{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ca2e5d69",
   "metadata": {},
   "source": [
    "# State-based transformations with ``brainstate``\n",
    "\n",
    "[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/chaobrain/brain-modeling-ecosystem/blob/main/docs/basics/brainstate_transformations.ipynb)\n",
    "[![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/chaobrain/brain-modeling-ecosystem/blob/main/docs/basics/brainstate_transformations.ipynb)\n",
    "\n",
    "Welcome! This tutorial introduces **state-based transformations** in `brainstate`, powerful tools that enable efficient simulation and compilation of brain models. You'll learn:\n",
    "\n",
    "- How to use `for_loop` for sequential time-step simulations\n",
    "- When and how to apply `jit` (Just-In-Time compilation) for performance\n",
    "- Using `vmap` for vectorization across multiple trials or batches\n",
    "- Using `cond` for conditional branching in JIT-compiled code\n",
    "- Using `grad` for automatic differentiation and optimization\n",
    "- Combining transformations for complex simulation workflows\n",
    "- Best practices and common patterns\n",
    "\n",
    "Prerequisites:\n",
    "- Basic Python knowledge\n",
    "- Familiarity with `brainstate.nn.Dynamics` (see the LIF neuron tutorial)\n",
    "- Understanding of neural dynamics concepts helps but is not required"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "setup",
   "metadata": {},
   "source": [
    "## Setup and Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 624,
   "id": "imports",
   "metadata": {},
   "outputs": [],
   "source": [
    "import braintools\n",
    "import brainstate\n",
    "import brainunit as u\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Set global simulation time step\n",
    "brainstate.environ.set(dt=0.1 * u.ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "what_are_transformations",
   "metadata": {},
   "source": [
    "## What are Transformations?\n",
    "\n",
    "In `brainstate`, **transformations** are function decorators and utilities that modify how your neural dynamics code executes:\n",
    "\n",
    "1. **`for_loop`**: Sequentially iterates over time steps or data, managing state updates automatically\n",
    "2. **`jit`**: Just-In-Time compiles your functions for faster execution on CPU/GPU/TPU\n",
    "3. **`vmap`**: Vectorizes (batches) computations across multiple trials or parameter sets\n",
    "4. **`map`**: Memory-efficient batching when full `vmap` would exceed memory\n",
    "5. **`cond`**: Enables conditional branching in JIT-compiled code for event-driven dynamics\n",
    "6. **`grad`**: Computes gradients automatically for optimization and learning\n",
    "\n",
    "These transformations handle the complex bookkeeping of stateful computations, allowing you to write simple, readable code while achieving high performance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "example_model",
   "metadata": {},
   "source": [
    "## Example Model: Simple LIF Neuron\n",
    "\n",
    "Let's define a simple LIF neuron model that we'll use throughout this tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 625,
   "id": "lif_model",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LIFDynamics(\n",
      "  in_size=(1,),\n",
      "  out_size=(1,),\n",
      "  R=1. * ohm,\n",
      "  tau=5. * msecond,\n",
      "  V_th=1. * mvolt,\n",
      "  V_reset=0. * mvolt,\n",
      "  V_rest=0. * mvolt,\n",
      "  V_initializer=Constant(value=0.0 * mvolt),\n",
      "  spk_fun=ReluGrad(alpha=0.3, width=1.0),\n",
      "  spk_reset=soft,\n",
      "  V=HiddenState(\n",
      "    value=~float32[1] * mvolt\n",
      "  )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "from typing import Callable\n",
    "\n",
    "class LIFDynamics(brainstate.nn.Dynamics):\n",
    "    \"\"\"\n",
    "    A leaky integrate-and-fire neuron implemented as a Dynamics module.\n",
    "    This implementation matches the working example from brainstate_LIF_neuron.ipynb.\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        in_size: brainstate.typing.Size,\n",
    "        R: brainstate.typing.ArrayLike = 1.0 * u.ohm,\n",
    "        tau: brainstate.typing.ArrayLike = 5.0 * u.ms,\n",
    "        V_th: brainstate.typing.ArrayLike = 1.0 * u.mV,\n",
    "        V_reset: brainstate.typing.ArrayLike = 0.0 * u.mV,\n",
    "        V_rest: brainstate.typing.ArrayLike = 0.0 * u.mV,\n",
    "        V_initializer: Callable = braintools.init.Constant(0.0 * u.mV),\n",
    "        spk_fun: Callable = braintools.surrogate.ReluGrad(),\n",
    "        spk_reset: str = \"soft\",\n",
    "        name: str | None = None,\n",
    "    ):\n",
    "        super().__init__(in_size, name=name)\n",
    "        # Parameters (unit-aware)\n",
    "        self.R = braintools.init.param(R, self.varshape)\n",
    "        self.tau = braintools.init.param(tau, self.varshape)\n",
    "        self.V_th = braintools.init.param(V_th, self.varshape)\n",
    "        self.V_reset = braintools.init.param(V_reset, self.varshape)\n",
    "        self.V_rest = braintools.init.param(V_rest, self.varshape)\n",
    "        self.V_initializer = V_initializer\n",
    "        # Spiking\n",
