ode_layers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "810d30cc-411f-4bd1-9b08-cbb8cffbb403",
   "metadata": {},
   "source": [
    "# Defining ODE layers in Jax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "894ed829-4f9c-4594-ad7d-b86a2a9144e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Defaulting to user installation because normal site-packages is not writeable\n",
      "Requirement already satisfied: jax in /home/dommiketa/.local/lib/python3.8/site-packages (0.2.16)\n",
      "Requirement already satisfied: jaxlib in /home/dommiketa/.local/lib/python3.8/site-packages (0.1.68)\n",
      "Requirement already satisfied: flax in /home/dommiketa/.local/lib/python3.8/site-packages (0.3.4)\n",
      "Requirement already satisfied: opt-einsum in /usr/local/lib/python3.8/dist-packages (from jax) (3.3.0)\n",
      "Requirement already satisfied: absl-py in /usr/local/lib/python3.8/dist-packages (from jax) (0.12.0)\n",
      "Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.8/dist-packages (from jax) (1.19.5)\n",
      "Requirement already satisfied: scipy in /usr/local/lib/python3.8/dist-packages (from jaxlib) (1.6.3)\n",
      "Requirement already satisfied: flatbuffers<3.0,>=1.12 in /usr/local/lib/python3.8/dist-packages (from jaxlib) (1.12)\n",
      "Requirement already satisfied: matplotlib in /usr/local/lib/python3.8/dist-packages (from flax) (3.4.2)\n",
      "Requirement already satisfied: optax in /home/dommiketa/.local/lib/python3.8/site-packages (from flax) (0.0.9)\n",
      "Requirement already satisfied: msgpack in /home/dommiketa/.local/lib/python3.8/site-packages (from flax) (1.0.2)\n",
      "Requirement already satisfied: six in /usr/local/lib/python3.8/dist-packages (from absl-py->jax) (1.15.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib->flax) (1.3.1)\n",
      "Requirement already satisfied: pyparsing>=2.2.1 in /usr/local/lib/python3.8/dist-packages (from matplotlib->flax) (2.4.7)\n",
      "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.8/dist-packages (from matplotlib->flax) (0.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.8/dist-packages (from matplotlib->flax) (2.8.1)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.8/dist-packages (from matplotlib->flax) (8.1.0)\n",
      "Requirement already satisfied: chex>=0.0.4 in /home/dommiketa/.local/lib/python3.8/site-packages (from optax->flax) (0.0.8)\n",
      "Requirement already satisfied: toolz>=0.9.0 in /home/dommiketa/.local/lib/python3.8/site-packages (from chex>=0.0.4->optax->flax) (0.11.1)\n",
      "Requirement already satisfied: dm-tree>=0.1.5 in /usr/local/lib/python3.8/dist-packages (from chex>=0.0.4->optax->flax) (0.1.6)\n",
      "\u001b[33mWARNING: You are using pip version 21.1.2; however, version 21.1.3 is available.\n",
      "You should consider upgrading via the '/usr/bin/python3 -m pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "!pip install jax jaxlib flax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "933245a7-f2c6-4374-8e2e-2ae9e738313c",
   "metadata": {},
   "source": [
    "## Toy dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24167fcc-f2af-49cf-9973-88973f593cf9",
   "metadata": {},
   "source": [
    "Based on the definitions in https://arxiv.org/pdf/1505.05770.pdf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad273b1a-8cc5-4a52-a652-07cfe4ee19c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import jax\n",
    "from typing import Any, Callable, Sequence, Optional\n",
    "from jax import lax,random,numpy as jnp\n",
    "import flax\n",
    "from flax import linen as nn\n",
    "\n",
    "def w1(z1,z2): return jnp.sin(2*jnp.pi*z1/4.)\n",
    "def w2(z1,z2): return 3*jnp.exp(-.5*(z1-1)**2/.36)\n",
    "def w3(z1,z2): return 3*jax.nn.sigmoid((z1-1)/.3)\n",
    "\n",
    "def U1(z1,z2): return .5*((jnp.linalg.norm(jnp.stack((z1,z2), axis=-1), axis=-1)-2)/.4)**2 - jnp.log(jnp.exp(-.5*((z1-2/.6))**2) + jnp.exp(-.5*((z1+2/.6))**2))\n",
    "def U2(z1,z2): return .5*((z2-w1(z1,z2))/.4)**2\n",
    "def U3(z1,z2): return -jnp.log(jnp.exp(-.5*((z2-w1(z1,z2))/.4)**2) + jnp.exp(-.5*((z2-w1(z1,z2)+w2(z1,z2))/.35)**2))\n",
