644
--- a/tamingllms/_build/jupyter_execute/markdown/intro.ipynb
+++ b/tamingllms/_build/jupyter_execute/markdown/intro.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d22d613b",
+   "id": "c51836b9",
    "metadata": {},
    "source": [
     "(intro)=\n",
diff --git a/tamingllms/_build/jupyter_execute/notebooks/alignment.ipynb b/tamingllms/_build/jupyter_execute/notebooks/alignment.ipynb
index 09385d4..cb46537 100644
--- a/tamingllms/_build/jupyter_execute/notebooks/alignment.ipynb
+++ b/tamingllms/_build/jupyter_execute/notebooks/alignment.ipynb
@@ -256,9 +256,9 @@
     "\n",
     "At a high-level DPO maximizes the probability of preferred output and minimize rejected output as defined in the following equation:\n",
     "\n",
-    "\\begin{gather*}\n",
+    "```{math}\n",
     "\\mathcal{L}_{\\text{DPO}}(\\pi_\\theta; \\pi_\\text{ref}) = -\\mathbb{E}_{(x,y_w,y_l) \\sim \\mathcal{D}} \\left[\\log \\sigma \\left(\\beta \\underbrace{\\log \\frac{\\pi_\\theta(y_w | x)}{\\pi_\\text{ref}(y_w | x)}}_{\\color{green}\\text{preferred}} - \\beta \\underbrace{\\log \\frac{\\pi_\\theta(y_l | x)}{\\pi_\\text{ref}(y_l | x)}}_{\\color{red}\\text{rejected}}\\right)\\right]\n",
-    "\\end{gather*}\n",
+    "```\n",
     "\n",
     "This approach is more straightforward than PPO, as it avoids the need for a reward model and instead uses a direct comparison of model outputs against human preferences.\n",
     "\n",
diff --git a/tamingllms/_config.yml b/tamingllms/_config.yml
index 9e9012a..68c3414 100644
--- a/tamingllms/_config.yml
+++ b/tamingllms/_config.yml
@@ -38,16 +38,16 @@ bibtex_bibfiles:
 only_build_toc_files: true
 
 
-parse:
-  myst_enable_extensions:
-    - amsmath
+#parse:
+#  myst_enable_extensions:
+#    - amsmath
 
 sphinx:
   extra_extensions:
     - sphinxcontrib.mermaid
     - sphinxcontrib.bibtex
   config:
-    mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
+    #mathjax_path: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
     bibtex_reference_style: author_year
     html_theme: 'press' #insipid
     #html_logo: '_static/logo_w.png'
diff --git a/tamingllms/notebooks/alignment.ipynb b/tamingllms/notebooks/alignment.ipynb
index e88d7fb..2eacf14 100644
--- a/tamingllms/notebooks/alignment.ipynb
+++ b/tamingllms/notebooks/alignment.ipynb
@@ -256,9 +256,9 @@
     "\n",
     "At a high-level DPO maximizes the probability of preferred output and minimize rejected output as defined in the following equation:\n",
     "\n",
-    "\\begin{gather*}\n",
+    "```{math}\n",
     "\\mathcal{L}_{\\text{DPO}}(\\pi_\\theta; \\pi_\\text{ref}) = -\\mathbb{E}_{(x,y_w,y_l) \\sim \\mathcal{D}} \\left[\\log \\sigma \\left(\\beta \\underbrace{\\log \\frac{\\pi_\\theta(y_w | x)}{\\pi_\\text{ref}(y_w | x)}}_{\\color{green}\\text{preferred}} - \\beta \\underbrace{\\log \\frac{\\pi_\\theta(y_l | x)}{\\pi_\\text{ref}(y_l | x)}}_{\\color{red}\\text{rejected}}\\right)\\right]\n",
-    "\\end{gather*}\n",
+    "```\n",
     "\n",
     "This approach is more straightforward than PPO, as it avoids the need for a reward model and instead uses a direct comparison of model outputs against human preferences.\n",
     "\n",