spiking_neurons.ipynb

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  "metadata": {
    "colab": {
      "name": "spiking_neurons.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "pPqT1BLe9VwL",
        "1R8eKuPw-CW7"
      ],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/jwalin12/stochastic_neurons/blob/main/spiking_neurons.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KinvzrKY5dQK",
        "outputId": "888504c8-39b9-4d4a-8cb7-a25bb91ed7af"
      },
      "source": [
        "!pip install brian2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting brian2\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/9a/c7/565012c479953d041d5e828938515d3c402d0c3f4942180f1c44cb0f472e/Brian2-2.4.2.tar.gz (1.2MB)\n",
            "\u001b[K     |████████████████████████████████| 1.2MB 5.4MB/s \n",
            "\u001b[?25hRequirement already satisfied: numpy>=1.15 in /usr/local/lib/python3.6/dist-packages (from brian2) (1.18.5)\n",
            "Requirement already satisfied: cython>=0.29 in /usr/local/lib/python3.6/dist-packages (from brian2) (0.29.21)\n",
            "Collecting sympy>=1.2\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/ff/69/b16fc81b939d3efdd0b552f2e3e54f7fa1423d0c320cced2e69e675dde26/sympy-1.7.1-py3-none-any.whl (5.9MB)\n",
            "\u001b[K     |████████████████████████████████| 5.9MB 16.9MB/s \n",
            "\u001b[?25hRequirement already satisfied: pyparsing in /usr/local/lib/python3.6/dist-packages (from brian2) (2.4.7)\n",
            "Requirement already satisfied: jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from brian2) (2.11.2)\n",
            "Requirement already satisfied: setuptools>=24.2 in /usr/local/lib/python3.6/dist-packages (from brian2) (50.3.2)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy>=1.2->brian2) (1.1.0)\n",
            "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from jinja2>=2.7->brian2) (1.1.1)\n",
            "Building wheels for collected packages: brian2\n",
            "  Building wheel for brian2 (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for brian2: filename=Brian2-2.4.2-cp36-cp36m-linux_x86_64.whl size=1257537 sha256=98feb4e57bc3e4fc70b36409987d6f0992188899e6b855cc2f10571dc2c46c76\n",
            "  Stored in directory: /root/.cache/pip/wheels/5d/4b/cf/ef50e71df5479d67f981cbb17b1d842381019d27ba144d57de\n",
            "Successfully built brian2\n",
            "Installing collected packages: sympy, brian2\n",
            "  Found existing installation: sympy 1.1.1\n",
            "    Uninstalling sympy-1.1.1:\n",
            "      Successfully uninstalled sympy-1.1.1\n",
            "Successfully installed brian2-2.4.2 sympy-1.7.1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YHfPgWG45Gl8"
      },
      "source": [
        "from __future__ import division\n",
        "\n",
        "from pylab import *\n",
        "from brian2 import *\n",
        "import time\n",
        "\n",
        "from brian2.units.allunits import henry\n",
        "from scipy.stats import vonmises\n",
        "from scipy.stats import norm as s_norm\n",
        "from sklearn.metrics.pairwise import cosine_similarity\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "plt.rcParams.update({'font.size': 18})\n",
        "plt.rcParams.update({'text.usetex': False})\n",
        "# matplotlib.rcParams['text.latex.preamble'] = [\n",
        "#     r'\\usepackage{amsmath}',\n",
        "#     r'\\usepackage{amssymb}']\n",
        "plt.rcParams.update({'font.family': 'serif', \n",
        "                     'font.serif':['Computer Modern']})"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YSwZtQOG5Lu6"
      },
      "source": [
        "def crvec(N, D=1):\n",
        "    rphase = 2*np.pi * np.random.rand(D, N)\n",
        "    return np.cos(rphase) + 1.0j * np.sin(rphase)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oNJD8Nk_5Ms-"
      },
      "source": [
        "def norm_range(v):\n",
        "    return (v-v.min())/(v.max()-v.min())"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AhayIB_H5hQR"
      },
      "source": [
        "def activation_thresh(x, sigma=0.0, c_thresh=None):\n",
        "    \n",
        "    if c_thresh is None:\n",
        "        N = x.shape[0]\n",
        "        c_thresh = 2.0 / N**0.5\n",
        "        \n",
        "    xn = np.abs(x)\n",
        "    \n",
        "    a = (x ) / (np.abs(x) + 1e-12)\n",
        "    a[xn < c_thresh] = 0\n",
        "    \n",
        "    return a"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SBx4pbjM5jNQ"
      },
      "source": [
        "def cviz_im(cvec):\n",
        "    ss = int(len(cvec)**0.5)\n",
        "    \n",
        "    ss_idx = ss**2\n",
        "    \n",
        "    im_cvec = np.zeros((ss, ss,3))\n",
        "#     im_cvec[:,:,3]=1\n",
        "    c=0\n",
        "    for i in range(ss):\n",
        "        for j in range(ss):\n",
        "            if np.abs(cvec[c]) > 0.05:\n",
        "                im_cvec[i,j,:] = matplotlib.colors.hsv_to_rgb([(np.angle(cvec[c])/2/pi + 1) % 1, 1, 1])\n",
        "                \n",
        "            c+=1\n",
        "                \n",
        "    return im_cvec"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4pu8tFGW5lJW"
      },
      "source": [
        "def phase2spikes(cv, freq=5.0):\n",
        "    st = np.angle(cv) / (2*pi*freq)\n",
        "    return st\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jb8tRTPaKdRT"
      },
      "source": [
        "def my_cosine_similarity(vec1, vec2):\n",
        "    return np.dot(vec1, vec2)/(np.linalg.norm(vec1)*np.linalg.norm(vec2))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "df-gPw5OOpMg"
      },
      "source": [
        "def phasor_similarity(vec1, vec2):\n",
        "  difference = np.abs(vec1 - vec2)\n",
        "  return np.abs(np.exp(1j*difference).sum())/len(vec1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8nnQMNSxXXWt"
      },
      "source": [
        "def angle_similarity(vec1, vec2):\n",
        "  diff = np.angle(vec1) - np.angle(vec2)\n",
        "  return np.cos(diff).sum()/len(diff)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qR_0QJfdfmfu"
      },
      "source": [
        "def hot_angle_similarity(input, target):\n",
        "  # Get indices where val in target != 0\n",
        "  indices = np.nonzero(target)\n",
        "  diff = np.angle(target[indices]) - np.angle(input[indices])\n",
        "  return np.cos(diff).sum()/len(diff)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nPrgBkIJ5n6N"
      },
      "source": [
        "# TPAM #"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SwBgAS-y5yyV"
      },
      "source": [
        "## Store random sparse phasor patterns in network ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yGW4GrxR5nV9"
      },
      "source": [
        "N=25**2\n",
        "D=201\n",
        "Ks=25\n",
        "\n",
        "letter_vectors_c = crvec(N, D)\n",
        "\n",
        "for d in range(D):\n",
        "    ip = np.random.choice(N, size=(N-Ks), replace=False)\n",
        "    letter_vectors_c[d, ip] = 0\n",
        "    \n",
        "letter_vectors = 2 * (np.random.randn(D,N) < 0) - 1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eh3ZIyaD5u7l"
      },
      "source": [
        "J_c = np.dot(letter_vectors_c.T, np.conj(letter_vectors_c))\n",
        "np.fill_diagonal(J_c, 0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9sw-fpvw53_9"
      },
      "source": [
        "## Network dynamics and simulations ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 290
        },
        "id": "Gyz03X3453LN",
        "outputId": "0e3b3443-d00f-4b61-8ed6-e5a968495903"
      },
      "source": [
        "max_steps = 20\n",
        "hop_hist = np.zeros((D, max_steps+1))\n",
        "hop_s_hist = np.zeros((N, max_steps+1), 'complex')\n",
        "\n",
        "target_idx = 100\n",
        "\n",
        "hop_state_i = letter_vectors_c[target_idx,:].copy()\n",
        "hop_state_i[:300] = 0\n",
        "\n",
        "noise_state = 0.0 * np.random.randn(N) * np.squeeze(crvec(N,1)) #2*(np.random.randn(N) < 0) - 1\n",
