{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spike Encoding Methods\n",
    "\n",
    "This tutorial demonstrates the comprehensive spike encoding capabilities available in ``braintools``. We'll cover:\n",
    "\n",
    "1. **Latency Encoding** - Time-to-first-spike coding\n",
    "2. **Rate Encoding** - Firing rate proportional to input intensity\n",
    "3. **Poisson Encoding** - Stochastic spike generation\n",
    "4. **Population Encoding** - Distributed representation across neurons\n",
    "5. **Bernoulli Encoding** - Independent spike probability\n",
    "6. **Delta Encoding** - Temporal difference encoding\n",
    "7. **Step Current Encoding** - Constant current injection\n",
    "8. **Spike Count Encoding** - Exact spike count distribution\n",
    "9. **Temporal Encoding** - Synchronized pattern encoding\n",
    "10. **Rank Order Encoding** - Relative timing based on magnitude\n",
    "\n",
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:42.215140Z",
     "start_time": "2025-09-23T15:39:39.153888Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import brainstate\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "\n",
    "# Import all spike encoders\n",
    "from braintools import (\n",
    "    LatencyEncoder,\n",
    "    RateEncoder,\n",
    "    PoissonEncoder,\n",
    "    PopulationEncoder,\n",
    "    BernoulliEncoder,\n",
    "    DeltaEncoder,\n",
    "    StepCurrentEncoder,\n",
    "    SpikeCountEncoder,\n",
    "    TemporalEncoder,\n",
    "    RankOrderEncoder\n",
    ")\n",
    "\n",
    "# Set up environment\n",
    "brainstate.environ.set(dt=0.1)  # 0.1 ms time step\n",
    "brainstate.random.seed(42)\n",
    "\n",
    "# Plotting setup\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "plt.rcParams['font.size'] = 10\n",
    "\n",
    "def plot_spikes(spikes, title=\"Spike Trains\", time_window=None):\n",
    "    \"\"\"Helper function to plot spike trains.\"\"\"\n",
    "    if spikes.ndim == 1:\n",
    "        spikes = spikes[:, None]\n",
    "    \n",
    "    n_time, n_neurons = spikes.shape\n",
    "    if time_window is not None:\n",
    "        spikes = spikes[:time_window]\n",
    "        n_time = time_window\n",
    "    \n",
    "    times = np.arange(n_time) * 0.1  # Convert to ms\n",
    "    \n",
    "    plt.figure(figsize=(10, min(6, max(2, n_neurons * 0.5))))\n",
    "    \n",
    "    for neuron in range(n_neurons):\n",
    "        spike_times = times[spikes[:, neuron] > 0]\n",
    "        plt.scatter(spike_times, [neuron] * len(spike_times), \n",
    "                   s=20, c='black', marker='|')\n",
    "    \n",
    "    plt.xlabel('Time (ms)')\n",
    "    plt.ylabel('Neuron ID')\n",
    "    plt.title(title)\n",
    "    plt.ylim(-0.5, n_neurons - 0.5)\n",
    "    if n_time > 0:\n",
    "        plt.xlim(0, times[-1])\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "print(\"Spike encoding tutorial setup complete!\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spike encoding tutorial setup complete!\n"
     ]
    }
   ],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Latency Encoding\n",
    "\n",
    "Latency encoding converts input intensity to spike timing. Higher intensity values result in earlier spike times."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:43.279926Z",
     "start_time": "2025-09-23T15:39:42.223638Z"
    }
   },
   "source": [
    "# Latency Encoding Examples\n",
    "print(\"=== LATENCY ENCODING ===\")\n",
    "\n",
    "# Test data with different intensities\n",
    "test_data = jnp.array([0.1, 0.3, 0.5, 0.7, 0.9])\n",
    "n_time = 100  # 10 ms simulation\n",
    "\n",
    "# Linear latency encoding\n",
    "linear_encoder = LatencyEncoder(method='linear', normalize=True)\n",
    "linear_spikes = linear_encoder(test_data, n_time=n_time)\n",
    "\n",
    "print(f\"Input data: {test_data}\")\n",
    "print(f\"Linear encoding spike times: {jnp.argmax(linear_spikes, axis=0) * 0.1} ms\")\n",
    "\n",
    "plot_spikes(linear_spikes, \"Latency Encoding (Linear Method)\")\n",
    "\n",
    "# Logarithmic latency encoding\n",
    "log_encoder = LatencyEncoder(method='log', normalize=True)\n",
