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1246 lines (1177 loc) · 45.7 KB
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>MRC Tutorial — Session 1: Linear Algebra</title>
<script>
MathJax = { tex: { inlineMath: [['$', '$']], displayMath: [['$$', '$$']] }, svg: { fontCache: 'global' } };
</script>
<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js" async></script>
<link rel="stylesheet" href="mrc_styles.css">
<style>
/* ============================================================
L1 deck shell — navigable presentation for Lecture 1.
Extends mrc_styles.css. Adds slide-specific structure:
- Title card layout (slide 1)
- Bulleted content slides (the majority)
- Dark section dividers (whiteboard transitions)
- Demo slides (full-iframe to existing interactive demos)
============================================================ */
body { padding: 0; }
.deck { position: relative; min-height: 100vh; }
/* base slide — each slide fills the viewport exactly (slideshow mode) */
.slide {
display: none;
height: 100vh;
overflow: auto; /* graceful fallback if content is too tall */
padding: 60px 48px;
}
.slide.active {
display: flex;
flex-direction: column;
}
.slide-inner {
max-width: 760px;
margin: 0 auto;
width: 100%;
}
.slide h2 {
font-family: var(--font-sans);
font-size: 32px;
font-weight: 500;
letter-spacing: -0.3px;
margin: 0 0 6px 0;
color: var(--text);
line-height: 1.2;
}
.slide .slide-subtitle {
font-family: var(--font-sans);
color: var(--text-muted);
font-size: 16px;
margin-bottom: 40px;
font-style: italic;
font-weight: 400;
line-height: 1.4;
}
/* bulleted content */
.slide ul.bullets {
font-size: 19px;
line-height: 1.85;
list-style: none;
padding: 0;
margin: 0;
}
.slide ul.bullets > li {
padding: 8px 0 8px 26px;
position: relative;
}
.slide ul.bullets > li::before {
content: "";
position: absolute;
left: 4px;
top: 19px;
width: 6px;
height: 6px;
background: var(--accent);
border-radius: 50%;
}
.slide ul.bullets ul {
margin: 6px 0 0 0;
padding-left: 0;
list-style: none;
}
.slide ul.bullets ul > li {
padding: 4px 0 4px 22px;
position: relative;
color: var(--text-muted);
font-size: 17px;
}
.slide ul.bullets ul > li::before {
content: "—";
position: absolute;
left: 0;
top: 4px;
color: var(--text-muted);
font-weight: 400;
background: none;
width: auto;
height: auto;
border-radius: 0;
}
.slide strong { font-weight: 700; color: var(--text); }
.slide em { font-style: italic; color: var(--text); }
/* equation block within content slides */
.eq-block {
background: white;
border-left: 3px solid var(--accent);
padding: 16px 24px;
margin: 18px 0;
font-size: 22px;
}
/* title card (slide 1) */
.slide.title-card {
align-items: center;
justify-content: center;
text-align: center;
}
.slide.title-card.active { display: flex; }
.slide.title-card .title-main {
font-family: var(--font-sans);
font-size: 54px;
font-weight: 400;
letter-spacing: -0.6px;
margin: 0 0 14px 0;
line-height: 1.15;
}
.slide.title-card .title-sub {
font-family: var(--font-sans);
font-size: 22px;
color: var(--text-muted);
margin-bottom: 64px;
font-style: italic;
font-weight: 300;
max-width: 600px;
margin-left: auto;
margin-right: auto;
line-height: 1.4;
}
.slide.title-card .author {
font-family: var(--font-serif);
font-size: 22px;
color: var(--text);
margin-bottom: 10px;
}
.slide.title-card .affiliation {
font-family: var(--font-serif);
font-size: 18px;
color: var(--text-muted);
margin: 0;
line-height: 1.65;
max-width: 540px;
margin-left: auto;
margin-right: auto;
}
.slide.title-card .term {
font-family: var(--font-sans);
margin-top: 36px;
color: var(--accent);
font-size: 14px;
letter-spacing: 1.5px;
text-transform: uppercase;
font-weight: 500;
}
/* dark section dividers */
.slide.divider {
background: var(--text);
color: white;
align-items: center;
justify-content: center;
text-align: center;
}
.slide.divider.active { display: flex; }