        "hop_state = hop_state_i + noise_state\n",
        "\n",
        "hop_state /= norm(hop_state)\n",
        "\n",
        "cols = get_cmap('copper', max_steps)\n",
        "\n",
        "c_thresh = 0.6/Ks**0.5\n",
        "for i in range(max_steps):\n",
        "    hop_hist[:,i] = np.real(np.dot(np.conj(letter_vectors_c), hop_state))    \n",
        "    hop_s_hist[:,i] = hop_state\n",
        "    \n",
        "    hop_u = np.dot(J_c, hop_state) / Ks\n",
        "    hop_state = activation_thresh(hop_u, c_thresh=c_thresh )\n",
        "    hop_state /= norm(hop_state)\n",
        "\n",
        "    plot(hop_hist[:,i], c=cols(i))\n",
        "\n",
        "hop_hist[:,i+1] =  np.real(np.dot(np.conj(letter_vectors_c), hop_state))\n",
        "plot(hop_hist[:,i], c=cols(i))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f4b75361080>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "stream",
          "text": [
            "findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 193
        },
        "id": "LDziAZwE6G8k",
        "outputId": "ea03a273-c280-494d-da8d-6a46c669e422"
      },
      "source": [
        "figure(figsize=(6,3))\n",
        "\n",
        "subplot(131)\n",
        "imshow(cviz_im(hop_state_i))\n",
        "title('Initial')\n",
        "subplot(132)\n",
        "imshow(cviz_im(hop_s_hist[:, -2]))\n",
        "title('Converged')\n",
        "subplot(133)\n",
        "imshow(cviz_im(letter_vectors_c[target_idx,:]))\n",
        "title('Target')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Target')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "output_type": "stream",
          "text": [
            "findfont: Font family ['serif'] not found. Falling back to DejaVu Sans.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x216 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rv5CPSzrAYBL"
      },
      "source": [
        "# Stochastic TPAM #"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NqrEWwGWA7HP"
      },
      "source": [
        "def stochastic_activation_thresh(x, k, sigma=0.0, type='vonmises'):\n",
        "  \"\"\"\n",
        "  Take a von mises distribution over the incoming data and sample\n",
        "  a threshold.\n",
        "  \"\"\"\n",
        "  top_k = np.sort(x)[-k:][::-1]\n",
        "  if type == 'vonmises':\n",
        "    norm_angle = (np.angle(top_k) + np.pi)/(2*np.pi)\n",
        "    dist = vonmises.fit(norm_angle, fscale=1)\n",
        "    # c_thresh = vonmises.rvs(kappa=dist[0], loc=dist[1])\n",
        "    c_thresh = vonmises.rvs(kappa=dist[0]*10, loc=0.2*dist[1])\n",
        "    # print(f'kappa: {dist[0]*10}, loc: {0.2*dist[1]}')\n",
        "  elif type == 'norm':\n",
        "    dist = s_norm.fit(np.abs(top_k), fscale=1)\n",
        "    c_thresh = s_norm.rvs(scale=dist[1], loc=0.2*dist[0])\n",
        "  else: \n",
        "    N = x.shape[0]\n",
        "    c_thresh = 2.0 / N**0.5\n",
        "  # c_thresh = 0.12\n",
        "  # print(\"stochastic threshold: \", c_thresh)\n",
        "      \n",
        "  xn = np.abs(x)\n",
        "  # print(\"x: \",x)\n",
        "  # print(\"xn: \",xn)\n",
        "  \n",
        "  a = (x) / (np.abs(x) + 1e-12)\n",
        "  a[xn < c_thresh] = 0\n",
        "  \n",
        "  return a"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gi__BpUErRbc"
      },
      "source": [
        "### Testing ###"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YvPHj21-FF7R",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        },
        "outputId": "a8f2215d-3cd6-4106-8b55-681f0f3e13eb"
      },
      "source": [
        "x=np.linspace(0,2*pi,num=1000)\n",
        "y= np.exp(1j*y)\n",
        "dist = s_norm.fit(np.abs(y), fscale=1)\n",
        "c_thresh = s_norm.rvs(scale=dist[1], loc=0.2*dist[0])\n",
        "\n",
        "fig, ax = plt.subplot(1,2, figsize=(9,4))\n",
        "\n",
        "ax0.plot(x, )"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-18-3a847e3a6ec9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mnum\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1j\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mdist\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ms_norm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mc_thresh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ms_norm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrvs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'y' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O4cbiN82S-gQ",
        "outputId": "fa66cec5-a155-474b-bddb-dd36264c73bc"
      },
      "source": [
        "x = np.array([-5,-4,-3,-2,-1,-0.3,0,0.3,1,2,3,4,5,6])\n",
        "\n",
        "D = 3\n",
        "N = 100\n",
        "rphase = 2*np.pi * np.random.rand(N)\n",
        "comp = np.cos(rphase) + 1.0j * np.sin(rphase)\n",
        "\n",
        "c_thresh = 0.6/Ks**0.5\n",
        "x = np.angle(comp)/(2*np.pi)\n",
        "stochastic_activation_thresh(x, k = Ks)\n",
        "activation_thresh(x, c_thresh=c_thresh)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING    /usr/local/lib/python3.6/dist-packages/scipy/stats/_continuous_distns.py:7497: RuntimeWarning: overflow encountered in exp\n",
            "  return np.exp(kappa * np.cos(x)) / (2*np.pi*sc.i0(kappa))\n",
            " [py.warnings]\n",
            "WARNING    /usr/local/lib/python3.6/dist-packages/scipy/stats/_continuous_distns.py:7497: RuntimeWarning: invalid value encountered in true_divide\n",
            "  return np.exp(kappa * np.cos(x)) / (2*np.pi*sc.i0(kappa))\n",
            " [py.warnings]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.,  0.,  1.,  1.,  1., -1.,  1.,  0.,  0.,  0.,  1., -1., -1.,\n",
              "        1.,  0., -1., -1.,  0.,  0.,  1.,  1.,  1., -1.,  1.,  1., -1.,\n",
              "       -1.,  1., -1.,  0.,  0., -1., -1., -1., -1.,  1., -1., -1.,  1.,\n",
              "        1.,  0.,  1.,  1., -1.,  0.,  0.,  1.,  1.,  0.,  1.,  0.,  0.,\n",
              "        1., -1.,  0.,  1.,  0.,  1., -1.,  1.,  1.,  1.,  0.,  1., -1.,\n",
              "       -1., -1., -1.,  1., -1., -1.,  0., -1., -1.,  1., -1.,  1., -1.,\n",
              "        0.,  0., -1., -1., -1.,  1., -1., -1., -1.,  1.,  0.,  1., -1.,\n",
              "        1.,  0.,  0.,  0.,  1., -1.,  0.,  1., -1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DdOuDAmmkb0s"
      },
      "source": [
        "kappa = 4\n",
        "x = np.linspace(vonmises.ppf(0.01, kappa), vonmises.ppf(0.99, kappa), 100)\n",
        "rphase = 2*np.pi * x\n",
        "comp = np.cos(rphase) + 1.0j * np.sin(rphase)\n",
        "x=np.angle(comp)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J1yxBKoeWky1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 215
        },
        "outputId": "37a2b0a9-0cc5-48e2-b6df-836625017483"
      },
      "source": [
        "dist = vonmises.fit(x, fscale=1)\n",
        "vonmises.rvs(kappa=10*dist[0], loc=1.5*dist[1])\n",
        "c_thresh = vonmises.rvs(kappa=dist[0]*10, loc=1.5*dist[1])\n",
        "# stochastic_activation_thresh(x)\n",
        "dist = s_norm.fit(np.abs(top_k), fscale=1)\n",
        "c_thresh = s_norm.rvs(scale=dist[1], loc=0.2*dist[0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-23-9c252bd16410>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mc_thresh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvonmises\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrvs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1.5\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;31m# stochastic_activation_thresh(x)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mdist\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ms_norm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtop_k\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mc_thresh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0ms_norm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrvs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'top_k' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 273
        },
        "id": "fK4uHljzWycq",