    "        self.spk_fun = spk_fun\n",
    "        self.spk_reset = spk_reset\n",
    "\n",
    "    def init_state(self, batch_size: int | None = None, **kwargs):\n",
    "        self.V = brainstate.HiddenState(\n",
    "            braintools.init.param(self.V_initializer, self.varshape, batch_size)\n",
    "        )\n",
    "\n",
    "    def reset_state(self, batch_size: int | None = None, **kwargs):\n",
    "        self.V.value = braintools.init.param(self.V_initializer, self.varshape, batch_size)\n",
    "\n",
    "    def get_spike(self, V=None):\n",
    "        V = self.V.value if V is None else V\n",
    "        v_scaled = (V - self.V_th) / (self.V_th - self.V_reset)\n",
    "        return self.spk_fun(v_scaled)\n",
    "\n",
    "    def update(self, x=0.0 * u.mA):\n",
    "        last_v = self.V.value\n",
    "        spk = self.get_spike(last_v)\n",
    "        # Reset policy\n",
    "        V_th_or_v = self.V_th if self.spk_reset == 'soft' else jax.lax.stop_gradient(last_v)\n",
    "        V = last_v - (V_th_or_v - self.V_reset) * spk\n",
    "        # Dynamics integration by exponential Euler\n",
    "        dv = lambda v: (-(v - self.V_rest) + self.R * x) / self.tau\n",
    "        V = brainstate.nn.exp_euler_step(dv, V)\n",
    "        self.V.value = V\n",
    "        return self.get_spike(V)\n",
    "\n",
    "\n",
    "# Helper function to run simulations\n",
    "def run_lif(lif_module, inputs, reset=True):\n",
    "    \"\"\"Run the LIF over a 1D array of input currents.\n",
    "    \n",
    "    Returns membrane potentials and spikes over time.\n",
    "    \"\"\"\n",
    "    if reset:\n",
    "        lif_module.reset_state()\n",
    "    \n",
    "    # Safely get the length of inputs (robust for all array types)\n",
    "    inputs = u.math.asarray(inputs)  # Ensure it's an array\n",
    "    n_steps = inputs.shape[0] if hasattr(inputs, 'shape') and len(inputs.shape) > 0 else 1\n",
    "    idx = np.arange(n_steps)\n",
    "\n",
    "    def step(i, x):\n",
    "        with brainstate.environ.context(i=i):\n",
    "            s = lif_module(x)\n",
    "            return lif_module.V.value, s\n",
    "\n",
    "    V_seq, S_seq = brainstate.transform.for_loop(step, idx, inputs)\n",
    "    return V_seq, S_seq\n",
    "\n",
    "\n",
    "# Create and initialize the model\n",
    "neuron = LIFDynamics(in_size=1)\n",
    "brainstate.nn.init_all_states(neuron)\n",
    "print(neuron)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "for_loop_intro",
   "metadata": {},
   "source": [
    "## Transformation 1: `for_loop`\n",
    "\n",
    "The `for_loop` transformation is the workhorse of sequential simulation. It:\n",
    "- Iterates over time steps or input sequences\n",
    "- Automatically manages state updates between iterations\n",
    "- Optionally displays progress bars\n",
    "- Returns collected outputs from each step\n",
    "\n",
    "### Basic Usage\n",
    "\n",
    "The typical pattern is:\n",
    "```python\n",
    "def step_function(index, *inputs):\n",
    "    # Your simulation logic here\n",
    "    with brainstate.environ.context(i=index):\n",
    "        output = model(*inputs)\n",
    "    return output\n",
    "\n",
    "results = brainstate.transform.for_loop(step_function, indices, inputs)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 626,
   "id": "for_loop_basic",
   "metadata": {},
   "outputs": [
    {
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g4wFAm1M0k3zgtUA5oVTmGtFT9ebaLKfDeki1hw2RH2FS5lpZ224Ep9rZ2K9jT1vGi4YDMjiw2VrabI0HZCKbbTHJ/TFf6d8AGAXUMWlXx4S5VnHTgKiHNOBUa2evGcy3HJR55SQA9/RMAESq5QE7ouVcY13LIsWk+z441cB02EdKldQU1DGpcGKJOl/1Ng2oPVUvwoS5Vi+zKH2uGTgfclDWsYebG3m4W51q3B9VtNlY19LA/VE9Uk2674NTDUyH/YmZ2U7RtABZAeqBqIeGHQSQFaBqpBp2RG6Eyc2NyL1QeqQaa1sasNnqgblWj5T0LACz7fvgVAPTYX/qjjpf+ZhVBVILsGlQD9RCareuGdhsufdHjlQr6d9Y2/KAzdbQZmOupWFJzbLHNokNgVMNzB2pdjfXKZouVCAR9ZCGWRU3tQBpm+qhzK0inMXAZsshJZuaaqxtecCOaDfXsCHysCiRamWuTbLvg1MNTMddLUMQ9ZAKItXqYVbFTS1AhEmLOt9CNkfPLJEPrey1h7tdpBprWxrIeNHOZmPfJw8LItUAmAP7DYK3yeo9tECZW2WusUGTB+ZaPZS5hQ1RL+rBTp6tzhfzLTlSnXGAATsih7S0tLvsCOZaHrDZ6ttsb5PNNZxqYFrDynszrhsTr5nkFE0LED1VD2QFqAeiHupHPdztI9WYb6nr2j4rADZbDvbTivujBjYb90dpWNKn1mz3RzjVwLSGlSMetk2DsmsDTgd1vhoobqJmTPV1jblWIVJtZ7Mx35Lvj3ZZAbDZcrDv/w07okFNtUnqfHVRU51qjrmGUw1MhxK9c7M/iTfH510XIkPYoMlD2aMpc22W02EtUKIctrlG1EMayplnJpuNtS35/mgnVIa1LQU7nxo2WwWUdQybLR+LSTVH4FQD06GoT2dOb0OkWhZmNa5aYNbekFqA/uvqodhnpCSrmf4NoTJVI9WwI9JRItOYa/lYTLrvg1MNTHtamSn9Gz61esYVp8PSMGsdkx7q13lZY77l2hBEqlWca7TUko79WT7qfOUDfRctUu3drd+bZF3DqQbmrc9zt68Zg1etllON02EV6phsc411rVak2kwbB63mWkSqUeereqQaNlvFSDVq0VSz2bAh8kgx6VzDqQbmVZLlSLU7ItWyURwNb9SMSUdZx7a5xlRLQ1nHylybaeOgVYQpU3YRDjCkZwXwIQYDmy0HZQ3zOZFneicSRKrVs9mw1/JINWlWAJxqYDqyVTfFjUzaTUyZWrMZV1201MJcS0OxGfaRamyI1WuphbUtd12zQ829qu1fA85FCVSLuca6Vt1mw16r1xM81STrGk41MLdTDaEyqdhvxuDoqS9UhrlWN/0babKSS3bsoqdY23KFPEWk2pbJhbmWaa/58EJZ17Ah8tc2StE0aF+Wao65hlMNzCtUlsmp1nhQBsV+M2brU43TYWko042e4CpmBdilf5vlNF7LSDUiehpEqjHX0iPVyl4ENkSFSDVK0aRjMalALZxqYDqyj3rAq5buVHukq0DiRqZCpNrdVKfD2kaq3e96DTgXRKo1yOSyi55iriVHqu2catgQ9Ww25loeFpOWosGpBqYj+6iHtmMyKkj/VhflbAg1Y/JRohzWiF7m14C87CLU+apXHoWsALko9tle1R42Wx7QHNEuK8Ai9HWMP99wqoFpT4czn8TDq5ZZw8Sgjkn9muoUnBZJIyWTSjLWtkyUeRU221bni7Ut26lGna9K6xqRalUwa5snLUjJUr/OmGG64VQD06HsxRD1UDlSnb4ZRjRPHooPbasZw1SrEmVK96mxSZOEYjO4BWJGna/GgzKRkCdsthww1+phP6/Qd1G/pZZZ7o9wqoF5I9Woz1N504BonmyU6J3SxkJZ60DeSbx9pBp2RIVINbKLVHf0YLPl169nzDXWtQzs17Byf4S9Vrc7hsUE8w2nGpj2BA01Y2pvGqyvoWZMPXEQ7M9UqPMtlFFTjciH5Eg1dDCko6xhzghAna869tpeqAzrWg72axjp3+rZbG+77hhmuD/CqQamjTChZkyjSLVdnTWQ61Qj6qFS7SlamKlWe5phs7G2Zc61tc0TsotkotgL+5ZayMCQg/0ahlOtUaTaYvz5hlMNzBuptku5Qh2TCk41oh7q9+FMI1Mobmqukox+vurbbKxr6VkBtuwirGv5kWqbvovGgzJDe08cgqqutM4gUg2AAYHipnpgrrWNVNu/BuRFmaDNoFJ2kbudHYH3oYLNRqRaNRsCVXv1nGpEqlXMeHGj9PMiU2QXwakGpiNbxU0TnKBpXb+OrACNnGqsbRXrITHXsuvXkfGifqQa61p+/TqyXeRiP6+eygEGbIg6e79Cyt6PDA+camA6skvbRNRDfv26skFD1EMOnOatTK2S3sZgkyY/yqS01MLaVsFmI+NFvUg1HD11onl2GRiYaxXstbKuse9TwY6Qnc02vlcNpxqYW2AIkWoVayGRcqV2elvW14GcKJPSUgt2REWbjXWtns3GupabFWCnFQB7Ldle27dAxLpWwWa72dlsMjxwqoHJI0yIesgEUQ+N1E0RqVbPjrhntNRCxoscYLO1ql+3voaInhxwf1QPZQ0js0iDdqqFEKkGwCQRJtzI1K5fx+mwen04GaxtyTXViFSrWr8Om61i/ToieurVr6POV7V1bbPXsCHy937uGWvbDPdHONXA1BEmpFxp0YcTcy0D+1N3XtuK4ibmWw6InmpkRxDRk4qiPg2hMm0i1ch2kbyuObMIkWqNItVpZHTgVANTR5jg6MkFCsnqYX/qbj2NR+RDJqjz1Sa7CBkvcrGkZ2jat9SCzZavkAx9F5XWtV2kmoHNlpwZ4GauvR+camA6EPVQD0Sq1cP+FBjK9upGmRCp1iC7COtaakTPen9UXsNcy+2O4QYbIhmlntc+K8D6Oubb2aSmppFyNgSnGgAzRk9xOiwF1K+rh3LiztNcyG6+EflQL8qEta1idhHWtdSInrg/pud/Y13LrvO1HmIwiJzKQdHIsq9fF6/Djjgdi92cwqkGwCwRJqR/q1qfp5zEY67lR04ZRD7kkpLufQhHDxkv6tWewo6oY7NNVgupBei/rn6k2t5eW1/HfDsbS5asOTPZbF041d9//z1VrlyZfHx8qFWrVrR79+5cr1+6dCnVrl1bXN+gQQNauXKlamMFro9yEgyhMnXr81Djq94GjUHkQy7KtGYqbcDalmuzTbZB07oWEtkucoEug3ooa9h+38fAjjgfi71oqslstuZO9eLFi2n06NE0fvx42r9/PzVq1Ii6d+9O4eHh2V6/fft2GjBgAA0bNowOHDhAffv2FY+jR4+qPnbgmignkxAqUzlSbRfNS8MmTarapviKyId6NXo2O2L8Ppya22xkBUgF0VON5hpZAerUr9vt+xjYEeeTYjenZrPZmjvVkydPpueee46GDh1KdevWpRkzZpCvry/Nnj072+u/+eYbevDBB+mtt96iOnXq0CeffEJNmzalqVOnqj524OInliY7QdNLpJrBdMuNMNl/xdpWoUbPNtfajskUUSalny/WtRQQPdVirt3E2maQFSD//mi3FYEdkUBqTpFqE6xtDy3fPCkpifbt20djxoyxvebm5kZdu3alHTt2ZPs7/DpHtu3hyPby5cvJKJwKi6GdITe1HoZhOXgpMkOIJf0E7XZ8Es3bfkHjkRmPI1eixFeeZyXqwczdfiGTkw0Kzo2YxMxOdfra/vvQVdp38bamYzMiydlEqrecuUFxiSkaj8y4a9s+6nH0ahRstgROX4+9K1J9JfIO5loCu85b93nsTyvrOi7RgrmWQMiNjHXNQp78lR3qxXtCqZiPp9bDMxSxdvdAe0HgNcfCKORG3F3Xe3m40YCWFckIaOpUR0REkMVioaCgoEyv8/cnT57M9nfCwsKyvZ5fz47ExETxUIiOjia9s/fiLRr/1zGth2F4Cnu6k6+X9SMQEZuEOZdIYS938vZwEyfEfIj5yT/HtR6Sode1+Opl/frD5hCNR2RsfDzcbXP958Gr4gFk2mzrXO8MuSUeQOJcp9uS8xFxuD9KhO2HYkPuJFsw1xLxSV/TvLZjElPoq39Paz0kw+9FfNPX9i87Q7O9zr+wJ5xqV2HChAn00UcfkStRsYQv9WpQRuthGJoi3u7iQ1wuoDC90rkaXYiI13pIhoXT2oa0rSxuZh/3qU87ziELQxqFiHo3LCuevt+rDv2+/wqR8TOuNKNZpeLk7+tJL3WsRp5uhSgZvZOlUb54YTHfFUv60uXbdygmARkBsuA1/VDDMlTE24OebVeFrkcnaD0kw+Lt6SbmuHxxX3qrey06flX/gR9XhaOmA1pUEM8/6Vuf1h6/rvWQDM39tQPF19EP1KKFu0NzLCNRDpSMQKE0DRWDOP2b66d/++03ITamMHjwYIqMjKQ///zzrt+pWLGiSP9+/fXXba+xyBmnfx86dChPkeoKFSpQVFQU+fn5Sfl3AQAAAAAAAABwXdhv9Pf3z5PfqKlQmZeXFzVr1ozWrVtney01NVV836ZNm2x/h1+3v55Zu3Ztjtd7e3uLSbB/AAAAAAAAAAAAhkj/5qgzR6abN29OLVu2pK+//pri4uKEGjgzaNAgKleunEjjZkaOHEkdO3akSZMmUa9evWjRokW0d+9e+vHHHzX+lwAAAAAAAAAAMBuaO9X9+/enGzdu0Lhx44TYWOPGjWn16tU2MbLQ0FChCK7Qtm1bWrhwIX3wwQf03nvvUY0aNUTqd/369TX8VwAAAAAAAAAAMCOa1lRrAefEBwQE0KVLl5AKDgAAAAAAAADgLhQtLtb64tpqXUeq1SYmJkZ85QkCAAAAAAAAAABy8x/v5VSbLlLNQmhXr16lYsWKiQbwej8ZQUQd6AWsSaBHsC6BHsG6BHoE6xLokWgdr0t2k9mhLlu2bKZy5OwwXaSaJ6R8+fLkKkCxHOgNrEmgR7AugR7BugR6BOsS6BE/na7Le0WoddFSCwA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      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulate for 500 time steps with constant input\n",
    "n_steps = 500\n",
    "inputs = np.ones(n_steps) * 1.5 * u.mA  # Constant input current\n",
    "\n",
    "# Run simulation using helper function\n",
    "V_trace, spike_trace = run_lif(neuron, inputs)\n",
    "\n",
    "# Plot results\n",
    "times = np.arange(n_steps) * brainstate.environ.get_dt()\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(times, V_trace)\n",
    "plt.axhline(neuron.V_th.mantissa, color='r', linestyle='--', label='V_th')\n",
    "plt.ylabel('Membrane Potential (mV)')\n",
    "plt.legend()\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(times, spike_trace)\n",
    "plt.ylabel('Spike')\n",
    "plt.xlabel('Time (ms)')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "for_loop_pbar",
   "metadata": {},
   "source": [
    "### Progress Bars\n",
    "\n",
    "For long simulations, you can add a progress bar:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 627,
   "id": "progress_bar",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "479726a7c2d845f5a733e3c9ce496b11",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulation completed: 10000 steps\n"
     ]
    }
   ],
   "source": [
    "# Long simulation with progress bar\n",
    "n_steps = 10000\n",
    "inputs = np.ones(n_steps) * 1.5 * u.mA\n",
    "\n",
    "neuron.reset_state()\n",
    "idx = np.arange(n_steps)\n",
    "\n",
    "def step(i, x):\n",
    "    with brainstate.environ.context(i=i):\n",
    "        s = neuron(x)\n",
    "        return neuron.V.value, s\n",
    "\n",
    "V_trace, spike_trace = brainstate.transform.for_loop(\n",
    "    step, \n",
    "    idx, \n",
    "    inputs,\n",
    "    pbar=brainstate.transform.ProgressBar(1000)  # Update every 1000 steps\n",
    "    # or simply\n",
    "    # pbar=1000\n",
    ")\n",
    "\n",
    "print(f\"Simulation completed: {n_steps} steps\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "jit_intro",
