demos/transformers.html at main · dlab-berkeley/demos · GitHub

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<!DOCTYPE html>
<html lang="en">
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    <title>D-Lab - Understanding Transformer Attention</title>
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<body>
    <div class="wrap">
        <div class="course-header">
            <img src="img/dlab-bubble-logo-2025.png" alt="D-Lab Logo" class="course-logo">
        </div>
        <h1>Understanding Transformer Attention</h1>
        <p class="lead">Interactive tutorial on how attention mechanisms work in transformers</p>

        <div class="progress-bar">
            <div class="progress-fill" id="progress" style="width: 20%"></div>
        </div>

        <!-- Introduction -->
        <div class="intro">
            <h2>What are we learning?</h2>
            <p>Transformers revolutionized AI by introducing the <strong>attention mechanism</strong>. Unlike earlier models that process words sequentially, transformers can look at all words simultaneously and decide which ones are most relevant for understanding each word.</p>

            <div class="goal">
                <h3>Learning Objective: Self-Attention</h3>
                <p>Understand how transformers use Query, Key, and Value matrices to compute attention scores, allowing the model to focus on relevant parts of the input when processing each word.</p>
            </div>
        </div>

        <!-- Step 1: Introduction -->
        <div class="stage">
            <h2><span class="step-number">1</span>What is Attention?</h2>
            <div class="explanation">
                <strong>Simple Definition:</strong> Attention is a mechanism that helps the model decide which words to "pay attention to" when understanding each word in a sentence.
            </div>
            <div class="card">
                <p>Let's work with this sentence that has clear relationships:</p>
                <div id="sentence">
                    <span class="chip" style="cursor: default;">The</span>
                    <span class="chip" style="cursor: default;">black</span>
                    <span class="chip" style="cursor: default;">cat</span>
                    <span class="chip" style="cursor: default;">ate</span>
                    <span class="chip" style="cursor: default;">fish</span>
                </div>
            <p style="color: var(--muted); margin-top: 20px; font-size: 14px;">
                <strong>Think about it:</strong> To understand "cat" fully, the model needs to know it's a "black cat" (not just any cat) that "ate fish" (not sleeping or playing). This is why attention matters - words get meaning from their context!
            </p>
            <button class="btn btn-primary" onclick="showStep1b()" style="margin-top: 15px;">Let's Learn How! →</button>
        </div>
    </div>

        <!-- Step 2: What are Transformers? -->
        <div class="stage hidden" id="step1b">
            <h2><span class="step-number">2</span>What are Transformers?</h2>
            <div class="explanation">
                <strong>The Big Picture:</strong> Transformers are a type of neural network architecture that revolutionized AI by processing all words in a sentence simultaneously, rather than one by one like older models. Previous models like RNNs (Recurrent Neural Networks) and LSTMs (Long Short-Term Memory networks) had to read text sequentially, word by word, which made them slower and less effective at understanding long-range relationships.
            </div>
            <div class="card">
                <div class="goal">
                    <h3>How Transformers Differ from Earlier Models</h3>
                    <div style="display: grid; grid-template-columns: 1fr 1fr; gap: 20px; margin-top: 15px;">
                        <div style="padding: 15px; background: rgba(239,68,68,.1); border-radius: 8px; border-left: 4px solid var(--red);">
                            <h4 style="color: var(--red); margin: 0 0 8px;">Old Way (RNNs/LSTMs)</h4>
                            <p style="margin: 0; font-size: 14px;">Process words sequentially: "The" → "black" → "cat" → "ate" → "fish"</p>
                            <p style="margin: 8px 0 0; font-size: 13px; color: var(--muted);">Slow, struggles with long sequences</p>
                        </div>
                        <div style="padding: 15px; background: rgba(25,135,84,.1); border-radius: 8px; border-left: 4px solid var(--emerald);">
                            <h4 style="color: var(--emerald); margin: 0 0 8px;">Transformer Way</h4>
                            <p style="margin: 0; font-size: 14px;">Process all words at once using <strong>self-attention</strong></p>
                            <p style="margin: 8px 0 0; font-size: 13px; color: var(--muted);">Fast, handles long sequences well</p>
                        </div>
                    </div>
                </div>

                <div style="margin-top: 20px;">
                    <h4 style="color: var(--blue); margin-bottom: 10px;">The Key Innovation: Self-Attention</h4>
                    <p>Instead of processing words in order, transformers ask: <em>"For each word, which other words in the sentence should I pay attention to?"</em></p>

                    <!-- Attention Mode Toggle -->
                    <div style="display: flex; justify-content: center; gap: 8px; margin: 15px 0;">
                        <button class="btn matrix-toggle active" data-mode="encoder" onclick="showAttentionMode('encoder')">
                            <span style="color: var(--emerald);">●</span> Encoder (Bidirectional)
                        </button>
                        <button class="btn matrix-toggle" data-mode="decoder" onclick="showAttentionMode('decoder')">
                            <span style="color: var(--orange);">●</span> Decoder (Causal)
                        </button>
                    </div>

                    <!-- Encoder Attention visualization (default) -->
                    <div id="attention-encoder" class="attention-mode-demo">
                        <div style="background: var(--panel); border: 1px solid var(--border); border-radius: 12px; padding: 20px; margin: 20px 0;">
                            <p style="text-align: center; margin-bottom: 15px; font-size: 14px;"><strong>Attention Matrix (Bidirectional)</strong></p>
                            <p style="text-align: center; margin-bottom: 20px; font-size: 12px; color: var(--muted);">Each row shows how that word attends to all other words. Darker = stronger attention.</p>

                            <div style="display: flex; justify-content: center;">
                                <div style="display: grid; grid-template-columns: 60px repeat(5, 65px); gap: 4px; font-size: 12px;">
                                    <!-- Header row -->
                                    <div></div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">the</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">black</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">cat</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">ate</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">fish</div>

                                    <!-- The row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">the</div>
                                    <div style="background: rgba(13,110,253,0.3); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.4);">0.30</div>
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                                    <div style="background: rgba(13,110,253,0.35); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.4);">0.35</div>
                                    <div style="background: rgba(13,110,253,0.1); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.10</div>

                                    <!-- Black row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">black</div>
                                    <div style="background: rgba(13,110,253,0.1); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.10</div>
                                    <div style="background: rgba(13,110,253,0.3); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.4);">0.30</div>
                                    <div style="background: rgba(13,110,253,0.5); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.6); font-weight: bold;">0.50</div>
                                    <div style="background: rgba(13,110,253,0.05); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.15);">0.05</div>
                                    <div style="background: rgba(13,110,253,0.05); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.15);">0.05</div>

