{"id":2793,"date":"2025-06-15T06:36:24","date_gmt":"2025-06-14T21:36:24","guid":{"rendered":"https:\/\/www.dogrow.net\/nnet\/?p=2793"},"modified":"2025-06-16T20:53:14","modified_gmt":"2025-06-16T11:53:14","slug":"blog60-%e5%a4%9a%e3%82%af%e3%83%a9%e3%82%b9%e5%88%86%e9%a1%9e%e3%81%a7%e4%bd%bf%e3%81%86softmax","status":"publish","type":"post","link":"https:\/\/www.dogrow.net\/nnet\/blog60-%e5%a4%9a%e3%82%af%e3%83%a9%e3%82%b9%e5%88%86%e9%a1%9e%e3%81%a7%e4%bd%bf%e3%81%86softmax\/","title":{"rendered":"(60) \u591a\u30af\u30e9\u30b9\u5206\u985e\u3067\u4f7f\u3046 Softmax"},"content":{"rendered":"

\u30101\u3011\u3084\u308a\u305f\u3044\u3053\u3068<\/h1>\n

PyTorch\u3084 TensorFlow\u306a\u3069\u306e\u6a5f\u68b0\u5b66\u7fd2\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u308f\u306a\u3044\u5834\u5408\u3001\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u63d0\u4f9b\u3057\u3066\u304f\u308c\u3066\u3044\u308b\u6a5f\u80fd\u3092\u81ea\u529b\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002
\n\u672c\u9805\u3067\u306f\u3001MNIST\u3084 CIFAR-10\u306e\u3088\u3046\u306a\u591a\u30af\u30e9\u30b9\u5206\u985e\u3067\u4f7f\u7528\u3059\u308b Softmax\u95a2\u6570\u3092\u5b9f\u88c5<\/span> \u3057\u3066\u307f\u308b\u3002<\/p>\n

\u6a5f\u68b0\u5b66\u7fd2\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u308f\u306a\u3044 Python\u81ea\u529b\u5b9f\u88c5\u30b7\u30ea\u30fc\u30ba<\/span> \u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002
\n(56) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 tanh(x)\u306e\u5fae\u5206<\/a>
\n(57) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 sigmoid(x)\u306e\u5fae\u5206<\/a>
\n(58) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 ReLU(x)\u306e\u5fae\u5206<\/a>
\n(59) \u9006\u4f1d\u64ad\u3067\u4f7f\u3046 MSE\uff08\u5e73\u5747\u4e8c\u4e57\u8aa4\u5dee\uff09\u306e\u5fae\u5206<\/a>
\n(60) \u4ed6\u30af\u30e9\u30b9\u5206\u985e\u3067\u4f7f\u3046 Softmax<\/a> \u2190\u4eca\u56de<\/span>
\n(61) \u6a5f\u68b0\u5b66\u7fd2\u3067\u591a\u7528\u3055\u308c\u308b\u30cd\u30a4\u30d4\u30a2\u6570\u3068\u306f\uff1f<\/a><\/p>\n

\u30102\u3011\u3084\u3063\u3066\u307f\u308b<\/h1>\n

\u591a\u30af\u30e9\u30b9\u5206\u985e\u30bf\u30b9\u30af\u3067\u306f\u3001
\n\u3000\u51fa\u529b\u5c64\u306b\u304a\u3051\u308b\u5404\u30af\u30e9\u30b9\u30b9\u30b3\u30a2\u3092 Softmax \u95a2\u6570\u306b\u901a\u3059\u3053\u3068\u3067\u3001
\n\u3000\u3000\u5168\u30af\u30e9\u30b9\u306b\u5bfe\u3059\u308b\u78ba\u7387\u5206\u5e03\u306b\u5909\u63db\u3059\u308b\u3002
\n\u2192 \u6271\u3044\u3084\u3059\u304f\u306a\u308b\uff01<\/span><\/p>\n