    "log_spikes = log_encoder(test_data, n_time=n_time)\n",
    "\n",
    "print(f\"Log encoding spike times: {jnp.argmax(log_spikes, axis=0) * 0.1} ms\")\n",
    "\n",
    "plot_spikes(log_spikes, \"Latency Encoding (Logarithmic Method)\")\n",
    "\n",
    "# Compare methods\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "ax1.plot(test_data, jnp.argmax(linear_spikes, axis=0) * 0.1, 'bo-', label='Linear')\n",
    "ax1.plot(test_data, jnp.argmax(log_spikes, axis=0) * 0.1, 'ro-', label='Logarithmic')\n",
    "ax1.set_xlabel('Input Intensity')\n",
    "ax1.set_ylabel('Spike Time (ms)')\n",
    "ax1.set_title('Latency Encoding: Input vs Spike Time')\n",
    "ax1.legend()\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Show encoding characteristics\n",
    "x_range = jnp.linspace(0.1, 1.0, 100)\n",
    "linear_times = (n_time - 1) * (1 - x_range) * 0.1\n",
    "log_times = (n_time - 1) * jnp.log(x_range / (x_range - 0.01)) * 0.1 / jnp.log(1 / 0.99)\n",
    "\n",
    "ax2.plot(x_range, linear_times, 'b-', label='Linear', linewidth=2)\n",
    "ax2.plot(x_range, log_times, 'r-', label='Logarithmic', linewidth=2)\n",
    "ax2.set_xlabel('Input Intensity')\n",
    "ax2.set_ylabel('Spike Time (ms)')\n",
    "ax2.set_title('Encoding Characteristic Curves')\n",
    "ax2.legend()\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nLatency encoding provides precise temporal coding where\")\n",
    "print(\"stimulus intensity determines the exact timing of the first spike.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== LATENCY ENCODING ===\n",
      "Input data: [0.1 0.3 0.5 0.7 0.9]\n",
      "Linear encoding spike times: [89.9 69.9 50.  30.  10. ] ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x250 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log encoding spike times: [10.5  3.4  2.   1.4  1.1] ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x250 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Latency encoding provides precise temporal coding where\n",
      "stimulus intensity determines the exact timing of the first spike.\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Rate Encoding\n",
    "\n",
    "Rate encoding converts input values to firing rates. Higher inputs produce higher firing rates."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:46.207768Z",
     "start_time": "2025-09-23T15:39:45.251907Z"
    }
   },
   "source": [
    "# Rate Encoding Examples\n",
    "print(\"=== RATE ENCODING ===\")\n",
    "\n",
    "test_inputs = jnp.array([0.2, 0.5, 0.8])\n",
    "n_time = 1000  # 100 ms simulation\n",
    "\n",
    "# Linear rate encoding\n",
    "linear_rate_encoder = RateEncoder(gain=200, method='linear')\n",
    "linear_rate_spikes = linear_rate_encoder(test_inputs, n_time=n_time)\n",
    "\n",
    "# Calculate actual firing rates\n",
    "actual_rates = jnp.sum(linear_rate_spikes, axis=0) * 10  # Convert to Hz\n",
    "expected_rates = test_inputs * 200\n",
    "\n",
    "print(f\"Input values: {test_inputs}\")\n",
    "print(f\"Expected rates (Hz): {expected_rates}\")\n",
    "print(f\"Actual rates (Hz): {actual_rates}\")\n",
    "\n",
    "plot_spikes(linear_rate_spikes, \"Rate Encoding (Linear)\", time_window=500)\n",
    "\n",
    "# Compare different rate encoding methods\n",
    "methods = ['linear', 'exponential', 'sqrt']\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
    "\n",
    "for i, method in enumerate(methods):\n",
    "    encoder = RateEncoder(gain=100, method=method)\n",
    "    spikes = encoder(test_inputs, n_time=1000)\n",
    "    rates = jnp.sum(spikes, axis=0) * 10  # Convert to Hz\n",
    "    \n",
    "    axes[i].bar(range(len(test_inputs)), rates, alpha=0.7)\n",
    "    axes[i].set_xlabel('Input Index')\n",
    "    axes[i].set_ylabel('Firing Rate (Hz)')\n",
    "    axes[i].set_title(f'{method.title()} Rate Encoding')\n",
    "    axes[i].set_xticks(range(len(test_inputs)))\n",
    "    axes[i].set_xticklabels([f'{x:.1f}' for x in test_inputs])\n",
    "    axes[i].grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nRate encoding is widely used in artificial neural networks and\")\n",