        "outputId": "ad604ec8-01b0-41f8-f57d-53f40ac936c9"
      },
      "source": [
        "fig, ax = plt.subplots(1, 1)\n",
        "rv = vonmises(dist[0])\n",
        "ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')\n",
        "ax.vlines(c_thresh, ymin=0, ymax=max(rv.pdf(x)), colors='red')\n",
        "r = vonmises.rvs(kappa=dist[0], loc=dist[1], size = 1000)\n",
        "ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)\n",
        "ax.legend(loc='best', frameon=False)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jqFnaw8QWxPI"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nAZHeJY1AlzJ"
      },
      "source": [
        "## Store random sparse phasors in network ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qhP7J81PAozZ"
      },
      "source": [
        "N=25**2\n",
        "D=201\n",
        "Ks=25\n",
        "\n",
        "letter_vectors_c = crvec(N, D)\n",
        "\n",
        "for d in range(D):\n",
        "    ip = np.random.choice(N, size=(N-Ks), replace=False)\n",
        "    letter_vectors_c[d, ip] = 0\n",
        "    \n",
        "letter_vectors = 2 * (np.random.randn(D,N) < 0) - 1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ymHHwLxaAtaf"
      },
      "source": [
        "J_c = np.dot(letter_vectors_c.T, np.conj(letter_vectors_c))\n",
        "np.fill_diagonal(J_c, 0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qc4mXKfVAw3A"
      },
      "source": [
        "## Network dynamics and simulations ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 784
        },
        "id": "x9-hTmb3AxP7",
        "outputId": "7632e8de-f5ea-4fb6-9769-6cbc1fb953ae"
      },
      "source": [
        "fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n",
        "\n",
        "\n",
        "max_steps = 20\n",
        "\n",
        "hop_hist = np.zeros((D, max_steps+1))\n",
        "hop_s_hist = np.zeros((N, max_steps+1), 'complex')\n",
        "\n",
        "target_idx = 100\n",
        "\n",
        "hop_state_i = letter_vectors_c[target_idx,:].copy()\n",
        "hop_state_i[:300] = 0\n",
        "\n",
        "noise_state = 0.2 * np.random.randn(N) * np.squeeze(crvec(N,1)) #2*(np.random.randn(N) < 0) - 1\n",
        "hop_state = hop_state_i + noise_state\n",
        "\n",
        "hop_state /= norm(hop_state)\n",
        "\n",
        "# Stochastic version\n",
        "hop_hist_stc = np.zeros((D, max_steps+1))\n",
        "hop_s_hist_stc = np.zeros((N, max_steps+1), 'complex')\n",
        "\n",
        "target_idx = 100\n",
        "\n",
        "hop_state_i_stc = letter_vectors_c[target_idx,:].copy()\n",
        "hop_state_i_stc[:300] = 0\n",
        "\n",
        "noise_state_stc = 0.2 * np.random.randn(N) * np.squeeze(crvec(N,1)) #2*(np.random.randn(N) < 0) - 1\n",
        "hop_state_stc = hop_state_i_stc + noise_state_stc\n",
        "\n",
        "hop_state_stc /= norm(hop_state_stc)\n",
        "\n",
        "cols = get_cmap('copper', max_steps)\n",
        "\n",
        "c_thresh = 0.6/Ks**0.5\n",
        "for i in range(max_steps):\n",
        "    hop_hist[:,i] = np.real(np.dot(np.conj(letter_vectors_c), hop_state))    \n",
        "    hop_s_hist[:,i] = hop_state\n",
        "    \n",
        "    hop_u = np.dot(J_c, hop_state) / Ks\n",
        "    # ax2.plot(hop_u[:,i], c=cols(i))\n",
        "    print(\"regular threshold: \", c_thresh)\n",
        "    # print(\"original: \",hop_u[:50])\n",
        "    hop_state = activation_thresh(hop_u, c_thresh=c_thresh )\n",
        "    # print(\"original: \",hop_state[:50])\n",
        "    hop_state /= norm(hop_state)\n",
        "\n",
        "    ax0.plot(hop_hist[:,i], c=cols(i))\n",
        "\n",
        "    # Stochastic version\n",
        "    hop_hist_stc[:,i] = np.real(np.dot(np.conj(letter_vectors_c), hop_state_stc))    \n",
        "    hop_s_hist_stc[:,i] = hop_state_stc\n",
        "\n",
        "    hop_u_stc = np.dot(J_c, hop_state_stc) / Ks\n",
        "    # ax3.plot(hop_u_stc[:,i], c=cols(i))\n",
        "    # print(\"Stochastic: \", hop_u_stc[:50])\n",
        "    hop_state_stc = stochastic_activation_thresh(hop_u_stc, k=Ks)\n",
        "    # print(\"Stochastic: \", hop_state_stc[:50])\n",
        "\n",
        "    hop_state_stc /= norm(hop_state_stc)\n",
        "\n",
        "    ax1.plot(hop_hist_stc[:,i], c=cols(i))\n",
        "\n",
        "ax0.set_title(\"Normal thresholding\")\n",
        "hop_hist[:,i+1] =  np.real(np.dot(np.conj(letter_vectors_c), hop_state))\n",
        "ax0.plot(hop_hist[:,i], c=cols(i))\n",
        "\n",
        "ax1.set_title(\"Stochastic thresholding from von mises \")\n",
        "hop_hist_stc[:,i+1] =  np.real(np.dot(np.conj(letter_vectors_c), hop_state_stc))\n",
        "ax1.plot(hop_hist_stc[:,i], c=cols(i))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING    /usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:46: RuntimeWarning: invalid value encountered in true_divide\n",
            " [py.warnings]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "regular threshold:  0.12\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "WARNING    /usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:60: RuntimeWarning: invalid value encountered in true_divide\n",
            " [py.warnings]\n",
            "WARNING    /usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in less\n",
            "  # Remove the CWD from sys.path while we load stuff.\n",
            " [py.warnings]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "regular threshold:  0.12\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "RuntimeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-26-be0cd5a3879c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     55\u001b[0m     \u001b[0;31m# ax3.plot(hop_u_stc[:,i], c=cols(i))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0;31m# print(\"Stochastic: \", hop_u_stc[:50])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 57\u001b[0;31m     \u001b[0mhop_state_stc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstochastic_activation_thresh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhop_u_stc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mKs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     58\u001b[0m     \u001b[0;31m# print(\"Stochastic: \", hop_state_stc[:50])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     59\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-17-14f84f9118f3>\u001b[0m in \u001b[0;36mstochastic_activation_thresh\u001b[0;34m(x, k, sigma, type)\u001b[0m\n\u001b[1;32m      7\u001b[0m   \u001b[0;32mif\u001b[0m \u001b[0mtype\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'vonmises'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m     \u001b[0mnorm_angle\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mangle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtop_k\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m     \u001b[0mdist\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvonmises\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnorm_angle\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfscale\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     10\u001b[0m     \u001b[0;31m# c_thresh = vonmises.rvs(kappa=dist[0], loc=dist[1])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m     \u001b[0mc_thresh\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvonmises\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrvs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkappa\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/scipy/stats/_distn_infrastructure.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, data, *args, **kwds)\u001b[0m\n\u001b[1;32m   2279\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2280\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2281\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The data contains non-finite values.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2282\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2283\u001b[0m         \u001b[0mstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mRuntimeError\u001b[0m: The data contains non-finite values."
