misc/graves_handwriting_generation.ipynb

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    "# Handwriting Generaton with Recurrent Neural Networks and Mixture of Gaussians\n",
    "\n",
    "*Thomas Viehmann* <tv@learnapparat.de>\n",
    "\n",
    "This is a PyTorch implementation of the handwriting generation in Alex Graves' classic paper [Generating Sequences with Recurrent Neural Networks](https://arxiv.org/abs/1308.0850).\n",
    "In addition to replicating the model, I wanted to explore recreating the visualisations that Graves uses.\n",
    "\n",
    "I also studied [Alexandre de Brébisson's Theano implementation](https://github.com/adbrebs/handwriting), but all errors are my own.\n",
    "\n",
    "I can highly recommend the original paper, I enjoyed reading it a lot.\n",
    "\n",
    "**Note:** This notebook is written using PyTorch 0.4 (master at the time of writing).\n",
    "\n",
    "At popular request, I have you can get [pretrained model weights](https://github.com/t-vi/pytorch-tvmisc/releases/download/2018-03-13/graves_handwriting_generation_2018-03-13-02-45epoch_49.hd5). Use them with the load_from_hdf5 code below. They are not particularly tweaked but just the ones that I got when I ran the notebook for the outputs you see below.\n",
    "\n",
    "## Overview\n",
    "Besically we have the following architecture (shown in the diagram):\n",
    "- The triplets of relative movements in $x$ and $y$ direction and $pen$ (note this is different to Graves' notation, who uses $x$ for the triple) and a (attention-) mixture $w$ of one-hot encoded characters are fed into an **LSTM**, producing a hidden state $h$.\n",
    "- The **Attention** takes the sequence of one-hot encoded characters ($c$ in Graves) and the hidden state $h$ to weight $c$ and give a new mixture $w$ of $c$ items. The attention component remembers the location of the attention modes.\n",
    "- A **Mixture Density Network** (see [a short notebook here](https://github.com/t-vi/pytorch-tvmisc/blob/master/misc/Mixture_Density_Network_Gaussian_1d.ipynb)) takes the LSTM output $h$ and the attention-modulated character information $w$ to compute a Gaussian density mixture for the coordinates and a Bernoulli parameter for pen up/pen down. In training the negative log likelihood of the actual movement and pen is used, and for prediction, movement and pen are sampled.\n",
    "- A module wraps the three components and steps through the sequence.\n",
    "\n",
    "(I honestly don't know how to make those esges between timesteps closer...)\n"
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       "<path fill=\"none\" stroke=\"black\" d=\"M414.149,-46.3728C424,-48.451 434.327,-50.4492 444.044,-52 482.868,-58.1959 586.817,-48.9858 620.044,-70 634.539,-79.1668 633.818,-87.0203 640.044,-103 701.694,-261.21 742.253,-326.302 674.044,-377 651.94,-393.429 577.491,-403.638 531.551,-408.531\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"530.962,-405.073 521.373,-409.577 531.679,-412.036 530.962,-405.073\"/>\n",
       "</g>\n",
       "<!-- h(t+1)&#45;&gt;GMMt+1 -->\n",
       "<g id=\"edge11\" class=\"edge\"><title>h(t+1)&#45;&gt;GMMt+1</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M334.704,-321.971C329.466,-291.9 321.263,-227.688 335.044,-176 337.621,-166.335 342.385,-156.602 347.419,-148.113\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"350.51,-149.774 352.896,-139.451 344.593,-146.033 350.51,-149.774\"/>\n",
       "</g>\n",
       "<!-- h(t+1)&#45;&gt;ATTt+1 -->\n",
       "<g id=\"edge9\" class=\"edge\"><title>h(t+1)&#45;&gt;ATTt+1</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M347.322,-322.533C352.079,-314.089 357.985,-303.605 363.344,-294.093\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"366.4,-295.799 368.259,-285.369 360.301,-292.363 366.4,-295.799\"/>\n",
       "</g>\n",
       "<!-- w(t+1)&#45;&gt;GMMt+1 -->\n",
       "<g id=\"edge13\" class=\"edge\"><title>w(t+1)&#45;&gt;GMMt+1</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M375.897,-175.813C374.428,-167.789 372.645,-158.047 371.001,-149.069\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"374.406,-148.235 369.162,-139.029 367.521,-149.496 374.406,-148.235\"/>\n",
       "</g>\n",
       "<!-- w(t+1)&#45;&gt;LSTMt+2 -->\n",
       "<g id=\"edge27\" class=\"edge\"><title>w(t+1)&#45;&gt;LSTMt+2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M408.971,-203.604C419.939,-206.551 432.493,-209.685 444.044,-212 582.472,-239.738 676.368,-197.027 742.044,-322 784.561,-402.904 610.125,-412.366 531.115,-412.604\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"531.085,-409.104 521.079,-412.586 531.072,-416.104 531.085,-409.104\"/>\n",
       "</g>\n",
       "<!-- h(t+2) -->\n",
       "<g id=\"node20\" class=\"node\"><title>h(t+2)</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"black\" cx=\"494.044\" cy=\"-340\" rx=\"33.2948\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"494.044\" y=\"-336.3\" font-family=\"Times,serif\" font-size=\"14.00\">h(t+2)</text>\n",
       "</g>\n",
       "<!-- LSTMt+2&#45;&gt;h(t+2) -->\n",
       "<g id=\"edge16\" class=\"edge\"><title>LSTMt+2&#45;&gt;h(t+2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M494.044,-394.813C494.044,-386.789 494.044,-377.047 494.044,-368.069\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"497.545,-368.029 494.044,-358.029 490.545,-368.029 497.545,-368.029\"/>\n",
       "</g>\n",
       "<!-- GMMt+2 -->\n",
       "<g id=\"node17\" class=\"node\"><title>GMMt+2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M563.544,-139C563.544,-139 480.544,-139 480.544,-139 474.544,-139 468.544,-133 468.544,-127 468.544,-127 468.544,-115 468.544,-115 468.544,-109 474.544,-103 480.544,-103 480.544,-103 563.544,-103 563.544,-103 569.544,-103 575.544,-109 575.544,-115 575.544,-115 575.544,-127 575.544,-127 575.544,-133 569.544,-139 563.544,-139\"/>\n",
       "<text text-anchor=\"middle\" x=\"522.044\" y=\"-117.3\" font-family=\"Times,serif\" font-size=\"14.00\">Mixture Density</text>\n",
       "</g>\n",
       "<!-- pts(t+2) -->\n",
       "<g id=\"node19\" class=\"node\"><title>pts(t+2)</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"black\" cx=\"522.044\" cy=\"-34\" rx=\"65.7887\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"522.044\" y=\"-30.3\" font-family=\"Times,serif\" font-size=\"14.00\">(X,Y,Pen)(t+2)</text>\n",
       "</g>\n",
       "<!-- GMMt+2&#45;&gt;pts(t+2) -->\n",
       "<g id=\"edge20\" class=\"edge\"><title>GMMt+2&#45;&gt;pts(t+2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" stroke-dasharray=\"5,2\" d=\"M522.044,-102.799C522.044,-91.1626 522.044,-75.5479 522.044,-62.2368\"/>\n",
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       "<text text-anchor=\"middle\" x=\"541.044\" y=\"-73.8\" font-family=\"Times,serif\" font-size=\"14.00\">predict</text>\n",
       "</g>\n",
       "<!-- w(t+2) -->\n",
       "<g id=\"node21\" class=\"node\"><title>w(t+2)</title>\n",
       "<ellipse fill=\"lightgrey\" stroke=\"black\" cx=\"535.044\" cy=\"-194\" rx=\"35.194\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"535.044\" y=\"-190.3\" font-family=\"Times,serif\" font-size=\"14.00\">w(t+2)</text>\n",
       "</g>\n",
       "<!-- ATTt+2&#45;&gt;w(t+2) -->\n",