.slide.divider .divider-eyebrow {
font-family: var(--font-sans);
color: var(--accent);
font-size: 13px;
letter-spacing: 3px;
text-transform: uppercase;
margin-bottom: 28px;
font-weight: 500;
}
.slide.divider .divider-title {
font-family: var(--font-sans);
font-size: 44px;
font-weight: 400;
color: white;
max-width: 760px;
line-height: 1.25;
margin: 0;
letter-spacing: -0.4px;
}
/* demo slides — full iframe sized to the fixed slide viewport */
.slide.demo { padding: 0; }
.slide.demo iframe {
display: block;
width: 100%;
height: 100%;
flex: 1;
border: none;
}
/* table for slide 23 */
table.summary {
width: 100%;
border-collapse: collapse;
margin: 14px 0;
font-size: 16px;
}
table.summary th, table.summary td {
text-align: left;
padding: 14px 14px;
border-bottom: 1px solid var(--rule);
vertical-align: top;
line-height: 1.5;
}
table.summary th {
font-family: var(--font-sans);
font-size: 11px;
letter-spacing: 1px;
text-transform: uppercase;
color: var(--text-muted);
font-weight: 500;
border-bottom: 1px solid var(--text);
}
table.summary td:first-child {
color: var(--text);
font-weight: 500;
width: 32%;
}
table.summary td:nth-child(2) { width: 38%; color: var(--text-muted); }
table.summary td:nth-child(3) { color: var(--text); }
/* deck chrome — counter + nav hint + present button */
.deck-counter {
position: fixed;
bottom: 22px;
right: 32px;
font-family: var(--font-sans);
font-size: 11px;
color: var(--text-muted);
letter-spacing: 1.5px;
z-index: 100;
pointer-events: none;
}
.deck-counter.on-dark { color: rgba(255,255,255,0.7); }
.deck-hint {
position: fixed;
bottom: 22px;
left: 32px;
font-family: var(--font-sans);
font-size: 11px;
color: var(--text-muted);
letter-spacing: 0.5px;
z-index: 100;
pointer-events: none;
}
.deck-hint.on-dark { color: rgba(255,255,255,0.7); }
.deck-present {
position: fixed;
top: 22px;
right: 32px;
z-index: 100;
font-family: var(--font-sans);
font-size: 11px;
letter-spacing: 1.2px;
text-transform: uppercase;
padding: 8px 14px;
border: 1px solid var(--rule);
background: white;
color: var(--text);
border-radius: 4px;
cursor: pointer;
transition: all 0.15s;
font-weight: 500;
}
.deck-present:hover {
border-color: var(--accent);
color: var(--accent);
}
/* hide the Present button when already in fullscreen */
:fullscreen .deck-present { display: none; }
/* On big screens / projector / fullscreen, use more of the available
width and bump font sizes so content reads from the back of the room. */
@media (min-width: 1400px) {
.slide-inner { max-width: 900px; }
.slide h2 { font-size: 38px; }
.slide .slide-subtitle { font-size: 18px; }
.slide ul.bullets { font-size: 21px; line-height: 1.85; }
.slide ul.bullets ul > li { font-size: 19px; }
.slide.title-card .title-main { font-size: 60px; }
.slide.title-card .title-sub { font-size: 24px; }
.eq-block { font-size: 25px; }
.identity-block .eq { font-size: 25px; }
table.summary { font-size: 18px; }
}
/* references / readings list at end of slide 24 */
.reading-list {
margin-top: 28px;
padding: 18px 22px;
border: 1px solid var(--rule);
border-radius: 4px;
font-size: 16px;
line-height: 1.65;
color: var(--text-muted);
}
.reading-list .label {
font-family: var(--font-sans);
color: var(--text);
font-weight: 500;
font-size: 11px;
letter-spacing: 1px;
text-transform: uppercase;
margin-bottom: 8px;
display: block;
}
/* identity slide (19): two equations side-by-side feel */
.identity-block {
border: 1px solid var(--rule);
border-radius: 4px;
padding: 16px 22px;
margin: 12px 0;
}
.identity-block .heading {
font-family: var(--font-sans);
font-size: 12px;
letter-spacing: 1.5px;
text-transform: uppercase;
color: var(--text-muted);
margin-bottom: 6px;
}
.identity-block .eq {
font-size: 22px;
color: var(--text);
}
/* ============ overview-deck component styles ============ */
/* ============================================================
Tutorial OVERVIEW deck — 7 slides.
