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| 2 | "providers": [ |
| 3 | "codecogs", |
| 4 | "quicklatex", |
| 5 | "mathpad", |
| 6 | "wikimedia" |
| 7 | ], |
| 8 | "items": [ |
| 9 | { |
| 10 | "id": "formula_001", |
| 11 | "latex": "h = W_0 x + \\Delta W x = W_0 x + B A x", |
| 12 | "display": "block", |
| 13 | "color": "#1B3A5C", |
| 14 | "background": "#FFFFFF", |
| 15 | "transparent": true, |
| 16 | "dpi": 400, |
| 17 | "filename": "formula_001.png", |
| 18 | "file": "images/formula_001.png", |
| 19 | "providers": [ |
| 20 | "codecogs", |
| 21 | "quicklatex", |
| 22 | "mathpad", |
| 23 | "wikimedia" |
| 24 | ], |
| 25 | "transparent_tolerance": 12, |
| 26 | "provider": "codecogs", |
| 27 | "pixel_width": 688, |
| 28 | "pixel_height": 44, |
| 29 | "ratio": 15.6364, |
| 30 | "status": "Rendered" |
| 31 | }, |
| 32 | { |
| 33 | "id": "formula_002", |
| 34 | "latex": "W_0 + \\Delta W = W_0 + BA,\\quad B \\in \\mathbb{R}^{d \\times r},\\; A \\in \\mathbb{R}^{r \\times k},\\; r \\ll \\min(d,k)", |
| 35 | "display": "block", |
| 36 | "color": "#1B3A5C", |
| 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", |
| 46 | "wikimedia" |
| 47 | ], |
| 48 | "transparent_tolerance": 12, |
| 49 | "provider": "codecogs", |
| 50 | "pixel_width": 1280, |
| 51 | "pixel_height": 55, |
| 52 | "ratio": 23.2727, |
| 53 | "status": "Rendered" |
| 54 | }, |
| 55 | { |
| 56 | "id": "formula_003", |
| 57 | "latex": "\\Delta W x \\;\\cdot\\; \\frac{\\alpha}{r}", |
| 58 | "display": "block", |
| 59 | "color": "#1B3A5C", |
| 60 | "background": "#FFFFFF", |
| 61 | "transparent": true, |
| 62 | "dpi": 400, |
| 63 | "filename": "formula_003.png", |
| 64 | "file": "images/formula_003.png", |
| 65 | "providers": [ |
| 66 | "codecogs", |
| 67 | "quicklatex", |
| 68 | "mathpad", |
| 69 | "wikimedia" |
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| 72 | "provider": "codecogs", |
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| 74 | "pixel_height": 91, |
| 75 | "ratio": 2.4176, |
| 76 | "status": "Rendered" |
| 77 | }, |
| 78 | { |
| 79 | "id": "formula_004", |
| 80 | "latex": "|\\Theta| = 2 \\times \\hat{L}_{\\mathrm{LoRA}} \\times d_{model} \\times r", |
| 81 | "display": "block", |
| 82 | "color": "#1B3A5C", |
| 83 | "background": "#FFFFFF", |
| 84 | "transparent": true, |
| 85 | "dpi": 400, |
| 86 | "filename": "formula_004.png", |
| 87 | "file": "images/formula_004.png", |
| 88 | "providers": [ |
| 89 | "codecogs", |
| 90 | "quicklatex", |
| 91 | "mathpad", |
| 92 | "wikimedia" |
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| 95 | "provider": "codecogs", |
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| 97 | "pixel_height": 60, |
| 98 | "ratio": 10.0667, |
| 99 | "status": "Rendered" |
| 100 | } |
| 101 | ], |
| 102 | "renderer": { |
| 103 | "providers": [ |
| 104 | "codecogs", |
| 105 | "quicklatex", |
| 106 | "mathpad", |
| 107 | "wikimedia" |
| 108 | ], |
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| 110 | "output_dir": "images" |
| 111 | } |
| 112 | } |
| 113 |