   "metadata": {},
   "source": [
    "## Transformation 2: `jit` (Just-In-Time Compilation)\n",
    "\n",
    "JIT compilation can dramatically speed up your simulations by compiling Python/NumPy code to optimized machine code. Use `jit` when:\n",
    "- You're running long simulations\n",
    "- The function will be called many times\n",
    "- Performance is critical\n",
    "\n",
    "### Basic JIT Usage\n",
    "\n",
    "You can JIT-compile simulation functions. Note that we need to be careful with how we structure the code for JIT:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 628,
   "id": "jit_basic",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No JIT: 0.0562s\n",
      "First JIT call (with compilation): 0.0520s\n",
      "Second JIT call (compiled): 0.0000s\n",
      "Speedup: Very fast (>1000x)\n"
     ]
    }
   ],
   "source": [
    "# Create a separate neuron for JIT example\n",
    "jit_neuron = LIFDynamics(in_size=1)\n",
    "brainstate.nn.init_all_states(jit_neuron)\n",
    "\n",
    "def run_simulation_nojit(inputs):\n",
    "    \"\"\"Non-JIT simulation function.\"\"\"\n",
    "    return run_lif(jit_neuron, inputs)\n",
    "\n",
    "@brainstate.transform.jit\n",
    "def run_simulation_jit(inputs):\n",
    "    \"\"\"JIT-compiled simulation function.\"\"\"\n",
    "    return run_lif(jit_neuron, inputs)\n",
    "\n",
    "# Benchmark\n",
    "import time\n",
    "inputs = np.ones(5000) * 1.5 * u.mA\n",
    "\n",
    "# Non-JIT\n",
    "start = time.time()\n",
    "V1, S1 = run_simulation_nojit(inputs)\n",
    "nojit_time = time.time() - start\n",
    "\n",
    "# First JIT call: includes compilation (slower)\n",
    "start = time.time()\n",
    "V2, S2 = run_simulation_jit(inputs)\n",
    "compile_time = time.time() - start\n",
    "\n",
    "# Second JIT call: uses compiled version (much faster)\n",
    "start = time.time()\n",
    "V3, S3 = run_simulation_jit(inputs)\n",
    "run_time = time.time() - start\n",
    "\n",
    "print(f\"No JIT: {nojit_time:.4f}s\")\n",
    "print(f\"First JIT call (with compilation): {compile_time:.4f}s\")\n",
    "print(f\"Second JIT call (compiled): {run_time:.4f}s\")\n",
    "if run_time > 0:\n",
    "    print(f\"Speedup: {nojit_time/run_time:.1f}x\")\n",
    "else:\n",
    "    print(f\"Speedup: Very fast (>1000x)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vmap_intro",
   "metadata": {},
   "source": [
    "## Transformation 3: `vmap` (Vectorization)\n",
    "\n",
    "`vmap` (vectorized map) runs your function in parallel over a batch dimension. This is incredibly useful for:\n",
    "- Running multiple trials with different random seeds\n",
    "- Sweeping parameters\n",
    "- Processing multiple inputs simultaneously\n",
    "\n",
    "### Running Multiple Trials\n",
    "\n",
    "Let's run multiple trials with different input currents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 629,
   "id": "vmap_basic",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output shape: V_batch=(10, 1000, 1), S_batch=(10, 1000, 1)\n",
      "Expected: (batch=10, time=1000, neurons=1)\n"
     ]
    }
   ],
   "source": [
    "# Different input currents for each trial\n",
    "batch_size = 10\n",
    "n_steps = 1000\n",
    "input_currents = np.linspace(0.1, 0.2, batch_size) * u.mA\n",
    "\n",
    "# Create batched inputs: shape (batch, time)\n",
    "inputs_list = []\n",
    "for I in input_currents:\n",
    "    inputs_list.append(np.ones(n_steps) * I)\n",
    "inputs_batched = u.math.asarray(inputs_list)\n",
    "\n",
    "# IMPORTANT: Create NEW neuron instances inside vmap to avoid state conflicts\n",
    "@brainstate.transform.vmap\n",
    "def run_batched_trial(inp_seq):\n",
    "    \"\"\"Run simulation for a single input sequence.\n",
    "    \n",
    "    Key Pattern: Create a fresh LIF instance for each vmap iteration.\n",
    "    This avoids BatchAxisError from shared state across iterations.\n",
    "    \"\"\"\n",
    "    lif_single = LIFDynamics(1)\n",
    "    brainstate.nn.init_all_states(lif_single)\n",
    "    \n",
    "    # Safely get sequence length\n",
    "    inp_seq = u.math.asarray(inp_seq)\n",
    "    n_steps_local = inp_seq.shape[0] if hasattr(inp_seq, 'shape') and len(inp_seq.shape) > 0 else 1\n",
    "    idx = np.arange(n_steps_local)\n",
    "\n",
    "    def step(i, x):\n",
    "        with brainstate.environ.context(i=i):\n",
    "            s = lif_single(x)\n",
    "            return lif_single.V.value, s\n",
    "    \n",
    "    return brainstate.transform.for_loop(step, idx, inp_seq)\n",
    "\n",
    "# Run all trials in parallel\n",
    "V_batch, S_batch = run_batched_trial(inputs_batched)\n",
    "\n",
    "print(f\"Output shape: V_batch={V_batch.shape}, S_batch={S_batch.shape}\")\n",
    "print(f\"Expected: (batch={batch_size}, time={n_steps}, neurons=1)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vmap_plotting",
   "metadata": {},
   "source": [
    "### Visualizing Batch Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 630,
   "id": "plot_vmap",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot membrane potentials for all trials\n",
    "times = np.arange(n_steps) * brainstate.environ.get_dt()\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "for i in range(batch_size):\n",