This is the introductory pitch deck for the Reddy Lab
Tutorial Course (advanced PhDs/postdocs). Each slide is a
self-contained content panel (no demos embedded).
============================================================ */
body { padding: 0; }
.deck { position: relative; min-height: 100vh; }
.slide {
display: none;
height: 100vh;
overflow: auto;
padding: 60px 48px;
}
.slide.active { display: flex; flex-direction: column; }
.slide-inner { max-width: 820px; margin: 0 auto; width: 100%; }
.slide h2 {
font-family: var(--font-sans);
font-size: 32px;
font-weight: 500;
letter-spacing: -0.3px;
margin: 0 0 8px 0;
color: var(--text);
line-height: 1.2;
}
.slide .slide-subtitle {
font-family: var(--font-sans);
color: var(--text-muted);
font-size: 16px;
margin-bottom: 32px;
font-style: italic;
font-weight: 400;
line-height: 1.4;
}
.slide ul.bullets {
font-size: 18px;
line-height: 1.75;
list-style: none;
padding: 0;
margin: 0;
}
.slide ul.bullets > li {
padding: 7px 0 7px 26px;
position: relative;
}
.slide ul.bullets > li::before {
content: "";
position: absolute;
left: 4px;
top: 18px;
width: 6px;
height: 6px;
background: var(--accent);
border-radius: 50%;
}
.slide strong { font-weight: 700; color: var(--text); }
.slide em { font-style: italic; color: var(--text); }
.lead-para {
font-size: 18px;
line-height: 1.7;
color: var(--text);
margin: 0 0 22px 0;
}
.eq-block {
background: white;
border-left: 3px solid var(--accent);
padding: 14px 22px;
margin: 14px 0;
font-size: 22px;
text-align: center;
}
/* Pillar grid for slide 2 (convergence equation) */
.pillar-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 14px;
margin: 14px 0 18px 0;
}
.pillar {
border: 1px solid var(--rule);
border-radius: 4px;
padding: 14px 18px;
}
.pillar .year {
font-family: var(--font-sans);
font-size: 11px;
letter-spacing: 1px;
color: var(--accent);
font-weight: 500;
text-transform: uppercase;
}
.pillar .name {
font-size: 18px;
font-weight: 700;
margin: 3px 0 2px 0;
color: var(--text);
}
.pillar .field {
font-style: italic;
color: var(--text-muted);
font-size: 13px;
margin-bottom: 6px;
}
.pillar .content {
font-size: 14px;
line-height: 1.55;
color: var(--text);
}
.convergence-tagline {
text-align: center;
margin: 8px 0 0 0;
font-size: 16px;
line-height: 1.6;
color: var(--text);
}
.convergence-tagline strong { color: var(--accent); font-weight: 700; }
/* Capability grid for slide 4 (the 4 things you'll own) */
.cap-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 14px;
margin: 12px 0 18px 0;
}
.cap {
border: 1px solid var(--rule);
border-radius: 4px;
padding: 16px 20px;
}
.cap .num {
font-family: var(--font-sans);
font-size: 32px;
color: var(--accent);
font-weight: 300;
line-height: 1;
margin-bottom: 6px;
}
.cap .title {
font-size: 17px;
font-weight: 700;
color: var(--text);
margin-bottom: 6px;
line-height: 1.3;
}
.cap .body {