    "print(\"provides a direct analog to biological firing rate modulation.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== RATE ENCODING ===\n",
      "Input values: [0.2 0.5 0.8]\n",
      "Expected rates (Hz): [ 40. 100. 160.]\n",
      "Actual rates (Hz): [ 40. 100. 170.]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x400 with 3 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Rate encoding is widely used in artificial neural networks and\n",
      "provides a direct analog to biological firing rate modulation.\n"
     ]
    }
   ],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Poisson Encoding\n",
    "\n",
    "Poisson encoding generates spike trains with Poisson-distributed inter-spike intervals."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:47.757534Z",
     "start_time": "2025-09-23T15:39:46.217784Z"
    }
   },
   "source": [
    "# Poisson Encoding Examples\n",
    "print(\"=== POISSON ENCODING ===\")\n",
    "\n",
    "rates = jnp.array([20, 50, 100])  # Hz\n",
    "n_time = 1000  # 100 ms\n",
    "\n",
    "poisson_encoder = PoissonEncoder()\n",
    "poisson_spikes = poisson_encoder(rates, n_time=n_time)\n",
    "\n",
    "print(f\"Input rates (Hz): {rates}\")\n",
    "actual_rates = jnp.sum(poisson_spikes, axis=0) * 10\n",
    "print(f\"Actual rates (Hz): {actual_rates}\")\n",
    "\n",
    "plot_spikes(poisson_spikes, \"Poisson Encoding\", time_window=500)\n",
    "\n",
    "# Analyze inter-spike intervals for Poisson process\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
    "\n",
    "for neuron in range(3):\n",
    "    spike_times = jnp.where(poisson_spikes[:, neuron])[0] * 0.1  # Convert to ms\n",
    "    if len(spike_times) > 1:\n",
    "        isis = jnp.diff(spike_times)\n",
    "        axes[neuron].hist(isis, bins=20, alpha=0.7, density=True)\n",
    "        axes[neuron].set_xlabel('Inter-Spike Interval (ms)')\n",
    "        axes[neuron].set_ylabel('Probability Density')\n",
    "        axes[neuron].set_title(f'ISI Distribution\\n({rates[neuron]} Hz)')\n",
    "        axes[neuron].grid(True, alpha=0.3)\n",
    "        \n",
    "        # Overlay theoretical exponential distribution\n",
    "        x = jnp.linspace(0, jnp.max(isis), 100)\n",
    "        rate_per_ms = rates[neuron] / 1000\n",
    "        theoretical = rate_per_ms * jnp.exp(-rate_per_ms * x)\n",
    "        axes[neuron].plot(x, theoretical, 'r-', linewidth=2, label='Theoretical')\n",
    "        axes[neuron].legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nPoisson encoding introduces natural variability and is commonly\")\n",
    "print(\"used to model stochastic neural activity.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== POISSON ENCODING ===\n",
      "Input rates (Hz): [ 20  50 100]\n",
      "Actual rates (Hz): [  0  30 140]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x400 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Poisson encoding introduces natural variability and is commonly\n",
      "used to model stochastic neural activity.\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Population Encoding\n",
    "\n",
    "Population encoding represents scalar values using a population of neurons with overlapping receptive fields."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:51.021727Z",
     "start_time": "2025-09-23T15:39:47.804884Z"
    }
   },
   "source": [
    "# Population Encoding Examples\n",
    "print(\"=== POPULATION ENCODING ===\")\n",
    "\n",
    "# Encode different values with a population\n",
    "pop_encoder = PopulationEncoder(n_neurons=10, min_val=0, max_val=1, sigma=0.2)\n",
    "test_values = [0.2, 0.5, 0.8]\n",
    "n_time = 500\n",
    "\n",
    "fig, axes = plt.subplots(2, len(test_values), figsize=(15, 8))\n",
    "\n",
    "for i, value in enumerate(test_values):\n",
    "    pop_spikes = pop_encoder(value, n_time=n_time)\n",
    "    \n",
    "    # Plot spike trains\n",
    "    for neuron in range(10):\n",
    "        spike_times = jnp.where(pop_spikes[:, neuron])[0] * 0.1\n",
    "        axes[0, i].scatter(spike_times, [neuron] * len(spike_times), \n",
    "                          s=10, c='black', marker='|')\n",
    "    \n",
