{
  "analytic": "multimodal-temperature",
  "kind": "declared_analytical_or_constructed_example",
  "experimental_model_result": false,
  "panels": [
    {
      "kind": "line",
      "x": [
        0.05,
        0.0595959595959596,
        0.0691919191919192,
        0.0787878787878788,
        0.08838383838383838,
        0.09797979797979797,
        0.10757575757575757,
        0.11717171717171716,
        0.12676767676767675,
        0.13636363636363635,
        0.14595959595959596,
        0.15555555555555556,
        0.16515151515151516,
        0.17474747474747476,
        0.1843434343434343,
        0.1939393939393939,
        0.2035353535353535,
        0.21313131313131312,
        0.22272727272727272,
        0.23232323232323232,
        0.24191919191919192,
        0.2515151515151515,
        0.26111111111111107,
        0.2707070707070707,
        0.2803030303030303,
        0.2898989898989899,
        0.2994949494949495,
        0.3090909090909091,
        0.31868686868686863,
        0.32828282828282823,
        0.33787878787878783,
        0.34747474747474744,
        0.35707070707070704,
        0.36666666666666664,
        0.37626262626262624,
        0.38585858585858585,
        0.39545454545454545,
        0.405050505050505,
        0.4146464646464646,
        0.4242424242424242,
        0.4338383838383838,
        0.4434343434343434,
        0.453030303030303,
        0.4626262626262626,
        0.47222222222222215,
        0.48181818181818176,
        0.49141414141414136,
        0.501010101010101,
        0.5106060606060606,
        0.5202020202020202,
        0.5297979797979798,
        0.5393939393939394,
        0.548989898989899,
        0.5585858585858586,
        0.5681818181818182,
        0.5777777777777778,
        0.5873737373737373,
        0.5969696969696969,
        0.6065656565656565,
        0.6161616161616161,
        0.6257575757575757,
        0.6353535353535353,
        0.6449494949494949,
        0.6545454545454545,
        0.6641414141414141,
        0.6737373737373737,
        0.6833333333333333,
        0.692929292929293,
        0.7025252525252526,
        0.7121212121212122,
        0.7217171717171718,
        0.7313131313131314,
        0.740909090909091,
        0.7505050505050505,
        0.76010101010101,
        0.7696969696969697,
        0.7792929292929293,
        0.7888888888888889,
        0.7984848484848485,
        0.8080808080808081,
        0.8176767676767677,
        0.8272727272727273,
        0.8368686868686869,
        0.8464646464646465,
        0.8560606060606061,
        0.8656565656565657,
        0.8752525252525253,
        0.8848484848484849,
        0.8944444444444444,
        0.904040404040404,
        0.9136363636363636,
        0.9232323232323232,
        0.9328282828282828,
        0.9424242424242424,
        0.952020202020202,
        0.9616161616161616,
        0.9712121212121212,
        0.9808080808080808,
        0.9904040404040404,
        1.0
      ],
      "series": [
        {
          "label": "Positive probability",
          "y": [
            0.999809565689181,
            0.9986865837151168,
            0.9947148002149302,
            0.9849527350408452,
            0.9662546317998256,
            0.9364175587618515,
            0.8950577069583995,
            0.8437900076527625,
            0.7856801961682508,
            0.7243240504227653,
            0.6630105859181475,
            0.6042381226940317,
            0.549596448882017,
            0.4998847017709305,
            0.4553213178577766,
            0.415751858410106,
            0.3808135896293408,
            0.35004956947870847,
            0.3229801660332302,
            0.2991437638143087,
            0.2781172002794294,
            0.2595238083976177,
            0.2430343905627038,
            0.2283644925286242,
            0.21526999855106743,
            0.20354219974454554,
            0.19300295245829724,
            0.18350022639268282,
            0.1749041614503855,
            0.16710365407653002,
            0.1600034440947361,
            0.15352165097201106,
            0.14758770158985615,
            0.14214059267091245,
            0.1371274358398632,
            0.13250223956846546,
            0.12822488873548743,
            0.12426028861260453,
            0.12057764550472155,
            0.11714986095386376,
            0.11395302038219343,
            0.11096596036880503,