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ArYK4Mg2AuEJ"
      },
      "source": [
        "figure(figsize=(6,6))\n",
        "\n",
        "subplot(231)\n",
        "imshow(cviz_im(hop_state_i))\n",
        "title('Initial')\n",
        "subplot(232)\n",
        "imshow(cviz_im(hop_s_hist[:, -2]))\n",
        "title('Converged')\n",
        "subplot(233)\n",
        "imshow(cviz_im(letter_vectors_c[target_idx,:]))\n",
        "title('Target')\n",
        "\n",
        "subplot(234)\n",
        "imshow(cviz_im(hop_state_i_stc))\n",
        "title('Initial')\n",
        "subplot(235)\n",
        "imshow(cviz_im(hop_s_hist_stc[:, -2]))\n",
        "title('Converged')\n",
        "subplot(236)\n",
        "imshow(cviz_im(letter_vectors_c[target_idx,:]))\n",
        "title('Target')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IuYP7Zs6PKnn"
      },
      "source": [
        "## Test similarity vs noise ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4xXfokNEJIkv"
      },
      "source": [
        "def test_thresholds(noise=0.0, layered = False):\n",
        "  max_steps = 20\n",
        "\n",
        "  hop_hist = np.zeros((D, max_steps+1))\n",
        "  hop_s_hist = np.zeros((N, max_steps+1), 'complex')\n",
        "\n",
        "  target_idx = 100\n",
        "\n",
        "  hop_state_i = letter_vectors_c[target_idx,:].copy()\n",
        "  hop_state_i[:300] = 0\n",
        "\n",
        "\n",
        "  if layered:\n",
        "    noise_state = noise*letter_vectors_c[target_idx-1,:].copy()\n",
        "    \n",
        "  else:\n",
        "    noise_state = noise * np.random.randn(N) * np.squeeze(crvec(N,1)) #2*(np.random.randn(N) < 0) - 1\n",
        "  hop_state = hop_state_i + noise_state\n",
        "\n",
        "  hop_state /= norm(hop_state)\n",
        "\n",
        "  # Stochastic version\n",
        "  hop_hist_stc = np.zeros((D, max_steps+1))\n",
        "  hop_s_hist_stc = np.zeros((N, max_steps+1), 'complex')\n",
        "\n",
        "  target_idx = 100\n",
        "\n",
        "  hop_state_i_stc = letter_vectors_c[target_idx,:].copy()\n",
        "  hop_state_i_stc[:300] = 0\n",
        "\n",
        "  if layered:\n",
        "    noise_state_stc = noise*letter_vectors_c[target_idx-1,:].copy()\n",
        "  else:\n",
        "     noise_state_stc = noise * np.random.randn(N) * np.squeeze(crvec(N,1)) #2*(np.random.randn(N) < 0) - 1\n",
        "\n",
        "  hop_state_stc = hop_state_i_stc + noise_state_stc\n",
        "\n",
        "  hop_state_stc /= norm(hop_state_stc)\n",
        "\n",
        "  cols = get_cmap('copper', max_steps)\n",
        "\n",
        "  c_thresh = 0.6/Ks**0.5\n",
        "  for i in range(max_steps):\n",
        "      hop_hist[:,i] = np.real(np.dot(np.conj(letter_vectors_c), hop_state))    \n",
        "      hop_s_hist[:,i] = hop_state\n",
        "      \n",
        "      hop_u = np.dot(J_c, hop_state) / Ks\n",
        "      # ax2.plot(hop_u[:,i], c=cols(i))\n",
        "      # print(\"regular threshold: \", c_thresh)\n",
        "      # print(\"original: \",hop_u[:50])\n",
        "      hop_state = activation_thresh(hop_u, c_thresh=c_thresh )\n",
        "      # print(\"original: \",hop_state[:50])\n",
        "\n",
        "      hop_state /= (norm(hop_state) + 1**-10)\n",
        "\n",
        "      # ax0.plot(hop_hist[:,i], c=cols(i))\n",
        "\n",
        "      # Stochastic version\n",
        "      hop_hist_stc[:,i] = np.real(np.dot(np.conj(letter_vectors_c), hop_state_stc))    \n",
        "      hop_s_hist_stc[:,i] = hop_state_stc\n",
        "\n",
        "      hop_u_stc = np.dot(J_c, hop_state_stc) / Ks\n",
        "      # ax3.plot(hop_u_stc[:,i], c=cols(i))\n",
        "      # print(\"Stochastic: \", hop_u_stc[:50])\n",
        "      hop_state_stc = stochastic_activation_thresh(hop_u_stc, k=Ks)\n",
        "      # print(\"Stochastic: \", hop_state_stc[:50])\n",
        "\n",
        "      hop_state_stc /= (norm(hop_state_stc) + 1**-10)\n",
        "\n",
        "      # ax1.plot(hop_hist_stc[:,i], c=cols(i))\n",
        "\n",
        "  # orig_output = np.angle(hop_s_hist[:, -2]).reshape(-1,1)\n",
        "  # stc_output = np.angle(hop_s_hist_stc[:, -2]).reshape(-1,1)\n",
        "  # target = np.angle(letter_vectors_c[target_idx,:]).reshape(-1,1)\n",
        "\n",
        "  # orig = cosine_similarity(orig_output, target)\n",
        "  # stochastic = cosine_similarity(stc_output, target)\n",
        "\n",
        "  orig_output = hop_s_hist[:, -2]\n",
        "  stc_output = hop_s_hist_stc[:, -2]\n",
        "  target = letter_vectors_c[target_idx,:]\n",
        "\n",
        "  # orig = my_cosine_similarity(orig_output, target)\n",
        "  # stochastic = my_cosine_similarity(stc_output, target)\n",
        "\n",
        "  orig = angle_similarity(orig_output, target)\n",
        "  stochastic = angle_similarity(stc_output, target)\n",
        "  hot_orig = hot_angle_similarity(orig_output, target)\n",
        "  hot_stochastic = hot_angle_similarity(stc_output, target)\n",
        "\n",
        "  # figure(figsize=(6,6))\n",
        "\n",
        "  # subplot(231)\n",
        "  # imshow(cviz_im(hop_state_i))\n",
        "  # title('Initial')\n",
        "  # subplot(232)\n",
        "  # imshow(cviz_im(hop_s_hist[:, -2]))\n",
        "  # title('Converged')\n",
        "  # subplot(233)\n",
        "  # imshow(cviz_im(letter_vectors_c[target_idx,:]))\n",
        "  # title('Target')\n",
        "\n",
        "  # subplot(234)\n",
        "  # imshow(cviz_im(hop_state_i_stc))\n",
        "  # title('Initial')\n",
        "  # subplot(235)\n",
        "  # imshow(cviz_im(hop_s_hist_stc[:, -2]))\n",
        "  # title('Converged')\n",
        "  # subplot(236)\n",
        "  # imshow(cviz_im(letter_vectors_c[target_idx,:]))\n",
        "  # title('Target')\n",
        "\n",
        "  return orig, stochastic, hot_orig, hot_stochastic"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tnrGXZE-OnyM"
      },
      "source": [
        "N=25**2\n",
        "D=201\n",
        "Ks=25\n",
        "\n",
        "letter_vectors_c = crvec(N, D)\n",
        "\n",
        "for d in range(D):\n",
        "    ip = np.random.choice(N, size=(N-Ks), replace=False)\n",
        "    letter_vectors_c[d, ip] = 0\n",
        "    \n",
        "letter_vectors = 2 * (np.random.randn(D,N) < 0) - 1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Phupj_XnPG9T"
      },
      "source": [
        "J_c = np.dot(letter_vectors_c.T, np.conj(letter_vectors_c))\n",
        "np.fill_diagonal(J_c, 0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RipNImIEKKu5"
      },
      "source": [
        "\n",
        "num_samples = 10\n",
        "o_means = []\n",
        "s_means = []\n",
        "o_h_means = []\n",
        "s_h_means = []\n",
        "o_medians = []\n",
        "s_medians = []\n",
        "o_h_medians = []\n",
        "s_h_medians  = []\n",
        "o_variance = []\n",
        "s_variance = []\n",
        "o_h_variance = []\n",
        "s_h_variance = []\n",
        "for _ in range(num_samples):\n",
        "  o_set = []\n",
        "  s_set = []\n",
        "  o_h_set = []\n",
        "  s_h_set = []\n",
        "  x = np.linspace(0,0.4,num=100)\n",