       "<g id=\"edge18\" class=\"edge\"><title>ATTt+2&#45;&gt;w(t+2)</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M534.286,-248.813C534.399,-240.789 534.537,-231.047 534.663,-222.069\"/>\n",
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       "<!-- h(t+2)&#45;&gt;GMMt+2 -->\n",
       "<g id=\"edge17\" class=\"edge\"><title>h(t+2)&#45;&gt;GMMt+2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M490.704,-321.971C485.466,-291.9 477.263,-227.688 491.044,-176 493.621,-166.335 498.385,-156.602 503.419,-148.113\"/>\n",
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       "</g>\n",
       "<!-- h(t+2)&#45;&gt;ATTt+2 -->\n",
       "<g id=\"edge15\" class=\"edge\"><title>h(t+2)&#45;&gt;ATTt+2</title>\n",
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       "<!-- w(t+2)&#45;&gt;GMMt+2 -->\n",
       "<g id=\"edge19\" class=\"edge\"><title>w(t+2)&#45;&gt;GMMt+2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M531.897,-175.813C530.428,-167.789 528.645,-158.047 527.001,-149.069\"/>\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x7f8e690057f0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "g = graphviz.Digraph(graph_attr=dict(size=\"12,12\"))\n",
    "with g.subgraph() as dot:\n",
    "    g.node(\"pts(t-1)\",label=\"(X,Y,Pen)(t-1)\", shape=\"ellipse\", style=\"filled\")\n",
    "    g.node(\"txt\",label=\"Text\", style=\"filled\")\n",
    "    g.node(\"w(t-1)\", style=\"filled\")\n",
    "    g.edge(\"pts(t-1)\",\"txt\", style=\"invis\")\n",
    "    g.edge(\"txt\",\"w(t-1)\", style=\"invis\")\n",
    "for i,timestep in enumerate([\"t\",\"t+1\", \"t+2\"]):\n",
    "    with g.subgraph(name=\"cluster_{}\".format(timestep)) as dot:\n",
    "        dot.attr(label='Step {}'.format(timestep))\n",
    "        dot.attr(sortv=str(i+1))\n",
    "        dot.node(\"LSTM{}\".format(timestep),label=\"LSTM\", shape=\"box\", style=\"rounded\")\n",
    "        dot.node(\"GMM{}\".format(timestep),label=\"Mixture Density\", shape=\"box\", style=\"rounded\")\n",
    "        dot.node(\"ATT{}\".format(timestep),label=\"Attention\", shape=\"box\", style=\"rounded\")\n",
    "        dot.node(\"pts({})\".format(timestep),label=\"(X,Y,Pen)({})\".format(timestep), shape=\"ellipse\", style=\"filled\")\n",
    "        dot.node(\"h({})\".format(timestep), shape=\"ellipse\", style=\"filled\")\n",
    "        dot.node(\"w({})\".format(timestep), shape=\"ellipse\", style=\"filled\")\n",
    "        dot.edge(\"h({})\".format(timestep), \"ATT{}\".format(timestep))\n",
    "        dot.edge(\"LSTM{}\".format(timestep),\"h({})\".format(timestep))\n",
    "        dot.edge(\"h({})\".format(timestep), \"GMM{}\".format(timestep))\n",
    "        dot.edge(\"ATT{}\".format(timestep), \"w({})\".format(timestep))\n",
    "        dot.edge(\"w({})\".format(timestep), \"GMM{}\".format(timestep))\n",
    "        dot.edge(\"GMM{}\".format(timestep), \"pts({})\".format(timestep), style=\"dashed\", label=\"predict\")\n",
    "\n",
    "\n",
    "g.edge(\"pts(t-1)\", \"LSTMt\", constraint=\"false\")\n",
    "g.edge(\"w(t-1)\", \"LSTMt\", constraint=\"false\")\n",
    "g.edge(\"txt\", \"ATTt\", constraint=\"false\")\n",
    "g.edge(\"txt\", \"ATTt+1\", constraint=\"false\")\n",
    "g.edge(\"txt\", \"ATTt+2\", constraint=\"false\")\n",
    "g.edge(\"w(t)\",\"LSTMt+1\",constraint=\"false\")\n",
    "g.edge(\"w(t+1)\",\"LSTMt+2\",constraint=\"false\")\n",
    "g.edge(\"pts(t)\",\"LSTMt+1\",constraint=\"false\")\n",
    "g.edge(\"pts(t+1)\",\"LSTMt+2\",constraint=\"false\")\n",
    "g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "310E031C764B4EC1B2A85C6D4173F490"
   },
   "source": [
    "First let us import something."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cell_id": "310E031C764B4EC1B2A85C6D4173F490"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x7f8e0ec5f650>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "import sys\n",
    "import pickle\n",
    "import time\n",
    "import collections\n",
    "import numpy\n",
    "import IPython\n",
    "import cairocffi as cairo\n",
    "from matplotlib import pyplot\n",
    "import matplotlib\n",
    "import torchtext\n",
    "import tqdm\n",
    "import glob\n",
    "import lxml.etree\n",
    "%matplotlib inline\n",
    "import torch\n",
    "torch.manual_seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The dataset\n",
    "\n",
    "The [IAM Online Handwriting Database](http://www.fki.inf.unibe.ch/databases/iam-online-document-database/iam-online-document-database) is provided by [E. Indermühle, M. Liwicki, and H. Bunke: IAMonDo-database: an Online Handwritten Document Database with Non-uniform Contents. Proc 9th Int. Workshop on Document Analysis Systems, 2010.](http://www.fki.inf.unibe.ch/databases/iam-online-document-database/das10db.pdf).\n",
    "\n",
    "The set is split into a training and three test sets, the latter being labeled *v*, *f*, and *t*. Following Graves, Section 4, we use the *v* set as validation and combine the other three for training.\n",
    "\n",
    "I used to have a separate preprocessing notebook, but preprocessing takes less than 30 seconds for me, so I just moved it here..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "iam_dir = \"/home/datasets/iam-online-handwriting-database/\"\n",
    "orig_trainset = [l.strip() for l in open(os.path.join(iam_dir, \"trainset.txt\"))]\n",
    "orig_testset_v = [l.strip() for l in open(os.path.join(iam_dir, \"testset_v.txt\"))] # smallest\n",
    "orig_testset_f = [l.strip() for l in open(os.path.join(iam_dir, \"testset_f.txt\"))]\n",
    "orig_testset_t = [l.strip() for l in open(os.path.join(iam_dir, \"testset_t.txt\"))]\n",
    "\n",
    "trainset = orig_trainset + orig_testset_f + orig_testset_t\n",
    "validset = orig_testset_v\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset contains ascii files with the text and xml-based representations of the strokes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "blacklist = {\"a08-551z-08\",\"a08-551z-09\"} # these seem broken\n",
    "\n",
    "def process_set(theset):\n",
    "    txts = {}\n",
    "    for i,n in enumerate(theset):\n",
    "        txtfn = \"/home/datasets/iam-online-handwriting-database/ascii/{}/{}/{}.txt\".format(n[:3], n[:7], n)\n",
    "        for j,t in enumerate(open(txtfn).read().split(\"CSR:\")[1].strip().split(\"\\n\")):\n",
    "            txts['{}-{:02d}'.format(n,j+1)] = t\n",
    "    samples = {}\n",
    "    for i,n in tqdm.tqdm(enumerate(theset),total=len(theset)):\n",
    "        globmask = \"/home/datasets/iam-online-handwriting-database/lineStrokes/{}/{}/{}-*.xml\".format(n[:3], n[:7], n)\n",
    "        for fn in glob.glob(globmask):\n",
    "            key = (os.path.splitext(os.path.basename(fn))[0])\n",
    "            if key not in blacklist:\n",
    "                root = lxml.etree.parse(fn).getroot()\n",
    "                strokes_list = []\n",
    "                for s in root.find(\"StrokeSet\").findall(\"Stroke\"):\n",
    "                    pts = torch.FloatTensor([(float(p.attrib['x']), float(p.attrib['y']),0.0) for p in s.findall(\"Point\")])\n",
    "                    pts[-1,-1] = 1\n",
    "                    strokes_list.append(pts)\n",
    "                strokes = torch.cat(strokes_list, dim=0)\n",
    "                (min_x,min_y),_ = torch.min(strokes[:,:2],dim=0)\n",