font-size: 14px;
line-height: 1.55;
color: var(--text-muted);
}
/* Session list for slide 5 */
.session-list {
margin: 6px 0 14px 0;
}
.session-item {
padding: 12px 0;
border-bottom: 1px solid var(--rail);
display: grid;
grid-template-columns: 110px 1fr;
gap: 18px;
align-items: baseline;
}
.session-item:last-child { border-bottom: none; }
.session-num {
font-family: var(--font-sans);
font-size: 11px;
letter-spacing: 1.2px;
color: var(--accent);
font-weight: 500;
text-transform: uppercase;
}
.session-body {
font-size: 16px;
line-height: 1.55;
color: var(--text);
}
.session-body .stitle {
font-weight: 700;
color: var(--text);
margin-right: 6px;
}
.session-body .stopic {
color: var(--text-muted);
}
/* 3-column reason grid for slide 7 */
.reason-grid {
display: grid;
grid-template-columns: 1fr 1fr 1fr;
gap: 14px;
margin: 12px 0 22px 0;
}
.reason {
border: 1px solid var(--rule);
border-radius: 4px;
padding: 14px 16px;
text-align: center;
}
.reason .label {
font-family: var(--font-sans);
font-size: 11px;
letter-spacing: 1px;
text-transform: uppercase;
color: var(--accent);
font-weight: 500;
margin-bottom: 8px;
}
.reason .body {
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<section class="slide title-card active" data-slide="1">
<div>
<div class="title-main">Molecular Recognition Computing</div>
<div class="title-sub">Tutorial Course · Session 1 — Linear Algebra for Machine Learning and Molecular Recognition</div>
<div class="author">Sai T. Reddy</div>
<p class="affiliation">Reddy Lab · ETH Zurich<br>Botnar Institute of Immune Engineering (BIIE)</p>
<div class="term">12 June 2026 · Session 1 of 4</div>
</div>
</section>
<section class="slide" data-slide="2">
<div class="slide-inner">
<h2>Why This Course Exists</h2>
<div class="slide-subtitle">Four foundational concepts. Four fields. One equation.</div>
<p class="lead-para">
This course is built on four concepts that are <strong>settled science</strong> — textbook material in their respective fields, none in dispute by working scientists in those fields.
</p>
<ul class="bullets">
<li><strong>Boltzmann's distribution (1877)</strong> — statistical mechanics</li>
<li><strong>Maximum entropy principle</strong> (Shannon 1948, Jaynes 1957) — information theory</li>
<li><strong>Softmax attention mechanism</strong> (Vaswani et al., 2017) — machine learning</li>
<li><strong>Luce's choice axiom (1959)</strong> — choice theory / econometrics</li>
</ul>
<p class="lead-para" style="margin-top: 24px;">
These four pillars are mathematically the <strong>same equation</strong> — the <strong>convergence equation</strong>. The course teaches you to see the identity, then shows that the identity, combined with five physical conditions, prescribes a complete neural architecture for predicting molecular binding: the <strong>Specificity Foundation Model (SFM)</strong>.