        "  for noise in x:\n",
        "    print(\"noise: \",noise)\n",
        "    o, s, o_h, s_h = test_thresholds(noise=noise)\n",
        "    # print(f'original similarity: {o}, stochastic similarity: {s}')\n",
        "    o_set.append(o)\n",
        "    s_set.append(s)\n",
        "    o_h_set.append(o_h)\n",
        "    s_h_set.append(s_h)\n",
        "    \n",
        "  o_means.append(np.mean(o_set))\n",
        "  s_means.append(np.mean(s_set))\n",
        "  print(f'original mean similarity: {np.mean(o_set)}')\n",
        "  print(f'stochastic mean similarity: {np.mean(s_set)}')\n",
        "\n",
        "  o_h_means.append(np.mean(o_h_set))\n",
        "  s_h_means.append(np.mean(s_h_set))\n",
        "  print(f'original one-hot mean similarity: {np.mean(o_h_set)}')\n",
        "  print(f'stochastic one-hot mean similarity: {np.mean(s_h_set)}')\n",
        "  o_medians.append(np.median(o_set))\n",
        "  s_medians.append(np.median(s_set))\n",
        "\n",
        "  print(f'original median similarity: {np.median(o_set)}')\n",
        "  print(f'stochastic median similarity: {np.median(s_set)}')\n",
        "  o_h_medians.append(np.median(o_h_set))\n",
        "  s_h_medians.append(np.median(s_h_set))\n",
        "\n",
        "  print(f'original one-hot median similarity: {np.median(o_h_set)}')\n",
        "  print(f'stochastic one-hot median similarity: {np.median(s_h_set)}')\n",
        "\n",
        "  o_variance.append(np.var(o_set))\n",
        "  s_variance.append(np.var(s_set))\n",
        "  print(f'original variance: {np.var(o_set)}')\n",
        "  print(f'stochastic variance: {np.var(s_set)}')\n",
        "\n",
        "  o_h_variance.append(np.var(o_h_set))\n",
        "  s_h_variance.append(np.var(s_h_set))\n",
        "  print(f'original one-hot variance: {np.var(o_h_set)}')\n",
        "  print(f'stochastic one-hot variance: {np.var(s_h_set)}')\n",
        "\n",
        "  # fig, (ax0, ax1) = plt.subplot(1, 2, figsize=(12,5))\n",
        "\n",
        "  # ax0.plot(x, np.array(o_set), label='original')\n",
        "  # ax0.plot(x, np.array(s_set), label='stochastic')\n",
        "  # ax0.xlabel(\"Noise\")\n",
        "  # ax0.ylabel(\"Similarity\")\n",
        "  # ax0.title(\"Similarity vs. Noise\")\n",
        "  # ax0.legend()\n",
        "\n",
        "  # ax1.plot(x, np.array(o_h_set), label='original')\n",
        "  # ax1.plot(x, np.array(s_h_set), label='stochastic')\n",
        "  # ax1.xlabel(\"Noise\")\n",
        "  # ax1.ylabel(\"Similarity\")\n",
        "  # ax1.title(\"Hot Similarity vs. Noise\")\n",
        "  # ax1.legend();\n",
        "\n",
        "\n",
        "print(f'original mean similarity across iterations: {np.mean(o_means)}')\n",
        "print(f'stochastic mean similarity across iterations: {np.mean(s_means)}')\n",
        "print(f'original mean hot similarity across iterations: {np.mean(o_h_means)}')\n",
        "print(f'stochastic mean hot similarity across iterations: {np.mean(s_h_means)}')\n",
        "print(f'original median similarity across iterations: {np.median(o_medians)}')\n",
        "print(f'stochastic median similarity across iterations: {np.mean(s_medians)}')\n",
        "print(f'original median hot similarity across iterations: {np.median(o_h_medians)}')\n",
        "print(f'stochastic median hot similarity across iterations: {np.mean(s_h_medians)}')\n",
        "print(f'average original similarity variance across iterations: {np.mean(o_variance)}')\n",
        "print(f'average stochastic similarity variance across iterations: {np.mean(s_variance)}')\n",
        "print(f'average original hot similarity variance across iterations: {np.mean(o_h_variance)}')\n",
        "print(f'average stochastic hot similarity variance across iterations: {np.mean(s_h_variance)}')\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JOOvo9yCjQu8",
        "outputId": "8800db35-bd53-4518-d4aa-1b0f0ce79a92"
      },
      "source": [
        "o_set = []\n",
        "s_set = []\n",
        "o_h_set = []\n",
        "s_h_set = []\n",
        "x = np.linspace(0,0.4,num=100)\n",
        "for noise in x:\n",
        "  print(\"noise: \",noise)\n",
        "  o, s, o_h, s_h = test_thresholds(noise=noise, layered = True)\n",
        "    # print(f'original similarity: {o}, stochastic similarity: {s}')\n",
        "  o_set.append(o)\n",
        "  s_set.append(s)\n",
        "  o_h_set.append(o_h)\n",
        "  s_h_set.append(s_h)\n",
        "    \n",
        "o_means.append(np.mean(o_set))\n",
        "s_means.append(np.mean(s_set))\n",
        "print(f'original mean similarity: {np.mean(o_set)}')\n",
        "print(f'stochastic mean similarity: {np.mean(s_set)}')\n",
        "\n",
        "o_h_means.append(np.mean(o_h_set))\n",
        "s_h_means.append(np.mean(s_h_set))\n",
        "print(f'original one-hot mean similarity: {np.mean(o_h_set)}')\n",
        "print(f'stochastic one-hot mean similarity: {np.mean(s_h_set)}')\n",
        "o_medians.append(np.median(o_set))\n",
        "s_medians.append(np.median(s_set))\n",
        "\n",
        "print(f'original median similarity: {np.median(o_set)}')\n",
        "print(f'stochastic median similarity: {np.median(s_set)}')\n",
        "o_h_medians.append(np.median(o_h_set))\n",
        "s_h_medians.append(np.median(s_h_set))\n",
        "\n",
        "print(f'original one-hot median similarity: {np.median(o_h_set)}')\n",
        "print(f'stochastic one-hot median similarity: {np.median(s_h_set)}')\n",
        "\n",
        "o_variance.append(np.var(o_set))\n",
        "s_variance.append(np.var(s_set))\n",
        "print(f'original variance: {np.var(o_set)}')\n",
        "print(f'stochastic variance: {np.var(s_set)}')\n",
        "\n",
        "o_h_variance.append(np.var(o_h_set))\n",
        "s_h_variance.append(np.var(s_h_set))\n",
        "print(f'original one-hot variance: {np.var(o_h_set)}')\n",
        "print(f'stochastic one-hot variance: {np.var(s_h_set)}')\n",
        "\n",
        "fig, (ax0, ax1) = plt.subplot(1,2,(1,2))\n",
        "\n",
        "ax0.plot(x, np.array(o_set), label='original')\n",
        "ax0.plot(x, np.array(s_set), label='stochastic')\n",
        "ax0.xlabel(\"Noise\")\n",
        "ax0.ylabel(\"Similarity\")\n",
        "ax0.title(\"Similarity vs. Noise\")\n",
        "ax0.legend()\n",
        "\n",
        "ax1.plot(x, np.array(o_h_set), label='original')\n",
        "ax1.plot(x, np.array(s_h_set), label='stochastic')\n",
        "ax1.xlabel(\"Noise\")\n",
        "ax1.ylabel(\"Similarity\")\n",
        "ax1.title(\"Hot Similarity vs. Noise\")\n",
        "ax1.legend();"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "noise:  0.0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "WARNING    /usr/local/lib/python3.6/dist-packages/scipy/stats/_continuous_distns.py:7497: RuntimeWarning: overflow encountered in exp\n",
            "  return np.exp(kappa * np.cos(x)) / (2*np.pi*sc.i0(kappa))\n",
            " [py.warnings]\n",
            "WARNING    /usr/local/lib/python3.6/dist-packages/scipy/stats/_continuous_distns.py:7497: RuntimeWarning: invalid value encountered in true_divide\n",
            "  return np.exp(kappa * np.cos(x)) / (2*np.pi*sc.i0(kappa))\n",