1) Softmax\u306e\u8a08\u7b97\u5f0f<\/h2>\n

Softmax\u3068\u306f\u3001
\n\u8907\u6570\u306e\u5165\u529b\u5024\u306b\u5bfe\u3057\u3066\u3001
\n\u3000\u51fa\u529b\u5024\u306e\u5408\u8a08\u304c 1\u306b\u306a\u308b\u3088\u3046\u306b\u5909\u63db\u30fb\u51fa\u529b\u3057\u3001
\n\u3000\u3000\u78ba\u7387\u3063\u307d\u3044\u5024\u3092\u4f5c\u308b\u30ed\u30b8\u30c3\u30af\u306e\u3053\u3068\u3002<\/span><\/p>\n

\n
n<\/span><\/td>\u51fa\u529b\u5c64\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u6570<\/td><\/tr>
zi<\/sub><\/span><\/td>\u51fa\u529b\u5c64\u306e\u30cb\u30e5\u30fc\u30ed\u30f3[i:1,2,3,…]\u306e\u51fa\u529b\u5024<\/td><\/tr>
pi<\/sub><\/span><\/td>softmax\u95a2\u6570\u306e\u51fa\u529b\u5024\uff08\uff1d\u4e88\u6e2c\u78ba\u7387\uff09 \u203b\u30e9\u30d9\u30eb\u3054\u3068\u306b\u78ba\u7387\u3092\u51fa\u3059\u3002<\/span><\/td><\/tr>\n<\/table>
\n\"\"<\/p>\n

2) \u5206\u304b\u308a\u3084\u3059\u3044\u4f8b\u3067\u78ba\u8a8d<\/h2>\n

\u51fa\u529b\u5c64\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u6570 3\u500b\u306e\u5834\u5408\u306b\u3064\u3044\u3066\u898b\u3066\u307f\u308b\u3002
\n\ud83d\udd38\u51fa\u529b\u5c64\u306e\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u4f4d\u7f6e\u306b\u3088\u3063\u3066\u5909\u308f\u308b\u306e\u306f\u3001\u5206\u5b50\u306e\u6307\u6570\u3060\u3051\u3002
\n\ud83d\udd38\u307e\u305f\u3001\u5206\u6bcd\u306b\u306f\u5168\u30cb\u30e5\u30fc\u30ed\u30f3\u306e\u51fa\u529b\u5024\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u78ba\u7387 p \u306e\u7b97\u51fa\u306b\u306f\u4ed6\u30e9\u30d9\u30eb\u306e\u51fa\u529b\u5024\u3082\u8003\u616e\u3055\u308c\u3066\u3044\u308b\u3002
\n\"\"<\/p>\n

\u4f8b\u3048\u3070\u30013\u30af\u30e9\u30b9\u5206\u985e\u30bf\u30b9\u30af\u306b\u304a\u3044\u3066\u3001\u51fa\u529b\u5c64\u304b\u3089\u5f97\u3089\u308c\u308b\u30b9\u30b3\u30a2\u304c [2, 3, 5]<\/span> \u3067\u3042\u3063\u305f\u3068\u3059\u308b\u3002
\n\u3053\u308c\u3089\u306e\u5024\u306f\u672a\u6b63\u898f\u5316\u306e\u30b9\u30b3\u30a2\uff08logits\uff09\u3067\u3042\u308a\u3001\u305d\u306e\u307e\u307e\u3067\u306f\u78ba\u7387\u3068\u3057\u3066\u89e3\u91c8\u3067\u304d\u306a\u3044<\/span> \u305f\u3081\u3001\u76f4\u63a5\u7684\u306a\u5229\u7528\u304c\u96e3\u3057\u3044\u3002<\/p>\n

