10b_mixup_label_smoothing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mixup / Label smoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export\n",
    "from exp.nb_10 import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = datasets.untar_data(datasets.URLs.IMAGENETTE_160)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "tfms = [make_rgb, ResizeFixed(128), to_byte_tensor, to_float_tensor]\n",
    "bs = 64\n",
    "\n",
    "il = ImageList.from_files(path, tfms=tfms)\n",
    "sd = SplitData.split_by_func(il, partial(grandparent_splitter, valid_name='val'))\n",
    "ll = label_by_func(sd, parent_labeler, proc_y=CategoryProcessor())\n",
    "data = ll.to_databunch(bs, c_in=3, c_out=10, num_workers=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mixup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Jump_to lesson 12 video](https://course.fast.ai/videos/?lesson=12&t=226)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is mixup?\n",
    "\n",
    "As the name kind of suggests, the authors of the [mixup article](https://arxiv.org/abs/1710.09412) propose to train the model on a mix of the pictures of the training set. Let's say we're on CIFAR10 for instance, then instead of feeding the model the raw images, we take two (which could be in the same class or not) and do a linear combination of them: in terms of tensor it's\n",
    "``` python\n",
    "new_image = t * image1 + (1-t) * image2\n",
    "```\n",
    "where t is a float between 0 and 1. Then the target we assign to that image is the same combination of the original targets:\n",
    "``` python\n",
    "new_target = t * target1 + (1-t) * target2\n",
    "```\n",
    "assuming your targets are one-hot encoded (which isn't the case in pytorch usually). And that's as simple as this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=160x160 at 0x19817B59908>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img1 = PIL.Image.open(ll.train.x.items[0])\n",
    "img1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=160x160 at 0x19817F597F0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img2 = PIL.Image.open(ll.train.x.items[4000])\n",
    "img2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mixed_up = ll.train.x[0] * 0.3 + ll.train.x[4000] * 0.7\n",
    "plt.imshow(mixed_up.permute(1,2,0));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "French horn or tench? The right answer is 70% french horn and 30% tench ;)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Jump_to lesson 12 video](https://course.fast.ai/videos/?lesson=12&t=490)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implementation relies on something called the *beta distribution* which in turns uses something which Jeremy still finds mildly terrifying called the *gamma function*. To get over his fears, Jeremy reminds himself that *gamma* is just a factorial function that (kinda) interpolates nice and smoothly to non-integers too. How it does that exactly isn't important..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# PyTorch has a log-gamma but not a gamma, so we'll create one\n",
    "Γ = lambda x: x.lgamma().exp()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NB: If you see math symbols you don't know you can google them like this: [Γ function](https://www.google.com/search?q=Γ+function).\n",
    "\n",
    "If you're not used to typing unicode symbols, on Mac type <kbd>ctrl</kbd>-<kbd>cmd</kbd>-<kbd>space</kbd> to bring up a searchable emoji box. On Linux you can use the [compose key](https://help.ubuntu.com/community/ComposeKey). On Windows you can also use a compose key, but you first need to install [WinCompose](https://github.com/samhocevar/wincompose). By default the <kbd>compose</kbd> key is the right-hand <kbd>Alt</kbd> key.\n",
    "\n",
    "You can search for symbol names in WinCompose. The greek letters are generally <kbd>compose</kbd>-<kbd>\\*</kbd>-<kbd>letter</kbd> (where *letter* is, for instance, <kbd>a</kbd> to get greek α alpha)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "facts = [math.factorial(i) for i in range(7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(7), facts, 'ro')\n",
    "plt.plot(torch.linspace(0,6), Γ(torch.linspace(0,6)+1))\n",
    "plt.legend(['factorial','Γ']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.0000, 0.1000, 0.2000, 0.3000, 0.4000, 0.5000, 0.6000, 0.7000, 0.8000,\n",
       "        0.9000])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.linspace(0,0.9,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the original article, the authors suggested three things:\n",
    " 1. Create two separate dataloaders and draw a batch from each at every iteration to mix them up\n",
    " 2. Draw a t value following a beta distribution with a parameter α (0.4 is suggested in their article)\n",
    " 3. Mix up the two batches with the same value t.\n",
    " 4. Use one-hot encoded targets\n",
    "\n",