                                    <!-- Cat row (highlighted) -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px; background: rgba(255,193,7,0.2); border-radius: 4px;">cat</div>
                                    <div style="background: rgba(13,110,253,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5);">0.10</div>
                                    <div style="background: rgba(13,110,253,0.7); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5); font-weight: bold; color: white;">0.45</div>
                                    <div style="background: rgba(13,110,253,0.05); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5);">0.00</div>
                                    <div style="background: rgba(13,110,253,0.5); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5); font-weight: bold;">0.30</div>
                                    <div style="background: rgba(13,110,253,0.25); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5);">0.15</div>

                                    <!-- Ate row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">ate</div>
                                    <div style="background: rgba(13,110,253,0.1); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.10</div>
                                    <div style="background: rgba(13,110,253,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.15</div>
                                    <div style="background: rgba(13,110,253,0.4); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.5);">0.40</div>
                                    <div style="background: rgba(13,110,253,0.2); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.3);">0.20</div>
                                    <div style="background: rgba(13,110,253,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.15</div>

                                    <!-- Fish row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">fish</div>
                                    <div style="background: rgba(13,110,253,0.05); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.15);">0.05</div>
                                    <div style="background: rgba(13,110,253,0.1); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.10</div>
                                    <div style="background: rgba(13,110,253,0.2); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.3);">0.20</div>
                                    <div style="background: rgba(13,110,253,0.5); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.6); font-weight: bold;">0.50</div>
                                    <div style="background: rgba(13,110,253,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.15</div>
                                </div>
                            </div>

                            <div style="text-align: center; margin-top: 15px; padding: 10px; background: rgba(255,193,7,0.1); border-radius: 6px; font-size: 12px;">
                                <strong>Focus on "cat" row:</strong> Can attend to ALL words (including future words "ate" and "fish")
                            </div>

                            <div style="background: rgba(25,135,84,.08); border: 1px solid rgba(25,135,84,.3); border-radius: 8px; padding: 12px; margin-top: 15px;">
                                <p style="margin: 0; font-size: 13px;"><strong style="color: var(--emerald);">✓ Bidirectional Attention:</strong> Each word sees the entire sentence. Perfect for understanding context when you have the full input (like BERT, for classification, understanding).</p>
                            </div>
                        </div>
                    </div>

                    <!-- Decoder Attention visualization (hidden) -->
                    <div id="attention-decoder" class="attention-mode-demo" style="display: none;">
                        <div style="background: var(--panel); border: 1px solid var(--border); border-radius: 12px; padding: 20px; margin: 20px 0;">
                            <p style="text-align: center; margin-bottom: 15px; font-size: 14px;"><strong>Attention Matrix (Causal/Masked)</strong></p>
                            <p style="text-align: center; margin-bottom: 20px; font-size: 12px; color: var(--muted);">Each row shows how that word attends ONLY to itself and previous words. Future positions are masked (⨯).</p>

                            <div style="display: flex; justify-content: center;">
                                <div style="display: grid; grid-template-columns: 60px repeat(5, 65px); gap: 4px; font-size: 12px;">
                                    <!-- Header row -->
                                    <div></div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">the</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">black</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">cat</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">ate</div>
                                    <div style="text-align: center; font-weight: bold; padding: 8px;">fish</div>

                                    <!-- The row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">the</div>
                                    <div style="background: rgba(13,110,253,0.9); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.6); font-weight: bold; color: white;">1.00</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>

                                    <!-- Black row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">black</div>
                                    <div style="background: rgba(13,110,253,0.25); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.3);">0.20</div>
                                    <div style="background: rgba(13,110,253,0.8); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.6); font-weight: bold; color: white;">0.80</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>

                                    <!-- Cat row (highlighted) -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px; background: rgba(255,193,7,0.2); border-radius: 4px;">cat</div>
                                    <div style="background: rgba(13,110,253,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5);">0.10</div>
                                    <div style="background: rgba(13,110,253,0.9); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5); font-weight: bold; color: white;">0.85</div>
                                    <div style="background: rgba(13,110,253,0.1); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5);">0.05</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5); color: var(--muted); font-weight: bold;">⨯</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 2px solid rgba(255,193,7,0.5); color: var(--muted); font-weight: bold;">⨯</div>

                                    <!-- Ate row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">ate</div>
                                    <div style="background: rgba(13,110,253,0.05); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.15);">0.05</div>
                                    <div style="background: rgba(13,110,253,0.25); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.3);">0.20</div>
                                    <div style="background: rgba(13,110,253,0.4); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.5);">0.40</div>
                                    <div style="background: rgba(13,110,253,0.45); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.5); font-weight: bold;">0.35</div>
                                    <div style="background: rgba(200,200,200,0.15); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(150,150,150,0.2); color: var(--muted);">⨯</div>

                                    <!-- Fish row -->
                                    <div style="font-weight: bold; display: flex; align-items: center; padding: 0 8px;">fish</div>
                                    <div style="background: rgba(13,110,253,0.05); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.15);">0.05</div>
                                    <div style="background: rgba(13,110,253,0.1); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.2);">0.10</div>
                                    <div style="background: rgba(13,110,253,0.2); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.3);">0.20</div>
                                    <div style="background: rgba(13,110,253,0.5); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.6); font-weight: bold;">0.50</div>
                                    <div style="background: rgba(13,110,253,0.25); padding: 12px; text-align: center; border-radius: 4px; border: 1px solid rgba(13,110,253,0.3);">0.15</div>
                                </div>
                            </div>

                            <div style="text-align: center; margin-top: 15px; padding: 10px; background: rgba(255,193,7,0.1); border-radius: 6px; font-size: 12px;">
                                <strong>Focus on "cat" row:</strong> Can ONLY attend to previous words "the" and "black". Future positions are masked (⨯).
                            </div>

                            <div style="background: rgba(253,126,20,.08); border: 1px solid rgba(253,126,20,.3); border-radius: 8px; padding: 12px; margin-top: 15px;">
                                <p style="margin: 0 0 8px; font-size: 13px;"><strong style="color: var(--orange);">⚡ Causal/Masked Attention:</strong> Each word can only see itself and previous words. Essential for text generation where you predict one word at a time (like GPT, Claude).</p>
                                <div style="background: var(--bg); padding: 8px; border-radius: 4px; margin-top: 8px; font-size: 12px; font-family: monospace; color: var(--muted);">
                                    Future tokens are masked with -∞ before softmax → attention weight becomes 0
                                </div>
                            </div>
                        </div>
                    </div>
                </div>

                <div style="background: rgba(102,16,242,.08); border: 1px solid rgba(102,16,242,.3); border-radius: 8px; padding: 15px; margin-top: 20px;">
                    <h4 style="color: var(--indigo); margin: 0 0 8px;">Real-World Impact</h4>
                    <p style="margin: 0; font-size: 14px;">This is what powers ChatGPT, Claude, Gemini and most other modern AI language models. The attention mechanism lets them understand complex relationships between words, no matter how far apart they are in a sentence!</p>
                </div>
            </div>
            <button class="btn btn-primary" onclick="showStep2()">Next: How Does Attention Work? →</button>
        </div>