\u305d\u3053\u3067\u3001Softmax\u95a2\u6570\u3092\u9069\u7528\u3059\u308b\u3053\u3068\u3067\u3001[0.04, 0.12, 0.84]<\/span> \u306e\u3088\u3046\u306a \u7dcf\u548c\u304c 1\u3068\u306a\u308b\u78ba\u7387\u5206\u5e03<\/span> \u306b\u5909\u63db\u3059\u308b\u3002
\n\u3053\u306e\u3088\u3046\u306b\u6b63\u898f\u5316\u3055\u308c\u305f\u51fa\u529b\u306f [0, 1, 0]<\/span> \u306e\u3088\u3046\u306a one-hot \u8868\u73fe\u306e\u6b63\u89e3\u30e9\u30d9\u30eb\u3068\u7167\u5408\u53ef\u80fd\u306b\u306a\u308a\u3001\u640d\u5931\u95a2\u6570\uff08\u4f8b\u3048\u3070\u4ea4\u5dee\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u640d\u5931\uff09\u306b\u3088\u308b\u5b66\u7fd2\u304c\u5bb9\u6613\u306b\u306a\u308b\u3002<\/p>\n

\"\"<\/p>\n

\u7a4d\u7b97\u5024\u304c 1 \u306b\u306a\u308b\u306e\u306f\u5f53\u7136<\/span> \u3060\u3002softmax\u306f\u305d\u3046\u5b9a\u7fa9\u3057\u3066\u3044\u308b\u306e\u3060\u304b\u3089\u30fb\u30fb\u30fb
\n\"\"<\/p>\n

3) Softmax\u306e\u7279\u5fb4<\/h2>\n

(1) \u305f\u3060\u306e Max\u3067\u306f\u306a\u304f Soft\u3068\u306f\uff1f<\/h3>\n\n
Max\u95a2\u6570<\/td>\u6700\u5927\u5024\u3092\u9078\u3076\u3002<\/td><\/tr>
Softmax\u95a2\u6570<\/td>\u6700\u5927\u5024\uff08\uff1d\u6700\u3082\u53ef\u80fd\u6027\u306e\u9ad8\u3044\u30e9\u30d9\u30eb\uff09\u3092\u9078\u3073\u3064\u3064\u3001\u4ed6\u30e9\u30d9\u30eb\u306e\u53ef\u80fd\u6027\u306e\u5927\u304d\u3055\u3082\u8868\u305b\u308b\u3002<\/td><\/tr>\n<\/table>\n

(2) e \u3092\u4f7f\u3046\u3068\u4f55\u304c\u5b09\u3057\u3044\uff1f<\/h3>\n

\u51fa\u529b\u5c64\u304b\u3089\u5f97\u3089\u308c\u308b\u30b9\u30b3\u30a2 zi<\/sub><\/span> \u304c [2, 3, 5]<\/span> \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u3001Softmax\u95a2\u6570\u306e\u51fa\u529b\u5024 pi<\/sub><\/span> \u3092\u4e0b\u56f3\u306b\u8a18\u3059\u3002
\nSoftmax\u306f\u7dda\u5f62\u6bd4\u7387\u3067\u306f\u306a\u304f\u6307\u6570\u95a2\u6570\u3067\u91cd\u307f\u4ed8\u3051\u3059\u308b<\/span> \u305f\u3081\u3001
\n\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b zi<\/sub><\/span> \u3088\u308a\u3082 pi<\/sub><\/span> \u306e\u65b9\u304c \u5f37\u8005\u304c\u5f37\u8abf<\/span> \u3055\u308c\u308b\u3002<\/p>\n

\u3053\u308c\u306b\u3088\u308a\u30fb\u30fb\u30fb
\n\u6b63\u89e3\u30e9\u30d9\u30eb\u306e\u78ba\u7387\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5206\u985e\u5668\u306e\u8a13\u7df4\u304c\u9032\u307f\u3084\u3059\u304f\u306a\u308b\u3002<\/span>
\n\"\"<\/p>\n

