neural_network_on_torus_3.ipynb

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    "accelerator": "GPU"
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        "<a href=\"https://colab.research.google.com/github/yukinaga/brain_ai_book/blob/master/neural_network_on_torus_3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# **馴化の導入**\n",
        "今回は、ニューロンの感度であるバイアスを調整することにより馴化を実現します。  \n",
        "バイアスの調整は以下の方法で行われます。\n",
        "\n",
        "* 興奮したニューロンのバイアスを、興奮しににくくなる方向に僅かに変化させる\n",
        "* 抑制されたニューロンのバイアスを、興奮しやすくなる方向に僅かに変化させる\n",
        "\n",
        "これにより、連続して興奮したニューロンは少しずつ興奮しにくくなり、連続して抑制されたニューロンは少しずつ興奮しやすくなります。\n"
      ]
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    {
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      "source": [
        "# import numpy as np  # CPU\n",
        "import cupy as np  # GPU\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib import animation, rc\n",
        "\n",
        "# @markdown ### **トーラス上のニューラルネットワーク**\n",
        "# @markdown 投射ニューロンの割合を入力してください。\n",
        "proj_ratio = 0.5 # @param {type:\"number\"}\n",
        "\n",
        "# @markdown 抑制性ニューロンの割合を入力してください。\n",
        "inhib_ratio = 0.2 # @param {type:\"number\"}\n",
        "\n",
        "# @markdown タイムステップ数を入力してください。\n",
        "steps = 240 # @param {type:\"number\"}\n",
        "\n",
        "# @markdown ### **恒常性の導入**\n",
        "# @markdown 興奮させるニューロンの割合を入力してください。\n",
        "excite_ratio = 0.5  # @param {type:\"number\"}\n",
        "\n",
        "# @markdown ### **馴化の導入**\n",
        "# @markdown 各ステップごとのバイアスの変化量を入力してください。\n",
        "delta_b = 0.01  # @param {type:\"number\"}\n",
        "\n",
        "# @markdown ### **動画の保存**\n",
        "# @markdown GIFアニメーションを保存しますか？\n",
        "save_gif = False #@param {type:\"boolean\"}\n",
        "# @markdown MP4形式の動画を保存しますか？\n",
        "save_mp4 = False #@param {type:\"boolean\"}\n",
        "\n",
        "n_h = 256  # 領域高さ\n",
        "n_w = 256  # 領域幅\n",
        "n_connect = 64  # ニューロンへの入力数\n",
        "sigma_inter = 4  # 介在ニューロンの軸索長の標準偏差\n",
        "w_mu = 0.25  # 重みの平均値 \n",
        "w_sigma = 0.08  # 重みの標準偏差\n",
        "\n",
        "matplotlib.rcParams[\"animation.embed_limit\"] = 2**128  # アニメーションのサイズの上限\n",
        "\n",
        "# トラース上のニューラルネットワークのクラス\n",
        "class TorusNetwork():\n",
        "    def __init__(self, n_h, n_w, n_connect):\n",
        "        n_neuron = n_h * n_w  # ニューロンの総数\n",
        "        self.params = (n_h, n_w, n_neuron, n_connect)\n",
        "\n",
        "        self.connect_ids = None  # シナプス前細胞のインデックス \n",
        "        self.w = None  # 重み\n",
        "        self.b = None  # バイアス\n",
        "        self.y = None  # ニューロンの出力\n",
        "        self.proj = None  # 投射ニューロンかどうか\n",
        "        self.proj_ids = None  # 投射ニューロンのインデックス\n",
        "        self.proj_to_ids = None  # 投射先のインデックス\n",
        "        self.inhib = None  # 抑制性ニューロンかどうか\n",
        "\n",
        "    def connect(self, proj_ratio, sigma_inter):\n",
        "        n_h, n_w, n_neuron, n_connect = self.params\n",
        "        \n",
        "        # 投射ニューロンをランダムに選択\n",
        "        n_proj= int(proj_ratio * n_neuron)\n",
        "        rand_ids = np.random.permutation(np.arange(n_neuron))\n",
        "        self.proj_ids = rand_ids[:n_proj]\n",
        "        self.proj_to_ids = np.random.permutation(self.proj_ids)\n",
        "        self.proj = np.zeros(n_neuron, dtype=np.bool)\n",
        "        self.proj[self.proj_ids] = True\n",
        "\n",
        "        # 介在ニューロンのx座標     \n",
        "        inter_dist_x = np.random.randn(n_neuron, n_connect) * sigma_inter\n",
        "        inter_dist_x = np.where(inter_dist_x<0, inter_dist_x-0.5, inter_dist_x+0.5).astype(np.int32) \n",
        "        x_connect = np.zeros((n_neuron, n_connect), dtype=np.int32)\n",
        "        x_connect += np.arange(n_neuron).reshape(-1, 1)\n",
        "        x_connect %= n_w\n",
        "        x_connect += inter_dist_x\n",
        "        x_connect = np.where(x_connect<0, x_connect+n_w, x_connect)\n",
        "        x_connect = np.where(x_connect>=n_w, x_connect-n_w, x_connect)\n",
        "\n",
        "        # 介在ニューロンのy座標        \n",