            " [py.warnings]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "noise:  0.00404040404040404\n",
            "noise:  0.00808080808080808\n",
            "noise:  0.012121212121212121\n",
            "noise:  0.01616161616161616\n",
            "noise:  0.0202020202020202\n",
            "noise:  0.024242424242424242\n",
            "noise:  0.028282828282828285\n",
            "noise:  0.03232323232323232\n",
            "noise:  0.03636363636363636\n",
            "noise:  0.0404040404040404\n",
            "noise:  0.044444444444444446\n",
            "noise:  0.048484848484848485\n",
            "noise:  0.052525252525252523\n",
            "noise:  0.05656565656565657\n",
            "noise:  0.06060606060606061\n",
            "noise:  0.06464646464646465\n",
            "noise:  0.06868686868686869\n",
            "noise:  0.07272727272727272\n",
            "noise:  0.07676767676767676\n",
            "noise:  0.0808080808080808\n",
            "noise:  0.08484848484848485\n",
            "noise:  0.08888888888888889\n",
            "noise:  0.09292929292929293\n",
            "noise:  0.09696969696969697\n",
            "noise:  0.10101010101010101\n",
            "noise:  0.10505050505050505\n",
            "noise:  0.10909090909090909\n",
            "noise:  0.11313131313131314\n",
            "noise:  0.11717171717171718\n",
            "noise:  0.12121212121212122\n",
            "noise:  0.12525252525252525\n",
            "noise:  0.1292929292929293\n",
            "noise:  0.13333333333333333\n",
            "noise:  0.13737373737373737\n",
            "noise:  0.1414141414141414\n",
            "noise:  0.14545454545454545\n",
            "noise:  0.1494949494949495\n",
            "noise:  0.15353535353535352\n",
            "noise:  0.15757575757575756\n",
            "noise:  0.1616161616161616\n",
            "noise:  0.16565656565656567\n",
            "noise:  0.1696969696969697\n",
            "noise:  0.17373737373737375\n",
            "noise:  0.17777777777777778\n",
            "noise:  0.18181818181818182\n",
            "noise:  0.18585858585858586\n",
            "noise:  0.1898989898989899\n",
            "noise:  0.19393939393939394\n",
            "noise:  0.19797979797979798\n",
            "noise:  0.20202020202020202\n",
            "noise:  0.20606060606060606\n",
            "noise:  0.2101010101010101\n",
            "noise:  0.21414141414141413\n",
            "noise:  0.21818181818181817\n",
            "noise:  0.2222222222222222\n",
            "noise:  0.22626262626262628\n",
            "noise:  0.23030303030303031\n",
            "noise:  0.23434343434343435\n",
            "noise:  0.2383838383838384\n",
            "noise:  0.24242424242424243\n",
            "noise:  0.24646464646464647\n",
            "noise:  0.2505050505050505\n",
            "noise:  0.2545454545454545\n",
            "noise:  0.2585858585858586\n",
            "noise:  0.26262626262626265\n",
            "noise:  0.26666666666666666\n",
            "noise:  0.27070707070707073\n",
            "noise:  0.27474747474747474\n",
            "noise:  0.2787878787878788\n",
            "noise:  0.2828282828282828\n",
            "noise:  0.2868686868686869\n",
            "noise:  0.2909090909090909\n",
            "noise:  0.29494949494949496\n",
            "noise:  0.298989898989899\n",
            "noise:  0.30303030303030304\n",
            "noise:  0.30707070707070705\n",
            "noise:  0.3111111111111111\n",
            "noise:  0.3151515151515151\n",
            "noise:  0.3191919191919192\n",
            "noise:  0.3232323232323232\n",
            "noise:  0.32727272727272727\n",
            "noise:  0.33131313131313134\n",
            "noise:  0.33535353535353535\n",
            "noise:  0.3393939393939394\n",
            "noise:  0.3434343434343434\n",
            "noise:  0.3474747474747475\n",
            "noise:  0.3515151515151515\n",
            "noise:  0.35555555555555557\n",
            "noise:  0.3595959595959596\n",
            "noise:  0.36363636363636365\n",
            "noise:  0.36767676767676766\n",
            "noise:  0.3717171717171717\n",
            "noise:  0.37575757575757573\n",
            "noise:  0.3797979797979798\n",
            "noise:  0.3838383838383838\n",
            "noise:  0.3878787878787879\n",
            "noise:  0.39191919191919194\n",
            "noise:  0.39595959595959596\n",
            "noise:  0.4\n",
            "original mean similarity: 0.953269621160836\n",
            "stochastic mean similarity: 0.953269621160836\n",
            "original one-hot mean similarity: -0.16825947097910127\n",
            "stochastic one-hot mean similarity: -0.16825947097910127\n",
            "original median similarity: 0.9532696211608359\n",
            "stochastic median similarity: 0.9532696211608359\n",
            "original one-hot median similarity: -0.16825947097910124\n",
            "stochastic one-hot median similarity: -0.16825947097910124\n",
            "original variance: 1.232595164407831e-32\n",
            "stochastic variance: 1.232595164407831e-32\n",
            "original one-hot variance: 7.703719777548943e-34\n",
            "stochastic one-hot variance: 7.703719777548943e-34\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-32-707df4c680ee>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     43\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf'stochastic one-hot variance: {np.var(s_h_set)}'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 45\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0max0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0max1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     46\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     47\u001b[0m \u001b[0max0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mo_set\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'original'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mTypeError\u001b[0m: 'AxesSubplot' object is not iterable"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IAfUVZwD9Uzz"
      },
      "source": [
        "# Spiking TPAM #"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pPqT1BLe9VwL"
      },
      "source": [
        "## Resonate-and-fire TPAM ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ytgi1Vzj8vEm"
      },
      "source": [
        "N_vec = 500\n",
        "N_inh_ff = 5\n",
        "N_out = 60\n",
        "\n",
        "pvecs = crvec(N_vec, N_out).T\n",
        "Ks = int(0.05 * N_vec)\n",
        "\n",
        "for d in range(N_out):\n",
        "    ip = np.random.choice(N_vec, size=(N_vec-Ks), replace=False)\n",
        "    pvecs[ip, d] = 0\n",
        "    \n",
        "pmat = np.dot(pvecs, np.conj(pvecs.T)) / Ks\n",
        "\n",
        "np.fill_diagonal(pmat, 0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EeTUavA482Q2"
      },
      "source": [
        "# Neuron parameters\n",
        "C_Sh = 4 * nF # Capacitance\n",
        "L_Sh = 10e-3/1e-9  * henry # Inductance\n",
        "\n",
        "g_l = 30.0 * nS # leak conductance\n",
        "E_l = -60.0 * mV # Resting potential\n",
        "\n",
        "V_t = -58.0 * mV # Threshold\n",
        "\n",
        "\n",
        "eqs_2_h = Equations('''\n",
