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| 2 | "providers": [ |
| 3 | "codecogs", |
| 4 | "quicklatex", |
| 5 | "mathpad", |
| 6 | "wikimedia" |
| 7 | ], |
| 8 | "items": [ |
| 9 | { |
| 10 | "id": "formula_001", |
| 11 | "latex": "\\text{Attention}(Q, K, V) = \\text{softmax}\\!\\left(\\frac{QK^{T}}{\\sqrt{d_k}}\\right) V", |
| 12 | "display": "block", |
| 13 | "color": "#1A365D", |
| 14 | "background": "#FFFFFF", |
| 15 | "transparent": true, |
| 16 | "dpi": 400, |
| 17 | "filename": "formula_001.png", |
| 18 | "file": "images/formula_001.png", |
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| 20 | "codecogs", |
| 21 | "quicklatex", |
| 22 | "mathpad", |
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| 26 | "provider": "codecogs", |
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| 28 | "pixel_height": 122, |
| 29 | "ratio": 7.2131, |
| 30 | "status": "Rendered" |
| 31 | }, |
| 32 | { |
| 33 | "id": "formula_002", |
| 34 | "latex": "\\begin{aligned}\\text{MultiHead}(Q, K, V) &= \\text{Concat}(\\text{head}_1, \\ldots, \\text{head}_h)\\,W^{O} \\\\ \\text{where}\\ \\text{head}_i &= \\text{Attention}(Q W_i^{Q},\\, K W_i^{K},\\, V W_i^{V})\\end{aligned}", |
| 35 | "display": "block", |
| 36 | "color": "#1A365D", |
| 37 | "background": "#FFFFFF", |
| 38 | "transparent": true, |
| 39 | "dpi": 400, |
| 40 | "filename": "formula_002.png", |
| 41 | "file": "images/formula_002.png", |
| 42 | "providers": [ |
| 43 | "codecogs", |
| 44 | "quicklatex", |
| 45 | "mathpad", |
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| 51 | "pixel_height": 137, |
| 52 | "ratio": 8.5255, |
| 53 | "status": "Rendered" |
| 54 | }, |
| 55 | { |
| 56 | "id": "formula_003", |
| 57 | "latex": "\\begin{aligned}PE_{(pos,\\, 2i)} &= \\sin\\!\\left(\\frac{pos}{10000^{2i/d_{\\text{model}}}}\\right) \\\\ PE_{(pos,\\, 2i+1)} &= \\cos\\!\\left(\\frac{pos}{10000^{2i/d_{\\text{model}}}}\\right)\\end{aligned}", |
| 58 | "display": "block", |
| 59 | "color": "#1A365D", |
| 60 | "background": "#FFFFFF", |
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| 64 | "file": "images/formula_003.png", |
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| 68 | "mathpad", |
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| 74 | "pixel_height": 201, |
| 75 | "ratio": 3.5124, |
| 76 | "status": "Rendered" |
| 77 | } |
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| 79 | "renderer": { |
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| 90 |