    "    plt.plot(times, V_batch[i, :, 0].mantissa, alpha=0.7,\n",
    "             label=f'I={input_currents[i].mantissa:.3f} mA')\n",
    "plt.axhline(1.0, color='r', linestyle='--', linewidth=2, label='V_th')\n",
    "plt.xlabel('Time (ms)')\n",
    "plt.ylabel('Membrane Potential (mV)')\n",
    "plt.title('Voltage Traces for Different Input Currents')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', fontsize=8)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "# Count spikes for each trial (threshold at 0.5)\n",
    "spike_counts = []\n",
    "for i in range(batch_size):\n",
    "    count = (np.asarray(S_batch[i]) >= 0.5).sum()\n",
    "    spike_counts.append(count)\n",
    "\n",
    "plt.plot(input_currents.mantissa, spike_counts, 'o-', markersize=8, linewidth=2)\n",
    "plt.xlabel('Input Current (mA)')\n",
    "plt.ylabel('Number of Spikes')\n",
    "plt.title('F-I Curve (Firing Rate vs Input)')\n",
    "plt.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "combining",
   "metadata": {},
   "source": [
    "## Combining Transformations\n",
    "\n",
    "The real power comes from combining transformations. A common pattern is `jit` + `vmap` for fast, batched simulations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 631,
   "id": "combined",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ran 50 trials of 2000 steps in 0.0010s\n",
      "Average time per trial: 0.02ms\n",
      "Time per step per trial: 0.01µs\n"
     ]
    }
   ],
   "source": [
    "# Combined JIT + vmap for maximum performance\n",
    "import time\n",
    "\n",
    "n_trials = 50\n",
    "n_steps = 2000\n",
    "\n",
    "# Create test inputs: same current for all trials\n",
    "test_inputs_list = []\n",
    "for _ in range(n_trials):\n",
    "    test_inputs_list.append(np.ones(n_steps) * 1.5 * u.mA)\n",
    "test_inputs = u.math.asarray(test_inputs_list)\n",
    "\n",
    "@brainstate.transform.jit\n",
    "@brainstate.transform.vmap\n",
    "def fast_batch_simulation(inp_seq):\n",
    "    \"\"\"JIT-compiled, vectorized simulation.\n",
    "    \n",
    "    Creates a fresh neuron for each vmap iteration (best practice).\n",
    "    \"\"\"\n",
    "    lif_fast = LIFDynamics(1)\n",
    "    brainstate.nn.init_all_states(lif_fast)\n",
    "    \n",
    "    # Safely get sequence length\n",
    "    inp_seq = u.math.asarray(inp_seq)\n",
    "    n_steps_local = inp_seq.shape[0] if hasattr(inp_seq, 'shape') and len(inp_seq.shape) > 0 else 1\n",
    "    idx = np.arange(n_steps_local)\n",
    "\n",
    "    def step(i, x):\n",
    "        with brainstate.environ.context(i=i):\n",
    "            s = lif_fast(x)\n",
    "            return lif_fast.V.value, s\n",
    "    \n",
    "    return brainstate.transform.for_loop(step, idx, inp_seq)\n",
    "\n",
    "# Warm-up compilation\n",
    "_ = fast_batch_simulation(test_inputs)\n",
    "\n",
    "# Timed run\n",
    "start = time.time()\n",
    "V_fast, S_fast = fast_batch_simulation(test_inputs)\n",
    "elapsed = time.time() - start\n",
    "\n",
    "print(f\"Ran {n_trials} trials of {n_steps} steps in {elapsed:.4f}s\")\n",
    "print(f\"Average time per trial: {elapsed/n_trials*1000:.2f}ms\")\n",
    "print(f\"Time per step per trial: {elapsed/(n_trials*n_steps)*1e6:.2f}µs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "map_intro",
   "metadata": {},
   "source": [
    "## Transformation 4: `map` for Memory-Efficient Batching\n",
    "\n",
    "When you have many trials but limited memory, use `map` instead of `vmap`. It processes data in smaller batches sequentially:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 632,
   "id": "map_example",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Processed 100 trials\n",
      "Output shape: (100, 1000, 1)\n",
      "Total spikes across all trials: 1800\n"
     ]
    }
   ],
   "source": [
    "# Simulate a scenario with many trials\n",
    "n_trials_map = 100\n",
    "n_steps_map = 1000\n",
    "\n",
    "# Create inputs for all trials\n",
    "large_inputs_list = []\n",
    "for _ in range(n_trials_map):\n",
    "    large_inputs_list.append(np.ones(n_steps_map) * 1.5 * u.mA)\n",
    "large_inputs = u.math.asarray(large_inputs_list)\n",
    "\n",
    "@brainstate.transform.vmap\n",
    "def single_trial_sim(inp_seq):\n",
    "    \"\"\"Single trial simulation - creates its own neuron instance.\"\"\"\n",
    "    lif_trial = LIFDynamics(1)\n",
    "    brainstate.nn.init_all_states(lif_trial)\n",
    "    \n",
    "    # Safely get sequence length\n",
    "    inp_seq = u.math.asarray(inp_seq)\n",
    "    n_steps_local = inp_seq.shape[0] if hasattr(inp_seq, 'shape') and len(inp_seq.shape) > 0 else 1\n",
    "    idx = np.arange(n_steps_local)\n",
    "\n",
    "    def step(i, x):\n",
    "        with brainstate.environ.context(i=i):\n",
    "            return lif_trial(x)\n",
    "    \n",
    "    return brainstate.transform.for_loop(step, idx, inp_seq)\n",
    "\n",
    "spike_results = single_trial_sim(large_inputs)\n",
    "print(f\"Processed {n_trials_map} trials\")\n",
    "print(f\"Output shape: {spike_results.shape}\")\n",
    "\n",
    "total_spikes = 0\n",
    "for i in range(n_trials_map):\n",