        "    dVs/dt = (g_l * (E_l - Vs) - 2*pi*Us + I_ext) / C_Sh : volt\n",
        "    dUs/dt = -2*pi*(E_l - Vs) / L_Sh : amp\n",
        "    I_ext : amp\n",
        "    ''')\n",
        "\n",
        "s_h = '''\n",
        "mag_v : 1\n",
        "mag_u : 1\n",
        "'''\n",
        "s_h_on_pre = '''\n",
        "Vs_post += mag_v * mV\n",
        "Us_post += mag_u * nA\n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tQPpM7K79cbC"
      },
      "source": [
        "cycle_freq = 1/(np.sqrt(L_Sh * C_Sh))\n",
        "VU_factor = sqrt(C_Sh/L_Sh) * mV/nA\n",
        "\n",
        "print(cycle_freq)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qDO96HlD9cp0"
      },
      "source": [
        "nreps = 1\n",
        "\n",
        "target_idx = 22\n",
        "\n",
        "init_vector = pvecs[:, target_idx].copy()\n",
        "\n",
        "init_vector[200:] = 0\n",
        "keep_idx = np.abs(init_vector) > 0.5\n",
        "\n",
        "stt = phase2spikes(init_vector)*second  +0.11*second\n",
        "#spike_indices = np.zeros_like(stt)\n",
        "spike_indices = np.arange(stt.shape[0])\n",
        "\n",
        "#keep_idx = np.random.rand(stt.shape[0]) < 1\n",
        "stt = stt[keep_idx]\n",
        "spike_indices = spike_indices[keep_idx]\n",
        "\n",
        "spike_times = np.tile(stt, (nreps))\n",
        "spike_indices = np.tile(spike_indices, (nreps))\n",
        "\n",
        "for i in range(nreps):\n",
        "    spike_times[(i*N_vec):((i+1)*N_vec)] = spike_times[:N_vec] + i * 200*ms"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q_S4kSf99foq"
      },
      "source": [
        "G_pre = SpikeGeneratorGroup(N_vec, spike_indices, spike_times)\n",
        "G_post = NeuronGroup(N_vec, model=eqs_2_h, threshold='Vs>V_t and Us>0*nA',  \n",
        "                     refractory=120*ms, method='euler')\n",
        "\n",
        "G_post.Vs = (E_l + 0.0*mV) * ones(N_vec)\n",
        "G_post.Us = 0.0 * VU_factor * nA * ones(N_vec)\n",
        "G_post.I_ext = 0\n",
        "\n",
        "S_pre_post = Synapses(G_pre, G_post, s_h, on_pre=s_h_on_pre, method='euler')\n",
        "S_recurrent = Synapses(G_post, G_post, s_h, on_pre=s_h_on_pre, method='euler')\n",
        "\n",
        "# Input connections\n",
        "S_pre_post.connect(j='i')\n",
        "S_pre_post.mag_u = -0.1 * VU_factor\n",
        "S_pre_post.mag_v = 3\n",
        "\n",
        "# Recurrent connections\n",
        "syn_thresh = 0.1 / (2*N_vec) ** 0.5\n",
        "synidxs = np.where(np.abs(pmat.T) > syn_thresh)\n",
        "S_recurrent.connect(i=synidxs[0], j=synidxs[1])\n",
        "\n",
        "syn_idxs_f = np.where(np.abs(pmat.T).flatten() > syn_thresh)[0]\n",
        "syn_abs = np.abs(pmat.T).flatten()\n",
        "syn_phase = -1*np.angle(pmat.T).flatten()\n",
        "\n",
        "syn_g = 5.0\n",
        "S_recurrent.mag_v = syn_g * syn_abs[syn_idxs_f] * np.cos(syn_phase[syn_idxs_f])\n",
        "S_recurrent.mag_u = syn_g * syn_abs[syn_idxs_f] * VU_factor * np.sin(syn_phase[syn_idxs_f])\n",
        "\n",
        "# Monitors\n",
        "SpM_post = SpikeMonitor(G_post)\n",
        "StM_post = StateMonitor(G_post, True, record=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QgDfFLlV9jqM"
      },
      "source": [
        "complex_net = Network()\n",
        "complex_net.add(G_pre)\n",
        "complex_net.add(G_post)\n",
        "\n",
        "complex_net.add(S_pre_post)\n",
        "complex_net.add(S_recurrent)\n",
        "\n",
        "complex_net.add(SpM_post)\n",
        "complex_net.add(StM_post)\n",
        "\n",
        "complex_net.store('init')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Otihg17l9rdd"
      },
      "source": [
        "run_time = 5.0 * second\n",
        "#complex_net.restore('init')\n",
        "tst = time.time()\n",
        "complex_net.run(run_time)\n",
        "print(\"elapsed\", time.time() - tst, \"seconds\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SzkxGMBV9vUe"
      },
      "source": [
        "figure(figsize=(3.5,3))\n",
        "\n",
        "spike_trains_post = SpM_post.spike_trains()\n",
        "\n",
        "for i in range(N_vec):\n",
        "    plot(spike_trains_post[i], i * ones(len(spike_trains_post[i])), '|', mew=2)\n",
        "\n",
        "ylim([0, N_vec])\n",
        "xlim([0, 1])\n",
        "\n",
        "xlabel('Time (s)')\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nCfq_LOy93g-"
      },
      "source": [
        "figure(figsize=(8,3.5))\n",
        "\n",
        "subplot(121)\n",
        "c=0\n",
        "for i in range(N_vec):\n",
        "    plot(spike_trains_post[i], i * ones(len(spike_trains_post[i])), '|', mew=2)\n",
        "    if len(spike_trains_post[i])>2:\n",
        "        c+=1\n",
        "        \n",
        "print(c, '==', Ks)\n",
        "\n",
        "xlim([4,5])\n",
        "ylim([0, N_vec])\n",
        "\n",
        "xlabel('Time (s)')\n",
        "title('Network')\n",
        "\n",
        "\n",
        "target_vector = pvecs[:, target_idx].copy()\n",
        "\n",
        "stt = phase2spikes(target_vector)*second  +0.11*second\n",
        "spike_indices = np.arange(stt.shape[0])\n",
        "\n",
        "keep_idx = np.abs(target_vector) > 0.5\n",
        "stt = stt[keep_idx]\n",
        "spike_indices = spike_indices[keep_idx]\n",
        "\n",
        "nreps = 10\n",
        "spike_times_target = np.tile(stt, (nreps))\n",
        "spike_indices_target = np.tile(spike_indices, (nreps))\n",
        "\n",
        "for i in range(nreps):\n",
        "    spike_times_target[(np.arange(len(stt)) + i * len(stt))] = spike_times_target[:len(stt)] + i * 200*ms\n",
        "\n",
        "    \n",
        "subplot(122)\n",
        "for i in range(N_vec):\n",
        "    sp_times = spike_times_target[spike_indices_target==i]\n",
        "    plot(sp_times, i*np.ones(sp_times.shape) , '|', mew=2)\n",
        "\n",
        "xlabel('Time (s)')\n",
        "xlim([0, 1])\n",
        "ylim([0, N_vec])\n",
        "title('Target')\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rymYCWMD95Eb"
      },
      "source": [
        "figure(figsize=(3.5,3))\n",
        "\n",
        "N_ex = spike_indices[0]\n",
        "ex=2\n",
        "\n",
        "plot(StM_post.Vs[N_ex]/mV, StM_post.Us[N_ex]/nA, c='cyan', lw=2)\n",
        "plot(StM_post.Vs[ex]/mV, StM_post.Us[ex]/nA, c=[0.3, 0.3, 0.3], lw=2)\n",
        "\n",
        "xl_V = 8*mV\n",
        "xlim([E_l/mV - xl_V/mV, E_l/mV + xl_V/mV])\n",
        "ylim([- xl_V * VU_factor /mV, xl_V * VU_factor/mV])\n",
        "\n",
        "xticks([])\n",
        "yticks([])\n",
        "xlabel('$V$ (mV)')\n",
        "ylabel('$U$ (nA)')\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1R8eKuPw-CW7"
      },
      "source": [
        "## Stochastic Resonate-and-Fire Neurons ##"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KRjm0sA-9__l"
      },
      "source": [
        "N_vec = 500\n",
        "N_inh_ff = 5\n",
        "N_out = 60\n",
        "\n",
        "pvecs = crvec(N_vec, N_out).T\n",
        "Ks = int(0.05 * N_vec)\n",
        "\n",
        "for d in range(N_out):\n",
        "    ip = np.random.choice(N_vec, size=(N_vec-Ks), replace=False)\n",
        "    pvecs[ip, d] = 0\n",
        "    \n",
        "pmat = np.dot(pvecs, np.conj(pvecs.T)) / Ks\n",