    "    axes[0, i].set_xlabel('Time (ms)')\n",
    "    axes[0, i].set_ylabel('Neuron ID')\n",
    "    axes[0, i].set_title(f'Population Response\\nInput = {value}')\n",
    "    axes[0, i].set_ylim(-0.5, 9.5)\n",
    "    axes[0, i].grid(True, alpha=0.3)\n",
    "    \n",
    "    # Plot population activity profile\n",
    "    firing_rates = jnp.sum(pop_spikes, axis=0) * 10  # Convert to Hz\n",
    "    neuron_ids = jnp.arange(10)\n",
    "    \n",
    "    axes[1, i].bar(neuron_ids, firing_rates, alpha=0.7)\n",
    "    axes[1, i].set_xlabel('Neuron ID')\n",
    "    axes[1, i].set_ylabel('Firing Rate (Hz)')\n",
    "    axes[1, i].set_title(f'Population Activity Profile')\n",
    "    axes[1, i].grid(True, alpha=0.3)\n",
    "    \n",
    "    # Mark the input value position\n",
    "    expected_peak = value * (10 - 1)\n",
    "    axes[1, i].axvline(expected_peak, color='red', linestyle='--', \n",
    "                      label=f'Input position: {expected_peak:.1f}')\n",
    "    axes[1, i].legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Demonstrate effect of receptive field width\n",
    "sigmas = [0.1, 0.2, 0.4]\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
    "\n",
    "test_value = 0.5\n",
    "for i, sigma in enumerate(sigmas):\n",
    "    encoder = PopulationEncoder(n_neurons=10, sigma=sigma)\n",
    "    spikes = encoder(test_value, n_time=500)\n",
    "    rates = jnp.sum(spikes, axis=0) * 10\n",
    "    \n",
    "    axes[i].bar(range(10), rates, alpha=0.7)\n",
    "    axes[i].set_xlabel('Neuron ID')\n",
    "    axes[i].set_ylabel('Firing Rate (Hz)')\n",
    "    axes[i].set_title(f'Receptive Field Width\\nσ = {sigma}')\n",
    "    axes[i].grid(True, alpha=0.3)\n",
    "    axes[i].axvline(5, color='red', linestyle='--', alpha=0.7)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nPopulation encoding provides robust representation and is\")\n",
    "print(\"commonly used in sensory systems and neural prosthetics.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== POPULATION ENCODING ===\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x800 with 6 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x400 with 3 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Population encoding provides robust representation and is\n",
      "commonly used in sensory systems and neural prosthetics.\n"
     ]
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Delta Encoding\n",
    "\n",
    "Delta encoding generates spikes when the input signal changes significantly."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:52.684579Z",
     "start_time": "2025-09-23T15:39:51.097274Z"
    }
   },
   "source": [
    "# Delta Encoding Examples\n",
    "print(\"=== DELTA ENCODING ===\")\n",
    "\n",
    "# Create a time-varying signal\n",
    "time_steps = 200\n",
    "t = jnp.arange(time_steps) * 0.1\n",
    "\n",
    "# Smooth signal with sudden changes\n",
    "signal = 0.5 + 0.3 * jnp.sin(0.1 * t) + 0.2 * jnp.sin(0.05 * t)\n",
    "# Add some step changes\n",
    "signal = signal.at[50:60].set(0.9)\n",
    "signal = signal.at[120:130].set(0.1)\n",
    "\n",
    "# Different delta encoding configurations\n",
    "encoders = {\n",
    "    'Standard': DeltaEncoder(threshold=0.05, absolute=False),\n",
    "    'Positive Only': DeltaEncoder(threshold=0.05, positive_only=True),\n",
    "    'Absolute': DeltaEncoder(threshold=0.05, absolute=True),\n",
    "}\n",
    "\n",
    "fig, axes = plt.subplots(len(encoders) + 1, 1, figsize=(12, 10))\n",
    "\n",
    "# Plot original signal\n",
    "axes[0].plot(t, signal, 'b-', linewidth=2)\n",
    "axes[0].set_ylabel('Signal Value')\n",
    "axes[0].set_title('Original Time-Varying Signal')\n",
    "axes[0].grid(True, alpha=0.3)\n",
    "\n",
    "# Plot delta encoded spike trains\n",
    "for i, (name, encoder) in enumerate(encoders.items()):\n",
    "    delta_spikes = encoder(signal)\n",
    "    \n",
    "    # Plot spikes\n",
    "    spike_times = t[delta_spikes > 0]\n",
    "    axes[i + 1].scatter(spike_times, [0] * len(spike_times), \n",
    "                       s=50, c='red', marker='|')\n",
    "    axes[i + 1].set_ylabel('Spikes')\n",
