notebooks-4/2-rnn-scratch.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "# Implementation of Recurrent Neural Networks from Scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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     "end_time": "2019-07-03T22:57:59.652142Z",
     "start_time": "2019-07-03T22:57:58.005167Z"
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   "source": [
    "%matplotlib inline\n",
    "import d2l\n",
    "import math\n",
    "from mxnet import autograd, np, npx, gluon\n",
    "npx.set_np()\n",
    "\n",
    "batch_size, num_steps = 32, 35\n",
    "train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "One-hot encoding: map each token to a unique unit vector. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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     "end_time": "2019-07-03T22:57:59.666677Z",
     "start_time": "2019-07-03T22:57:59.654202Z"
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    "attributes": {
     "classes": [],
     "id": "",
     "n": "21"
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   "outputs": [
    {
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      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npx.one_hot(np.array([0, 2]), len(vocab))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Map a (batch size, time step) mini-batch to (time step, batch size, vocabulary size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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     "start_time": "2019-07-03T22:57:59.668386Z"
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    "attributes": {
     "classes": [],
     "id": "",
     "n": "18"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 2, 28)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.arange(10).reshape((2, 5))\n",
    "npx.one_hot(X.T, 28).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Initializing the model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:57:59.681788Z",
     "start_time": "2019-07-03T22:57:59.675320Z"
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   "source": [
    "def get_params(vocab_size, num_hiddens, ctx):\n",
    "    num_inputs = num_outputs = vocab_size\n",
    "    normal = lambda shape: np.random.normal(\n",
    "        scale=0.01, size=shape, ctx=ctx)\n",
    "    # Hidden layer parameters\n",
    "    W_xh = normal((num_inputs, num_hiddens))\n",
    "    W_hh = normal((num_hiddens, num_hiddens))\n",
    "    b_h = np.zeros(num_hiddens, ctx=ctx)\n",
    "    # Output layer parameters\n",
    "    W_hq = normal((num_hiddens, num_outputs))\n",
    "    b_q = np.zeros(num_outputs, ctx=ctx)\n",
    "    # Attach a gradient\n",
    "    params = [W_xh, W_hh, b_h, W_hq, b_q]\n",
    "    for param in params: param.attach_grad()\n",
    "    return params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Initialize the hidden state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:57:59.686448Z",
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   "outputs": [],
   "source": [
    "def init_rnn_state(batch_size, num_hiddens, ctx):\n",
    "    return (np.zeros(shape=(batch_size, num_hiddens), ctx=ctx), )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The forward function for one time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:57:59.692239Z",
     "start_time": "2019-07-03T22:57:59.687818Z"
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    "attributes": {
     "classes": [],
     "id": "",
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   },
   "outputs": [],
   "source": [
    "def rnn(inputs, state, params):\n",
    "    # inputs shape: (num_steps, batch_size, vocab_size)\n",
    "    W_xh, W_hh, b_h, W_hq, b_q = params\n",
    "    H, = state\n",
    "    outputs = []\n",
    "    for X in inputs:\n",
    "        H = np.tanh(np.dot(X, W_xh) + np.dot(H, W_hh) + b_h)\n",
    "        Y = np.dot(H, W_hq) + b_q\n",
    "        outputs.append(Y)\n",
    "    return np.concatenate(outputs, axis=0), (H,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Wrap these functions and store parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:57:59.698680Z",
     "start_time": "2019-07-03T22:57:59.693585Z"
    }
   },
   "outputs": [],
   "source": [
    "class RNNModelScratch(object):\n",
    "    def __init__(self, vocab_size, num_hiddens, ctx,\n",
    "                 get_params, init_state, forward):\n",
    "        self.vocab_size, self.num_hiddens = vocab_size, num_hiddens\n",
    "        self.params = get_params(vocab_size, num_hiddens, ctx)\n",
    "        self.init_state, self.forward_fn = init_state, forward\n",
    "\n",
    "    def __call__(self, X, state):\n",
    "        X = npx.one_hot(X.T, self.vocab_size)\n",
    "        return self.forward_fn(X, state, self.params)\n",
    "\n",
    "    def begin_state(self, batch_size, ctx):\n",
    "        return self.init_state(batch_size, self.num_hiddens, ctx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Check whether inputs and outputs have the correct dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:58:03.222717Z",
     "start_time": "2019-07-03T22:57:59.700717Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10, 28), 1, (2, 512))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vocab_size, num_hiddens, ctx = len(vocab), 512, d2l.try_gpu()\n",
