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<!DOCTYPE html>
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<title>MRC Tutorial Course — Overview</title>
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Tutorial OVERVIEW deck — 7 slides.
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<body>
<div class="deck">
<!-- ================== SLIDE 1 — Why This Course Exists ================== -->
<section class="slide active" data-slide="1">
<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>
<!-- ================== SLIDE 2 — The Convergence Equation ================== -->
<section class="slide" data-slide="2">
<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>
<!-- ================== SLIDE 3 — Why No Existing Training Prepares You ================== -->
<section class="slide" data-slide="3">
<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>
<!-- ================== SLIDE 4 — The 4 Capabilities ================== -->
<section class="slide" data-slide="4">
<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>
<!-- ================== SLIDE 5 — Course Structure ================== -->
<section class="slide" data-slide="5">
<div class="slide-inner">
<h2>Course Structure</h2>
<div class="slide-subtitle">Six 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</div>
<div class="session-body"><span class="stitle">Linear Algebra for ML & Molecular Recognition.</span><span class="stopic">Dot products, matrix multiplication, cosine similarity, softmax with temperature.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 2</div>
<div class="session-body"><span class="stitle">Neural Networks, Transformers, & Attention.</span><span class="stopic">Forward passes, scaled dot-product attention, why $\sqrt{d_k}$, multi-head attention.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 3</div>
<div class="session-body"><span class="stitle">Language Models, Protein LMs, & Contrastive Learning.</span><span class="stopic">BERT, GPT, ESM-2, AntiBERTy, DNABERT-2, CLIP, CALM, the InfoNCE loss.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 4</div>
<div class="session-body"><span class="stitle">Thermodynamics of Molecular Recognition.</span><span class="stopic">Free energy, $K_d$, competitive binding as softmax, the identity moment, SPR/ITC/BLI.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 5</div>
<div class="session-body"><span class="stitle">Given & Emergent Bilinearity.</span><span class="stopic">SantaLucia, position weight matrices, the encoding problem for antibody–antigen.</span></div>
</div>
<div class="session-item">
<div class="session-num">Session 6</div>
<div class="session-body"><span class="stitle">The Convergence Equation, the SFM Architecture, & the Ten Domains.</span><span class="stopic">Luce's proof, deriving the 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 lab member builds an SFM on their own data and presents results.</span></div>
</div>
</div>
</div>
</section>
<!-- ================== SLIDE 6 — Final Project ================== -->
<section class="slide" data-slide="6">
<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>
<!-- ================== SLIDE 7 — SFMs as Infrastructure ================== -->
<section class="slide" data-slide="7">
<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>
</div>
<div class="deck-counter" id="counter">SLIDE 1 / 7</div>
<div class="deck-hint" id="hint">← → navigate · F fullscreen</div>
<button class="deck-present" id="presentBtn">▶ Present</button>
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