    "    axes[i + 1].set_title(f'Delta Encoding - {name}')\n",
    "    axes[i + 1].set_ylim(-0.5, 0.5)\n",
    "    axes[i + 1].grid(True, alpha=0.3)\n",
    "    \n",
    "    print(f\"{name}: {jnp.sum(delta_spikes)} spikes generated\")\n",
    "\n",
    "axes[-1].set_xlabel('Time (ms)')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Multi-channel delta encoding\n",
    "print(\"\\nMulti-channel Delta Encoding:\")\n",
    "# Create multiple signals\n",
    "signals = jnp.array([\n",
    "    0.5 + 0.3 * jnp.sin(0.1 * t),\n",
    "    0.5 + 0.3 * jnp.cos(0.1 * t),\n",
    "    0.5 + 0.2 * jnp.sin(0.2 * t)\n",
    "]).T\n",
    "\n",
    "multi_encoder = DeltaEncoder(threshold=0.1)\n",
    "multi_spikes = multi_encoder(signals)\n",
    "\n",
    "plot_spikes(multi_spikes, \"Multi-channel Delta Encoding\", time_window=150)\n",
    "\n",
    "print(\"\\nDelta encoding is efficient for representing dynamic signals\")\n",
    "print(\"and is inspired by retinal ganglion cell responses.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== DELTA ENCODING ===\n",
      "Standard: 4.0 spikes generated\n",
      "Positive Only: 2.0 spikes generated\n",
      "Absolute: 4.0 spikes generated\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x1000 with 4 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Multi-channel Delta Encoding:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Delta encoding is efficient for representing dynamic signals\n",
      "and is inspired by retinal ganglion cell responses.\n"
     ]
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Rank Order Encoding\n",
    "\n",
    "Rank order encoding preserves the relative ordering of input features through spike timing."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:39:54.373129Z",
     "start_time": "2025-09-23T15:39:52.776441Z"
    }
   },
   "source": [
    "# Rank Order Encoding Examples\n",
    "print(\"=== RANK ORDER ENCODING ===\")\n",
    "\n",
    "# Test with different input patterns\n",
    "patterns = {\n",
    "    'Ascending': jnp.array([0.1, 0.3, 0.5, 0.7, 0.9]),\n",
    "    'Descending': jnp.array([0.9, 0.7, 0.5, 0.3, 0.1]),\n",
    "    'Random': jnp.array([0.3, 0.8, 0.1, 0.9, 0.4]),\n",
    "}\n",
    "\n",
    "n_time = 50  # 5 ms encoding window\n",
    "\n",
    "fig, axes = plt.subplots(2, len(patterns), figsize=(15, 8))\n",
    "\n",
    "rank_encoder = RankOrderEncoder(use_values=True, normalize=True)\n",
    "\n",
    "for i, (name, pattern) in enumerate(patterns.items()):\n",
    "    # Encode pattern\n",
    "    rank_spikes = rank_encoder(pattern, n_time=n_time)\n",
    "    \n",
    "    # Plot input pattern\n",
    "    axes[0, i].bar(range(len(pattern)), pattern, alpha=0.7)\n",
    "    axes[0, i].set_xlabel('Feature Index')\n",
    "    axes[0, i].set_ylabel('Feature Value')\n",
    "    axes[0, i].set_title(f'{name} Pattern')\n",
    "    axes[0, i].grid(True, alpha=0.3)\n",
    "    \n",
    "    # Plot spike times\n",
    "    spike_times = jnp.argmax(rank_spikes, axis=0) * 0.1  # Convert to ms\n",
    "    for feature in range(len(pattern)):\n",
    "        axes[1, i].scatter(spike_times[feature], feature, s=100, c='red', marker='|')\n",
    "    \n",
    "    axes[1, i].set_xlabel('Spike Time (ms)')\n",
    "    axes[1, i].set_ylabel('Feature Index')\n",
    "    axes[1, i].set_title(f'Rank Order Spikes')\n",
    "    axes[1, i].set_ylim(-0.5, len(pattern) - 0.5)\n",
    "    axes[1, i].grid(True, alpha=0.3)\n",
    "    \n",
    "    # Print spike order\n",
    "    order = jnp.argsort(spike_times)\n",
    "    print(f\"{name} pattern - Spike order: {order}\")\n",
    "    print(f\"  Corresponds to values: {pattern[order]}\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Compare value-based vs rank-based encoding\n",
    "test_pattern = jnp.array([0.1, 0.11, 0.9, 0.91])\n",
    "\n",
    "value_encoder = RankOrderEncoder(use_values=True)\n",
    "rank_encoder = RankOrderEncoder(use_values=False)\n",
    "\n",
    "value_spikes = value_encoder(test_pattern, n_time=20)\n",
    "rank_spikes = rank_encoder(test_pattern, n_time=20)\n",
    "\n",