        <!-- Step 3: Query, Key, Value -->
        <div class="stage hidden" id="step2">
            <h2><span class="step-number">3</span>The Three Components: Query, Key, Value</h2>
            <div class="explanation">
                <strong>The Problem with Traditional Embeddings:</strong> In traditional word embeddings, each token gets just one static vector - but a single vector can't capture how words relate to each other in different contexts. The word "bank" means something different in "river bank" vs "bank account", but traditional embeddings can't adapt.
            </div>

            <div class="card">
                <!-- Traditional vs Transformer comparison -->
                <div style="background: var(--panel); border: 1px solid var(--border); border-radius: 12px; padding: 20px; margin-bottom: 25px;">
                    <h4 style="color: var(--blue); margin: 0 0 15px;">Traditional Embeddings vs Transformers</h4>

                    <div style="display: grid; grid-template-columns: 1fr 1fr; gap: 20px;">
                        <div style="padding: 15px; background: rgba(239,68,68,.08); border-radius: 8px; border-left: 4px solid var(--red);">
                            <h5 style="color: var(--red); margin: 0 0 10px;">Traditional: Single Vector</h5>
                            <div style="display: flex; align-items: center; gap: 10px; margin: 10px 0;">
                                <span class="chip" style="font-size: 12px;">cat</span>
                                <span style="color: var(--muted);">→</span>
                                <div style="background: white; border: 1px solid var(--border); padding: 8px; border-radius: 6px; font-family: monospace; font-size: 11px;">
                                    [0.2, -0.5, 0.8]
                                </div>
                            </div>
                            <p style="margin: 10px 0 0; font-size: 12px; color: var(--muted);">
                                Same vector regardless of context.<br>
                                Can't ask questions or provide answers.
                            </p>
                        </div>

                        <div style="padding: 15px; background: rgba(25,135,84,.08); border-radius: 8px; border-left: 4px solid var(--emerald);">
                            <h5 style="color: var(--emerald); margin: 0 0 10px;">Transformers: Three Vectors</h5>
                            <div style="display: flex; flex-direction: column; gap: 5px; margin: 10px 0;">
                                <div style="display: flex; align-items: center; gap: 10px;">
                                    <span class="chip" style="font-size: 12px;">cat</span>
                                    <span style="color: var(--muted);">→</span>
                                    <div style="display: flex; flex-direction: column; gap: 3px;">
                                        <div style="background: rgba(239,68,68,.1); border: 1px solid rgba(239,68,68,.3); padding: 4px 8px; border-radius: 4px; font-family: monospace; font-size: 10px;">
                                            Q: [0.1, 0.9, -0.2]
                                        </div>
                                        <div style="background: rgba(34,197,94,.1); border: 1px solid rgba(34,197,94,.3); padding: 4px 8px; border-radius: 4px; font-family: monospace; font-size: 10px;">
                                            K: [0.8, -0.3, 0.5]
                                        </div>
                                        <div style="background: rgba(59,130,246,.1); border: 1px solid rgba(59,130,246,.3); padding: 4px 8px; border-radius: 4px; font-family: monospace; font-size: 10px;">
                                            V: [0.3, 0.6, -0.1]
                                        </div>
                                    </div>
                                </div>
                            </div>
                            <p style="margin: 10px 0 0; font-size: 12px; color: var(--muted);">
                                Dynamic representations for each role.<br>
                                Can query, be queried, and provide values.
                            </p>
                        </div>
                    </div>
                </div>

                <h4 style="color: var(--blue); margin-bottom: 15px;">How Q, K, V Are Created</h4>
                <p>Each word's embedding is transformed by three learned matrices to create these specialized representations:</p>

                <div style="display: grid; grid-template-columns: 1fr 1fr 1fr; gap: 15px; margin: 20px 0;">
                    <div style="text-align: center; padding: 15px; background: rgba(239,68,68,.08); border-radius: 8px; border: 1px solid rgba(239,68,68,.3);">
                        <div class="chip query" style="margin-bottom: 10px;">Query (Q)</div>
                        <p style="font-size: 13px; color: var(--muted); margin: 8px 0;"><strong>W<sub>Q</sub></strong> matrix</p>
                        <p style="font-size: 12px; margin: 0;">"What am I looking for?"</p>
                    </div>
                    <div style="text-align: center; padding: 15px; background: rgba(34,197,94,.08); border-radius: 8px; border: 1px solid rgba(34,197,94,.3);">
                        <div class="chip key" style="margin-bottom: 10px;">Key (K)</div>
                        <p style="font-size: 13px; color: var(--muted); margin: 8px 0;"><strong>W<sub>K</sub></strong> matrix</p>
                        <p style="font-size: 12px; margin: 0;">"What do I offer?"</p>
                    </div>
                    <div style="text-align: center; padding: 15px; background: rgba(59,130,246,.08); border-radius: 8px; border: 1px solid rgba(59,130,246,.3);">
                        <div class="chip value" style="margin-bottom: 10px;">Value (V)</div>
                        <p style="font-size: 13px; color: var(--muted); margin: 8px 0;"><strong>W<sub>V</sub></strong> matrix</p>
                        <p style="font-size: 12px; margin: 0;">"What information do I contain?"</p>
                    </div>
                </div>

                <!-- Embedding Values Explanation -->
                <div style="background: rgba(255,193,7,.08); border: 1px solid rgba(255,193,7,.3); border-radius: 8px; padding: 15px; margin: 20px 0;">
                    <h4 style="color: var(--orange); margin: 0 0 12px;">Understanding Embedding Values</h4>
                    <p style="margin: 0 0 8px; font-size: 13px; line-height: 1.5;">Embeddings are <strong>learned representations</strong> where each dimension captures some learned concept. The numbers are <em>relative strengths</em> - higher means stronger association. In real models, there are 768-12,288 dimensions!</p>
                    <div style="background: var(--bg); padding: 10px; border-radius: 6px; margin-top: 10px;">
                        <div style="font-size: 11px; color: var(--muted); margin-bottom: 6px;">Example comparison:</div>
                        <div style="display: grid; grid-template-columns: auto 1fr 1fr 1fr; gap: 8px; font-size: 11px;">
                            <div style="font-weight: 600;"></div>
                            <div style="text-align: center; font-weight: 600;">animal-like</div>
                            <div style="text-align: center; font-weight: 600;">noun-like</div>
                            <div style="text-align: center; font-weight: 600;">domestic</div>

