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Similar words/sentences have vectors that are close together — useful for semantic search, clustering, and similarity comparisons.",[227,228,230],"h2",{"id":229},"install-an-embedding-provider","Install an Embedding Provider",[232,233,238],"pre",{"className":234,"code":235,"language":236,"meta":237,"style":237},"language-bash shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","pnpm add @ai-sdk/openai\n","bash","",[239,240,241],"code",{"__ignoreMap":237},[242,243,246,250,254],"span",{"class":244,"line":245},"line",1,[242,247,249],{"class":248},"sBMFI","pnpm",[242,251,253],{"class":252},"sfazB"," add",[242,255,256],{"class":252}," @ai-sdk/openai\n",[227,258,260],{"id":259},"generate-a-single-embedding","Generate a Single Embedding",[232,262,266],{"className":263,"code":264,"language":265,"meta":237,"style":237},"language-typescript shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","import { embed } from \"ai\";\nimport { openai } from \"@ai-sdk/openai\";\n\nconst { embedding } = await embed({\n  model: openai.embedding(\"text-embedding-3-small\"),\n  value: \"Artificial intelligence is transforming the world.\",\n});\n\nconsole.log(embedding);        // → [0.023, -0.041, 0.334, ...]\nconsole.log(embedding.length); // → 1536 dimensions\n","typescript",[239,267,268,300,323,330,360,393,410,419,424,445],{"__ignoreMap":237},[242,269,270,274,278,282,285,288,291,294,297],{"class":244,"line":245},[242,271,273],{"class":272},"s7zQu","import",[242,275,277],{"class":276},"sMK4o"," {",[242,279,281],{"class":280},"sTEyZ"," embed",[242,283,284],{"class":276}," }",[242,286,287],{"class":272}," from",[242,289,290],{"class":276}," \"",[242,292,293],{"class":252},"ai",[242,295,296],{"class":276},"\"",[242,298,299],{"class":276},";\n",[242,301,303,305,307,310,312,314,316,319,321],{"class":244,"line":302},2,[242,304,273],{"class":272},[242,306,277],{"class":276},[242,308,309],{"class":280}," openai",[242,311,284],{"class":276},[242,313,287],{"class":272},[242,315,290],{"class":276},[242,317,318],{"class":252},"@ai-sdk/openai",[242,320,296],{"class":276},[242,322,299],{"class":276},[242,324,326],{"class":244,"line":325},3,[242,327,329],{"emptyLinePlaceholder":328},true,"\n",[242,331,333,337,339,342,345,348,351,354,357],{"class":244,"line":332},4,[242,334,336],{"class":335},"spNyl","const",[242,338,277],{"class":276},[242,340,341],{"class":280}," embedding ",[242,343,344],{"class":276},"}",[242,346,347],{"class":276}," =",[242,349,350],{"class":272}," await",[242,352,281],{"class":353},"s2Zo4",[242,355,356],{"class":280},"(",[242,358,359],{"class":276},"{\n",[242,361,363,367,370,372,375,378,380,382,385,387,390],{"class":244,"line":362},5,[242,364,366],{"class":365},"swJcz","  model",[242,368,369],{"class":276},":",[242,371,309],{"class":280},[242,373,374],{"class":276},".",[242,376,377],{"class":353},"embedding",[242,379,356],{"class":280},[242,381,296],{"class":276},[242,383,384],{"class":252},"text-embedding-3-small",[242,386,296],{"class":276},[242,388,389],{"class":280},")",[242,391,392],{"class":276},",\n",[242,394,396,399,401,403,406,408],{"class":244,"line":395},6,[242,397,398],{"class":365},"  value",[242,400,369],{"class":276},[242,402,290],{"class":276},[242,404,405],{"class":252},"Artificial intelligence is transforming the world.",[242,407,296],{"class":276},[242,409,392],{"class":276},[242,411,413,415,417],{"class":244,"line":412},7,[242,414,344],{"class":276},[242,416,389],{"class":280},[242,418,299],{"class":276},[242,420,422],{"class":244,"line":421},8,[242,423,329],{"emptyLinePlaceholder":328},[242,425,427,430,432,435,438,441],{"class":244,"line":426},9,[242,428,429],{"class":280},"console",[242,431,374],{"class":276},[242,433,434],{"class":353},"log",[242,436,437],{"class":280},"(embedding)",[242,439,440],{"class":276},";",[242,442,444],{"class":443},"sHwdD","        // → [0.023, -0.041, 0.334, ...]