        "\n",
        "np.fill_diagonal(pmat, 0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LnaBpLbo-l3C"
      },
      "source": [
        "# Neuron parameters\n",
        "C_Sh = 4 * nF # Capacitance\n",
        "L_Sh = 10e-3/1e-9  * henry # Inductance\n",
        "\n",
        "g_l = 30.0 * nS # leak conductance\n",
        "E_l = -60.0 * mV # Resting potential\n",
        "\n",
        "V_t = -58.0 * mV # Threshold\n",
        "\n",
        "\n",
        "eqs_2_h = Equations('''\n",
        "    dVs/dt = (g_l * (E_l - Vs) - 2*pi*Us + I_ext) / C_Sh : volt\n",
        "    dUs/dt = -2*pi*(E_l - Vs) / L_Sh : amp\n",
        "    I_ext : amp\n",
        "    ''')\n",
        "\n",
        "s_h = '''\n",
        "mag_v : 1\n",
        "mag_u : 1\n",
        "'''\n",
        "s_h_on_pre = '''\n",
        "Vs_post += mag_v * mV\n",
        "Us_post += mag_u * nA\n",
        "'''"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BWlUrtZ--qz4"
      },
      "source": [
        "cycle_freq = 1/(np.sqrt(L_Sh * C_Sh))\n",
        "VU_factor = sqrt(C_Sh/L_Sh) * mV/nA\n",
        "\n",
        "print(cycle_freq)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aOquxilZ-xym"
      },
      "source": [
        "nreps = 1\n",
        "\n",
        "target_idx = 22\n",
        "\n",
        "init_vector = pvecs[:, target_idx].copy()\n",
        "\n",
        "init_vector[200:] = 0\n",
        "keep_idx = np.abs(init_vector) > 0.5\n",
        "\n",
        "stt = phase2spikes(init_vector)*second  +0.11*second\n",
        "#spike_indices = np.zeros_like(stt)\n",
        "spike_indices = np.arange(stt.shape[0])\n",
        "\n",
        "#keep_idx = np.random.rand(stt.shape[0]) < 1\n",
        "stt = stt[keep_idx]\n",
        "spike_indices = spike_indices[keep_idx]\n",
        "\n",
        "spike_times = np.tile(stt, (nreps))\n",
        "spike_indices = np.tile(spike_indices, (nreps))\n",
        "\n",
        "for i in range(nreps):\n",
        "    spike_times[(i*N_vec):((i+1)*N_vec)] = spike_times[:N_vec] + i * 200*ms"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "guXwrrF8-1DC"
      },
      "source": [
        "G_pre = SpikeGeneratorGroup(N_vec, spike_indices, spike_times)\n",
        "G_post = NeuronGroup(N_vec, model=eqs_2_h, threshold='Vs>V_t and Us>0*nA',  \n",
        "                     refractory=120*ms, method='euler')\n",
        "\n",
        "G_post.Vs = (E_l + 0.0*mV) * ones(N_vec)\n",
        "G_post.Us = 0.0 * VU_factor * nA * ones(N_vec)\n",
        "G_post.I_ext = 0\n",
        "\n",
        "S_pre_post = Synapses(G_pre, G_post, s_h, on_pre=s_h_on_pre, method='euler')\n",
        "S_recurrent = Synapses(G_post, G_post, s_h, on_pre=s_h_on_pre, method='euler')\n",
        "\n",
        "# Input connections\n",
        "S_pre_post.connect(j='i')\n",
        "S_pre_post.mag_u = -0.1 * VU_factor\n",
        "S_pre_post.mag_v = 3\n",
        "\n",
        "# Recurrent connections\n",
        "syn_thresh = 0.1 / (2*N_vec) ** 0.5\n",
        "synidxs = np.where(np.abs(pmat.T) > syn_thresh)\n",
        "S_recurrent.connect(i=synidxs[0], j=synidxs[1])\n",
        "\n",
        "syn_idxs_f = np.where(np.abs(pmat.T).flatten() > syn_thresh)[0]\n",
        "syn_abs = np.abs(pmat.T).flatten()\n",
        "syn_phase = -1*np.angle(pmat.T).flatten()\n",
        "\n",
        "syn_g = 5.0\n",
        "S_recurrent.mag_v = syn_g * syn_abs[syn_idxs_f] * np.cos(syn_phase[syn_idxs_f])\n",
        "S_recurrent.mag_u = syn_g * syn_abs[syn_idxs_f] * VU_factor * np.sin(syn_phase[syn_idxs_f])\n",
        "\n",
        "# Monitors\n",
        "SpM_post = SpikeMonitor(G_post)\n",
        "StM_post = StateMonitor(G_post, True, record=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RaR50Zzd-3N5"
      },
      "source": [
        "complex_net = Network()\n",
        "complex_net.add(G_pre)\n",
        "complex_net.add(G_post)\n",
        "\n",
        "complex_net.add(S_pre_post)\n",
        "complex_net.add(S_recurrent)\n",
        "\n",
        "complex_net.add(SpM_post)\n",
        "complex_net.add(StM_post)\n",
        "\n",
        "complex_net.store('init')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jfT-_9pZ-5WI"
      },
      "source": [
        "run_time = 5.0 * second\n",
        "#complex_net.restore('init')\n",
        "tst = time.time()\n",
        "complex_net.run(run_time)\n",
        "print(\"elapsed\", time.time() - tst, \"seconds\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SSnZ6Sao-7bO"
      },
      "source": [
        "figure(figsize=(3.5,3))\n",
        "\n",
        "spike_trains_post = SpM_post.spike_trains()\n",
        "\n",
        "for i in range(N_vec):\n",
        "    plot(spike_trains_post[i], i * ones(len(spike_trains_post[i])), '|', mew=2)\n",
        "\n",
        "ylim([0, N_vec])\n",
        "xlim([0, 1])\n",
        "\n",
        "xlabel('Time (s)')\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o5xmz6xG--xA"
      },
      "source": [
        "figure(figsize=(8,3.5))\n",
        "\n",
        "subplot(121)\n",
        "c=0\n",
        "for i in range(N_vec):\n",
        "    plot(spike_trains_post[i], i * ones(len(spike_trains_post[i])), '|', mew=2)\n",
        "    if len(spike_trains_post[i])>2:\n",
        "        c+=1\n",
        "        \n",
        "print(c, '==', Ks)\n",
        "\n",
        "xlim([4,5])\n",
        "ylim([0, N_vec])\n",
        "\n",
        "xlabel('Time (s)')\n",
        "title('Network')\n",
        "\n",
        "\n",
        "target_vector = pvecs[:, target_idx].copy()\n",
        "\n",
        "stt = phase2spikes(target_vector)*second  +0.11*second\n",
        "spike_indices = np.arange(stt.shape[0])\n",
        "\n",
        "keep_idx = np.abs(target_vector) > 0.5\n",
        "stt = stt[keep_idx]\n",
        "spike_indices = spike_indices[keep_idx]\n",
        "\n",
        "nreps = 10\n",
        "spike_times_target = np.tile(stt, (nreps))\n",
        "spike_indices_target = np.tile(spike_indices, (nreps))\n",
        "\n",
        "for i in range(nreps):\n",
        "    spike_times_target[(np.arange(len(stt)) + i * len(stt))] = spike_times_target[:len(stt)] + i * 200*ms\n",
        "\n",
        "    \n",
        "subplot(122)\n",
        "for i in range(N_vec):\n",
        "    sp_times = spike_times_target[spike_indices_target==i]\n",
        "    plot(sp_times, i*np.ones(sp_times.shape) , '|', mew=2)\n",
        "\n",
        "xlabel('Time (s)')\n",
        "xlim([0, 1])\n",
        "ylim([0, N_vec])\n",
        "title('Target')\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9dQExsCw_A8x"
      },
      "source": [
        "figure(figsize=(3.5,3))\n",
        "\n",
        "N_ex = spike_indices[0]\n",
        "ex=2\n",
        "\n",
        "plot(StM_post.Vs[N_ex]/mV, StM_post.Us[N_ex]/nA, c='cyan', lw=2)\n",
        "plot(StM_post.Vs[ex]/mV, StM_post.Us[ex]/nA, c=[0.3, 0.3, 0.3], lw=2)\n",
        "\n",
        "xl_V = 8*mV\n",
        "xlim([E_l/mV - xl_V/mV, E_l/mV + xl_V/mV])\n",
        "ylim([- xl_V * VU_factor /mV, xl_V * VU_factor/mV])\n",
        "\n",
        "xticks([])\n",
        "yticks([])\n",
        "xlabel('$V$ (mV)')\n",
        "ylabel('$U$ (nA)')\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}