                            <div style="font-weight: 600; background: rgba(255,193,7,.15); padding: 4px 6px; border-radius: 3px; border: 2px solid rgba(255,193,7,.4);">cat</div>
                            <div style="text-align: center; background: rgba(102,16,242,.15); padding: 2px; border-radius: 3px; border: 2px solid rgba(255,193,7,.4);">0.2</div>
                            <div style="text-align: center; background: rgba(102,16,242,.25); padding: 2px; border-radius: 3px; border: 2px solid rgba(255,193,7,.4);">0.8</div>
                            <div style="text-align: center; background: rgba(102,16,242,.15); padding: 2px; border-radius: 3px; border: 2px solid rgba(255,193,7,.4);">0.1</div>

                            <div style="font-weight: 600;">wolf</div>
                            <div style="text-align: center; background: rgba(102,16,242,.25); padding: 2px; border-radius: 3px;">0.7</div>
                            <div style="text-align: center; background: rgba(102,16,242,.25); padding: 2px; border-radius: 3px;">0.6</div>
                            <div style="text-align: center; background: rgba(102,16,242,.05); padding: 2px; border-radius: 3px;">-0.4</div>

                            <div style="font-weight: 600;">runs</div>
                            <div style="text-align: center; background: rgba(102,16,242,.05); padding: 2px; border-radius: 3px;">-0.1</div>
                            <div style="text-align: center; background: rgba(102,16,242,.05); padding: 2px; border-radius: 3px;">-0.3</div>
                            <div style="text-align: center; background: rgba(102,16,242,.15); padding: 2px; border-radius: 3px;">0.0</div>
                        </div>
                        <div style="font-size: 10px; color: var(--muted); margin-top: 6px;">→ "cat" scores high on noun-like (0.8), "wolf" scores high on animal-like (0.7) and wild (-0.4), "runs" is a verb (low noun score)</div>
                    </div>
                    <div style="background: rgba(255,193,7,.12); border-left: 3px solid rgba(255,193,7,.6); padding: 8px 12px; border-radius: 4px; margin-top: 12px;">
                        <p style="margin: 0; font-size: 12px; color: var(--text);"><strong>↓ We'll use the cat embedding [0.2, 0.8, 0.1] in the transformation example below</strong></p>
                    </div>
                </div>

                <div class="goal">
                    <h3>Matrix Transformation Example</h3>
                    <p>Let's see how the word "cat" gets transformed (simplified 3D example):</p>

                    <!-- Matrix Toggle Buttons -->
                    <div style="display: flex; justify-content: center; gap: 8px; margin: 15px 0;">
                        <button class="btn matrix-toggle active" data-matrix="query" onclick="showMatrix('query')">
                            <span style="color: var(--red);">●</span> W<sub>Q</sub> Query
                        </button>
                        <button class="btn matrix-toggle" data-matrix="key" onclick="showMatrix('key')">
                            <span style="color: var(--emerald);">●</span> W<sub>K</sub> Key
                        </button>
                        <button class="btn matrix-toggle" data-matrix="value" onclick="showMatrix('value')">
                            <span style="color: var(--blue);">●</span> W<sub>V</sub> Value
                        </button>
                    </div>

                    <div style="margin: 20px 0; font-family: ui-monospace, monospace; font-size: 13px;">
                        <!-- Query Matrix (default visible) -->
                        <div id="matrix-query" class="matrix-demo">
                            <div style="display: grid; grid-template-columns: 1fr auto 1fr auto 1fr; gap: 10px; align-items: center; margin: 15px 0;">
                                <!-- Word Embedding -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 8px; color: var(--text);">Embedding</div>
                                    <div style="font-size: 11px; color: var(--muted); margin-bottom: 4px;">"cat"</div>
                                    <div style="background: var(--panel); padding: 8px 12px; border-radius: 6px; border: 1px solid var(--border); display: inline-block;">
                                        <div style="padding: 2px 0; font-size: 12px;">0.2</div>
                                        <div style="padding: 2px 0; font-size: 12px;">0.8</div>
                                        <div style="padding: 2px 0; font-size: 12px;">0.1</div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3 dimensions</div>
                                </div>

                                <!-- × symbol -->
                                <div style="text-align: center; font-size: 20px; color: var(--blue);">×</div>

                                <!-- W_Q Matrix -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 4px; color: var(--red);">W<sub>Q</sub> (weights)</div>
                                    <div style="font-size: 9px; color: var(--muted); margin-bottom: 6px;">learned, shared</div>
                                    <div style="background: repeating-linear-gradient(45deg, rgba(239,68,68,.06), rgba(239,68,68,.06) 10px, rgba(239,68,68,.12) 10px, rgba(239,68,68,.12) 20px); padding: 8px 12px; border-radius: 6px; border: 2px dashed rgba(239,68,68,.5); display: inline-block;">
                                        <div style="padding: 2px 0; border-left: 3px solid rgba(239,68,68,0.5); padding-left: 6px; margin-bottom: 2px; font-size: 12px;">
                                            <span style="background: rgba(239,68,68,0.15); padding: 1px 3px; border-radius: 2px; font-size: 9px; margin-right: 4px;">row 1</span>[1.0, 0.2, 0.5]
                                        </div>
                                        <div style="padding: 2px 0; padding-left: 6px; margin-bottom: 2px; font-size: 12px; opacity: 0.5;">
                                            <span style="font-size: 9px; margin-right: 4px; opacity: 0.6;">row 2</span>[0.1, 1.5, 0.3]
                                        </div>
                                        <div style="padding: 2px 0; padding-left: 6px; font-size: 12px; opacity: 0.5;">
                                            <span style="font-size: 9px; margin-right: 4px; opacity: 0.6;">row 3</span>[0.4, 0.2, 0.9]
                                        </div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3×3 weight matrix</div>
                                </div>

                                <!-- = symbol -->
                                <div style="text-align: center; font-size: 20px; color: var(--blue);">=</div>

                                <!-- Query Result -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 8px; color: var(--red);">Query Output</div>
                                    <div style="font-size: 11px; color: var(--muted); margin-bottom: 4px;">Q<sub>cat</sub></div>
                                    <div style="background: rgba(239,68,68,.15); padding: 8px 12px; border-radius: 6px; border: 1px solid rgba(239,68,68,.4); display: inline-block;">
                                        <div style="padding: 2px 0; color: var(--red); font-weight: bold; font-size: 13px; border-left: 3px solid var(--red); padding-left: 6px; margin-bottom: 2px;">0.41</div>
                                        <div style="padding: 2px 0; color: var(--red); font-size: 12px; padding-left: 6px; margin-bottom: 2px; opacity: 0.5;">1.25</div>
                                        <div style="padding: 2px 0; color: var(--red); font-size: 12px; padding-left: 6px; opacity: 0.5;">0.33</div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3 dimensions</div>
                                </div>
                            </div>
                            <div style="text-align: center; color: var(--muted); font-size: 12px; margin: 10px 0;">
                                The <strong>Query</strong> represents "what this word is looking for" in other words
                            </div>
                        </div>