</p>
</div>
</section>
<section class="slide" data-slide="3">
<div class="slide-inner">
<h2>The Convergence Equation</h2>
<div class="slide-subtitle">Four independent derivations. One function.</div>
<div class="pillar-grid">
<div class="pillar">
<div class="year">1877 · Physics</div>
<div class="name">Boltzmann</div>
<div class="field">statistical mechanics</div>
<div class="content">$P(\text{state}) \propto \exp(-E/k_BT)$ at thermal equilibrium</div>
</div>
<div class="pillar">
<div class="year">1948–57 · Information theory</div>
<div class="name">Shannon · Jaynes</div>
<div class="field">maximum entropy principle</div>
<div class="content">Most-rational distribution under partial info → exponential form</div>
</div>
<div class="pillar">
<div class="year">1959 · Choice theory</div>
<div class="name">Luce</div>
<div class="field">independence of irrelevant alternatives</div>
<div class="content">IIA + monotonicity force the softmax form (uniqueness theorem)</div>
</div>
<div class="pillar">
<div class="year">2017 · Machine learning</div>
<div class="name">Vaswani et al.</div>
<div class="field">transformer attention</div>
<div class="content">$\mathrm{Attention}(Q, K, V) = \mathrm{softmax}(QK^\top / \sqrt{d_k})\, V$</div>
</div>
</div>
<div class="eq-block">$$P(j) \;=\; \frac{\exp(s_j)}{\sum_k \exp(s_k)}$$</div>
<div class="convergence-tagline">
Four derivations, four fields, 140 years apart. <strong>Not analogies — an algebraic identity.</strong>
</div>
</div>
</section>
<section class="slide" data-slide="4">
<div class="slide-inner">
<h2>Why No Existing Training Prepares You</h2>
<div class="slide-subtitle">A structural gap, not a failure of anyone's preparation</div>
<ul class="bullets">
<li>Standard <strong>ML courses</strong> teach attention — but not its identity with Boltzmann</li>
<li>Standard <strong>biophysics</strong> teaches Boltzmann — but not its identity with attention</li>
<li>Standard <strong>information theory</strong> teaches max entropy — but not its prescriptive consequences for neural architectures</li>
<li><strong>No existing curriculum stitches these together</strong> — because none was designed to. The implications of <em>Level 3 alignment</em> — where the architecture <em>is</em> the governing equation rather than approximating it — have to be learned explicitly.</li>
</ul>
<p class="lead-para" style="margin-top: 26px;">
The math used in this course is at the level of <strong>college algebra and basic calculus</strong> — dot products, exponential functions, derivatives. Detailed step-by-step derivations are provided in writing for every key result. <strong>Anyone in the lab can take this course.</strong> Wet-lab researchers, computational biologists, and immunologists will all start from the same place.
</p>
</div>
</section>
<section class="slide" data-slide="5">
<div class="slide-inner">
<h2>What You Will Learn</h2>
<div class="slide-subtitle">Four capabilities not currently taught anywhere as a unified curriculum</div>
<div class="cap-grid">
<div class="cap">
<div class="num">1</div>
<div class="title">Mathematical foundations of modern AI</div>
<div class="body">Linear algebra (dot products, matrix multiplication, cosine similarity, softmax with temperature). Transformers, attention, multi-head attention. Contrastive learning and the InfoNCE loss. <em>Read transformer papers and follow them.</em></div>
</div>
<div class="cap">
<div class="num">2</div>
<div class="title">The physics of molecular binding</div>
<div class="body">Boltzmann distribution, $K_d$ and free energy ($\Delta G = RT \ln K_d$), competitive binding as softmax. Bilinearity: TF–DNA decomposes by position exactly; antibody–antigen requires a learned encoder.</div>
</div>
<div class="cap">
<div class="num">3</div>
<div class="title">A new paradigm: physics-derived AI architectures</div>
<div class="body">Luce's proof. The SFM derived from the convergence equation + five physical conditions. <strong>Parameter estimation in a known governing equation</strong> vs. function approximation. Predicts exponential (not power-law) data scaling, fast convergence, OOD robustness.</div>
</div>
<div class="cap">
<div class="num">4</div>
<div class="title">Build, validate, implement your own SFM</div>
<div class="body">Final project: build an SFM on your own molecular recognition data using Claude Code with the CALM codebase as reference. The architecture is prescribed; you make the domain-expert decisions.</div>
</div>
</div>
</div>
</section>
<section class="slide" data-slide="6">
<div class="slide-inner">
<h2>Course Structure</h2>
<div class="slide-subtitle">Four sessions plus the final project · run as an informal tutorial</div>
<div class="session-list">
<div class="session-item">
<div class="session-num">Session 1<br><span style="color:var(--text-muted);font-weight:400;font-size:10px;">12 Jun</span></div>