    "                (max_x,max_y),_ = torch.max(strokes[:,:2],dim=0)\n",
    "                rel_strokes = torch.cat([torch.zeros(1,3),\n",
    "                                         torch.cat([strokes[1:,:2]-strokes[:-1,:2],strokes[1:,2:]],dim=1)], dim=0)\n",
    "                if rel_strokes.abs().max()<1000: # we assume that such large moves are broken\n",
    "                    samples[key] = {\"strokes\":strokes_list, \"minmax\":(min_x,min_y,max_x,max_y), \"rel_strokes\":rel_strokes,\n",
    "                                    \"txt\": txts[key]}\n",
    "    return samples\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1535/1535 [00:17<00:00, 88.31it/s]\n",
      "100%|██████████| 192/192 [00:02<00:00, 83.38it/s]\n"
     ]
    }
   ],
   "source": [
    "training_samples = process_set(trainset)\n",
    "#torch.save(training_samples, \"preprocessed-training.pt\")\n",
    "val_samples = process_set(validset)\n",
    "#torch.save(val_samples, \"preprocessed-validation.pt\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean \n",
      " 8.1842\n",
      " 0.1145\n",
      "[torch.FloatTensor of size (2,)]\n",
      " std \n",
      " 40.3660\n",
      " 37.0441\n",
      "[torch.FloatTensor of size (2,)]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = torch.cat([d[\"rel_strokes\"] for d in training_samples.values()], dim=0)\n",
    "mean,std = x[:,:2].mean(0),x[:,:2].std(0)\n",
    "print (\"mean\", mean, \"std\", std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use a torchtext dataset to use our preprocessed IAM online handwriting data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cell_id": "BB01C85EE70F4A9686266712878C69A9"
   },
   "outputs": [],
   "source": [
    "char_dict = {k:v for v,k in enumerate(' !\"#%&\\'()+,-./0123456789:;?ABCDEFGHIJKLMNOPQRSTUVWXYZ[]abcdefghijklmnopqrstuvwxyz')}\n",
    "inv_char_dict = {v:k for k,v in char_dict.items()}\n",
    "n_chars = len(char_dict)\n",
    "\n",
    "class DS(torchtext.data.Dataset):\n",
    "    def __init__(self, samples, mean, std):\n",
    "        self.myfields = [('txt',torchtext.data.Field(use_vocab=True,tokenize=list, eos_token='<eos>')), \n",
    "                         ('txtn',torchtext.data.Field(use_vocab=False,pad_token=0)), \n",
    "                         ('txtlen',torchtext.data.Field(use_vocab=False)),\n",
    "                         ('txtmask',torchtext.data.Field(use_vocab=False,pad_token=0, tensor_type=torch.FloatTensor)),\n",
    "                         ('xs',torchtext.data.Field(use_vocab=False, pad_token=-1, tensor_type=torch.FloatTensor)),\n",
    "                         ('ys',torchtext.data.Field(use_vocab=False, pad_token=-1, tensor_type=torch.FloatTensor)),\n",
    "                         ('pen',torchtext.data.Field(use_vocab=False,pad_token=-1)),\n",
    "                         ('ptslen',torchtext.data.Field(use_vocab=False))\n",
    "                        ]\n",
    "        self.coord_mean = mean\n",
    "        self.coord_std  = std\n",
    "        examples = []\n",
    "        for s in samples.values():\n",
    "            txt = [c for c in s[\"txt\"] if c in char_dict]\n",
    "            txtn = torch.LongTensor([char_dict[i] for i in txt])\n",
    "            txtlen = torch.LongTensor([len(txt)])\n",
    "            txtmask = torch.ones(len(txt))\n",
    "            stroke = s['rel_strokes']\n",
    "            xs = stroke[:,0]\n",
    "            ys = stroke[:,1]\n",
    "            pen = stroke[:,2]\n",
    "            ptslen = torch.LongTensor([len(pen)])\n",
    "            if xs.abs().max()<1000 and ys.abs().max()<1000 and len(txt)>=20:\n",
    "                xs = (xs-self.coord_mean[0])/self.coord_std[0]\n",
    "                ys = (ys-self.coord_mean[1])/self.coord_std[1]\n",
    "                examples.append(torchtext.data.Example.fromlist([txt, txtn, txtlen, txtmask,\n",
    "                                                            xs, ys, pen, ptslen\n",
    "                                                            ], self.myfields))        \n",
    "        super(DS, self).__init__(examples, self.myfields)\n",
    "        self.myfields[0][1].build_vocab(self)\n",
    "    def sort_key(self, ex):\n",
    "        return len(ex.txt)\n",
    "    def tensor_to_str(self,t):\n",
    "        return ''.join([self.fields['txt'].vocab.itos[c] for c in t if c >= 3])\n",
    "    def tensor_to_str2(self,t):\n",
    "        return ''.join([inv_char_dict[c] for c in t])\n",
    "\n",
    "train_ds = DS(training_samples, mean, std)\n",
    "val_ds   = DS(val_samples, mean, std)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is both a matplotlib-based and a cairo-based function to display a stroke.\n",
    "The cairo-based function is a lot faster and optionally add random shear and rotation, the matplotlib-based one offers color."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cell_id": "9C2DFE5CE8B645A28C47AAA32ED8CE32"
   },
   "outputs": [],
   "source": [
    "def show_stroke(x, colors=None):   \n",
    "    x= x[:(torch.arange(0,x.size(0))[x[:,2]>-0.0001].size(0))] # only used bits\n",
    "    stroke = (x[:,:2]*train_ds.coord_std.unsqueeze(0)+train_ds.coord_mean.unsqueeze(0)).cumsum(0)\n",
    "    stroke[:,1] *= -1\n",
    "    pen = x[:,2]\n",
    "    xmin,ymin = stroke.min(0)[0]\n",
    "    xmax,ymax = stroke.max(0)[0]\n",
    "    \n",
    "    actions = [matplotlib.path.Path.MOVETO]\n",
    "    coords = []\n",
    "    for c,p in zip(stroke, pen):\n",
    "        if p >=-0.0001:\n",
    "          if p==1 or len(actions)==0:\n",
    "            actions.append(matplotlib.path.Path.MOVETO)\n",
    "          else:\n",
    "            actions.append(matplotlib.path.Path.LINETO)\n",
    "          coords.append((c[0],c[1]))\n",
    "    actions = actions[:-1]\n",
    "    ax = pyplot.gca()\n",
    "    ax.set_xlim(xmin, xmax)\n",
    "    ax.set_ylim(ymin, ymax)\n",
    "\n",
    "    if colors is None:\n",
    "        path = matplotlib.path.Path(coords, actions)\n",
    "        patch = matplotlib.patches.PathPatch(path, facecolor='none')\n",
    "        ax.add_patch(patch)\n",
    "    else:\n",
    "        pos = coords[0]\n",
    "        curpos = pos\n",
    "        for pos,a,col in zip(coords, actions, colors):\n",
    "            if a == matplotlib.path.Path.LINETO:\n",
    "                ax.add_line(matplotlib.lines.Line2D((curpos[0],pos[0]), (curpos[1],pos[1]), axes=ax, color=col))\n",
    "            curpos = pos\n",
    "\n",
    "\n",
    "def stroke_to_image(x, target_size = (1280,64), randomize=False):\n",
    "    stroke = (x[:,:2]*train_ds.coord_std.unsqueeze(0)+train_ds.coord_mean.unsqueeze(0)).cumsum(0)\n",
    "    pen = x[:,2]\n",
    "    if randomize:\n",
    "        shear_prob = 0.5\n",
    "        shear_prec = 4.0\n",
    "        if torch.rand(1)[0] > shear_prob:\n",
    "            shear_sigma = 1/shear_prec**0.5\n",
    "            shear_theta = 0.5*torch.randn(1)    \n",
    "        else:\n",
    "            shear_theta = torch.zeros(1)\n",
    "        rot_prob = 0.5\n",
    "        rot_prec = 4.0\n",
    "        if torch.rand(1)[0] > rot_prob:\n",
    "            rot_sigma = 1/rot_prec**0.5\n",
    "            rot_theta = 0.5*torch.randn(1)    \n",