    "    spike_trace = spike_results[i]\n",
    "    if hasattr(spike_trace, '__len__'):\n",
    "        total_spikes += (np.asarray(spike_trace) >= 0.5).sum()\n",
    "print(f\"Total spikes across all trials: {total_spikes}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "advanced",
   "metadata": {},
   "source": [
    "## Advanced Pattern: Nested Loops\n",
    "\n",
    "Sometimes you need nested iteration (e.g., trials × time steps). Here's a practical example with random noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 633,
   "id": "nested_loops",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spike counts per trial: [9 9 9 9 9]\n",
      "Mean: 9.0, Std: 0.00\n"
     ]
    }
   ],
   "source": [
    "nested_neuron = LIFDynamics(1)\n",
    "brainstate.nn.init_all_states(nested_neuron)\n",
    "\n",
    "n_trials_nest = 5\n",
    "n_steps_nest = 500\n",
    "\n",
    "def run_single_trial_noise(trial_idx):\n",
    "    \"\"\"Run one trial with a specific random seed.\"\"\"\n",
    "    nested_neuron.reset_state()\n",
    "    \n",
    "    # Generate noisy input for this trial\n",
    "    key = jax.random.PRNGKey(trial_idx)\n",
    "    base_current = 1.5 * u.mA\n",
    "    noise = jax.random.normal(key, (n_steps_nest,)) * 0.03 * u.mA\n",
    "    inputs = base_current + noise\n",
    "    \n",
    "    # Run simulation and return spike count\n",
    "    _, spikes = run_lif(nested_neuron, inputs, reset=False)\n",
    "    # return (np.asarray(spikes) >= 0.5).sum()\n",
    "    spike_mask = spikes >= 0.5\n",
    "    spike_count = spike_mask.sum()\n",
    "    return spike_count\n",
    "\n",
    "# Outer loop: iterate over trials\n",
    "trial_indices = jnp.arange(n_trials_nest)\n",
    "spike_counts = brainstate.transform.for_loop(\n",
    "    lambda i: run_single_trial_noise(i), \n",
    "    trial_indices\n",
    ")\n",
    "\n",
    "print(f\"Spike counts per trial: {spike_counts}\")\n",
    "print(f\"Mean: {spike_counts.mean():.1f}, Std: {spike_counts.std():.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "i030b4ap54q",
   "metadata": {},
   "source": [
    "## Transformation 5: `cond` for Conditional Branching\n",
    "\n",
    "The `cond` transformation enables efficient conditional execution in JIT-compiled code. Unlike Python's `if/else`, which are resolved at trace time, `cond` supports runtime conditionals that work seamlessly with JIT compilation.\n",
    "\n",
    "Use `cond` when:\n",
    "- You need data-dependent branching inside JIT-compiled functions\n",
    "- Implementing different update rules based on runtime conditions\n",
    "- Switching between computational modes (e.g., training vs inference)\n",
    "\n",
    "### Basic Usage\n",
    "\n",
    "The basic pattern is:\n",
    "```python\n",
    "result = brainstate.transform.cond(\n",
    "    predicate,      # Boolean condition\n",
    "    true_fun,       # Function called if True  \n",
    "    false_fun,      # Function called if False\n",
    "    operand         # Passed to whichever function is called\n",
    ")\n",
    "```\n",
    "\n",
    "Both `true_fun` and `false_fun` must accept the same input and return the same output type/shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 634,
   "id": "l11op7zxfpd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input | Condition | Output\n",
      "------|-----------|-------\n",
      "0.5   | low       | 0.2\n",
      "1.0   | low       | 0.5\n",
      "1.5   | low       | 0.8\n",
      "2.0   | high      | 4.0\n",
      "2.5   | high      | 5.0\n"
     ]
    }
   ],
   "source": [
    "# Simple example: Apply different scaling factors based on a threshold\n",
    "def adaptive_scale(x, threshold):\n",
    "    \"\"\"Apply 2x scaling if x > threshold, otherwise apply 0.5x scaling.\"\"\"\n",
    "    \n",
    "    def high_branch(val):\n",
    "        return val * 2.0\n",
    "    \n",
    "    def low_branch(val):\n",
    "        return val * 0.5\n",
    "    \n",
    "    return brainstate.transform.cond(\n",
    "        x > threshold,\n",
    "        high_branch,\n",
    "        low_branch,\n",
    "        x\n",
    "    )\n",
    "\n",
    "# Test with different values\n",
    "test_vals = jnp.array([0.5, 1.0, 1.5, 2.0, 2.5])\n",
    "threshold = 1.5\n",
    "\n",
    "print(\"Input | Condition | Output\")\n",
    "print(\"------|-----------|-------\")\n",
    "for val in test_vals:\n",
    "    result = adaptive_scale(val, threshold)\n",
    "    cond_str = \"high\" if val > threshold else \"low\"\n",
    "    print(f\"{val:.1f}   | {cond_str:9s} | {result:.1f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aqa4jvc3t4b",
   "metadata": {},
   "source": [
    "### Using `cond` in Simulations\n",
    "\n",
    "A practical use case: applying different input currents to a neuron based on time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 635,
   "id": "j6ywe6ngefj",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1200x900 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Spikes in early phase (low current): 5\n",
      "Spikes in late phase (high current): 12\n"
     ]
    }
   ],
   "source": [
    "# Simulate neuron with time-varying input using cond\n",
    "cond_neuron = LIFDynamics(1)\n",