                        <!-- Key Matrix (hidden by default) -->
                        <div id="matrix-key" class="matrix-demo" style="display: none;">
                            <div style="display: grid; grid-template-columns: 1fr auto 1fr auto 1fr; gap: 10px; align-items: center; margin: 15px 0;">
                                <!-- Word Embedding -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 8px; color: var(--text);">Embedding</div>
                                    <div style="font-size: 11px; color: var(--muted); margin-bottom: 4px;">"cat"</div>
                                    <div style="background: var(--panel); padding: 8px 12px; border-radius: 6px; border: 1px solid var(--border); display: inline-block;">
                                        <div style="padding: 2px 0; font-size: 12px;">0.2</div>
                                        <div style="padding: 2px 0; font-size: 12px;">0.8</div>
                                        <div style="padding: 2px 0; font-size: 12px;">0.1</div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3 dimensions</div>
                                </div>

                                <!-- × symbol -->
                                <div style="text-align: center; font-size: 20px; color: var(--blue);">×</div>

                                <!-- W_K Matrix -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 4px; color: var(--emerald);">W<sub>K</sub> (weights)</div>
                                    <div style="font-size: 9px; color: var(--muted); margin-bottom: 6px;">learned, shared</div>
                                    <div style="background: repeating-linear-gradient(45deg, rgba(34,197,94,.06), rgba(34,197,94,.06) 10px, rgba(34,197,94,.12) 10px, rgba(34,197,94,.12) 20px); padding: 8px 12px; border-radius: 6px; border: 2px dashed rgba(34,197,94,.5); display: inline-block;">
                                        <div style="padding: 2px 0; border-left: 3px solid rgba(34,197,94,0.6); padding-left: 6px; margin-bottom: 2px; font-size: 12px;">
                                            <span style="background: rgba(34,197,94,0.15); padding: 1px 3px; border-radius: 2px; font-size: 9px; margin-right: 4px;">row 1</span>[0.8, 1.1, 0.2]
                                        </div>
                                        <div style="padding: 2px 0; padding-left: 6px; margin-bottom: 2px; font-size: 12px; opacity: 0.5;">
                                            <span style="font-size: 9px; margin-right: 4px; opacity: 0.6;">row 2</span>[0.3, 0.7, 1.2]
                                        </div>
                                        <div style="padding: 2px 0; padding-left: 6px; font-size: 12px; opacity: 0.5;">
                                            <span style="font-size: 9px; margin-right: 4px; opacity: 0.6;">row 3</span>[1.0, 0.1, 0.6]
                                        </div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3×3 weight matrix</div>
                                </div>

                                <!-- = symbol -->
                                <div style="text-align: center; font-size: 20px; color: var(--blue);">=</div>

                                <!-- Key Result -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 8px; color: var(--emerald);">Key Output</div>
                                    <div style="font-size: 11px; color: var(--muted); margin-bottom: 4px;">K<sub>cat</sub></div>
                                    <div style="background: rgba(34,197,94,.15); padding: 8px 12px; border-radius: 6px; border: 1px solid rgba(34,197,94,.4); display: inline-block;">
                                        <div style="padding: 2px 0; color: var(--emerald); font-weight: bold; font-size: 13px; border-left: 3px solid var(--emerald); padding-left: 6px; margin-bottom: 2px;">1.06</div>
                                        <div style="padding: 2px 0; color: var(--emerald); font-size: 12px; padding-left: 6px; margin-bottom: 2px; opacity: 0.5;">0.74</div>
                                        <div style="padding: 2px 0; color: var(--emerald); font-size: 12px; padding-left: 6px; opacity: 0.5;">0.34</div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3 dimensions</div>
                                </div>
                            </div>
                            <div style="text-align: center; color: var(--muted); font-size: 12px; margin: 10px 0;">
                                The <strong>Key</strong> represents "what type of information this word can provide"
                            </div>
                        </div>

                        <!-- Value Matrix (hidden by default) -->
                        <div id="matrix-value" class="matrix-demo" style="display: none;">
                            <div style="display: grid; grid-template-columns: 1fr auto 1fr auto 1fr; gap: 10px; align-items: center; margin: 15px 0;">
                                <!-- Word Embedding -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 8px; color: var(--text);">Embedding</div>
                                    <div style="font-size: 11px; color: var(--muted); margin-bottom: 4px;">"cat"</div>
                                    <div style="background: var(--panel); padding: 8px 12px; border-radius: 6px; border: 1px solid var(--border); display: inline-block;">
                                        <div style="padding: 2px 0; font-size: 12px;">0.2</div>
                                        <div style="padding: 2px 0; font-size: 12px;">0.8</div>
                                        <div style="padding: 2px 0; font-size: 12px;">0.1</div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3 dimensions</div>
                                </div>

                                <!-- × symbol -->
                                <div style="text-align: center; font-size: 20px; color: var(--blue);">×</div>

                                <!-- W_V Matrix -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 4px; color: var(--blue);">W<sub>V</sub> (weights)</div>
                                    <div style="font-size: 9px; color: var(--muted); margin-bottom: 6px;">learned, shared</div>
                                    <div style="background: repeating-linear-gradient(45deg, rgba(59,130,246,.06), rgba(59,130,246,.06) 10px, rgba(59,130,246,.12) 10px, rgba(59,130,246,.12) 20px); padding: 8px 12px; border-radius: 6px; border: 2px dashed rgba(59,130,246,.5); display: inline-block;">
                                        <div style="padding: 2px 0; border-left: 3px solid rgba(59,130,246,0.6); padding-left: 6px; margin-bottom: 2px; font-size: 12px;">
                                            <span style="background: rgba(59,130,246,0.15); padding: 1px 3px; border-radius: 2px; font-size: 9px; margin-right: 4px;">row 1</span>[0.6, 0.9, 1.1]
                                        </div>
                                        <div style="padding: 2px 0; padding-left: 6px; margin-bottom: 2px; font-size: 12px; opacity: 0.5;">
                                            <span style="font-size: 9px; margin-right: 4px; opacity: 0.6;">row 2</span>[1.3, 0.4, 0.7]
                                        </div>
                                        <div style="padding: 2px 0; padding-left: 6px; font-size: 12px; opacity: 0.5;">
                                            <span style="font-size: 9px; margin-right: 4px; opacity: 0.6;">row 3</span>[0.2, 1.5, 0.3]
                                        </div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3×3 weight matrix</div>
                                </div>