    "        else:\n",
    "            rot_theta = torch.zeros(1)\n",
    "\n",
    "        (min_x,min_y),_ = torch.min(stroke[:,:2],dim=0)\n",
    "        (max_x,max_y),_ = torch.max(stroke[:,:2],dim=0)\n",
    "        stroke[:,0] -= min_x\n",
    "        stroke[:,1] -= min_y  \n",
    "        min_x, min_y = 0.0,0.0\n",
    "        max_x, max_y = max_x-min_x, max_y-min_y\n",
    "\n",
    "        stroke[:,0] += stroke[:,1]*torch.sin(shear_theta)\n",
    "\n",
    "        stroke[:,0] = stroke[:,0]*torch.cos(rot_theta)+stroke[:,1]*torch.sin(rot_theta)\n",
    "        stroke[:,1] = stroke[:,1]*torch.cos(rot_theta)-stroke[:,0]*torch.sin(rot_theta)\n",
    "\n",
    "    (min_x,min_y),_ = torch.min(stroke[:,:2],dim=0)\n",
    "    (max_x,max_y),_ = torch.max(stroke[:,:2],dim=0)\n",
    "    stroke[:,0] -= min_x\n",
    "    stroke[:,1] -= min_y  \n",
    "    min_x, min_y = 0.0,0.0\n",
    "    max_x, max_y = max_x-min_x, max_y-min_y\n",
    "\n",
    "    factor = min(target_size[0]/max(max_x-min_x,0.001),target_size[1]/max(max_y-min_y,0.001),1)\n",
    "    xmin,ymin = stroke.min(0)[0]\n",
    "    xmax,ymax = stroke.max(0)[0]\n",
    "\n",
    "    imwidth, imheight = int(xmax*factor)+2, int(ymax*factor)+2\n",
    "    surface = cairo.ImageSurface (cairo.FORMAT_A8, imwidth, imheight)\n",
    "    ctx = cairo.Context(surface)\n",
    "\n",
    "    ctx.scale (factor, factor) # Normalizing the canvas\n",
    "    ctx.rectangle (0, 0, xmax+5/factor, ymax+5/factor) # Rectangle(x0, y0, x1, y1)\n",
    "    ctx.set_source_rgba (0.0, 0.0, 0.0, 0.0) # Solid color\n",
    "    ctx.fill ()\n",
    "    next_action = 1\n",
    "    coords = []\n",
    "    for c,p in zip(stroke, pen):\n",
    "        if p >=-0.0001:\n",
    "          if next_action:\n",
    "            ctx.move_to(c[0]+1,c[1]+1)\n",
    "          else:\n",
    "            ctx.line_to(c[0]+1,c[1]+1)\n",
    "          next_action = p>0.5\n",
    "    ctx.set_source_rgba(1.0, 1.0, 1.0, 1.0) # Solid color\n",
    "\n",
    "    \n",
    "    if randomize:\n",
    "        linewidth = (1+torch.rand(1)[0])/factor\n",
    "    else:\n",
    "        linewidth = 2/factor\n",
    "    ctx.set_line_width (linewidth)\n",
    "    ctx.stroke ()\n",
    "\n",
    "    buf = surface.get_data()\n",
    "    data = numpy.ndarray(shape=(imheight, (imwidth+3)//4*4),#(WIDTH+7)//8),\n",
    "                         dtype=numpy.uint8,\n",
    "                         buffer=buf)[:,:imwidth]\n",
    "    data = 1-(data>0)\n",
    "    data = torch.FloatTensor(data)\n",
    "    return data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "7FAF0988C7FF480982084244884101F3"
   },
   "source": [
    "Let us see an example of our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cell_id": "449FD1CD6C2D440795EA35A83BF5A100"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'at Lancaster House despite the crisis which'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlMAAABECAYAAAClDbDiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAADXhJREFUeJzt3VvMHHUZx/HvYysg9VCqQLAFKbGxIpFD3xQUYxQUChLKBZoSEhtt0huNaEy0hAvipdGImiimAaQaBLSCNASBppJ4BbarBsuh8HIQXlspSEGiiVB9vJj/wjCd3Z3zYd/fJ9n0ndnZnf8+88x/nvnP7NbcHREREREp5i1tN0BERESkz1RMiYiIiJSgYkpERESkBBVTIiIiIiWomBIREREpQcWUiIiISAmliikzW2Nme8xs1sw2VdUoERERkb6wor8zZWYLgMeATwNzwE7gMnd/uLrmiYiIiHRbmZGp1cCsuz/p7q8CtwBrq2mWiIiISD8sLPHapcCzsek54MzkQma2EdgIsGjRolUrV64sscrmDQYDAFatWtVyS0RERPplMBj0+vg5GAxecPejJy1XppiylHmHXDN0983AZoCZmRnftWtXiVU2zyz6mH1rt4iISNvMrNfHTzP7a5blylzmmwOOj00vA/aWeL+RhgWNdIuZvf4QmWbTkufT8jlEuqZMMbUTWGFmy83sMGAdsK2aZkkfuDvDLzCog5Zp15f/FF77okg2VZ5cFL7M5+4HzezLwD3AAuAGd3+oklbFqGOQouK5Ez8QmllvDozSPvVBIjJJmXumcPe7gLsqaov0lLt3+oCTVjipoBIRkaroF9CltC4XUqOokCpvPt1/07d8mS/bRbqtD3lY1b6tYiqDvnWkInXTyJ5I9fpQfLSl6thU/X6lLvNNOyV2/+mAX735WEil9QXzLQYiRVS1n9Sxv1X5nr0YmVKnJdIN03KCMekS5bif/Yh/i1Xmpzr3g2nax8ZNTxuNTE0wHzvNIiMPXYvTfBw9qduwM5yGn8OYlBvxz6g8kqThl26qzo1RX5YZ9VzXJb+c1JX9qY6+S8WUpOpC0tfRifS5ABDpulH7V9t9SVJfLtv2tZBKxreL3/iuOqatFlNdOGBPgz7ucJO2fZ2fqU9x6prkqFSeWI763a+u6lrnX7ey26cv8aoyD4scw/rYXxfRxQIK6svTVoqpLg77JXW1XUlZd8y6z8TydFDDZSfFuA/xny/KdEBZXtu3QitNV0Y7xh3ERj0X70fybutJ266JA2rW/rqu0e4yxeekPnB4717f9ovk52uiuKqqHynSzsaLqaLJ3MfONm2os+jri/7w5LhfAR+l6A6ctzMb1YayO1wXz4aq0tQBOy1vkuspcvAad1NqmVGvNo3bx/pwEBxVXLVVnOSRZ/1525r1ZC/vds6bI03uF1Xna9kfTM6bh6PWmfW9yxw7enPPVJM3vVa9jrJnLWk7XNGdN2ub8p5FVFV0denMsei6oN4Cp+59YdJnKHqgnTQ9VEWhPSnHqto+fTrJS14RGCXryVSWXG+iv2477vF41dmeptaTV1qejGpbkRP1qm8Jifcv405O8+ZuK8VUkRGaUWfHXZW2gYuOJKV9IyJPG8a99zjD9dbRWU7qzKtQVdu6kHNNdaBZCqki71Okw5u07nHLZMnbqk4oxrWjydwZt7+PU9clqrpjUKQoLnPsmfS+WXOvjORoWHxeWeMu/45aTxPbYJyiMShSeE3SaDE1GAyaXF0pdWzw+N9ZOvJx75O1KIsnQ9Fr1lmHofO8X9rrqjyLzXIwzvraug4KZUd46mjTuPfMGodR+ZZnBCrreyZlufRSdD9Ia1NXCqnk+sq2IcsIQpaCuwsnItD8CFmdfUbavKrWM6qPmVRotaGJkcA8Gv/Rzjar2CoMO5j4mcEoaQePokOI8dfmiUmXhoSzdLJl21nHDp5nODrP8nklz0ab6KjLvEfWtmYd/WljO0wqvJKft0v7W9k2pI2CTNLFQqoNWfr5KgreqvqB+KhalqsjXdGlHMs0MmVmTwOvAP8FDrr7jJktAW4FTgSeBj7n7gcyvh9Qbsi/SXmTKO16bJUJn1d83W3HcpQu7qhZ1Tmsn9T29qv6ZKjqTrruEYHkvpRWaLS9jaqUvHwVN2q7NX1psysjE01ook15Tnzqbk/WUfA8r6lLnpGpT7r7ae4+E6Y3ATvcfQWwI0xPFE/+Lh9Ak6NP8bOASWcEyQ533AjVpNfneV3asm0ne3LZtG3fpbP5ovJ+hrSDQHLUc9RZYh3GXXpN21aT5M29KkfFqo5TMm9HjUw3sb+1IUvf11R/k1wn5Bs5a0LWEcou5UuW7Zd8vu225zkmN6HMZb61wJbw9xbgkjwv7nJBVcUGanvDdlmdnWAbcc+bJ8kh9XEH5vh7Nr2vpJ1IDOePG5Vo+uy5yOW1Mvv0qP5hXCE8jbLmRN1tGOpKzLtwYK/TNH+2MrIWUw7ca2YDM9sY5h3r7vsAwr/HpL3QzDaa2S4z23XCCSekVrZd2AFktDp2nC6dUcSldchVjZqM6uyznPXXLa0gSFt32sGrbHyKbP+mR+4mSW67LuV03dr+rFlOOtpuo0y/rN/mO9vd95rZMcB2M3s06wrcfTOwGWBmZuaQbHbv5m9ntKULn1/FbaSOA/Uw3/O+Zxt5Me5yc5eoPd3Q9udue/0yv2Uqptx9b/h3v5ndDqwGnjOz49x9n5kdB+wv2gjtBN0yrdsjy+eqq7iPj/x0Nb5dbVeaPrW1DYqPSLMmXuYzs0Vm9o7h38B5wG5gG7A+LLYeuKOuRoo0qc5LjzrIiYhMnywjU8cCt4cz9YXAL9z9bjPbCfzSzDYAzwCfra+ZIiLdHtkTkflrYjHl7k8Cp6bM/wdwbh2NEhEREemLxn8BXURERGSaqJgSERERKUHFlIj0gn6yQ0S6SsWUiIiISAkqpkRERERKUDElIr2hn0UQkS6yJjsnM3sF2NPYCueP9wAvtN2IKaS41kexrYfiWg/FtR59iOv73P3oSQtl/b/5qrLH3WcaXufUM7Ndimv1FNf6KLb1UFzrobjWY5riqst8IiIiIiWomBIREREpoelianPD65svFNd6KK71UWzrobjWQ3Gtx9TEtdEb0EVERESmjS7ziYiIiJSgYkpERESkhMaKKTNbY2Z7zGzWzDY1td5pYGbHm9l9ZvaImT1kZleE+UvMbLuZPR7+PSrMNzP7YYj1g2Z2RrufoLvMbIGZ/cnM7gzTy83sgRDTW83ssDD/8DA9G54/sc12d52ZLTazrWb2aMjbjyhfyzOzr4U+YLeZ3WxmRyhn8zOzG8xsv5ntjs3LnZ9mtj4s/7iZrW/js3TNiNh+J/QFD5rZ7Wa2OPbclSG2e8zs/Nj8XtUMjRRTZrYA+BFwAXAycJmZndzEuqfEQeDr7v5B4CzgSyF+m4Ad7r4C2BGmIYrzivDYCFzbfJN74wrgkdj0t4FrQkwPABvC/A3AAXd/P3BNWE5G+wFwt7uvBE4lirHytQQzWwp8BZhx91OABcA6lLNF3AisSczLlZ9mtgS4GjgTWA1cPSzA5rkbOTS224FT3P3DwGPAlQDhOLYO+FB4zY/DCW7vaoamRqZWA7Pu/qS7vwrcAqxtaN295+773P2P4e9XiA5MS4liuCUstgW4JPy9FviZR+4HFpvZcQ03u/PMbBnwGeC6MG3AOcDWsEgypsNYbwXODctLgpm9E/g4cD2Au7/q7i+hfK3CQuBtZrYQOBLYh3I2N3f/PfBiYnbe/Dwf2O7uL7r7AaKCIVlEzDtpsXX3e939YJi8H1gW/l4L3OLu/3H3p4BZonqhdzVDU8XUUuDZ2PRcmCc5haH604EHgGPdfR9EBRdwTFhM8c7m+8A3gP+F6XcDL8V2+njcXo9peP7lsLwc6iTgeeCn4RLqdWa2COVrKe7+N+C7wDNERdTLwADlbFXy5qfytpgvAr8Nf09NbJsqptLOhvSbDDmZ2duBXwNfdfd/jls0ZZ7iHWNmFwH73X0Qn52yqGd4Tt5sIXAGcK27nw78izcumaRRbDMIl5DWAsuB9wKLiC6DJClnqzUqjopvTmZ2FdFtKzcNZ6Us1svYNlVMzQHHx6aXAXsbWvdUMLO3EhVSN7n7bWH2c8PLIeHf/WG+4j3Z2cDFZvY00RDyOUQjVYvDJRR4c9xej2l4/l0ceplAInPAnLs/EKa3EhVXytdyPgU85e7Pu/trwG3AR1HOViVvfipvcwg36F8EXO5v/MDl1MS2qWJqJ7AifOvkMKIbzrY1tO7eC/c5XA884u7fiz21DRh+g2Q9cEds/ufDt1DOAl4eDl9LxN2vdPdl7n4iUT7+zt0vB+4DLg2LJWM6jPWlYflOnym1xd3/DjxrZh8Is84FHkb5WtYzwFlmdmToE4ZxVc5WI29+3gOcZ2ZHhVHD88I8STCzNcA3gYvd/d+xp7YB68I3T5cT3eT/B/pYM7h7Iw/gQqK7+J8ArmpqvdPwAD5GNMT5IPDn8LiQ6P6HHcDj4d8lYXkj+ibEE8BfiL790/rn6OoD+ARwZ/j7JKKdeRb4FXB4mH9EmJ4Nz5/Udru7/ABOA3aFnP0NcJTytZK4fgt4FNgN/Bw4XDlbKI43E9139hrRKMiGIvlJdP/PbHh8oe3P1YXHiNjOEt0DNTx+/SS2/FUhtnuAC2Lze1Uz6L+TERERESlBv4AuIiIiUoKKKREREZESVEyJiIiIlKBiSkRERKQEFVMiIiIiJaiYEhERESlBxZSIiIhICf8Hgtn9ns9cGlQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8e03f06780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b = train_ds[0]\n",