    "def U4(z1,z2): return -jnp.log(jnp.exp(-.5*((z2-w1(z1,z2))/.4)**2) + jnp.exp(-.5*((z2-w1(z1,z2)+w3(z1,z2))/.35)**2))\n",
    "Us = (U1,U2,U3,U4)\n",
    "\n",
    "def f(U,z1,z2): return jnp.exp(-U(z1,z2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "88450682-05c8-4aa1-9760-dc7a35488076",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1728x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = ys = jnp.linspace(-4,4)\n",
    "\n",
    "fig,axs = plt.subplots(ncols=len(Us), figsize=(24,6))\n",
    "xgrid,ygrid = jnp.meshgrid(xs,ys)\n",
    "\n",
    "for ax,U in zip(axs,Us):\n",
    "    ax.set_aspect('equal')\n",
    "    zs = jnp.exp(-U(xgrid,ygrid))\n",
    "    plot = ax.contourf(xgrid,ygrid,zs,30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "dff3be04-fe3d-428c-8f26-d16fdae02f2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_batch(n_samples, U, key):\n",
    "    \"Get uniformly distributed batch\"\n",
    "    key1,key2 = random.split(key) \n",
    "    pts = random.uniform(key, (n_samples, 2), minval=-4, maxval=4) # sample uniformly from (-4,4)^2\n",
    "    log_pz = jnp.zeros((n_samples,))\n",
    "    return key2, (pts,log_pz)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fa0c906-2981-4a2a-af0b-ea08fda81902",
   "metadata": {},
   "source": [
    "## Continuous normalizing flow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c3df1f4-c547-4d4a-a606-cb37bffc56dc",
   "metadata": {},
   "source": [
    "$$ \\frac{d\\mathbf{z}(t)}{dt} = \\sum_{n=1}^M f_n(\\mathbf{z}(t)), \\frac{d\\log p(\\mathbf{z}(t))}{dt} = \\sum_{n=1}^M \\mathrm{tr} \\left( \\frac{\\partial f_n}{\\partial \\mathbf{z}} \\right) $$\n",
    "\n",
    "The paper https://arxiv.org/pdf/1806.07366.pdf uses $M=64$.\n",
    "\n",
    "Currently reading https://github.com/rtqichen/torchdiffeq/blob/master/examples/cnf.py to determine CNF architecture and hyperparameter settings.\n",
    "\n",
    "That repo implements the CNF by first defining a `hypernet: t->W` which outputs a set of weights. In Jax we'll have `hypernet: (t,H)->W`. The CNF is then defined as `f: (t,H,z)-> dz/dt, dlogp_z/dt`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "951bbe75-9b34-40f6-8a6b-d3957a024c8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initialised parameter shapes:\n",
      " {'params': {'Dense_0': {'bias': (32,), 'kernel': (1, 32)}, 'Dense_1': {'bias': (32,), 'kernel': (32, 32)}, 'Dense_2': {'bias': (448,), 'kernel': (32, 448)}}}\n",
      "output:\n",
      " ['(64, 2, 1)', '(64, 1, 1)', '(64, 1, 2)']\n"
     ]
    }
   ],
   "source": [
    "from flax.core import freeze,unfreeze\n",
    "\n",
    "class HyperNetwork(nn.Module):\n",
    "    in_out_dim: int\n",
    "    hidden_dim: int\n",
    "    width: int\n",
    "        \n",
    "    @property\n",
    "    def blocksize(self): return self.width*self.in_out_dim\n",
    "    \n",
    "    @nn.compact\n",
    "    def __call__(self, inputs):\n",
    "        # predict params\n",
    "        x = inputs\n",
    "        features = [self.hidden_dim, self.hidden_dim, 3*self.blocksize + self.width]\n",
    "        for i,feat in enumerate(features):\n",
    "            x = nn.Dense(feat)(x)\n",
    "            if i!= 2:\n",
    "                x = nn.tanh(x)\n",
    "                \n",
    "        # restructure\n",
    "        x = x.reshape(-1)\n",
    "        W = x[:self.blocksize].reshape(self.width, self.in_out_dim, 1) \n",
    "        \n",
    "        U = x[self.blocksize:2*self.blocksize].reshape(self.width, 1, self.in_out_dim) \n",
    "        G = x[2*self.blocksize:3*self.blocksize].reshape(self.width, 1, self.in_out_dim) \n",
    "        U = U * nn.sigmoid(G)\n",
    "        \n",
    "        B = x[3*self.blocksize:].reshape(self.width, 1, 1)\n",
    "        \n",
    "        return [W,B,U]\n",
    "    \n",
    "key1,key2 = random.split(random.PRNGKey(0), 2)\n",
    "x = random.uniform(key1, (1,1))\n",
    "\n",
    "hidden_dim = 32\n",
    "width = 64\n",
    "\n",
    "hyper_net = HyperNetwork(2, hidden_dim, width)\n",
    "params = hyper_net.init(key2,x)\n",
    "y = hyper_net.apply(params, x)\n",
    "print('initialised parameter shapes:\\n', jax.tree_map(jnp.shape, unfreeze(params)))\n",