<div class="session-body"><span class="stitle">Linear Algebra for ML & Molecular Recognition <span style="font-family:var(--font-sans);font-size:10px;color:var(--accent);font-weight:600;">L1</span></span><span class="stopic">Vectors, dot products, matrix multiplication, cosine similarity, softmax with temperature.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 2<br><span style="color:var(--text-muted);font-weight:400;font-size:10px;">17 Jun</span></div>
<div class="session-body"><span class="stitle">Transformers & Contrastive Learning <span style="font-family:var(--font-sans);font-size:10px;color:var(--accent);font-weight:600;">L2 + L3</span></span><span class="stopic">Attention, why $\sqrt{d_k}$, multi-head; protein language models (ESM-2, AntiBERTy); CLIP, CALM, the InfoNCE loss.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 3<br><span style="color:var(--text-muted);font-weight:400;font-size:10px;">19 Jun</span></div>
<div class="session-body"><span class="stitle">Thermodynamics & Bilinearity <span style="font-family:var(--font-sans);font-size:10px;color:var(--accent);font-weight:600;">L4 + L5</span></span><span class="stopic">Boltzmann from maximum entropy, $K_d$ and free energy, competitive binding as softmax; SantaLucia, PWMs, the encoding problem.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 4<br><span style="color:var(--text-muted);font-weight:400;font-size:10px;">01 Jul</span></div>
<div class="session-body"><span class="stitle">Convergence Equation, SFM Architecture & Ten Domains <span style="font-family:var(--font-sans);font-size:10px;color:var(--accent);font-weight:600;">L6</span></span><span class="stopic">Luce's proof, deriving the SFM architecture, ten validated domains.</span></div>
</div>
<div class="session-item">
<div class="session-num">Final Project</div>
<div class="session-body"><span class="stitle">Build, Validate & Present Your SFM.</span><span class="stopic">Each of you builds an SFM on your own molecular-recognition data with Claude Code, and presents the results.</span></div>
</div>
</div>
</div>
</section>
<section class="slide" data-slide="7">
<div class="slide-inner">
<h2>Final Project — Build Your Own SFM</h2>
<div class="slide-subtitle">With Claude Code · using CALM as the reference implementation</div>
<p class="lead-para">
Each of you builds an SFM on <strong>your own molecular recognition data</strong> — antibody–antigen pairs from repertoire or display screening, TCR–pMHC pairs, peptide–MHC pairs, cytokine or other ligand binding to receptors, whatever fits your project.
</p>
<ul class="bullets">
<li>You decide the <strong>domain-expert decisions</strong>: encoder selection, data curation, masking strategy, train/test split design and leakage prevention, hard-negative strategy, evaluation design</li>
<li>The <strong>architecture itself does not change</strong> — that part is prescribed by the convergence equation</li>
<li>You evaluate with retrieval metrics, out-of-distribution splits at sequence-identity-clustered thresholds, and pseudo-prospective validation against held-out experiments</li>
<li>You <strong>present your results</strong> to the lab. We then discuss the cross-domain comparison: what training behaviors emerge from your data, what they tell us about the framework, and what comes next.</li>
</ul>
<p class="lead-para" style="margin-top: 22px;">
<em>This is the only test of understanding that matters: did you build a model that works on data nobody has seen before?</em>
</p>
</div>
</section>
<section class="slide" data-slide="8">
<div class="slide-inner">
<h2>SFMs as Infrastructure</h2>
<div class="slide-subtitle">A method like PCR or CRISPR</div>
<div class="reason-grid">
<div class="reason">
<div class="label">Broad applicability</div>
<div class="body">Any molecular recognition system at thermal equilibrium — antibodies, TCRs, MHC, TFs, miRNAs, CRISPR guides, enzymes, drug–target pairs. <strong>Six SFM domains demonstrated</strong>, four more in active development.</div>
</div>
<div class="reason">
<div class="label">Low resource</div>
<div class="body">CALM trained on ~4,000 antibody–antigen pairs vs. CLIP's ~400,000,000 image-text pairs. Single GPU node, pretrained encoders. <strong>Bottleneck is data curation by a domain expert.</strong></div>
</div>
<div class="reason">
<div class="label">Open source</div>
<div class="body">CALM, the SFM template, training and evaluation pipelines, validation harness, pretrained encoders — all public. <strong>No proprietary infrastructure needed.</strong></div>
</div>
</div>
<div class="infra-block">
<div class="lead">The natural division of labor</div>
<strong>AlphaFold</strong> and the structure predictors solve <em>structure</em>. <strong>ESM-2, AntiBERTy, DNABERT-2, MoLFormer, RNA-FM</strong> solve <em>sequence representation</em>. Neither solves <strong>specificity</strong> — which partner does this molecule recognize from a pool of candidates? <strong>SFMs sit on top of this infrastructure</strong> and produce the specificity prediction itself.