    "brainstate.nn.init_all_states(cond_neuron)\n",
    "\n",
    "n_steps_cond = 1000\n",
    "switch_time = 500  # Switch input current at this step\n",
    "\n",
    "def get_input_current(step_idx):\n",
    "    \"\"\"Return different input currents before/after switch_time.\"\"\"\n",
    "    \n",
    "    def early_phase(_):\n",
    "        return 1.2 * u.mA  # Lower current\n",
    "    \n",
    "    def late_phase(_):\n",
    "        return 1.8 * u.mA  # Higher current\n",
    "    \n",
    "    return brainstate.transform.cond(\n",
    "        step_idx < switch_time,\n",
    "        early_phase,\n",
    "        late_phase,\n",
    "        None  # Operand (not used here)\n",
    "    )\n",
    "\n",
    "# Run simulation\n",
    "cond_neuron.reset_state()\n",
    "idx_cond = np.arange(n_steps_cond)\n",
    "\n",
    "def step_with_cond(i, _):\n",
    "    with brainstate.environ.context(i=i):\n",
    "        current = get_input_current(i)\n",
    "        spike = cond_neuron(current)\n",
    "        return current, cond_neuron.V.value, spike\n",
    "\n",
    "currents, V_cond, spikes_cond = brainstate.transform.for_loop(\n",
    "    step_with_cond, idx_cond, jnp.zeros(n_steps_cond)\n",
    ")\n",
    "\n",
    "# Plot results\n",
    "times_cond = np.arange(n_steps_cond) * brainstate.environ.get_dt()\n",
    "\n",
    "fig, axes = plt.subplots(3, 1, figsize=(12, 9))\n",
    "plt.subplots_adjust(left=0.08, right=0.98, top=0.95, bottom=0.05)\n",
    "\n",
    "# Input current\n",
    "axes[0].plot(times_cond, currents.mantissa,linewidth=1.5)\n",
    "axes[0].axvline(switch_time * 0.1, color='r', linestyle='--', alpha=0.5)\n",
    "axes[0].set_ylabel('Input (mA)')\n",
    "axes[0].set_title('Time-Varying Input with cond')\n",
    "axes[0].text(30, 1.5, 'Low current', ha='center')\n",
    "axes[0].text(80, 1.5, 'High current', ha='center')\n",
    "\n",
    "# Voltage\n",
    "axes[1].plot(times_cond, V_cond[:, 0].mantissa)\n",
    "axes[1].axhline(1.0, color='r', linestyle='--', alpha=0.5, label='V_th')\n",
    "axes[1].axvline(switch_time * 0.1, color='r', linestyle='--', alpha=0.5)\n",
    "axes[1].set_ylabel('Voltage (mV)')\n",
    "axes[1].legend()\n",
    "\n",
    "# Spikes\n",
    "axes[2].plot(times_cond, spikes_cond[:, 0])\n",
    "axes[2].axvline(switch_time * 0.1, color='r', linestyle='--', alpha=0.5, label='Switch point')\n",
    "axes[2].set_ylabel('Spike')\n",
    "axes[2].set_xlabel('Time (ms)')\n",
    "axes[2].legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Count spikes in each phase\n",
    "early_spikes = (spikes_cond[:switch_time] >= 0.5).sum()\n",
    "late_spikes = (spikes_cond[switch_time:] >= 0.5).sum()\n",
    "print(f\"Spikes in early phase (low current): {early_spikes}\")\n",
    "print(f\"Spikes in late phase (high current): {late_spikes}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "z8djoh13tqb",
   "metadata": {},
   "source": [
    "## Transformation 6: `grad` for Automatic Differentiation\n",
    "\n",
    "The `grad` transformation computes gradients automatically, enabling optimization and learning in neural models. It supports differentiation with respect to:\n",
    "- Function arguments (standard autodiff)\n",
    "- Model parameters (`ParamState` objects)\n",
    "- Combinations of both\n",
    "\n",
    "### Basic Usage\n",
    "\n",
    "The basic pattern is:\n",
    "```python\n",
    "grad_fn = brainstate.transform.grad(\n",
    "    fun,                  # Function to differentiate\n",
    "    argnums=None,         # Which arguments to differentiate (int or list)\n",
    "    grad_states=None,     # Which State objects to differentiate\n",
    "    has_aux=False,        # Whether function returns (loss, aux_data)\n",
    "    return_value=False    # Whether to return loss value with gradients\n",
    ")\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 636,
   "id": "zz51r447vfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example 1: Computing gradients w.r.t. function arguments\n",
    "\n",
    "def quadratic_loss(x, y):\n",
    "    \"\"\"Simple quadratic loss function.\"\"\"\n",
    "    return jnp.sum((x - y) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 637,
   "id": "8fedf842",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input x: [1. 2. 3.]\n",
      "Target y: [0.5 1.5 2.5]\n",
      "Gradient ∂L/∂x: [1. 1. 1.]\n",
      "Loss: 0.7500\n"
     ]
    }
   ],
   "source": [
    "# Gradient w.r.t. first argument (x)\n",
    "grad_fn_x = brainstate.transform.grad(quadratic_loss, argnums=0)\n",
    "\n",
    "x = jnp.array([1.0, 2.0, 3.0])\n",
    "y = jnp.array([0.5, 1.5, 2.5])\n",
    "\n",
    "grad_x = grad_fn_x(x, y)\n",
    "print(f\"Input x: {x}\")\n",
    "print(f\"Target y: {y}\")\n",
    "print(f\"Gradient ∂L/∂x: {grad_x}\")\n",
    "print(f\"Loss: {quadratic_loss(x, y):.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 638,
   "id": "cfb6fcd1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Gradients w.r.t. both arguments:\n",
      "∂L/∂x: [1. 1. 1.]\n",
      "∂L/∂y: [-1. -1. -1.]\n"
     ]
    }
   ],
   "source": [
    "# Gradient w.r.t. multiple arguments\n",
    "grad_fn_both = brainstate.transform.grad(quadratic_loss, argnums=[0, 1])\n",
    "grad_x, grad_y = grad_fn_both(x, y)\n",