    "pts = torch.stack([b.xs,b.ys,b.pen.float()],dim=-1)\n",
    "pyplot.figure(figsize=(10,5))\n",
    "pyplot.imshow(stroke_to_image(pts[:b.ptslen[0]].cpu()), cmap=pyplot.cm.gray)\n",
    "''.join(b.txt)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The network\n",
    "\n",
    "### Mixture Density Network\n",
    "\n",
    "The mixture density network, described in Graves Section 4.1, consists of a linear layer and parameter transforms in `compute_params`.\n",
    "The parameters are\n",
    "- a vector $\\pi$ with the weights of the mixture components, \n",
    "- vectors (one element per mixture component)`mean_x, mean_y` ($\\mu$ in Graves), `std_x, std_y` ($\\sigma$), and $\\rho$,\n",
    "- a probaility `bernoulli` ($e$ in Graves) of the pen being up (i.e. $1$ means no pen).\n",
    "\n",
    "Then for training (in `forward`), the negative log likelihood is computer. For prediction (`predict`), movement and pen indicator are sampled.\n",
    "In the prediction, we allow for bias ($b$) as in Graves Section 5.4.\n",
    "\n",
    "We found that the training sometimes runs into `NaN` unless we use some regularisation, we do so via a parameter `eps`.\n",
    "This may be due to us using single precision floating point numbers rather than double precision or a too aggressive learning rate.\n",
    "We also see below that we do not seem to achieve the deterministic outputs when the bias is high.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MixtureGaussians2DandPen(torch.nn.Module):\n",
    "    \"\"\"Gaussian mixture module as in Graves Section 4.1\"\"\"\n",
    "    def __init__(self, n_inputs, n_mixture_components, eps=1e-6):\n",
    "        # n_inputs = dimension N of h^n_t in Graves eq. (17)\n",
    "        # n_mixture_components = number M of mixture components in Graves eq. (16)\n",
    "        super().__init__()\n",
    "        self.n_mixture_components = n_mixture_components\n",
    "        self.eps = eps\n",
    "        # linear layer as in Graves eq. (17)\n",
    "        # ((proportions, m_x, m_y, s_x, s_y, rho)*n_mixture_components, pen)\n",
    "        self.linear = torch.nn.Linear(n_inputs, n_mixture_components *6 + 1) \n",
    "\n",
    "    def compute_parameters(self, h, bias):\n",
    "        # h: batch x n_inputs\n",
    "        # The output of the input layer is batch x ...\n",
    "        y_hat = self.linear(h)\n",
    "        if y_hat.requires_grad:\n",
    "            y_hat.register_hook(lambda x: x.clamp(min=-100, max=100))\n",
    "        \n",
    "        M = self.n_mixture_components\n",
    "        # note that our ordering within y_hat is different to Graves eq (17)\n",
    "        # we also incorporate the bias b given in Graves eq (61) and (62)\n",
    "        # we have a regularisation self.eps that Graves does not have in the paper\n",
    "        pi = torch.nn.functional.softmax(y_hat[:, :M]*(1 + bias),1) # Graves eq (19)\n",
    "        mean_x = y_hat[:, M:M*2]                                      # Graves eq (20)\n",
    "        mean_y = y_hat[:, M*2:M*3]\n",
    "        std_x = torch.exp(y_hat[:, M*3:M*4] - bias) + self.eps        # Graves eq (21)\n",
    "        std_y = torch.exp(y_hat[:, M*4:M*5] - bias) + self.eps\n",
    "        rho = torch.tanh(y_hat[:, M*5:M*6])                           # Graves eq (22)\n",
    "        rho = rho/(1+self.eps)\n",
    "        bernoulli = torch.sigmoid(y_hat[:, -1])                       # Graves eq (18)\n",
    "        bernoulli = (bernoulli + self.eps) / (1 + 2*self.eps)\n",
    "        #bernoulli = 1/(1+torch.exp(-(1+bias)*((torch.log(bernoulli)-torch.log(1-bernoulli))+3*(1-torch.exp(-bias))))) # this is NOT covered by Graves: Bias in the Bernoulli\n",
    "        return pi, mean_x, mean_y, std_x, std_y, rho, bernoulli\n",
    "\n",
    "    def predict(self, h, bias=0.0):\n",
    "        pi, mean_x, mean_y, std_x, std_y, rho, bernoulli = self.compute_parameters(h, bias)\n",
    "\n",
    "        mode = torch.multinomial(pi.data,1) # choose one mixture component\n",
    "\n",
    "        m_x = mean_x.gather(1, mode).squeeze(1) # data for the chosen mixture component\n",
    "        m_y = mean_y.gather(1, mode).squeeze(1)\n",
    "        s_x = std_x.gather(1, mode).squeeze(1)\n",
    "        s_y = std_y.gather(1, mode).squeeze(1)\n",
    "        r   = rho.gather(1, mode).squeeze(1)\n",
    "\n",
    "        normal = rho.new().resize_((h.size(0), 2)).normal_()\n",
    "        x = normal[:, 0]\n",
    "        y = normal[:, 1]\n",
    "\n",
    "        x_n = (m_x + s_x * x).unsqueeze(-1)\n",
    "        y_n = (m_y + s_y * (x * r + y * (1.-r**2)**0.5)).unsqueeze(-1)\n",
    "\n",
    "        uniform = bernoulli.data.new(h.size(0)).uniform_()\n",
    "        pen = torch.autograd.Variable((bernoulli.data > uniform).float().unsqueeze(-1))\n",
    "\n",
    "        return torch.cat([x_n, y_n, pen], dim=1)\n",
    "\n",
    "    def forward(self, h_seq, mask_seq, tg_seq, hidden_dict=None):\n",
    "        # h_seq: (seq, batch, features),  mask_seq: (seq, batch), tg_seq: (seq, batch, features=3)\n",
    "        batch_size = h_seq.size(1)\n",
    "        h_seq = h_seq.view(-1, h_seq.size(-1))\n",
    "        tg_seq = tg_seq.view(-1, tg_seq.size(-1))\n",
    "        mask_seq = mask_seq.view(-1,)\n",
    "\n",
    "        atensor = next(self.parameters())\n",
    "        bias = torch.zeros((),device=atensor.get_device(), dtype=atensor.dtype)\n",
    "        pi, mean_x, mean_y, std_x, std_y, rho, bernoulli = self.compute_parameters(h_seq, bias)\n",
    "\n",
    "        if hidden_dict is not None:\n",
    "            hidden_dict[\"pi\"].append(pi.data.cpu())\n",
    "            hidden_dict[\"mean_x\"].append(mean_x.data.cpu())\n",
    "            hidden_dict[\"mean_y\"].append(mean_y.data.cpu())\n",
    "            hidden_dict[\"std_x\"].append(std_x.data.cpu())\n",
    "            hidden_dict[\"std_y\"].append(std_y.data.cpu())\n",
    "            hidden_dict[\"rho\"].append(rho.data.cpu())\n",
    "            hidden_dict[\"bernoulli\"].append(bernoulli.data.cpu())\n",
    "\n",
    "        tg_x = tg_seq[:, 0:1]\n",
    "        tg_y = tg_seq[:, 1:2]\n",
    "        tg_pen = tg_seq[:, 2]\n",
    "\n",
    "        tg_x_s = (tg_x - mean_x) / std_x \n",
    "        tg_y_s = (tg_y - mean_y) / std_y\n",
    "\n",
    "        z = tg_x_s**2 + tg_y_s**2 - 2*rho*tg_x_s*tg_y_s # Graves eq (25)\n",
    "        \n",
    "        if hidden_dict is not None:\n",
    "            hidden_dict[\"z\"].append(z.data.cpu())            \n",
    "\n",
    "        tmp = 1-rho**2\n",
    "        # tmp is ln (pi N(x, mu, sigma, rho)) with N as in Graves eq (24) (this is later used for eq (26))\n",
    "        mixture_part_loglikelihood = (-z / (2 * tmp) \n",
    "                              -numpy.log(2*numpy.pi) - torch.log(std_x) - torch.log(std_y) - 0.5*torch.log(tmp)\n",