                                <!-- = symbol -->
                                <div style="text-align: center; font-size: 20px; color: var(--blue);">=</div>

                                <!-- Value Result -->
                                <div style="text-align: center;">
                                    <div style="font-weight: bold; margin-bottom: 8px; color: var(--blue);">Value Output</div>
                                    <div style="font-size: 11px; color: var(--muted); margin-bottom: 4px;">V<sub>cat</sub></div>
                                    <div style="background: rgba(59,130,246,.15); padding: 8px 12px; border-radius: 6px; border: 1px solid rgba(59,130,246,.4); display: inline-block;">
                                        <div style="padding: 2px 0; color: var(--blue); font-weight: bold; font-size: 13px; border-left: 3px solid var(--blue); padding-left: 6px; margin-bottom: 2px;">0.95</div>
                                        <div style="padding: 2px 0; color: var(--blue); font-size: 12px; padding-left: 6px; margin-bottom: 2px; opacity: 0.5;">0.65</div>
                                        <div style="padding: 2px 0; color: var(--blue); font-size: 12px; padding-left: 6px; opacity: 0.5;">1.27</div>
                                    </div>
                                    <div style="font-size: 10px; color: var(--muted); margin-top: 4px;">3 dimensions</div>
                                </div>
                            </div>
                            <div style="text-align: center; color: var(--muted); font-size: 12px; margin: 10px 0;">
                                The <strong>Value</strong> represents "the actual content/meaning this word contributes"
                            </div>
                        </div>
                    </div>

                    <!-- Interactive "What's Really Happening" Explanations -->
                    <div style="margin-top: 20px;">
                        <!-- Query Explanation (default visible) -->
                        <div id="explanation-query" class="matrix-demo">
                            <div style="background: rgba(239,68,68,.08); border: 1px solid rgba(239,68,68,.3); border-radius: 8px; padding: 15px;">
                                <h4 style="color: var(--red); margin: 0 0 12px;">What is W<sub>Q</sub> Really Doing?</h4>
                                <p style="margin: 0 0 12px; font-size: 14px;"><strong>W<sub>Q</sub></strong> creates a "search pattern" by recombining embedding dimensions.</p>

                                <div style="background: rgba(239,68,68,.05); border-left: 3px solid rgba(239,68,68,0.5); padding: 10px 12px; border-radius: 4px; margin: 12px 0;">
                                    <p style="margin: 0 0 8px; font-size: 13px;">
                                        <span style="background: rgba(239,68,68,0.15); padding: 2px 6px; border-radius: 3px; font-size: 10px; margin-right: 6px; font-weight: 600;">row 1</span>
                                        <strong>Row 1 of W<sub>Q</sub></strong> [1.0, 0.2, 0.5] creates the first Query dimension:
                                    </p>
                                </div>
                                <div style="background: var(--bg); padding: 12px; border-radius: 6px; margin: 8px 0;">
                                    <div style="margin-bottom: 8px; font-size: 12px; font-family: monospace;">1.0×(0.2) + 0.2×(0.8) + 0.5×(0.1) = <strong style="color: var(--red);">0.41</strong></div>
                                    <div style="display: flex; align-items: center; gap: 8px;">
                                        <div style="flex: 1; height: 24px; background: linear-gradient(90deg, rgba(239,68,68,0.3) 0%, rgba(239,68,68,0.3) 48.8%, rgba(239,68,68,0.2) 48.8%, rgba(239,68,68,0.2) 87.8%, rgba(239,68,68,0.1) 87.8%); border-radius: 4px; border: 1px solid rgba(239,68,68,0.4); position: relative;">
                                            <span style="position: absolute; left: 24%; font-size: 10px; font-weight: bold; color: var(--red);">0.2 (49%)</span>
                                            <span style="position: absolute; left: 68%; font-size: 10px; font-weight: bold; color: var(--red);">0.16 (39%)</span>
                                            <span style="position: absolute; left: 93%; font-size: 10px; font-weight: bold; color: var(--red);">0.05 (12%)</span>
                                        </div>
                                    </div>
                                    <div style="font-size: 11px; color: var(--muted); margin-top: 6px;">→ Creates a "search filter" heavily weighing animalness</div>
                                </div>

                                <div style="background: rgba(13,110,253,.08); border-left: 3px solid var(--blue); padding: 10px 12px; border-radius: 4px; margin-top: 12px;">
                                    <p style="margin: 0; font-size: 13px;"><strong>Metaphor:</strong> W<sub>Q</sub> turns "cat" into a magnet <em>asking</em> "I'm looking for animal-related, noun-like words"</p>
                                </div>
                            </div>
                        </div>

                        <!-- Key Explanation (hidden by default) -->
                        <div id="explanation-key" class="matrix-demo" style="display: none;">
                            <div style="background: rgba(34,197,94,.08); border: 1px solid rgba(34,197,94,.3); border-radius: 8px; padding: 15px;">
                                <h4 style="color: var(--emerald); margin: 0 0 12px;">What is W<sub>K</sub> Really Doing?</h4>
                                <p style="margin: 0 0 12px; font-size: 14px;"><strong>W<sub>K</sub></strong> creates an "identity tag" by recombining embedding dimensions.</p>

                                <div style="background: rgba(34,197,94,.05); border-left: 3px solid rgba(34,197,94,0.6); padding: 10px 12px; border-radius: 4px; margin: 12px 0;">
                                    <p style="margin: 0 0 8px; font-size: 13px;">
                                        <span style="background: rgba(34,197,94,0.15); padding: 2px 6px; border-radius: 3px; font-size: 10px; margin-right: 6px; font-weight: 600;">row 1</span>
                                        <strong>Row 1 of W<sub>K</sub></strong> [0.8, 1.1, 0.2] creates the first Key dimension:
                                    </p>
                                </div>
                                <div style="background: var(--bg); padding: 12px; border-radius: 6px; margin: 8px 0;">
                                    <div style="margin-bottom: 8px; font-size: 12px; font-family: monospace;">0.8×(0.2) + 1.1×(0.8) + 0.2×(0.1) = <strong style="color: var(--emerald);">1.06</strong></div>
                                    <div style="display: flex; align-items: center; gap: 8px;">
                                        <div style="flex: 1; height: 24px; background: linear-gradient(90deg, rgba(34,197,94,0.2) 0%, rgba(34,197,94,0.2) 15.1%, rgba(34,197,94,0.4) 15.1%, rgba(34,197,94,0.4) 98.1%, rgba(34,197,94,0.15) 98.1%); border-radius: 4px; border: 1px solid rgba(34,197,94,0.4); position: relative;">
                                            <span style="position: absolute; left: 7%; font-size: 10px; font-weight: bold; color: var(--emerald);">0.16 (15%)</span>
                                            <span style="position: absolute; left: 56%; font-size: 10px; font-weight: bold; color: var(--emerald);">0.88 (83%)</span>
                                            <span style="position: absolute; left: 99%; font-size: 10px; font-weight: bold; color: var(--emerald); transform: translateX(-100%);">0.02 (2%)</span>
                                        </div>
                                    </div>
                                    <div style="font-size: 11px; color: var(--muted); margin-top: 6px;">→ Creates an "identity signal" emphasizing noun-ness with some animalness</div>
                                </div>