\n",[242,446,448,450,452,454,457,459,462,464],{"class":244,"line":447},10,[242,449,429],{"class":280},[242,451,374],{"class":276},[242,453,434],{"class":353},[242,455,456],{"class":280},"(embedding",[242,458,374],{"class":276},[242,460,461],{"class":280},"length)",[242,463,440],{"class":276},[242,465,466],{"class":443}," // → 1536 dimensions\n",[227,468,470],{"id":469},"batch-embeddings","Batch Embeddings",[218,472,473,474,369],{},"Embed multiple texts in one call with ",[239,475,476],{},"embedMany",[232,478,480],{"className":263,"code":479,"language":265,"meta":237,"style":237},"import { embedMany } from \"ai\";\nimport { openai } from \"@ai-sdk/openai\";\n\nconst { embeddings } = await embedMany({\n  model: openai.embedding(\"text-embedding-3-small\"),\n  values: [\n    \"Artificial intelligence\",\n    \"Machine learning\",\n    \"Deep neural networks\",\n  ],\n});\n\n// embeddings is an array aligned with values\nconsole.log(embeddings[0]); // → vector for \"Artificial intelligence\"\n",[239,481,482,503,523,527,548,572,582,594,605,616,623,632,637,643],{"__ignoreMap":237},[242,483,484,486,488,491,493,495,497,499,501],{"class":244,"line":245},[242,485,273],{"class":272},[242,487,277],{"class":276},[242,489,490],{"class":280}," embedMany",[242,492,284],{"class":276},[242,494,287],{"class":272},[242,496,290],{"class":276},[242,498,293],{"class":252},[242,500,296],{"class":276},[242,502,299],{"class":276},[242,504,505,507,509,511,513,515,517,519,521],{"class":244,"line":302},[242,506,273],{"class":272},[242,508,277],{"class":276},[242,510,309],{"class":280},[242,512,284],{"class":276},[242,514,287],{"class":272},[242,516,290],{"class":276},[242,518,318],{"class":252},[242,520,296],{"class":276},[242,522,299],{"class":276},[242,524,525],{"class":244,"line":325},[242,526,329],{"emptyLinePlaceholder":328},[242,528,529,531,533,536,538,540,542,544,546],{"class":244,"line":332},[242,530,336],{"class":335},[242,532,277],{"class":276},[242,534,535],{"class":280}," embeddings ",[242,537,344],{"class":276},[242,539,347],{"class":276},[242,541,350],{"class":272},[242,543,490],{"class":353},[242,545,356],{"class":280},[242,547,359],{"class":276},[242,549,550,552,554,556,558,560,562,564,566,568,570],{"class":244,"line":362},[242,551,366],{"class":365},[242,553,369],{"class":276},[242,555,309],{"class":280},[242,557,374],{"class":276},[242,559,377],{"class":353},[242,561,356],{"class":280},[242,563,296],{"class":276},[242,565,384],{"class":252},[242,567,296],{"class":276},[242,569,389],{"class":280},[242,571,392],{"class":276},[242,573,574,577,579],{"class":244,"line":395},[242,575,576],{"class":365},"  values",[242,578,369],{"class":276},[242,580,581],{"class":280}," [\n",[242,583,584,587,590,592],{"class":244,"line":412},[242,585,586],{"class":276},"    \"",[242,588,589],{"class":252},"Artificial intelligence",[242,591,296],{"class":276},[242,593,392],{"class":276},[242,595,596,598,601,603],{"class":244,"line":421},[242,597,586],{"class":276},[242,599,600],{"class":252},"Machine learning",[242,602,296],{"class":276},[242,604,392],{"class":276},[242,606,607,609,612,614],{"class":244,"line":426},[242,608,586],{"class":276},[242,610,611],{"class":252},"Deep neural networks",[242,613,296],{"class":276},[242,615,392],{"class":276},[242,617,618,621],{"class":244,"line":447},[242,619,620],{"class":280},"  ]",[242,622,392],{"class":276},[242,624,626,628,630],{"class":244,"line":625},11,[242,627,344],{"class":276},[242,629,389],{"class":280},[242,631,299],{"class":276},[242,633,635],{"class":244,"line":634},12,[242,636,329],{"emptyLinePlaceholder":328},[242,638,640],{"class":244,"line":639},13,[242,641,642],{"class":443},"// embeddings is an array aligned with values\n",[242,644,646,648,650,652,655,659,662,664],{"class":244,"line":645},14,[242,647,429],{"class":280},[242,649,374],{"class":276},[242,651,434],{"class":353},[242,653,654],{"class":280},"(embeddings[",[242,656,658],{"class":657},"sbssI","0",[242,660,661],{"class":280},"])",[242,663,440],{"class":276},[242,665,666],{"class":443}," // → vector for \"Artificial intelligence\"\n",[227,668,670],{"id":669},"cosine-similarity-measure-closeness","Cosine Similarity (Measure Closeness)",[232,672,674],{"className":263,"code":673,"language":265,"meta":237,"style":237},"function cosineSimilarity(a: number[], b: number[]): number {\n  const dot = a.reduce((sum, val, i) => sum + val * b[i], 0);\n  const magA = Math.sqrt(a.reduce((sum, val) => sum + val * val, 0));\n  const magB = Math.sqrt(b.reduce((sum, val) => sum + val * val, 0));\n  return dot / (magA * magB);\n}\n\nconst { embeddings } = await embedMany({\n  model: openai.embedding(\"text-embedding-3-small\"),\n  values: [\"cat\", \"kitten\", \"car\"],\n});\n\nconsole.log(cosineSimilarity(embeddings[0], embeddings[1])); // → ~0.92 (similar)\nconsole.log(cosineSimilarity(embeddings[0], embeddings[2])); // → ~0.41 (different)\n",[239,675,676,718,789,847,903,927,932,936,956,980,1018,1026,1030,1065],{"__ignoreMap":237},[242,677,678,681,684,686,690,692,695,698,701,704,706,708,710,713,715],{"class":244,"line":245},[242,679,680],{"class":335},"function",[242,682,683],{"class":353}," cosineSimilarity",[242,685,356],{"class":276},[242,687,689],{"class":688},"sHdIc","a",[242,691,369],{"class":276},[242,693,694],{"class":248}," number",[242,696,697],{"class":280},"[]",[242,699,700],{"class":276},",",[242,702,703],{"class":688}," b",[242,705,369],{"class":276},[242,707,694],{"class":248},[242,709,697],{"class":280},[242,711,712],{"class":276},"):",[242,714,694],{"class":248},[242,716,717],{"class":276}," {\n",[242,719,720,723,726,728,731,733,736,738,740,743,745,748,750,753,755,758,761,764,766,769,771,774,777,780,782,785,787],{"class":244,"line":302},[242,721,722],{"class":335},"  const",[242,724,725],{"class":280}," dot",[242,727,347],{"class":276},[242,729,730],{"class":280}," a",[242,732,374],{"class":276},[242,734,735],{"class":353},"reduce",[242,737,356],{"class":365},[242,739,356],{"class":276},[242,741,742],{"class":688},"sum",[242,744,700],{"class":276},[242,746,747],{"class":688}," val",[242,749,700],{"class":276},[242,751,752],{"class":688}," i",[242,754,389],{"class":276},[242,756,757],{"class":335}," =>",[242,759,760],{"class":280}," sum",[242,762,763],{"class":276}," +",[242,765,747],{"class":280},[242,767,768],{"class":276}," *",[242,770,703],{"class":280},[242,772,773],{"class":365},"[",[242,775,776],{"class":280},"i",[242,778,779],{"class":365},"]",[242,781,700],{"class":276},[242,783,784],{"class":657}," 0",[242,786,389],{"class":365},[242,788,299],{"class":276},[242,790,791,793,796,798,801,803,806,808,810,812,814,816,818,820,822,824,826,828,830,832,834,836,838,840,842,845],{"class":244,"line":325},[242,792,722],{"class":335},[242,794,795],{"class":280}," magA",[242,797,347],{"class":276},[242,799,800],{"class":280}," Math",[242,802,374],{"class":276},[242,804,805],{"class":353},"sqrt",[242,807,356],{"class":365},[242,809,689],{"class":280},[242,811,374],{"class":276},[242,813,735],{"class":353},[242,815,356],{"class":365},[242,817,356],{"class":276},[242,819,742],{"class":688},[242,821,700],{"class":276},[242,823,747],{"class":688},