    "                              +torch.log(pi))\n",
    "\n",
    "        # logsumexp over the mixture components\n",
    "        # mixture_log_likelihood the log in the first part of Graves eq (26)\n",
    "        mpl_max,_ = mixture_part_loglikelihood.max(1, keepdim=True)                                 \n",
    "        mixture_log_likelihood = (mixture_part_loglikelihood-mpl_max).exp().sum(1).log()+mpl_max.squeeze(1)\n",
    "\n",
    "        # these are the summands in Graves eq (26)\n",
    "        loss_per_timestep = (-mixture_log_likelihood - tg_pen * torch.log(bernoulli) - (1-tg_pen) * torch.log(1 - bernoulli))\n",
    "\n",
    "        if hidden_dict is not None:\n",
    "            hidden_dict[\"loss_per_timestep\"].append(loss_per_timestep.data.cpu())\n",
    "        # loss as in Graves eq (26)\n",
    "        loss = torch.sum(loss_per_timestep * mask_seq)/batch_size\n",
    "        return loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attention Mechanism\n",
    "\n",
    "Graves Section 5.1 describes a straightforward attention mechanism using a mixture-type weighting scheme and with moving modes.\n",
    "In addition to the one-hot encoded character sequence, the input for the attention mechanism is the LSTM-output $h$ and the previous time-steps mode locations $\\kappa_{t-1}^k$.\n",
    "More precisely, weights $\\phi$ are computed as\n",
    "$$\n",
    "\\phi(t, u) = \\sum_k \\alpha_t^k \\exp(-\\beta_t^k (\\kappa_t^k-u)^2)\n",
    "$$\n",
    "with $t$ being the recurrence time step, $u$ the character location and $k$ is used to sum over the components.\n",
    "Here, $\\alpha_t^k, \\beta_t^k$ and $\\kappa_t^k-\\kappa_{t-1}^k$ are positive - mapped by $\\exp$ from the output of a linear layer. For the $\\kappa_t^k$, the difference is modelled to achieve better stationarity.\n",
    "The module returns the weight vector $\\phi$ and the mode location vector $\\kappa$.\n",
    "\n",
    "Graves notes he does not normalize the weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Attention(torch.nn.Module):\n",
    "    def __init__(self, n_inputs, n_mixture_components):\n",
    "        super().__init__()\n",
    "        self.n_mixture_components = n_mixture_components\n",
    "        # linear layer from Graves eq (28)\n",
    "        self.linear = torch.nn.Linear(n_inputs, n_mixture_components*3)\n",
    "    def forward(self, h_1, kappa_prev, c_seq_len):\n",
    "        # h_1: batch x n_inputs, kappa_prev batch x n_mixture_components\n",
    "        K = self.n_mixture_components\n",
    "        params = torch.exp(self.linear(h_1)) # exp of Graves eq (48)\n",
    "        alpha = params[:,:K]                 # Graves eq (49)\n",
    "        beta  = params[:,K:2*K]              # Graves eq (50)\n",
    "        kappa = kappa_prev + 0.1*params[:,2*K:]  # Graves eq (51)\n",
    "        u = torch.arange(0,c_seq_len, out=kappa.new()).view(-1,1,1)\n",
    "        phi = torch.sum(alpha * torch.exp(-beta*(kappa-u)**2), dim=-1)\n",
    "        return phi, kappa\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LSTM\n",
    "\n",
    "In order to be able to trade the LSTM cell for a GRU, I have a thin wraper around the LSTMCell module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RNNCell(torch.nn.Module):\n",
    "    def __init__(self, input_size, hidden_size, bias=True):\n",
    "        super().__init__()\n",
    "        self.input_size = input_size\n",
    "        self.hidden_size = hidden_size\n",
    "        self.cell = torch.nn.LSTMCell(input_size, hidden_size, bias)\n",
    "    def forward(self, inp, hidden = None):\n",
    "        if hidden is None:\n",
    "            batch_size = inp.size(0)\n",
    "            hx = inp.new(batch_size, self.hidden_size).zero_()\n",
    "            cx = inp.new(batch_size, self.hidden_size).zero_()\n",
    "            hidden = (hx, cx)\n",
    "        return self.cell(inp, hidden)\n",
    "    def get_hidden(self, hidden):\n",
    "        return hidden[0]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Main Module\n",
    "\n",
    "Tying things together is the main module. It is disappointingly heavyweight given that it mostly does administraton.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cell_id": "4AFBD0DFCE2147588AB92E4813E9041F"
   },
   "outputs": [],
   "source": [
    "class HandwritingModel(torch.nn.Module):\n",
    "    def __init__(self, n_hidden, n_chars, n_attention_components, n_gaussians, grad_clipping=10):\n",
    "        super(HandwritingModel, self).__init__()\n",
    "        self.n_hidden = n_hidden\n",
    "        self.n_chars = n_chars\n",
    "        self.n_attention_components = n_attention_components\n",
    "        self.n_gaussians = n_gaussians\n",
    "\n",
    "        self.attention = Attention(n_hidden, n_attention_components)\n",
    "        self.rnn_cell = RNNCell(3+self.n_chars, n_hidden)\n",
    "        self.grad_clipping = grad_clipping\n",
    "        self.mixture = MixtureGaussians2DandPen(n_hidden+self.n_chars, n_gaussians)\n",
    "\n",
    "    def rnn_step(self, inputs, h_state_pre, k_pre, w_pre, c, c_mask, mask=None, hidden_dict=None):\n",
    "        # inputs: (batch_size, n_in + n_in_c)\n",
    "        inputs = torch.cat([inputs, w_pre], dim=1)\n",
    "\n",
    "        # h: (batch_size, n_hidden)\n",
    "        h_state = self.rnn_cell(inputs, h_state_pre)\n",
    "        h = self.rnn_cell.get_hidden(h_state)\n",
    "        if h.requires_grad:\n",
    "            h.register_hook(lambda x: x.clamp(min=-self.grad_clipping, max=self.grad_clipping))\n",
    "            \n",
    "        # update attention\n",
    "        phi, k =  self.attention(h, k_pre, c.size(0))\n",
    "        phi = phi * c_mask\n",
    "        # w: (batch_size, n_chars)\n",
    "        w = torch.sum(phi.unsqueeze(-1) * c, dim=0)\n",
    "        if mask is not None:\n",
    "            k = mask.unsqueeze(1)*k + (1-mask.unsqueeze(1))*k_pre\n",
    "            w = mask.unsqueeze(1)*w + (1-mask.unsqueeze(1))*w_pre\n",
    "        if w.requires_grad:\n",
    "            w.register_hook(lambda x: x.clamp(min=-100, max=100))\n",
    "        return h_state, k, phi, w\n",
    "    \n",
    "    def forward(self, seq_pt, seq_mask, seq_pt_target, c, c_mask,\n",
    "                h_ini=None, k_ini=None, w_ini=None, hidden_dict=None):       \n",
    "        batch_size = seq_pt.size(1)\n",
    "        atensor = next(m.parameters())\n",
    "        \n",
    "        #if h_ini is None:\n",
    "        #    h_ini = self.mixture.linear.weight.data.new(batch_size, self.n_hidden).zero_()\n",
    "        if k_ini is None:\n",
    "            k_ini = atensor.new(batch_size, self.n_attention_components).zero_()\n",
    "        if w_ini is None:\n",
    "            w_ini = atensor.new(batch_size, self.n_chars).zero_()\n",
    "\n",
    "        # Convert the integers representing chars into one-hot encodings\n",
    "        # seq_str will have shape (seq_length, batch_size, n_chars)\n",
    "        \n",
    "        c_idx = c\n",
    "        c = c.data.new(c.size(0), c.size(1), self.n_chars).float().zero_()\n",
    "        c.scatter_(2, c_idx.view(c.size(0), c.size(1), 1), 1)\n",
    "\n",