    "value_times = jnp.argmax(value_spikes, axis=0) * 0.1\n",
    "rank_times = jnp.argmax(rank_spikes, axis=0) * 0.1\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "# Value-based timing\n",
    "for i in range(len(test_pattern)):\n",
    "    ax1.scatter(value_times[i], i, s=100, c='blue', marker='|')\n",
    "ax1.set_xlabel('Spike Time (ms)')\n",
    "ax1.set_ylabel('Feature Index')\n",
    "ax1.set_title('Value-Based Timing')\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Rank-based timing\n",
    "for i in range(len(test_pattern)):\n",
    "    ax2.scatter(rank_times[i], i, s=100, c='red', marker='|')\n",
    "ax2.set_xlabel('Spike Time (ms)')\n",
    "ax2.set_ylabel('Feature Index')\n",
    "ax2.set_title('Rank-Based Timing')\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(f\"Test pattern: {test_pattern}\")\n",
    "print(f\"Value-based times: {value_times}\")\n",
    "print(f\"Rank-based times: {rank_times}\")\n",
    "\n",
    "print(\"\\nRank order encoding preserves feature relationships and\")\n",
    "print(\"is useful for pattern recognition tasks.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== RANK ORDER ENCODING ===\n",
      "Ascending pattern - Spike order: [4 3 2 1 0]\n",
      "  Corresponds to values: [0.9 0.7 0.5 0.3 0.1]\n",
      "Descending pattern - Spike order: [0 1 2 3 4]\n",
      "  Corresponds to values: [0.9 0.7 0.5 0.3 0.1]\n",
      "Random pattern - Spike order: [3 1 4 0 2]\n",
      "  Corresponds to values: [0.9 0.8 0.4 0.3 0.1]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1500x800 with 6 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test pattern: [0.1  0.11 0.9  0.91]\n",
      "Value-based times: [1.9       1.8000001 0.        0.       ]\n",
      "Rank-based times: [1.4        0.90000004 0.4        0.        ]\n",
      "\n",
      "Rank order encoding preserves feature relationships and\n",
      "is useful for pattern recognition tasks.\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Temporal Pattern Encoding\n",
    "\n",
    "Temporal encoding creates synchronized spike patterns for sequence representation."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:40:26.327366Z",
     "start_time": "2025-09-23T15:40:25.066330Z"
    }
   },
   "source": [
    "# Temporal Encoding Examples\n",
    "print(\"=== TEMPORAL ENCODING ===\")\n",
    "\n",
    "# Create a temporal encoder for 4 different patterns\n",
    "temporal_encoder = TemporalEncoder(n_patterns=4, pattern_length=20, jitter=0.1)\n",
    "\n",
    "# Encode a sequence\n",
    "sequence = jnp.array([0, 1, 2, 3, 1, 0, 2])\n",
    "temporal_spikes = temporal_encoder(sequence)\n",
    "\n",
    "print(f\"Input sequence: {sequence}\")\n",
    "print(f\"Temporal spikes shape: {temporal_spikes.shape}\")\n",
    "\n",
    "# Plot the temporal patterns\n",
    "plot_spikes(temporal_spikes, \"Temporal Pattern Encoding\", time_window=140)\n",
    "\n",
    "# Analyze patterns for each symbol\n",
    "fig, axes = plt.subplots(2, 2, figsize=(12, 8))\n",
    "axes = axes.ravel()\n",
    "\n",
    "pattern_length = 20\n",
    "for pattern_id in range(4):\n",
    "    # Find occurrences of this pattern in the sequence\n",
    "    occurrences = jnp.where(sequence == pattern_id)[0]\n",
    "    \n",
    "    if len(occurrences) > 0:\n",
    "        # Extract all instances of this pattern\n",
    "        for occ in occurrences:\n",
    "            start_time = occ * pattern_length\n",
    "            end_time = start_time + pattern_length\n",
    "            pattern_spikes = temporal_spikes[start_time:end_time, pattern_id]\n",
    "            spike_times = jnp.where(pattern_spikes)[0] * 0.1\n",
    "            axes[pattern_id].scatter(spike_times, [occ] * len(spike_times), \n",
    "                                   s=50, alpha=0.7)\n",
    "    \n",
    "    axes[pattern_id].set_xlabel('Time within Pattern (ms)')\n",
    "    axes[pattern_id].set_ylabel('Occurrence')\n",
    "    axes[pattern_id].set_title(f'Pattern {pattern_id} Instances')\n",
    "    axes[pattern_id].set_xlim(0, pattern_length * 0.1)\n",
    "    axes[pattern_id].grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Compare with and without jitter\n",