    "Why the beta distribution with the same parameters α? Well it looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_,axs = plt.subplots(1,2, figsize=(12,4))\n",
    "x = torch.linspace(0,1, 100)\n",
    "for α,ax in zip([0.1,0.8], axs):\n",
    "    α = tensor(α)\n",
    "#     y = (x.pow(α-1) * (1-x).pow(α-1)) / (gamma_func(α ** 2) / gamma_func(α))\n",
    "    y = (x**(α-1) * (1-x)**(α-1)) / (Γ(α)**2 / Γ(2*α))\n",
    "    ax.plot(x,y)\n",
    "    ax.set_title(f\"α={α:.1}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a low `α`, we pick values close to 0. and 1. with a high probability, and the values in the middle  all have the same kind of probability. With a greater `α`, 0. and 1. get a lower probability ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the approach above works very well, it's not the fastest way we can do this. The main point that slows down this process is wanting two different batches at every iteration (which means loading twice the amount of images and applying to them the other data augmentation function). To avoid this slow down, we can be a little smarter and mixup a batch with a shuffled version of itself (this way the images mixed up are still different). This was a trick suggested in the MixUp paper.\n",
    "\n",
    "Then pytorch was very careful to avoid one-hot encoding targets when it could, so it seems a bit of a drag to undo this. Fortunately for us, if the loss is a classic cross-entropy, we have\n",
    "```python\n",
    "loss(output, new_target) = t * loss(output, target1) + (1-t) * loss(output, target2)\n",
    "```\n",
    "so we won't one-hot encode anything and just compute those two losses then do the linear combination.\n",
    "\n",
    "Using the same parameter t for the whole batch also seemed a bit inefficient. In our experiments, we noticed that the model can train faster if we draw a different t for every image in the batch (both options get to the same result in terms of accuracy, it's just that one arrives there more slowly).\n",
    "The last trick we have to apply with this is that there can be some duplicates with this strategy: let's say or shuffle say to mix image0 with image1 then image1 with image0, and that we draw t=0.1 for the first, and t=0.9 for the second. Then\n",
    "```python\n",
    "image0 * 0.1 + shuffle0 * (1-0.1) = image0 * 0.1 + image1 * 0.9\n",
    "image1 * 0.9 + shuffle1 * (1-0.9) = image1 * 0.9 + image0 * 0.1\n",
    "```\n",
    "will be the same. Of course, we have to be a bit unlucky but in practice, we saw there was a drop in accuracy by using this without removing those near-duplicates. To avoid them, the tricks is to replace the vector of parameters we drew by\n",
    "``` python\n",
    "t = max(t, 1-t)\n",
    "```\n",
    "The beta distribution with the two parameters equal is symmetric in any case, and this way we insure that the biggest coefficient is always near the first image (the non-shuffled batch).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In `Mixup` we have handle loss functions that have an attribute `reduction` (like `nn.CrossEntropy()`). To deal with the `reduction=None` with various types of loss function without modifying the actual loss function outside of the scope we need to perform those operations with no reduction, we create a context manager:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export\n",
    "class NoneReduce():\n",
    "    def __init__(self, loss_func): \n",
    "        self.loss_func,self.old_red = loss_func,None\n",
    "        \n",
    "    def __enter__(self):\n",
    "        if hasattr(self.loss_func, 'reduction'):\n",
    "            self.old_red = getattr(self.loss_func, 'reduction')\n",
    "            setattr(self.loss_func, 'reduction', 'none')\n",
    "            return self.loss_func\n",
    "        else: return partial(self.loss_func, reduction='none')\n",
    "        \n",
    "    def __exit__(self, type, value, traceback):\n",
    "        if self.old_red is not None: setattr(self.loss_func, 'reduction', self.old_red)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can use it in `MixUp`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export\n",
    "from torch.distributions.beta import Beta\n",
    "\n",
    "def unsqueeze(input, dims):\n",
    "    for dim in listify(dims): input = torch.unsqueeze(input, dim)\n",
    "    return input\n",
    "\n",
    "def reduce_loss(loss, reduction='mean'):\n",
    "    return loss.mean() if reduction=='mean' else loss.sum() if reduction=='sum' else loss    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export\n",
    "class MixUp(Callback):\n",
    "    _order = 90 #Runs after normalization and cuda\n",
    "    def __init__(self, α:float=0.4): self.distrib = Beta(tensor([α]), tensor([α]))\n",
    "    \n",
    "    def begin_fit(self): self.old_loss_func,self.run.loss_func = self.run.loss_func,self.loss_func\n",