            0.10816990150964628,
            0.10554813608417486,
            0.10308576162397584,
            0.10076945301615504,
            0.0985872670366882,
            0.09652847424546122,
            0.09458341402651728,
            0.092743369257807,
            0.09100045767217912,
            0.08934753744801077,
            0.08777812496213351,
            0.08628632296450213,
            0.08486675770552891,
            0.08351452377305076,
            0.08222513558455187,
            0.08099448463809658,
            0.0798188017577797,
            0.07869462368076131,
            0.07761876342669909,
            0.07658828396957057,
            0.07560047479890959,
            0.07465283101435996,
            0.07374303464582542,
            0.07286893793272915,
            0.07202854833112309,
            0.07122001504754633,
            0.07044161692440738,
            0.06969175152391303,
            0.06896892527673311,
            0.06827174457813717,
            0.06759890772865237,
            0.06694919762869479,
            0.06632147514739799,
            0.06571467309523182,
            0.06512779073816936,
            0.06455988879828961,
            0.0640100848919371,
            0.06347754936202206,
            0.0629615014658374,
            0.062461205883981,
            0.06197596951968099,
            0.061505138561091,
            0.061048095782010155,
            0.0606042580590367,
            0.06017307408542525,
            0.059754022263924435,
            0.059346608762653304,
            0.05895036571965996,
            0.058564849583217164,
            0.05818963957616849,
            0.05782433627376322,
            0.057468560285422236,
            0.05712195103177788,
            0.0567841656091364,
            0.05645487773423558,
            0.056133776762820366,
            0.055820566776143506,
            0.05551496573002562
          ]
        }
      ],
      "xlabel": "Temperature",
      "ylabel": "Softmax probability",
      "logx": false,
      "logy": false
    },
    {
      "kind": "line",
      "x": [
        0.05,
        0.0595959595959596,
        0.0691919191919192,
        0.0787878787878788,
        0.08838383838383838,
        0.09797979797979797,
        0.10757575757575757,
        0.11717171717171716,
        0.12676767676767675,
        0.13636363636363635,
        0.14595959595959596,
        0.15555555555555556,
        0.16515151515151516,
        0.17474747474747476,
        0.1843434343434343,
        0.1939393939393939,
        0.2035353535353535,
        0.21313131313131312,
        0.22272727272727272,
        0.23232323232323232,
        0.24191919191919192,
        0.2515151515151515,
        0.26111111111111107,
        0.2707070707070707,
        0.2803030303030303,
        0.2898989898989899,
        0.2994949494949495,
        0.3090909090909091,
        0.31868686868686863,
        0.32828282828282823,
        0.33787878787878783,
        0.34747474747474744,
        0.35707070707070704,
        0.36666666666666664,
        0.37626262626262624,
        0.38585858585858585,
        0.39545454545454545,
        0.405050505050505,
        0.4146464646464646,
        0.4242424242424242,
        0.4338383838383838,
        0.4434343434343434,
        0.453030303030303,
        0.4626262626262626,
        0.47222222222222215,
        0.48181818181818176,
        0.49141414141414136,
        0.501010101010101,
        0.5106060606060606,
        0.5202020202020202,
        0.5297979797979798,
        0.5393939393939394,
        0.548989898989899,
        0.5585858585858586,
        0.5681818181818182,
        0.5777777777777778,
        0.5873737373737373,
        0.5969696969696969,
        0.6065656565656565,
        0.6161616161616161,
        0.6257575757575757,
        0.6353535353535353,
        0.6449494949494949,
        0.6545454545454545,
        0.6641414141414141,
        0.6737373737373737,
        0.6833333333333333,
        0.692929292929293,
        0.7025252525252526,
        0.7121212121212122,
        0.7217171717171718,
        0.7313131313131314,
        0.740909090909091,
        0.7505050505050505,
        0.76010101010101,
        0.7696969696969697,
        0.7792929292929293,
        0.7888888888888889,
        0.7984848484848485,
        0.8080808080808081,
        0.8176767676767677,
        0.8272727272727273,
        0.8368686868686869,
        0.8464646464646465,