    "        seq_h = []\n",
    "        seq_k = []\n",
    "        seq_w = []\n",
    "        seq_phi = []\n",
    "        h_state, k, w = h_ini, k_ini, w_ini\n",
    "        for inputs, mask in zip(seq_pt, seq_mask):\n",
    "            h_state, k, phi, w = self.rnn_step(inputs, h_state, k, w, c, c_mask, mask=mask, hidden_dict=hidden_dict)\n",
    "            h = self.rnn_cell.get_hidden(h_state)\n",
    "            seq_h.append(h)\n",
    "            seq_k.append(k)\n",
    "            seq_w.append(w)\n",
    "            if hidden_dict is not None:\n",
    "                seq_phi.append(phi)\n",
    "        seq_h = torch.stack(seq_h,0)\n",
    "        seq_k = torch.stack(seq_k,0)\n",
    "        seq_w = torch.stack(seq_w,0)\n",
    "        if hidden_dict is not None:\n",
    "            hidden_dict['seq_h'].append(seq_h.data.cpu())\n",
    "            hidden_dict['seq_k'].append(seq_k.data.cpu())\n",
    "            hidden_dict['seq_w'].append(seq_w.data.cpu())\n",
    "            hidden_dict['seq_phi'].append(torch.stack(seq_phi,0).data.cpu())\n",
    "        seq_hw = torch.cat([seq_h, seq_w], dim=-1)\n",
    "\n",
    "        loss = self.mixture(seq_hw, seq_mask, seq_pt_target, hidden_dict=hidden_dict)\n",
    "        return loss\n",
    "\n",
    "    def predict(self, pt_ini, seq_str, seq_str_mask,\n",
    "                   h_ini=None, k_ini=None, w_ini=None, bias=.0, n_steps=10000, hidden_dict=None):\n",
    "        # pt_ini: (batch_size, 3), seq_str: (length_str_seq, batch_size), seq_str_mask: (length_str_seq, batch_size)\n",
    "        # h_ini: (batch_size, n_hidden), k_ini: (batch_size, n_mixture_attention), w_ini: (batch_size, n_chars)\n",
    "        # bias: float    The bias that controls the variance of the generation\n",
    "        # n_steps: int   The maximal number of generation steps.\n",
    "        atensor = next(m.parameters())\n",
    "        bias = bias*torch.ones((),device=atensor.get_device(), dtype=atensor.dtype)\n",
    "        batch_size = pt_ini.size(0)\n",
    "        if k_ini is None:\n",
    "            k_ini = atensor.new(batch_size, self.n_attention_components).zero_()\n",
    "        if w_ini is None:\n",
    "            w_ini = atensor.new(batch_size, self.n_chars).zero_()\n",
    "\n",
    "        # Convert the integers representing chars into one-hot encodings\n",
    "        # seq_str will have shape (seq_length, batch_size, n_chars)\n",
    "        \n",
    "        input_seq_str = seq_str\n",
    "        seq_str = pt_ini.data.new(input_seq_str.size(0), input_seq_str.size(1), self.n_chars).float().zero_()\n",
    "        seq_str.scatter_(2, input_seq_str.data.view(seq_str.size(0), seq_str.size(1) ,1), 1)\n",
    "        seq_str = torch.autograd.Variable(seq_str)        \n",
    "\n",
    "        mask = torch.autograd.Variable(self.mixture.linear.weight.data.new(batch_size).fill_(1))\n",
    "        seq_pt = [pt_ini]\n",
    "        seq_mask = [mask]\n",
    "\n",
    "        last_char = seq_str_mask.long().sum(0)-1\n",
    "\n",
    "        pt, h_state, k, w = pt_ini, h_ini, k_ini, w_ini\n",
    "        for i in range(n_steps):\n",
    "            h_state, k, phi, w = self.rnn_step(pt, h_state, k, w, seq_str, seq_str_mask, mask=mask, hidden_dict=hidden_dict)\n",
    "            h = self.rnn_cell.get_hidden(h_state)\n",
    "            hw = torch.cat([h, w], dim=-1)\n",
    "            pt = self.mixture.predict(hw, bias)\n",
    "            seq_pt.append(pt)\n",
    "            \n",
    "            last_phi = torch.gather(phi, 0, last_char.unsqueeze(0)).squeeze(0)\n",
    "            max_phi,_ = phi.max(0)\n",
    "            mask = mask * (1-(last_phi >= 0.95*max_phi).float())\n",
    "            seq_mask.append(mask)\n",
    "            if mask.data.sum()==0:\n",
    "                break\n",
    "        seq_pt   = torch.stack(seq_pt,0)\n",
    "        seq_mask = torch.stack(seq_mask,0)\n",
    "        return seq_pt, seq_mask        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "478F522049C049AA8B8F818CEB567B22"
   },
   "source": [
    "## Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "cell_id": "998AED33563E45F78A2CE8759B69A4BF"
   },
   "outputs": [],
   "source": [
    "n_hidden = 900\n",
    "n_mixt_attention = 10\n",
    "n_mixt_output = 20\n",
    "batch_size = 50\n",
    "\n",
    "train_it, = torchtext.data.BucketIterator.splits((train_ds,), batch_size=batch_size, repeat=False)\n",
    "val_it,   = torchtext.data.BucketIterator.splits((val_ds,),   batch_size=batch_size, repeat=False)\n",
    "\n",
    "m = HandwritingModel(n_hidden, n_chars, n_mixt_attention, n_mixt_output)\n",
    "m.cuda()\n",
    "# These are based on Graves Section 4.2.\n",
    "opt = torch.optim.RMSprop(m.parameters(), lr=1e-4, eps=1e-4, alpha=0.95, momentum=0.9, centered=True) \n",
    "losses = []\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the training. If you want to skip the training, skip the next cell and enable the loading below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "cell_id": "496A24D27A3B4D938DD9629F08DAF456",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smoothloss -1209.02839966\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbf432a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time per minibatch 1.329148292541504\n",
      "49 / 180 (of 208) : -1224.4349365234375\n",
      "epoch 49 took 277.51844930648804 seconds\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(50):\n",
    "    lasttime = time.time()\n",
    "    lastbatch = -1\n",
    "    epochstart = lasttime\n",
    "    for batch,i in enumerate(train_it):\n",
    "        #i_seq_pt, i_seq_tg, i_seq_mask, i_seq_str, i_seq_str_mask = [torch.autograd.Variable(torch.from_numpy(i).cuda()) for i in inputs]\n",
    "        #i_seq_str = i_seq_str.long()\n",
    "        i_seq_pt = torch.stack([i.xs, i.ys, i.pen.float()], dim=2)\n",
    "        i_seq_tg = i_seq_pt[1:]\n",
    "        i_seq_pt = i_seq_pt[:-1]\n",
    "        i_seq_mask = (i.pen[:-1]>=0).float()\n",
    "        i_seq_str = i.txtn\n",
    "        i_seq_str_mask = i.txtmask\n",
    "        \n",
    "        opt.zero_grad()\n",
    "        res = m(i_seq_pt, i_seq_mask, i_seq_tg, i_seq_str, i_seq_str_mask)\n",
    "        res.backward()\n",
    "        losses.append(res.data)\n",
    "        if batch % 10 == 0:\n",
    "            losses = [float(l) for l in losses]\n",
    "            IPython.display.clear_output(wait=True)\n",
    "            pyplot.figure(figsize=(15,5))\n",
    "            pyplot.subplot(1,2,1)\n",
    "            pyplot.plot(losses)\n",
    "            if len(losses)>=50:\n",
    "                smoothed = (numpy.convolve(losses,numpy.ones(50)/50,'valid'))\n",
    "                pyplot.plot(numpy.arange(len(losses)-len(smoothed),len(losses)),smoothed)\n",
    "                print (\"smoothloss\", smoothed[-1])\n",
    "            pyplot.subplot(1,2,2)\n",
    "            with torch.no_grad():\n",
    "                i_seq_str = torch.autograd.Variable(torch.LongTensor([int(char_dict[c]) for c in \"Die Katzen von Kopenhagen. \"]).view(-1,1).cuda())\n",
    "                i_seq_str_mask = torch.autograd.Variable(torch.ones(i_seq_str.size()).cuda())\n",