    "    \n",
    "    def begin_batch(self):\n",
    "        if not self.in_train: return #Only mixup things during training\n",
    "        λ = self.distrib.sample((self.yb.size(0),)).squeeze().to(self.xb.device)\n",
    "        λ = torch.stack([λ, 1-λ], 1)\n",
    "        self.λ = unsqueeze(λ.max(1)[0], (1,2,3))\n",
    "        shuffle = torch.randperm(self.yb.size(0)).to(self.xb.device)\n",
    "        xb1,self.yb1 = self.xb[shuffle],self.yb[shuffle]\n",
    "        self.run.xb = lin_comb(self.xb, xb1, self.λ)\n",
    "        \n",
    "    def after_fit(self): self.run.loss_func = self.old_loss_func\n",
    "    \n",
    "    def loss_func(self, pred, yb):\n",
    "        if not self.in_train: return self.old_loss_func(pred, yb)\n",
    "        with NoneReduce(self.old_loss_func) as loss_func:\n",
    "            loss1 = loss_func(pred, yb)\n",
    "            loss2 = loss_func(pred, self.yb1)\n",
    "        loss = lin_comb(loss1, loss2, self.λ)\n",
    "        return reduce_loss(loss, getattr(self.old_loss_func, 'reduction', 'mean'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "nfs = [32,64,128,256,512]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_learner(nfs, data, lr, layer, loss_func=F.cross_entropy,\n",
    "                cb_funcs=None, opt_func=optim.SGD, **kwargs):\n",
    "    model = get_cnn_model(data, nfs, layer, **kwargs)\n",
    "    init_cnn(model)\n",
    "    return Learner(model, data, loss_func, lr=lr, cb_funcs=cb_funcs, opt_func=opt_func)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "cbfs = [partial(AvgStatsCallback,accuracy),\n",
    "        CudaCallback, \n",
    "        ProgressCallback,\n",
    "        partial(BatchTransformXCallback, norm_imagenette),\n",
    "        MixUp]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "learn = get_learner(nfs, data, 0.4, conv_layer, cb_funcs=cbfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.826746</td>\n",
       "      <td>0.249651</td>\n",
       "      <td>3.599925</td>\n",
       "      <td>0.266000</td>\n",
       "      <td>00:46</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.fit(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.941251</td>\n",
       "      <td>0.244998</td>\n",
       "      <td>2.846736</td>\n",
       "      <td>0.270000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.958097</td>\n",
       "      <td>0.228944</td>\n",
       "      <td>2.375943</td>\n",
       "      <td>0.302000</td>\n",
       "      <td>00:41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>3.061006</td>\n",
       "      <td>0.208314</td>\n",
       "      <td>2.677350</td>\n",
       "      <td>0.214000</td>\n",
       "      <td>00:41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.898490</td>\n",
       "      <td>0.243602</td>\n",
       "      <td>2.305692</td>\n",
       "      <td>0.232000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.874297</td>\n",
       "      <td>0.256786</td>\n",
       "      <td>2.297105</td>\n",
       "      <td>0.352000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.878167</td>\n",
       "      <td>0.244532</td>\n",
       "      <td>4.278208</td>\n",
       "      <td>0.262000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.970739</td>\n",
       "      <td>0.219404</td>\n",
       "      <td>2.329896</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.844333</td>\n",
       "      <td>0.248333</td>\n",
       "      <td>9.874415</td>\n",
       "      <td>0.212000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>3.028004</td>\n",
       "      <td>0.212735</td>\n",
       "      <td>3.071312</td>\n",
       "      <td>0.198000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>3.015177</td>\n",
       "      <td>0.222351</td>\n",
       "      <td>3.155881</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for jj in range(10):\n",
    "    learn = get_learner(nfs, data, 0.4, conv_layer, cb_funcs=cbfs)\n",
    "    learn.fit(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.2612) tensor(0.0506)\n"
     ]
    }
   ],
   "source": [
    "# mean and std dev \n",
    "validation = torch.FloatTensor([0.270, 0.302, 0.214, 0.232, 0.352, 0.262, 0.320, 0.212, 0.198, 0.250])\n",
    "print(validation.mean(), validation.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Questions: How does softmax interact with all this? Should we jump straight from mixup to inference?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Label smoothing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another regularization technique that's often used is label smoothing. It's designed to make the model a little bit less certain of it's decision by changing a little bit its target: instead of wanting to predict 1 for the correct class and 0 for all the others, we ask it to predict `1-ε` for the correct class and `ε` for all the others, with `ε` a (small) positive number and N the number of classes. This can be written as:\n",