</div>
<div class="closing-line">
Ten years from now: every recognition problem in biology has an SFM.<br>
<strong>The model you build at the end of this course is the prototype.</strong>
</div>
</div>
</section>
<section class="slide divider" data-slide="9">
<div>
<div class="divider-eyebrow">Part 2 · The Mathematics</div>
<h2 class="divider-title">Linear Algebra for Machine Learning and Molecular Recognition</h2>
</div>
</section>
<section class="slide demo" data-slide="10">
<iframe src="L1/interactive_demos/L1_demo_uat.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="11">
<iframe src="L1/interactive_demos/L1_demo_uat_flexibility.html" loading="lazy"></iframe>
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<iframe src="L1/interactive_demos/L1_demo_known_equation.html" loading="lazy"></iframe>
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<section class="slide demo" data-slide="13">
<iframe src="L1/interactive_demos/L1_demo_coverage.html" loading="lazy"></iframe>
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<section class="slide demo" data-slide="14">
<iframe src="L1/interactive_demos/L1_demo_function_approximation.html" loading="lazy"></iframe>
</section>
<section class="slide" data-slide="15">
<div class="slide-inner">
<h2>One Equation Governs Both</h2>
<ul class="bullets">
<li>The <strong>softmax attention mechanism</strong> in transformers (Vaswani et al., 2017)</li>
<li>is <strong>mathematically identical</strong> to</li>
<li>the <strong>Boltzmann distribution</strong> governing molecular binding (Boltzmann, 1877)</li>
<li>This identity is not approximate — it is <strong>algebraic</strong></li>
<li>This course will prove it, derive its consequences, and show it prescribes a complete neural architecture across ten biological domains</li>
</ul>
</div>
</section>
<section class="slide" data-slide="16">
<div class="slide-inner">
<h2>Four Operations Build the Entire Course</h2>
<div class="slide-subtitle">Everything that follows is constructed from these</div>
<ul class="bullets">
<li><strong>Dot product:</strong> measures compatibility between two vectors</li>
<li><strong>Matrix multiplication:</strong> computes all pairwise compatibilities simultaneously</li>
<li><strong>Cosine similarity:</strong> normalizes the comparison to a [−1, +1] scale</li>
<li><strong>Softmax:</strong> converts compatibility scores into a probability distribution</li>
</ul>
</div>
</section>
<section class="slide demo" data-slide="17">
<iframe src="L1/interactive_demos/L1_demo_three_systems.html" loading="lazy"></iframe>
</section>
<section class="slide" data-slide="18">
<div class="slide-inner">
<h2>What Is a Vector?</h2>
<div class="slide-subtitle">Just an ordered list of numbers — and a direction in space</div>
<ul class="bullets">
<li>A <strong>vector</strong> is an ordered list of numbers. Nothing more mysterious than that.</li>
<li>You already use them. Describe an amino acid by its measurable properties:
<ul>
<li>Leucine → [ hydrophobicity 3.8, volume 167, charge 0, polarity 0 ]</li>
<li>Lysine → [ hydrophobicity −3.9, volume 169, charge +1, polarity 1 ]</li>
</ul>
</li>
<li>Each number is one <strong>coordinate</strong>; each property is one <strong>axis</strong>. The list places the molecule as a point — or an arrow from the origin — in "property space."</li>
<li>Two molecules with similar properties → nearby points → arrows that <strong>point the same way</strong>.</li>
<li>The whole game of this course: turn molecules into geometry, then compare them geometrically.</li>
</ul>
</div>
</section>
<section class="slide demo" data-slide="19">