        0.8560606060606061,
        0.8656565656565657,
        0.8752525252525253,
        0.8848484848484849,
        0.8944444444444444,
        0.904040404040404,
        0.9136363636363636,
        0.9232323232323232,
        0.9328282828282828,
        0.9424242424242424,
        0.952020202020202,
        0.9616161616161616,
        0.9712121212121212,
        0.9808080808080808,
        0.9904040404040404,
        1.0
      ],
      "series": [
        {
          "label": "Magnitude (1-p)/temperature",
          "y": [
            0.003808686216379975,
            0.02203868003448148,
            0.07638463922947601,
            0.19098451678927195,
            0.3818047373505444,
            0.6489341940800722,
            0.9755199071472724,
            1.3331714864117687,
            1.69065024536599,
            2.021623630233055,
            2.3087856051282625,
            2.5441834969669395,
            2.727214162732741,
            2.8619314754149063,
            2.954695316826308,
            3.0125294800728915,
            3.0421565571560927,
            3.049530456000373,
            3.039680887197742,
            3.016729016625367,
            2.9839831804733397,
            2.9440619666118812,
            2.8990172276321986,
            2.8504445984950078,
            2.7995773024664623,
            2.7473631437383275,
            2.694526398199952,
            2.6416169146119084,
            2.589048748539203,
            2.5371304075822625,
            2.4860884614236514,
            2.4360859463305498,
            2.3872367055899364,
            2.339616565442966,
            2.293272049714189,
            2.2482271801759666,
            2.204488787105664,
            2.1620506590362134,
            2.1208967867243014,
            2.0810038991801787,
            2.042343445451987,
            2.0048831417651094,
            1.9685881772696774,
            1.9334221512590979,
            1.8993477989139338,
            1.8663275503438295,
            1.834323958137058,
            1.8033000211632932,
            1.773219426535604,
            1.7440467270578077,
            1.7157474678828268,
            1.6882882732705415,
            1.6616369020928936,
            1.6357622789604753,
            1.610634506438269,
            1.586224862700489,
            1.56250578808477,
            1.5394508632965895,
            1.5170347814484566,
            1.4952333156656497,
            1.4740232836280356,
            1.453382510127385,
            1.4332897884872036,
            1.413724841505839,
            1.3946682824344225,
            1.3761015763817064,
            1.358007002442259,
            1.3403676167681182,
            1.3231672167431152,
            1.3063903063706752,
            1.2900220629475636,
            1.274048305065807,
            1.258455461961328,
            1.2432305442094107,
            1.228361115752925,
            1.2138352672384785,
            1.1996415906276245,
            1.1857691550444216,
            1.1722074838165493,
            1.1589465326644977,
            1.1459766689917492,
            1.133288652228155,
            1.1208736151786551,
            1.108723046329976,
            1.0968287730688022,
            1.0851829457661069,
            1.0737780226837033,
            1.0626067556606333,
            1.0516621765386485,
            1.0409375842877506,
            1.0304265327944888,
            1.0201228192774543,
            1.0100204732961282,
            1.0001137463209346,
            0.9903971018339947,
            0.9808652059316755,
            0.9715129184015671,
            0.9623352842479999,
            0.9533275256416297,
            0.9444850342699744
          ]
        }
      ],
      "xlabel": "Temperature",
      "ylabel": "Positive-logit gradient magnitude",
      "logx": false,
      "logy": false
    }
  ],
  "title": "Temperature changes both relative probability and gradient",
  "assumptions": "One fixed positive logit 0.8 and 31 negative logits 0.2. No learned embedding or retrieval result.",
  "worked": "固定正样本相似度0.8、31个负样本均0.2，温度0.1时正样本概率约0.929，温度1时约0.056。分数被归一化后的变化不证明表示或真实识别能力改变。",
  "source_ids": [
    "vit",
    "clip",
    "perceiver",
    "arxiv-2304.02643"
  ],
  "formula_source": "Article equations and this versioned script",
  "diagram_nodes": [
    "图像 patch / 文本词元",
    "各自编码与表示压缩",
    "配对相似度矩阵",
    "温度与负样本归一化",
    "检索 / 定位 / 计数接口",
    "组合与跨域失效分析"
  ]
}