4) Softmax\u3092 Python\u3067\u5b9f\u88c5<\/h2>\n
\r\n"""\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\r\nsoftmax\u95a2\u6570\r\n\u5165\u529b: x \u306f 1\u6b21\u5143\u307e\u305f\u306f 2\u6b21\u5143\u306enumpy\u914d\u5217\r\n\u51fa\u529b: \u5404\u8981\u7d20\u3092\u78ba\u7387\u306b\u5909\u63db\u3057\u305f numpy\u914d\u5217\uff08\u5168\u8981\u7d20\u306e\u5408\u8a08=1\uff09\r\n- 1\u6b21\u5143: [z0, z1, z2] \u2192 [p0, p1, p2]\r\n- 2\u6b21\u5143: \u5404\u884c\u3054\u3068\u306bsoftmax\uff08\u30d0\u30c3\u30c1\u30c7\u30fc\u30bf\u5bfe\u5fdc\uff09\r\n\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/"""\r\ndef softmax(x):\r\n    x = np.asarray(x)\r\n    #---------------------------------------------------------------------------\r\n    if x.ndim == 1:                                         # \u5165\u529b\u30c7\u30fc\u30bf\u304c 1\u6b21\u5143\uff1f\uff08\u5358\u4e00\u30c7\u30fc\u30bf\uff09\r\n        e_x = np.exp(x - np.max(x))                         # \u6570\u5024\u5b89\u5b9a\u5316(1)\r\n        #e_x = np.exp(x)                                    # \u6570\u5024\u5b89\u5b9a\u5316(2) \u203b(1),(2)\u306e\u3069\u3061\u3089\u3067\u3082\u540c\u3058\u51fa\u529b\u5024\u306b\u306a\u308b\u3002\r\n        return e_x \/ e_x.sum()\r\n    #---------------------------------------------------------------------------\r\n    elif x.ndim == 2:                                       # \u5165\u529b\u30c7\u30fc\u30bf\u304c 2\u6b21\u5143\uff1f\uff08\u8907\u6570\u30c7\u30fc\u30bf\uff09\r\n        e_x = np.exp(x - np.max(x, axis=1, keepdims=True))\r\n        return e_x \/ e_x.sum(axis=1, keepdims=True)\r\n    #---------------------------------------------------------------------------\r\n    else:\r\n        raise ValueError('\u5165\u529b\u306f1\u6b21\u5143\u307e\u305f\u306f2\u6b21\u5143\u306e\u914d\u5217\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002')\r\n<\/pre>\n
\u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5\u306b\u898b\u3048\u308b\u304c\u3001\u3053\u3053\u306b\u306f Python + Numpy\u306e\u5e95\u529b\u304c\u96a0\u308c\u3066\u3044\u308b\u3002
\nnumpy\u306e\u30d9\u30af\u30c8\u30eb\u5316\u95a2\u6570\u3092\u4f7f\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u5165\u529b\u5024 x\u306f\u591a\u6b21\u5143\u914d\u5217\uff08ndarray\uff09\u3092\u4f7f\u3048\u308b\u3002
\n \u2192 \u30df\u30cb\u30d0\u30c3\u30c1\u30c7\u30fc\u30bf\u7b49\u3001\u8907\u6570\u30c7\u30fc\u30bf\u3092\u307e\u3068\u3081\u3066\u51e6\u7406\u3067\u304d\u308b\u3002<\/span>
\n\u203b\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u4e26\u5217\u51e6\u7406\u306f\u30e9\u30a4\u30d6\u30e9\u30ea\u5185\u90e8\u306b\u96a0\u853d\u3055\u308c\u3066\u3044\u308b\u3002<\/span><\/p>\n