    "no_jitter_encoder = TemporalEncoder(n_patterns=2, pattern_length=15, jitter=0.0)\n",
    "jitter_encoder = TemporalEncoder(n_patterns=2, pattern_length=15, jitter=0.3)\n",
    "\n",
    "test_sequence = jnp.array([0, 1, 0, 1])\n",
    "\n",
    "no_jitter_spikes = no_jitter_encoder(test_sequence)\n",
    "jitter_spikes = jitter_encoder(test_sequence)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 6))\n",
    "\n",
    "# Plot without jitter\n",
    "for neuron in range(2):\n",
    "    spike_times = jnp.where(no_jitter_spikes[:, neuron])[0] * 0.1\n",
    "    ax1.scatter(spike_times, [neuron] * len(spike_times), s=30, marker='|')\n",
    "ax1.set_ylabel('Pattern ID')\n",
    "ax1.set_title('Temporal Encoding - No Jitter')\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Plot with jitter\n",
    "for neuron in range(2):\n",
    "    spike_times = jnp.where(jitter_spikes[:, neuron])[0] * 0.1\n",
    "    ax2.scatter(spike_times, [neuron] * len(spike_times), s=30, marker='|')\n",
    "ax2.set_xlabel('Time (ms)')\n",
    "ax2.set_ylabel('Pattern ID')\n",
    "ax2.set_title('Temporal Encoding - With Jitter')\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nTemporal encoding provides robust sequence representation\")\n",
    "print(\"with optional jitter for noise tolerance.\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== TEMPORAL ENCODING ===\n",
      "Input sequence: [0 1 2 3 1 0 2]\n",
      "Temporal spikes shape: (140, 4)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x800 with 4 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Temporal encoding provides robust sequence representation\n",
      "with optional jitter for noise tolerance.\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Comparison and Summary\n",
    "\n",
    "Let's compare different encoding methods on the same input data."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-23T15:40:29.398622Z",
     "start_time": "2025-09-23T15:40:26.967089Z"
    }
   },
   "source": [
    "# Comparison of Encoding Methods\n",
    "print(\"=== ENCODING METHOD COMPARISON ===\")\n",
    "\n",
    "# Common test data\n",
    "test_data = jnp.array([0.2, 0.5, 0.8])\n",
    "n_time = 200\n",
    "\n",
    "# Configure encoders\n",
    "encoders = {\n",
    "    'Rate (Linear)': RateEncoder(gain=100, method='linear'),\n",
    "    'Poisson': PoissonEncoder(normalize=True, max_rate=100),\n",
    "    'Bernoulli': BernoulliEncoder(scale=0.2),\n",
    "    'Rank Order': RankOrderEncoder(use_values=True),\n",
    "}\n",
    "\n",
    "fig, axes = plt.subplots(len(encoders), 1, figsize=(12, 2 * len(encoders)))\n",
    "\n",
    "print(f\"Input data: {test_data}\")\n",
    "\n",
    "for i, (name, encoder) in enumerate(encoders.items()):\n",
    "    # Generate spikes\n",
    "    if hasattr(encoder, '__call__'):\n",
    "        if 'Poisson' in name or 'Bernoulli' in name:\n",
    "            spikes = encoder(test_data, n_time=n_time)\n",
    "        elif 'Rank' in name:\n",
    "            spikes = encoder(test_data, n_time=50)  # Shorter for rank order\n",
    "        else:\n",
    "            spikes = encoder(test_data, n_time=n_time)\n",
    "    \n",
    "    # Plot spike trains\n",
    "    plot_window = min(n_time, spikes.shape[0])\n",
    "    for neuron in range(spikes.shape[1]):\n",
    "        spike_times = jnp.where(spikes[:plot_window, neuron])[0] * 0.1\n",
    "        axes[i].scatter(spike_times, [neuron] * len(spike_times), \n",
    "                       s=20, marker='|')\n",
    "    \n",
    "    axes[i].set_ylabel('Neuron')\n",
    "    axes[i].set_title(f'{name} Encoding')\n",
    "    axes[i].set_ylim(-0.5, 2.5)\n",
    "    axes[i].grid(True, alpha=0.3)\n",
    "    \n",
    "    # Calculate and print statistics\n",
    "    total_spikes = jnp.sum(spikes)\n",
    "    spike_rates = jnp.sum(spikes, axis=0) * 1000 / spikes.shape[0]\n",
    "    print(f\"{name}: Total spikes = {total_spikes}, Rates = {spike_rates} Hz\")\n",
    "\n",
    "axes[-1].set_xlabel('Time (ms)')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Summary table of encoding characteristics\n",
    "print(\"\\n\" + \"=\"*60)\n",