                                <div style="background: rgba(13,110,253,.08); border-left: 3px solid var(--blue); padding: 10px 12px; border-radius: 4px; margin-top: 12px;">
                                    <p style="margin: 0; font-size: 13px;"><strong>Metaphor:</strong> W<sub>K</sub> turns "cat" into a magnet <em>offering</em> "I provide noun-related, animal information"</p>
                                </div>
                            </div>
                        </div>

                        <!-- Value Explanation (hidden by default) -->
                        <div id="explanation-value" class="matrix-demo" style="display: none;">
                            <div style="background: rgba(59,130,246,.08); border: 1px solid rgba(59,130,246,.3); border-radius: 8px; padding: 15px;">
                                <h4 style="color: var(--blue); margin: 0 0 12px;">What is W<sub>V</sub> Really Doing?</h4>
                                <p style="margin: 0 0 12px; font-size: 14px;"><strong>W<sub>V</sub></strong> creates the "content package" that will be passed forward.</p>

                                <div style="background: rgba(59,130,246,.05); border-left: 3px solid rgba(59,130,246,0.6); padding: 10px 12px; border-radius: 4px; margin: 12px 0;">
                                    <p style="margin: 0 0 8px; font-size: 13px;">
                                        <span style="background: rgba(59,130,246,0.15); padding: 2px 6px; border-radius: 3px; font-size: 10px; margin-right: 6px; font-weight: 600;">row 1</span>
                                        <strong>Row 1 of W<sub>V</sub></strong> [0.6, 0.9, 1.1] creates the first Value dimension:
                                    </p>
                                </div>
                                <div style="background: var(--bg); padding: 12px; border-radius: 6px; margin: 8px 0;">
                                    <div style="margin-bottom: 8px; font-size: 12px; font-family: monospace;">0.6×(0.2) + 0.9×(0.8) + 1.1×(0.1) = <strong style="color: var(--blue);">0.95</strong></div>
                                    <div style="display: flex; align-items: center; gap: 8px;">
                                        <div style="flex: 1; height: 24px; background: linear-gradient(90deg, rgba(59,130,246,0.2) 0%, rgba(59,130,246,0.2) 12.6%, rgba(59,130,246,0.35) 12.6%, rgba(59,130,246,0.35) 88.4%, rgba(59,130,246,0.25) 88.4%); border-radius: 4px; border: 1px solid rgba(59,130,246,0.4); position: relative;">
                                            <span style="position: absolute; left: 6%; font-size: 10px; font-weight: bold; color: var(--blue);">0.12 (13%)</span>
                                            <span style="position: absolute; left: 50%; font-size: 10px; font-weight: bold; color: var(--blue);">0.72 (76%)</span>
                                            <span style="position: absolute; left: 94%; font-size: 10px; font-weight: bold; color: var(--blue);">0.11 (11%)</span>
                                        </div>
                                    </div>
                                    <div style="font-size: 11px; color: var(--muted); margin-top: 6px;">→ Packages a balanced blend of all features for downstream layers</div>
                                </div>

                                <div style="background: rgba(13,110,253,.08); border-left: 3px solid var(--blue); padding: 10px 12px; border-radius: 4px; margin-top: 12px;">
                                    <p style="margin: 0; font-size: 13px;"><strong>Metaphor:</strong> W<sub>V</sub> packages "cat's" actual semantic content to be delivered based on attention weights</p>
                                </div>
                            </div>
                        </div>
                    </div>
                </div>

                <div class="goal" style="margin-top: 20px;">
                    <h3>What Happens Next: Q · K<sup>T</sup></h3>
                    <p style="margin: 0 0 15px;">Now that we have Query, Key, and Value vectors for each word, we use them to calculate <strong>attention scores</strong> through dot products.</p>

                    <div style="background: var(--bg); border-radius: 8px; padding: 15px; margin: 15px 0;">
                        <h4 style="color: var(--blue); margin: 0 0 12px; font-size: 15px;">The Attention Score Formula</h4>
                        <div style="background: rgba(13,110,253,.08); padding: 12px; border-radius: 6px; font-family: monospace; font-size: 14px; text-align: center; border: 1px solid rgba(13,110,253,.3);">
                            Attention(Q, K, V) = softmax(Q · K<sup>T</sup> / √d<sub>k</sub>) · V
                        </div>
                        <p style="margin: 12px 0 0; font-size: 13px; color: var(--muted);">where d<sub>k</sub> is the dimension of the key vectors (scaling factor)</p>
                    </div>

                    <div style="display: grid; grid-template-columns: 1fr 1fr; gap: 15px; margin: 15px 0;">
                        <div style="background: rgba(239,68,68,.08); border: 1px solid rgba(239,68,68,.3); border-radius: 8px; padding: 12px;">
                            <h5 style="color: var(--red); margin: 0 0 8px; font-size: 14px;">Step 1: Q · K<sup>T</sup></h5>
                            <p style="margin: 0; font-size: 12px;">Compare "cat's" Query with all Keys via dot product:</p>
                            <div style="background: var(--bg); padding: 8px; border-radius: 4px; margin-top: 8px; font-size: 11px; font-family: monospace;">
                                Q<sub>cat</sub> · K<sub>the</sub> = low score<br>
                                Q<sub>cat</sub> · K<sub>black</sub> = <strong>high score</strong><br>
                                Q<sub>cat</sub> · K<sub>cat</sub> = <strong>very high score</strong><br>
                                Q<sub>cat</sub> · K<sub>ate</sub> = medium score<br>
                                Q<sub>cat</sub> · K<sub>fish</sub> = medium score
                            </div>
                            <p style="margin: 8px 0 0; font-size: 11px; color: var(--muted);">Higher dot product = better match between what "cat" is looking for and what that word offers</p>
                        </div>