    "\n",
    "$$loss = (1-ε) ce(i) + ε \\sum ce(j) / N$$\n",
    "\n",
    "where `ce(x)` is cross-entropy of `x` (i.e. $-\\log(p_{x})$), and `i` is the correct class. This can be coded in a loss function:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Jump_to lesson 12 video](https://course.fast.ai/videos/?lesson=12&t=1121)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "#export\n",
    "class LabelSmoothingCrossEntropy(nn.Module):\n",
    "    def __init__(self, ε:float=0.1, reduction='mean'):\n",
    "        super().__init__()\n",
    "        self.ε,self.reduction = ε,reduction\n",
    "    \n",
    "    def forward(self, output, target):\n",
    "        c = output.size()[-1]\n",
    "        log_preds = F.log_softmax(output, dim=-1)\n",
    "        loss = reduce_loss(-log_preds.sum(dim=-1), self.reduction)\n",
    "        nll = F.nll_loss(log_preds, target, reduction=self.reduction)\n",
    "        return lin_comb(loss/c, nll, self.ε)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: we implement the various reduction attributes so that it plays nicely with MixUp after."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "cbfs = [partial(AvgStatsCallback,accuracy),\n",
    "        CudaCallback,\n",
    "        ProgressCallback,\n",
    "        partial(BatchTransformXCallback, norm_imagenette)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "learn = get_learner(nfs, data, 0.4, conv_layer, cb_funcs=cbfs, loss_func=LabelSmoothingCrossEntropy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.959759</td>\n",
       "      <td>0.237475</td>\n",
       "      <td>3.106079</td>\n",
       "      <td>0.262000</td>\n",
       "      <td>00:41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.842752</td>\n",
       "      <td>0.264697</td>\n",
       "      <td>2.673313</td>\n",
       "      <td>0.260000</td>\n",
       "      <td>00:41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>3.017319</td>\n",
       "      <td>0.237397</td>\n",
       "      <td>2.489758</td>\n",
       "      <td>0.254000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.798567</td>\n",
       "      <td>0.285869</td>\n",
       "      <td>2.140577</td>\n",
       "      <td>0.394000</td>\n",
       "      <td>00:41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.788396</td>\n",
       "      <td>0.289980</td>\n",
       "      <td>2.631723</td>\n",
       "      <td>0.298000</td>\n",
       "      <td>00:41</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.940310</td>\n",
       "      <td>0.263921</td>\n",
       "      <td>4.108496</td>\n",
       "      <td>0.288000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.895419</td>\n",
       "      <td>0.266558</td>\n",
       "      <td>5.307915</td>\n",
       "      <td>0.216000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.914987</td>\n",
       "      <td>0.259811</td>\n",
       "      <td>2.442337</td>\n",
       "      <td>0.318000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.898996</td>\n",
       "      <td>0.263456</td>\n",
       "      <td>2.841800</td>\n",
       "      <td>0.302000</td>\n",
       "      <td>00:44</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>train_accuracy</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>valid_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>2.974465</td>\n",
       "      <td>0.260276</td>\n",
       "      <td>141.745484</td>\n",
       "      <td>0.146000</td>\n",
       "      <td>00:42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# quantify results\n",
    "for jj in range(10):\n",
    "    learn = get_learner(nfs, data, 0.4, conv_layer, cb_funcs=cbfs, loss_func=LabelSmoothingCrossEntropy())\n",
    "    learn.fit(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can check our loss function `reduction` attribute hasn't changed outside of the training loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(0.2926) tensor(0.0408)\n",
      "tensor(0.2738) tensor(0.0653)\n"
     ]
    }
   ],
   "source": [
    "# mean and std dev \n",
    "validation = torch.FloatTensor([0.252, 0.334, 0.250, 0.286, 0.264, 0.238, 0.340, 0.302, 0.350, 0.310])\n",
    "print(validation.mean(), validation.std())\n",
    "validation = torch.FloatTensor([0.262, 0.260, 0.254, 0.394, 0.298, 0.288, 0.216, 0.318, 0.302, 0.146])\n",
    "print(validation.mean(), validation.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert learn.loss_func.reduction == 'mean'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Export"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "'.' is not recognized as an internal or external command,\n",
      "operable program or batch file.\n"
     ]
    }
   ],
   "source": [
    "!./notebook2script.py 10b_mixup_label_smoothing.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}