    "print(f\"\\nGradients w.r.t. both arguments:\")\n",
    "print(f\"∂L/∂x: {grad_x}\")\n",
    "print(f\"∂L/∂y: {grad_y}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0xm8goo3n5",
   "metadata": {},
   "source": [
    "### Computing Gradients w.r.t. Model Parameters\n",
    "\n",
    "To train neural models, we need to differentiate with respect to `ParamState` objects. BrainState extends JAX's autodiff to handle stateful parameters seamlessly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 641,
   "id": "xfmbjipvld",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial: weight=0.1623, bias=0.0000\n",
      "Epoch   0: loss=4.882305, weight=0.4485, bias=0.4302\n",
      "Epoch  20: loss=0.053904, weight=1.3369, bias=1.4566\n",
      "Epoch  40: loss=0.039217, weight=1.4816, bias=1.3671\n",
      "Epoch  60: loss=0.028541, weight=1.6041, bias=1.2893\n",
      "Epoch  80: loss=0.020774, weight=1.7085, bias=1.2229\n",
      "Epoch 100: loss=0.015124, weight=1.7976, bias=1.1663\n",
      "Epoch 120: loss=0.011013, weight=1.8736, bias=1.1180\n",
      "Epoch 140: loss=0.008023, weight=1.9384, bias=1.0768\n",
      "\n",
      "Final: weight=1.9644, bias=1.0603\n",
      "True parameters: weight=2.0000, bias=1.0000\n"
     ]
    }
   ],
   "source": [
    "# Example 2: Training a simple linear model\n",
    "\n",
    "class LinearRegressor(brainstate.nn.Module):\n",
    "    \"\"\"Simple linear regression model: y = wx + b\"\"\"\n",
    "\n",
    "    def __init__(self, in_features: int):\n",
    "        super().__init__()\n",
    "        # Initialize parameters with small random values\n",
    "        key = jax.random.PRNGKey(0)\n",
    "        self.weight = brainstate.ParamState(jax.random.normal(key, (in_features, 1)) * 0.1)\n",
    "        self.bias = brainstate.ParamState(jnp.zeros((1,)))\n",
    "\n",
    "    def __call__(self, x):\n",
    "        return jnp.dot(x, self.weight.value) + self.bias.value\n",
    "\n",
    "# Create model and training data\n",
    "model = LinearRegressor(in_features=1)\n",
    "\n",
    "# Generate synthetic data: y = 2x + 1 + noise\n",
    "# Normalize input to [0, 1] for stability\n",
    "key = jax.random.PRNGKey(42)\n",
    "x_train = jax.random.uniform(key, (20, 1))  # Range [0, 1]\n",
    "y_train = 2.0 * x_train + 1.0 + jax.random.normal(key, (20, 1)) * 0.1\n",
    "\n",
    "# Define loss function\n",
    "def compute_loss(x_data, y_data):\n",
    "    \"\"\"MSE loss for the model.\"\"\"\n",
    "    predictions = model(x_data)\n",
    "    return jnp.mean((predictions - y_data) ** 2)\n",
    "\n",
    "# Create gradient function w.r.t. all ParamState in model\n",
    "# Gradients are returned as a list in the same order as grad_states\n",
    "grad_fn = brainstate.transform.grad(\n",
    "    compute_loss,\n",
    "    grad_states=[model.weight, model.bias],  # Explicit list order\n",
    "    return_value=True\n",
    ")\n",
    "\n",
    "# Training loop \n",
    "learning_rate = 0.1  \n",
    "n_epochs = 150\n",
    "\n",
    "print(f\"Initial: weight={model.weight.value[0, 0]:.4f}, bias={model.bias.value[0]:.4f}\")\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    # Compute gradients - returns tuple (grads_list, loss)\n",
    "    grads, loss = grad_fn(x_train, y_train)\n",
    "    \n",
    "    # Unpack gradients list: [grad_weight, grad_bias]\n",
    "    grad_w, grad_b = grads\n",
    "    \n",
    "    # Update parameters\n",
    "    model.weight.value = model.weight.value - learning_rate * grad_w\n",
    "    model.bias.value = model.bias.value - learning_rate * grad_b\n",
    "    \n",
    "    if epoch % 20 == 0:\n",
    "        print(f\"Epoch {epoch:3d}: loss={loss:.6f}, \"\n",
    "              f\"weight={model.weight.value[0, 0]:.4f}, \"\n",
    "              f\"bias={model.bias.value[0]:.4f}\")\n",
    "\n",
    "print(f\"\\nFinal: weight={model.weight.value[0, 0]:.4f}, bias={model.bias.value[0]:.4f}\")\n",
    "print(f\"True parameters: weight=2.0000, bias=1.0000\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c516be7",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "You've learned the core transformations in `brainstate`:\n",
    "\n",
    "| Transformation | Purpose | When to Use |\n",
    "|---------------|---------|-------------|\n",
    "| `for_loop` | Sequential iteration with state | Time-step simulations, sequential data |\n",
    "| `jit` | Compile to fast machine code | Long/repeated simulations, performance critical |\n",
    "| `vmap` | Vectorize over batch dimension | Multiple trials, parameter sweeps, batching |\n",
    "| `map` | Memory-efficient batching | Large number of trials, limited memory |\n",
    "| `cond` | Conditional branching in JIT code | Event-driven dynamics, mode switching, adaptive behavior |\n",
    "| `grad` | Automatic differentiation | Training networks, optimizing parameters, learning rules |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d5o54ktx1qu",
   "metadata": {},
   "source": [
    "For more detailed information about `brainstate` transformations and advanced features, please visit:\n",
    "\n",
    "*[BrainState Documentation](https://brainstate.readthedocs.io)*\n"
   ]
  }
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