    "model = RNNModelScratch(len(vocab), num_hiddens, ctx, get_params,\n",
    "                        init_rnn_state, rnn)\n",
    "state = model.begin_state(X.shape[0], ctx)\n",
    "Y, new_state = model(X.as_in_context(ctx), state)\n",
    "Y.shape, len(new_state), new_state[0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Predicting the next `num_predicts` characters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:58:03.230183Z",
     "start_time": "2019-07-03T22:58:03.224452Z"
    }
   },
   "outputs": [],
   "source": [
    "def predict_ch8(prefix, num_predicts, model, vocab, ctx):\n",
    "    state = model.begin_state(batch_size=1, ctx=ctx)\n",
    "    outputs = [vocab[prefix[0]]]\n",
    "    get_input = lambda: np.array([outputs[-1]], ctx=ctx).reshape((1, 1))\n",
    "    for y in prefix[1:]:  # Warmup state with prefix\n",
    "        _, state = model(get_input(), state)\n",
    "        outputs.append(vocab[y])\n",
    "    for _ in range(num_predicts):  # Predict num_predicts steps\n",
    "        Y, state = model(get_input(), state)\n",
    "        outputs.append(int(Y.argmax(axis=1).reshape(1)))\n",
    "    return ''.join([vocab.idx_to_token[i] for i in outputs])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Gradient clipping:\n",
    "\n",
    "$$\\mathbf{g} \\leftarrow \\min\\left(1, \\frac{\\theta}{\\|\\mathbf{g}\\|}\\right) \\mathbf{g}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:58:03.235877Z",
     "start_time": "2019-07-03T22:58:03.231513Z"
    },
    "attributes": {
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   },
   "outputs": [],
   "source": [
    "def grad_clipping(model, theta):\n",
    "    if isinstance(model, gluon.Block):\n",
    "        params = [p.data() for p in model.collect_params().values()]\n",
    "    else:\n",
    "        params = model.params\n",
    "    norm = math.sqrt(sum((p.grad ** 2).sum() for p in params))\n",
    "    if norm > theta:\n",
    "        for param in params:\n",
    "            param.grad[:] *= theta / norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Training one epoch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:58:03.243416Z",
     "start_time": "2019-07-03T22:58:03.237209Z"
    }
   },
   "outputs": [],
   "source": [
    "def train_epoch_ch8(model, train_iter, loss, updater, ctx):\n",
    "    state, timer = None, d2l.Timer()\n",
    "    metric = d2l.Accumulator(2)  # loss_sum, num_examples\n",
    "    for X, Y in train_iter:\n",
    "        if not state:\n",
    "            state = model.begin_state(batch_size=X.shape[0], ctx=ctx)\n",
    "        y = Y.T.reshape((-1,))\n",
    "        X, y = X.as_in_context(ctx), y.as_in_context(ctx)\n",
    "        with autograd.record():\n",
    "            py, state = model(X, state)\n",
    "            l = loss(py, y).mean()\n",
    "        l.backward()\n",
    "        grad_clipping(model, 1)\n",
    "        updater(batch_size=1)  # Since used mean already.\n",
    "        metric.add(l * y.size, y.size)\n",
    "    return math.exp(metric[0]/metric[1]), metric[1]/timer.stop()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The training function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T22:58:03.252788Z",
     "start_time": "2019-07-03T22:58:03.244750Z"
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   },
   "outputs": [],
   "source": [
    "def train_ch8(model, train_iter, vocab, lr, num_epochs, ctx):\n",
    "    # Initialize\n",
    "    loss = gluon.loss.SoftmaxCrossEntropyLoss()\n",
    "    animator = d2l.Animator(xlabel='epoch', ylabel='perplexity',\n",
    "                            legend=['train'], xlim=[1, num_epochs])\n",
    "    if isinstance(model, gluon.Block):\n",
    "        model.initialize(ctx=ctx, force_reinit=True, init=init.Normal(0.01))\n",
    "        trainer = gluon.Trainer(model.collect_params(), 'sgd', {'learning_rate': lr})\n",
    "        updater = lambda batch_size : trainer.step(batch_size)\n",
    "    else:\n",
    "        updater = lambda batch_size : d2l.sgd(model.params, lr, batch_size)\n",
    "\n",
    "    predict = lambda prefix: predict_ch8(prefix, 50, model, vocab, ctx)\n",
    "    # Train and check the progress.\n",
    "    for epoch in range(num_epochs):\n",
    "        ppl, speed = train_epoch_ch8(model, train_iter, loss, updater, ctx)\n",
    "        if epoch % 10 == 0:\n",
    "            print(predict('time traveller'))\n",
    "            animator.add(epoch+1, [ppl])\n",
    "    print('Perplexity %.1f, %d tokens/sec on %s' % (ppl, speed, ctx))\n",
    "    print(predict('time traveller'))\n",
    "    print(predict('traveller'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Finally we can train a model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-03T23:00:31.379846Z",
     "start_time": "2019-07-03T22:58:03.254109Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Perplexity 1.0, 32620 tokens/sec on gpu(0)\n",
      "time traveller for so it will be convenient to speak of him was \n",
      "traveller  it s against reason said filby  what reason said\n"
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