[242,825,389],{"class":276},[242,827,757],{"class":335},[242,829,760],{"class":280},[242,831,763],{"class":276},[242,833,747],{"class":280},[242,835,768],{"class":276},[242,837,747],{"class":280},[242,839,700],{"class":276},[242,841,784],{"class":657},[242,843,844],{"class":365},"))",[242,846,299],{"class":276},[242,848,849,851,854,856,858,860,862,864,867,869,871,873,875,877,879,881,883,885,887,889,891,893,895,897,899,901],{"class":244,"line":332},[242,850,722],{"class":335},[242,852,853],{"class":280}," magB",[242,855,347],{"class":276},[242,857,800],{"class":280},[242,859,374],{"class":276},[242,861,805],{"class":353},[242,863,356],{"class":365},[242,865,866],{"class":280},"b",[242,868,374],{"class":276},[242,870,735],{"class":353},[242,872,356],{"class":365},[242,874,356],{"class":276},[242,876,742],{"class":688},[242,878,700],{"class":276},[242,880,747],{"class":688},[242,882,389],{"class":276},[242,884,757],{"class":335},[242,886,760],{"class":280},[242,888,763],{"class":276},[242,890,747],{"class":280},[242,892,768],{"class":276},[242,894,747],{"class":280},[242,896,700],{"class":276},[242,898,784],{"class":657},[242,900,844],{"class":365},[242,902,299],{"class":276},[242,904,905,908,910,913,916,919,921,923,925],{"class":244,"line":362},[242,906,907],{"class":272},"  return",[242,909,725],{"class":280},[242,911,912],{"class":276}," /",[242,914,915],{"class":365}," (",[242,917,918],{"class":280},"magA",[242,920,768],{"class":276},[242,922,853],{"class":280},[242,924,389],{"class":365},[242,926,299],{"class":276},[242,928,929],{"class":244,"line":395},[242,930,931],{"class":276},"}\n",[242,933,934],{"class":244,"line":412},[242,935,329],{"emptyLinePlaceholder":328},[242,937,938,940,942,944,946,948,950,952,954],{"class":244,"line":421},[242,939,336],{"class":335},[242,941,277],{"class":276},[242,943,535],{"class":280},[242,945,344],{"class":276},[242,947,347],{"class":276},[242,949,350],{"class":272},[242,951,490],{"class":353},[242,953,356],{"class":280},[242,955,359],{"class":276},[242,957,958,960,962,964,966,968,970,972,974,976,978],{"class":244,"line":426},[242,959,366],{"class":365},[242,961,369],{"class":276},[242,963,309],{"class":280},[242,965,374],{"class":276},[242,967,377],{"class":353},[242,969,356],{"class":280},[242,971,296],{"class":276},[242,973,384],{"class":252},[242,975,296],{"class":276},[242,977,389],{"class":280},[242,979,392],{"class":276},[242,981,982,984,986,989,991,994,996,998,1000,1003,1005,1007,1009,1012,1014,1016],{"class":244,"line":447},[242,983,576],{"class":365},[242,985,369],{"class":276},[242,987,988],{"class":280}," [",[242,990,296],{"class":276},[242,992,993],{"class":252},"cat",[242,995,296],{"class":276},[242,997,700],{"class":276},[242,999,290],{"class":276},[242,1001,1002],{"class":252},"kitten",[242,1004,296],{"class":276},[242,1006,700],{"class":276},[242,1008,290],{"class":276},[242,1010,1011],{"class":252},"car",[242,1013,296],{"class":276},[242,1015,779],{"class":280},[242,1017,392],{"class":276},[242,1019,1020,1022,1024],{"class":244,"line":625},[242,1021,344],{"class":276},[242,1023,389],{"class":280},[242,1025,299],{"class":276},[242,1027,1028],{"class":244,"line":634},[242,1029,329],{"emptyLinePlaceholder":328},[242,1031,1032,1034,1036,1038,1040,1043,1045,1047,1049,1051,1054,1057,1060,1062],{"class":244,"line":639},[242,1033,429],{"class":280},[242,1035,374],{"class":276},[242,1037,434],{"class":353},[242,1039,356],{"class":280},[242,1041,1042],{"class":353},"cosineSimilarity",[242,1044,654],{"class":280},[242,1046,658],{"class":657},[242,1048,779],{"class":280},[242,1050,700],{"class":276},[242,1052,1053],{"class":280}," 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