\u3044\u304f\u3064\u304b\u8a66\u3057\u3066\u307f\u308b\u3002
\n
\n>>> z = np.array([5, 5])\n>>> p = softmax(z)\n>>> p\narray([0.5, 0.5])\n>>>\n>>> z = np.array([2, 3, 5])\n>>> p = softmax(z)\n>>> p\narray([0.04201007, 0.1141952 , 0.84379473])\n<\/pre><\/p>\n
\u30df\u30cb\u30d0\u30c3\u30c1\u306e\u5834\u5408\uff08\uff1d\u8907\u6570\u306e\u8a13\u7df4\u30c7\u30fc\u30bf\u3092\u4e00\u62ec\u51e6\u7406\u3059\u308b\u5834\u5408\uff09
\n
\n>>> z = np.array([[2, 3, 5],[1, 5, 7]])\n>>> p = softmax(z)\n>>> p\narray([[0.04201007, 0.1141952 , 0.84379473],\n       [0.00217852, 0.11894324, 0.87887824]])\n<\/pre><\/p>\n
\u30103\u3011\u6240\u611f<\/h1>\n
\u672c\u5f53\u306f\u3001Softmax \u2192 CrossEntropy \u2192 \u8aa4\u5dee\u7b97\u51fa \u2192 \u52fe\u914d\u521d\u671f\u5024\u7b97\u51fa\uff08CrossEntropy, Softmax\u306e\u5fae\u5206\uff09\u307e\u3067\u3092\u4e00\u6c17\u901a\u8cab\u3067\u8a18\u9332\u3057\u3066\u304a\u304d\u305f\u304b\u3063\u305f\u3002
\n\u3067\u3082…
\n\u6587\u91cf\u304c\u304b\u306a\u308a\u5897\u3048\u305d\u3046\u3060\u3063\u305f\u306e\u3067\u3001\u672c\u9805\u3067\u306f\u9806\u4f1d\u64ad\u6642\u306e Softmax\u3060\u3051\u3092\u6271\u3063\u305f\u3002<\/p>\n
\u4eca\u5f8c\u306f\u3001\u4ee5\u4e0b\u306e\u9806\u306b\u6295\u7a3f\u3057\u3066\u3044\u3053\u3046\u3002
\n\u30fbSoftmax\u306e\u5fae\u5206
\n\u30fb\u9806\u4f1d\u64ad\uff1a CrossEntropyLoss\u306b\u3088\u308b\u640d\u5931\u7b97\u51fa
\n\u30fbCrossEntropyLoss\u306e\u5fae\u5206
\n\u30fbCrossEntropyLoss + Softmax\u306e\u5c0e\u95a2\u6570\u3092\u4f7f\u3063\u305f\u52fe\u914d\u521d\u671f\u5024\u7b97\u51fa<\/p>\n
\u305d\u306e\u5f8c\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5168\u4f53\u306e\u8a13\u7df4\u306e\u6d41\u308c\u306b\u3064\u3044\u3066\u6295\u7a3f\u3059\u308b\u3002
\n\u30fb\u9806\u4f1d\u64ad
\n\u30fb\u9006\u4f1d\u64ad
\n\u30fb\u30d1\u30e9\u30e1\u30fc\u30bf\u66f4\u65b0<\/p>\n
\u3067\u30fb\u30fb\u30fb
\n\u3053\u308c\u3089\u3092\u7528\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u5fdc\u7528\u4f8b\uff08\u57fa\u790e\u7de8\u3060\u304c\uff09\u3092\u4f5c\u308b\u3002
\n\u30fbSin\u95a2\u6570\u306e\u8fd1\u4f3c\uff08\u56de\u5e30\u30bf\u30b9\u30af\uff09
\n\u30fbMNIST\u5206\u985e\uff08\u5206\u985e\u30bf\u30b9\u30af\uff09<\/p>\n
\u307e\u305a\u306f \u6a5f\u68b0\u5b66\u7fd2\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u4f7f\u308f\u306a\u3044 Python\u81ea\u529b\u5b9f\u88c5\u30b7\u30ea\u30fc\u30ba<\/span> \u3092\u3053\u3053\u307e\u3067\u9032\u3081\u3088\u3046\u3002
\n\u76ee\u6a19\u306f 7\/\u672b\u307e\u3067\u3002<\/p>\n
\u3042\u3063\u3001\u30aa\u30bb\u30edAI\u3092\u5168\u7136\u9032\u3081\u3066\u3044\u306a\u3044\u305e\u30fb\u30fb\u30fb<\/p>\n
\n","protected":false},"excerpt":{"rendered":"
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