    "print('output:\\n', [f'{t.shape}' for t in y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "01e25d9b-4abf-4466-9361-0f597a4d700c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(2,), ()]\n",
      "[(2,), ()]\n",
      "initialised parameter shapes:\n",
      " {'params': {'hyper_net': {'Dense_0': {'bias': (32,), 'kernel': (1, 32)}, 'Dense_1': {'bias': (32,), 'kernel': (32, 32)}, 'Dense_2': {'bias': (448,), 'kernel': (32, 448)}}}}\n",
      "output:\n",
      " ['(2,)', '()']\n"
     ]
    }
   ],
   "source": [
    "class CNF(nn.Module):\n",
    "    in_out_dim: int\n",
    "    hidden_dim: int\n",
    "    width: int\n",
    "    \n",
    "    def setup(self):\n",
    "        self.hyper_net = HyperNetwork(self.in_out_dim,self.hidden_dim,self.width)\n",
    "    \n",
    "    def __call__(self, inputs, *t):\n",
    "        z = inputs[0]\n",
    "        logp_z = inputs[1]\n",
    "        \n",
    "        W,B,U = self.hyper_net(t)\n",
    "        \n",
    "        z_blocks = compute_zblocks(W,B,U,t,z)\n",
    "        z_blocks_grad = jax.jacfwd(compute_zblocks,-1)(W,B,U,t,z)\n",
    "        \n",
    "        dz_dt = z_blocks.mean(0)\n",
    "        d_log_p_dt = -jnp.einsum('mjj->m',z_blocks_grad).mean(0)\n",
    "        \n",
    "        print(f'{[t.shape for t in (dz_dt, d_log_p_dt)]}')\n",
    "        \n",
    "        return (dz_dt,d_log_p_dt)\n",
    "    \n",
    "def compute_zblocks(W,B,U,t,z):\n",
    "    Z = jnp.expand_dims(z, 0)\n",
    "    h = nn.tanh(Z@W + B)\n",
    "    z_blocks = (h@U).squeeze(1)\n",
    "    return z_blocks\n",
    "    \n",
    "key1,key2 = random.split(random.PRNGKey(0), 2)\n",
    "\n",
    "in_out_dim = 2\n",
    "hidden_dim = 32\n",
    "width = 64\n",
    "\n",
    "key1,(z,log_pdiff) = get_batch(1,U1,key1)\n",
    "t = jnp.zeros((1,))\n",
    "\n",
    "cnf = CNF(in_out_dim, hidden_dim, width)\n",
    "params = cnf.init(key2,(z[0],log_pdiff[0]),t)\n",
    "y = cnf.apply(params,(z[0],log_pdiff[0]),t)\n",
    "print('initialised parameter shapes:\\n', jax.tree_map(jnp.shape, unfreeze(params)))\n",
    "print('output:\\n', [f'{t.shape}' for t in y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "150d2ae1-a187-4c7c-96de-0280b2202727",
   "metadata": {},
   "outputs": [],
   "source": [
    "from jax.experimental.ode import odeint\n",
    "from functools import partial\n",
    "\n",
    "def full_cnf(params,inputs):\n",
    "    start_and_end_times = jnp.array([0.,1.])\n",
    "    cnf = CNF(in_out_dim, hidden_dim, width)\n",
    "    cnf_func = partial(cnf.apply,params) \n",
    "    print(f'{[t.shape for t in inputs]}')\n",
    "    init_state, final_state = odeint(cnf_func, inputs, start_and_end_times, atol=1e-3, rtol=1e-3)\n",
    "    return final_state\n",
    "\n",
    "def cnf_loss(params, inputs):\n",
    "    def single_loss(params, inputs):\n",
    "        _,log_pz0 = inputs\n",
    "        z1,delta_log_pz1 = full_cnf(params,inputs)\n",
    "        log_pz1 = log_pz0 + delta_log_pz1\n",
    "        loss = -log_pz1.mean()\n",
    "        return loss\n",
    "        \n",
    "    full_loss = jax.vmap(single_loss, in_axes=(None,0))(params,inputs)\n",
    "    return full_loss\n",
    "\n",
    "\n",
    "key,key_init = random.split(random.PRNGKey(0))\n",
    "\n",
    "key,(z,log_pdiff) = get_batch(1,U1,key)\n",
    "t = jnp.zeros((1,))\n",
    "\n",
    "params = cnf.init(key_init,(z[0],log_pdiff[0]),t)\n",
    "\n",
    "n_samples = 10\n",
    "U_func = U1\n",
    "\n",
    "def train_step(key, params)\n",
    "    key, inputs = get_batch(n_samples, U_func, key)\n",
    "    cnf_loss(params, inputs)\n",
    "    \n",
    "    return key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "8f5ca7cc-47de-4052-bb85-7e239e59ab80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[0.29765356, 0.508113  ],\n",
       "             [0.301397  , 0.5101015 ]], dtype=float32)"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50ce2e82-4a4e-4781-b50b-1d33c8ad5845",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_iters = 10\n",
    "\n",
    "for i in range(n_iters):\n",
    "    "
   ]
  }
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