    "print(\"SPIKE ENCODING METHOD SUMMARY\")\n",
    "print(\"=\"*60)\n",
    "\n",
    "summary_data = [\n",
    "    [\"Method\", \"Input Type\", \"Output\", \"Key Features\"],\n",
    "    [\"-\"*15, \"-\"*12, \"-\"*15, \"-\"*25],\n",
    "    [\"Latency\", \"Scalar/Vector\", \"Time-to-spike\", \"Precise timing, energy efficient\"],\n",
    "    [\"Rate\", \"Scalar/Vector\", \"Firing rate\", \"Intuitive, noise robust\"],\n",
    "    [\"Poisson\", \"Rates (Hz)\", \"Stochastic spikes\", \"Natural variability\"],\n",
    "    [\"Population\", \"Scalar\", \"Distributed\", \"Robust, biologically inspired\"],\n",
    "    [\"Bernoulli\", \"Probabilities\", \"Independent\", \"Simple, controllable\"],\n",
    "    [\"Delta\", \"Time series\", \"Change detection\", \"Efficient for dynamics\"],\n",
    "    [\"Step Current\", \"Scalar/Vector\", \"Constant current\", \"For LIF neurons\"],\n",
    "    [\"Spike Count\", \"Scalar/Vector\", \"Exact counts\", \"Deterministic totals\"],\n",
    "    [\"Temporal\", \"Sequences\", \"Patterns\", \"Sequence encoding\"],\n",
    "    [\"Rank Order\", \"Vectors\", \"Relative timing\", \"Order preservation\"],\n",
    "]\n",
    "\n",
    "for row in summary_data:\n",
    "    print(f\"{row[0]:15} {row[1]:12} {row[2]:15} {row[3]}\")\n",
    "\n",
    "print(\"\\n\" + \"=\"*60)\n",
    "print(\"USAGE RECOMMENDATIONS:\")\n",
    "print(\"• Rate/Poisson: General-purpose, biologically realistic\")\n",
    "print(\"• Latency: Time-critical applications, energy efficiency\")\n",
    "print(\"• Population: Robust encoding, sensory processing\")\n",
    "print(\"• Delta: Dynamic signals, event-driven processing\")\n",
    "print(\"• Rank Order: Feature relationships, pattern recognition\")\n",
    "print(\"• Temporal: Sequence learning, temporal patterns\")\n",
    "print(\"=\"*60)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== ENCODING METHOD COMPARISON ===\n",
      "Input data: [0.2 0.5 0.8]\n",
      "Rate (Linear): Total spikes = 4.0, Rates = [ 5. 10.  5.] Hz\n",
      "Poisson: Total spikes = 3.0, Rates = [ 5.  0. 10.] Hz\n",
      "Bernoulli: Total spikes = 60.0, Rates = [ 40. 105. 155.] Hz\n",
      "Rank Order: Total spikes = 3.0, Rates = [20. 20. 20.] Hz\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x800 with 4 Axes>"
      ],
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "============================================================\n",
      "SPIKE ENCODING METHOD SUMMARY\n",
      "============================================================\n",
      "Method          Input Type   Output          Key Features\n",
      "--------------- ------------ --------------- -------------------------\n",
      "Latency         Scalar/Vector Time-to-spike   Precise timing, energy efficient\n",
      "Rate            Scalar/Vector Firing rate     Intuitive, noise robust\n",
      "Poisson         Rates (Hz)   Stochastic spikes Natural variability\n",
      "Population      Scalar       Distributed     Robust, biologically inspired\n",
      "Bernoulli       Probabilities Independent     Simple, controllable\n",
      "Delta           Time series  Change detection Efficient for dynamics\n",
      "Step Current    Scalar/Vector Constant current For LIF neurons\n",
      "Spike Count     Scalar/Vector Exact counts    Deterministic totals\n",
      "Temporal        Sequences    Patterns        Sequence encoding\n",
      "Rank Order      Vectors      Relative timing Order preservation\n",
      "\n",
      "============================================================\n",
      "USAGE RECOMMENDATIONS:\n",
      "• Rate/Poisson: General-purpose, biologically realistic\n",
      "• Latency: Time-critical applications, energy efficiency\n",
      "• Population: Robust encoding, sensory processing\n",
      "• Delta: Dynamic signals, event-driven processing\n",
      "• Rank Order: Feature relationships, pattern recognition\n",
      "• Temporal: Sequence learning, temporal patterns\n",
      "============================================================\n"
     ]
    }
   ],
   "execution_count": 10
  }
 ],
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