        "        inter_dist_y = np.random.randn(n_neuron, n_connect) * sigma_inter\n",
        "        inter_dist_y = np.where(inter_dist_y<0, inter_dist_y-0.5, inter_dist_y+0.5).astype(np.int32)        \n",
        "        y_connect = np.zeros((n_neuron, n_connect), dtype=np.int32)\n",
        "        y_connect += np.arange(n_neuron).reshape(-1, 1)\n",
        "        y_connect //= n_w\n",
        "        y_connect += inter_dist_y\n",
        "        y_connect = np.where(y_connect<0, y_connect+n_h, y_connect)\n",
        "        y_connect = np.where(y_connect>=n_h, y_connect-n_h, y_connect)        \n",
        "\n",
        "          # シナプス前細胞のインデックス\n",
        "        self.connect_ids = x_connect + n_w * y_connect\n",
        "        \n",
        "    def initialize_network(self, inhib_ratio, w_mu, w_sigma):\n",
        "        n_h, n_w, n_neuron, n_connect = self.params\n",
        "\n",
        "        # 抑制性ニューロンをランダムに選択\n",
        "        n_inhib = int(inhib_ratio * n_neuron)\n",
        "        rand_ids = np.random.permutation(np.arange(n_neuron))\n",
        "        inhib_ids = rand_ids[:n_inhib]\n",
        "        self.inhib = np.zeros(n_neuron, dtype=np.bool)\n",
        "        self.inhib[inhib_ids] = True\n",
        "        \n",
        "        # 重みとバイアスの初期化\n",
        "        self.w = np.random.randn(n_neuron, n_connect) * w_sigma + w_mu\n",
        "        self.w = np.where(self.inhib[self.connect_ids], -self.w, self.w)\n",
        "        self.w /= np.sum(self.w, axis=1, keepdims=True)\n",
        "        self.b = np.zeros(n_neuron)\n",
        "        \n",
        "        # 出力を初期化\n",
        "        self.y = np.random.randint(0, 2, n_neuron)\n",
        "\n",
        "    def forward(self, delta_b, excite_ratio):\n",
        "        n_h, n_w, n_neuron, n_connect = self.params\n",
        "        n_excite = int(excite_ratio * n_neuron)  # 興奮したニューロン数\n",
        "\n",
        "        # ニューラルネットワークの計算\n",
        "        self.y[self.proj_to_ids] = self.y[self.proj_ids]  # 投射\n",
        "        x = self.y[self.connect_ids]\n",
        "        u = np.sum(self.w*x, axis=1) - self.b\n",
        "        larger_ids = np.argpartition(-u, n_excite)[:n_excite]  # 恒常性\n",
        "        self.y[:] = 0\n",
        "        self.y[larger_ids] = 1\n",
        "        \n",
        "        # 馴化\n",
        "        self.b = np.where(self.y, self.b+delta_b, self.b-delta_b)\n",
        "        self.b -= np.mean(self.b)\n",
        "\n",
        "# ネットワークの設定\n",
        "tnet = TorusNetwork(n_h, n_w, n_connect)\n",
        "tnet.connect(proj_ratio, sigma_inter)\n",
        "tnet.initialize_network(inhib_ratio, w_mu, w_sigma)\n",
        "\n",
        "# 結果表示のための設定\n",
        "figure = plt.figure()\n",
        "plt.tick_params(labelbottom=False, labelleft=False, labelright=False, labeltop=False)\n",
        "plt.tick_params(bottom=False, left=False, right=False, top=False)\n",
        "\n",
        "# 興奮したニューロンのカラー\n",
        "c_excite = np.array([30, 144, 255]).reshape(1, -1)\n",
        "c_map = np.zeros((n_h*n_w, 3)) + c_excite\n",
        "\n",
        "# 画像を格納するリスト\n",
        "images = []\n",
        "\n",
        "for i in range(steps):\n",
        "    tnet.forward(delta_b, excite_ratio)\n",
        "    y = tnet.y.reshape(-1, 1)\n",
        "\n",
        "    image = np.zeros((n_h*n_w, 3))\n",
        "    image = np.where(y, c_map, image)\n",
        "    image = image.reshape(n_h, n_w, -1).astype(np.uint8)\n",
        "    image = plt.imshow(image.tolist())\n",
        "    images.append([image])\n",
        "\n",
        "anim = animation.ArtistAnimation(figure, images, interval=100)\n",
        "rc(\"animation\", html=\"jshtml\")\n",
        "if save_gif:\n",
        "    anim.save(\"torus_network3.gif\", writer=\"pillow\", fps=10)\n",
        "if save_mp4:\n",
        "    anim.save(\"torus_network3.mp4\", writer=\"ffmpeg\")\n",
        "plt.close()  # 通常のグラフを非表示に\n",
        "anim"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
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      "source": [
        "結果がうまく表示されない場合は、「ランタイム」→「ランタイムを出荷時設定にリセット」を選択し、ランタイムをリセットしましょう。  \n",
        "なお、計算にはGPUを利用していますが、連続で使用するとランタイムが途中で切断されることがあります。タイムステップ数を少なくするか、しばらく時間を置いてから再びお試しください。"
      ]
    }
  ]
}