                        <div style="background: rgba(59,130,246,.08); border: 1px solid rgba(59,130,246,.3); border-radius: 8px; padding: 12px;">
                            <h5 style="color: var(--blue); margin: 0 0 8px; font-size: 14px;">Step 2: Softmax → Weights</h5>
                            <p style="margin: 0; font-size: 12px;">Convert scores to probabilities (sum to 1):</p>
                            <div style="background: var(--bg); padding: 8px; border-radius: 4px; margin-top: 8px; font-size: 11px;">
                                <div style="margin-bottom: 4px;">the: 10% <div style="height: 6px; width: 10%; background: rgba(13,110,253,0.3); border-radius: 3px;"></div></div>
                                <div style="margin-bottom: 4px;">black: <strong>45%</strong> <div style="height: 6px; width: 45%; background: rgba(13,110,253,0.6); border-radius: 3px;"></div></div>
                                <div style="margin-bottom: 4px;">cat: <strong>30%</strong> <div style="height: 6px; width: 30%; background: rgba(13,110,253,0.5); border-radius: 3px;"></div></div>
                                <div style="margin-bottom: 4px;">ate: 10% <div style="height: 6px; width: 10%; background: rgba(13,110,253,0.3); border-radius: 3px;"></div></div>
                                <div>fish: 5% <div style="height: 6px; width: 5%; background: rgba(13,110,253,0.2); border-radius: 3px;"></div></div>
                            </div>
                            <p style="margin: 8px 0 0; font-size: 11px; color: var(--muted);">These are the attention weights!</p>
                        </div>
                    </div>

                    <div style="background: rgba(25,135,84,.08); border: 1px solid rgba(25,135,84,.3); border-radius: 8px; padding: 12px; margin-top: 15px;">
                        <h5 style="color: var(--emerald); margin: 0 0 8px; font-size: 14px;">Step 3: Weighted Sum of Values</h5>
                        <p style="margin: 0; font-size: 12px;">Multiply each word's Value by its attention weight and sum:</p>
                        <div style="background: var(--bg); padding: 10px; border-radius: 6px; margin-top: 8px; font-family: monospace; font-size: 12px; text-align: center;">
                            Output<sub>cat</sub> = 0.10×V<sub>the</sub> + 0.45×V<sub>black</sub> + 0.30×V<sub>cat</sub> + 0.10×V<sub>ate</sub> + 0.05×V<sub>fish</sub>
                        </div>
                        <p style="margin: 8px 0 0; font-size: 11px; color: var(--muted);">The output for "cat" is now enriched with information from "black" (its most attended word) and other context!</p>
                    </div>

                    <div style="background: rgba(102,16,242,.08); border-left: 3px solid var(--indigo); padding: 10px 12px; border-radius: 4px; margin-top: 15px;">
                        <p style="margin: 0; font-size: 13px;"><strong>Why This Works:</strong> The Query-Key dot product is high when both vectors point in similar directions - meaning "cat's" query matches well with "black's" key. This automatically determines which words provide the most relevant context!</p>
                    </div>
                </div>
            </div>
            <button class="btn btn-primary" onclick="showCalculator()">Next: Try the Live Calculator! →</button>
    </div>

        <!-- Step 5: Live Attention Calculator -->
        <div class="stage hidden" id="calculator">
            <h2><span class="step-number">5</span>Live Attention Calculator</h2>
            <div class="explanation">
                <strong>The Real Mechanism:</strong> Attention scores come from dot products between Query and Key vectors. Let's see how changing the Query or Key vectors affects attention!
            </div>
            <div class="card">
                <!-- Show Current Vectors -->
                <div style="display: grid; grid-template-columns: 1fr 1fr; gap: 20px; margin: 20px 0;">
                    <div style="padding: 15px; background: rgba(239,68,68,.08); border-radius: 8px; border: 1px solid rgba(239,68,68,.3);">
                        <h4 style="color: var(--red); margin: 0 0 10px;">Query vector for "cat"</h4>
                        <div style="font-family: ui-monospace, monospace; font-size: 13px;">
                            Q_cat = [<span id="q-cat-0">0.41</span>, <span id="q-cat-1">1.25</span>, <span id="q-cat-2">0.33</span>]
                        </div>
                        <div style="margin-top: 10px;">
                            <label style="display: block; font-size: 12px; margin-bottom: 5px;">Adjust Q_cat[0]:</label>
                            <input type="range" min="-2" max="2" step="0.01" value="0.41"
                                   oninput="updateQueryValue(0, this.value)"
                                   style="width: 100%;">
                        </div>
                        <div style="margin-top: 8px;">
                            <label style="display: block; font-size: 12px; margin-bottom: 5px;">Adjust Q_cat[1]:</label>
                            <input type="range" min="-2" max="2" step="0.01" value="1.25"
                                   oninput="updateQueryValue(1, this.value)"
                                   style="width: 100%;">
                        </div>
                        <div style="margin-top: 8px;">
                            <label style="display: block; font-size: 12px; margin-bottom: 5px;">Adjust Q_cat[2]:</label>
                            <input type="range" min="-2" max="2" step="0.01" value="0.33"
                                   oninput="updateQueryValue(2, this.value)"
                                   style="width: 100%;">
                        </div>

                        <div style="margin-top: 12px; padding: 10px; background: rgba(255,193,7,.1); border-radius: 6px; border-left: 3px solid var(--orange);">
                            <p style="margin: 0; font-size: 12px; color: var(--text);"><strong>What's happening:</strong> When you adjust Q_cat values, you're changing what "cat" is "looking for". Higher values in dimensions where Key vectors also have high values = stronger attention!</p>
                        </div>
                    </div>

                    <div style="padding: 15px; background: rgba(34,197,94,.08); border-radius: 8px; border: 1px solid rgba(34,197,94,.3);">
                        <h4 style="color: var(--emerald); margin: 0 0 10px;">Key vectors (fixed)</h4>
                        <div style="font-family: ui-monospace, monospace; font-size: 12px;">
                            K_the = [0.1, 0.2, 0.1]<br>
                            K_black = [0.8, 1.0, 0.3]<br>
                            K_cat = [1.06, 0.74, 0.34]<br>
                            K_ate = [0.4, 0.6, 0.8]<br>
                            K_fish = [0.2, 0.3, 0.9]
                        </div>
                    </div>
                </div>

                <div class="goal">
                    <h3>Live Dot Product Calculation</h3>
                    <div id="dot-products" style="margin: 15px 0; padding: 15px; background: var(--bg); border-radius: 8px; border: 1px solid var(--border);">
                        <div style="font-family: ui-monospace, monospace; font-size: 13px;" id="calculations">
                            <!-- Will be populated by JavaScript -->
                        </div>
                    </div>

                    <div style="background: rgba(59,130,246,.08); border: 1px solid rgba(59,130,246,.3); border-radius: 8px; padding: 12px; margin-top: 10px;">
                        <p style="margin: 0; font-size: 12px; color: var(--text);"><strong>Example:</strong> If you increase Q_cat[1] to match K_black[1] (both = 1.0), "cat" will pay more attention to "black" because they align in that dimension. This is how transformers learn semantic relationships!</p>
                    </div>
                </div>