<iframe src="L1/interactive_demos/L1_demo_vector.html" loading="lazy"></iframe>
</section>
<section class="slide" data-slide="20">
<div class="slide-inner">
<h2>What Is a Compatibility Score?</h2>
<div class="slide-subtitle">In every system, it is a dot product of feature vectors</div>
<ul class="bullets">
<li>Antibody surface features <strong>·</strong> Antigen surface features = binding compatibility</li>
<li>TF positional preferences <strong>·</strong> DNA nucleotide identities = binding energy</li>
<li>Transformer query vector <strong>·</strong> key vector = attention score</li>
<li>The dot product is the <strong>universal compatibility measure</strong></li>
<li>This is not a modeling choice — it follows from the <strong>bilinear decomposition of binding energy</strong> (Lecture 5)</li>
</ul>
</div>
</section>
<section class="slide demo" data-slide="21">
<iframe src="L1/interactive_demos/L1_demo_vector_dotproduct.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="22">
<iframe src="L1/interactive_demos/L1_demo_dotproduct.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="23">
<iframe src="L1/whiteboard_demos/L1_wb1_proof_dotproduct.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="24">
<iframe src="L1/interactive_demos/L1_demo_similarity_build.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="25">
<iframe src="L1/interactive_demos/L1_demo_matmul.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="26">
<iframe src="L1/whiteboard_demos/L1_wb2_qkt_visual.html" loading="lazy"></iframe>
</section>
<section class="slide" data-slide="27">
<div class="slide-inner">
<h2>The Magnitude Problem</h2>
<div class="slide-subtitle">Should longer vectors always mean higher compatibility?</div>
<div class="eq-block">$$\mathbf{a} \cdot \mathbf{b} = \|\mathbf{a}\|\,\|\mathbf{b}\|\,\cos\theta$$</div>
<ul class="bullets">
<li>The dot product conflates <strong>alignment</strong> ($\cos\theta$) and <strong>magnitude</strong> ($\|\mathbf{a}\|\,\|\mathbf{b}\|$)</li>
<li>A very "loud" vector dominates all dot products regardless of direction</li>
<li>In molecular binding: we care about <strong>direction</strong> (what features match), not magnitude</li>
<li>Solution: <strong>normalize to unit length</strong> → dot product = pure alignment</li>
</ul>
</div>
</section>
<section class="slide demo" data-slide="28">
<iframe src="L1/interactive_demos/L1_demo_cosine.html" loading="lazy"></iframe>
</section>
<section class="slide demo" data-slide="29">
<iframe src="L1/whiteboard_demos/L1_wb3_proof_l2norm.html" loading="lazy"></iframe>
</section>
<section class="slide" data-slide="30">
<div class="slide-inner">
<h2>The Conversion Problem</h2>
<div class="slide-subtitle">We have scores. We need probabilities.</div>
<ul class="bullets">
<li>Agent has compatibility scores with $M$ candidates: $\mathbf{s} = [s_1, s_2, \ldots, s_M]$</li>
<li>We need a probability distribution: $\mathbf{P} = [P_1, P_2, \ldots, P_M]$</li>
<li>Requirements:
<ul>
<li>All probabilities positive</li>
<li>Sum to 1</li>
<li>Accept any real-valued scores — including negatives (unrestricted domain)</li>
<li>Higher score → higher probability</li>
<li>Relative preference between two candidates shouldn't change when a third enters or leaves</li>
</ul>
</li>
<li>How many functions satisfy all five? → <strong>Exactly one</strong> (Lecture 6)</li>
</ul>
</div>
</section>
<section class="slide demo" data-slide="31">
<iframe src="L1/whiteboard_demos/L1_wb4_softmax_example.html" loading="lazy"></iframe>
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<iframe src="L1/interactive_demos/L1_demo_softmax.html" loading="lazy"></iframe>