    "                seq_pt, seq_mask = m.predict(i_seq_pt[0,:1], i_seq_str, i_seq_str_mask, bias=0.8)\n",
    "                lengths = seq_mask.sum(0).data.long()\n",
    "                idx = 0\n",
    "                show_stroke(seq_pt.data.cpu()[:lengths[idx],idx])\n",
    "                #''.join([inv_char_dict[c] for c in i_seq_str.data.cpu()[:,idx]])\n",
    "            pyplot.show()\n",
    "            print (\"time per minibatch\",(time.time()-lasttime)/(batch-lastbatch))\n",
    "            lastbatch = batch\n",
    "            lasttime = time.time()\n",
    "            print (epoch,'/', batch,'(of 208) :', res.item())\n",
    "\n",
    "        torch.nn.utils.clip_grad_norm(m.parameters(),5)\n",
    "        opt.step()\n",
    "    print (\"epoch\", epoch, \"took\", time.time()-epochstart, \"seconds\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes I miss the output above, so here is the loss graph again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cell_id": "E210C2A610FE401A924EA97DC8998CB4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smoothloss -1229.02942749\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8e03e9acf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49 / 189 (of 208) : -1108.754150390625\n"
     ]
    }
   ],
   "source": [
    "IPython.display.clear_output(wait=True)\n",
    "pyplot.plot(numpy.fmin(losses,3000))\n",
    "if len(losses)>=50:\n",
    "    smoothed = (numpy.convolve(losses,numpy.ones(50)/50,'valid'))\n",
    "    pyplot.plot(numpy.arange(len(losses)-len(smoothed),len(losses)),numpy.fmin(smoothed,3000))\n",
    "    print (\"smoothloss\", smoothed[-1])\n",
    "pyplot.show()\n",
    "print (epoch,'/', batch,'(of 208) :', res.item())            \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can evaluate the negative log likelihood on the validation set. We should reach the same ballpark as Graves, who reports -1096.9 for the non-adaptive weight noise, albeit for a three-layer network) in Table 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 25/25 [00:18<00:00,  1.37it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Negative log likelihood on validation set -1123.9588082752182\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    totalweight = 0.0\n",
    "    totalweightedloss = 0.0\n",
    "    for i in tqdm.tqdm(val_it): #, total=len(val_it)):\n",
    "        i_seq_pt = torch.stack([i.xs, i.ys, i.pen.float()], dim=2)\n",
    "        i_seq_tg = i_seq_pt[1:]\n",
    "        i_seq_pt = i_seq_pt[:-1]\n",
    "        i_seq_mask = (i.pen[:-1]>=0).float()\n",
    "        i_seq_str = i.txtn\n",
    "        i_seq_str_mask = i.txtmask\n",
    "        loss = m(i_seq_pt, i_seq_mask, i_seq_tg, i_seq_str, i_seq_str_mask).item()\n",
    "        lossweight = i.batch_size/val_it.batch_size\n",
    "        totalweight += lossweight\n",
    "        totalweightedloss += loss*lossweight\n",
    "print(\"Negative log likelihood on validation set\", totalweightedloss/totalweight)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want, you can load and save the model with the code below. It is more customary to use torch.save, but sometimes I like to save the weights only."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import h5py\n",
    "def save_to_hdf5(fn, d):\n",
    "    f = h5py.File(fn, \"w\")\n",
    "    for k,v in d.items():\n",
    "        f.create_dataset(k, data=v)\n",
    "def load_from_hdf5(fn):\n",
    "    f = h5py.File(fn, \"r\")\n",
    "    print (list(f.keys()))\n",
    "    return {k:v[:] for k,v in f.items()}\n",
    "\n",
    "if 0:\n",
    "    save_to_hdf5(\"graves_handwriting_generation_\"+time.strftime(\"%Y-%m-%d-%H-%M\",time.localtime())+\"epoch_{}\".format(epoch)+\".hd5\", {n:p.data.cpu().numpy() for n,p in m.named_parameters()})\n",
    "if 0:\n",
    "    d =load_from_hdf5(\"graves_handwriting_generation_2018-03-13-02-45epoch_49.hd5\")\n",
    "    for n,p in m.named_parameters():\n",
    "        p.data.copy_(torch.from_numpy(d[n]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visual model evaluation\n",
    "\n",
    "Nw that we have a model, we may show some samples.\n",
    "First we use the bias parameter as Graves describes in Section 5.4 and shows in Figure 16."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8e71e98e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbf659828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbed5eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8e0abe2e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbe9b34a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8e71e98e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbfa455f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbe02d2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbfa76b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbf6592e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for bias in [0,2,2,2,5,5,5,100,100,100]:\n",
    "    with torch.no_grad():\n",
    "        i = next(iter(train_it))\n",
    "        i_seq_pt = torch.stack([i.xs, i.ys, i.pen.float()], dim=2)\n",
    "        i_seq_pt = i_seq_pt[:-1]\n",
    "\n",
    "        i_seq_str = torch.autograd.Variable(torch.LongTensor([int(char_dict[c]) for c in \"Die Katzen von Kopenhagen. \"]).view(-1,1).cuda())\n",
    "        i_seq_str_mask = torch.autograd.Variable(torch.ones(i_seq_str.size()).cuda())\n",
    "        seq_pt, seq_mask = m.predict(i_seq_pt[0,:1], i_seq_str, i_seq_str_mask, bias=bias)\n",
    "        lengths = seq_mask.sum(0).data.long()\n",
    "        idx = 0\n",
    "        pyplot.figure(figsize=(10,2))\n",
    "        show_stroke(seq_pt.data.cpu()[:lengths[idx],idx])\n",
    "        #''.join([inv_char_dict[c] for c in i_seq_str.data.cpu()[:,idx]])\n",
    "        pyplot.title(\"bias={}\".format(bias))\n",
    "        pyplot.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that even with an extreme bias, the generated writing is not identical. This is in contrast to Graves' observation in Figure 16. I tentatively believe this is due to several modes sharing the top spot for the weights (e.g. two having mass almost exactly 0.5). Also the pen write vs. move probability is not biased."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "4F00536FD70B4DDA8447E83163E4E4AD"
   },
   "source": [
    "### Model internal state\n",
    "\n",
    "In Order to look at model internals, we can a pass a Python defaultdict to the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['seq_h', 'seq_k', 'seq_w', 'seq_phi', 'pi', 'mean_x', 'mean_y', 'std_x', 'std_y', 'rho', 'bernoulli', 'z', 'loss_per_timestep'])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = collections.defaultdict(list)\n",
    "with torch.no_grad():\n",
    "        i = next(iter(train_it))\n",
    "        i_seq_pt = torch.stack([i.xs, i.ys, i.pen.float()], dim=2)\n",
    "        i_seq_tg = i_seq_pt[1:]\n",
    "        i_seq_pt = i_seq_pt[:-1]\n",
    "        i_seq_mask = (i.pen[:-1]>=0).float()\n",
    "        i_seq_str = i.txtn\n",
    "        i_seq_str_mask = i.txtmask\n",
    "        \n",
    "        opt.zero_grad()\n",
    "        res = m(i_seq_pt, i_seq_mask, i_seq_tg, i_seq_str, i_seq_str_mask, hidden_dict=d)\n",
    "d.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx=1\n",
    "this_batch_size = i_seq_pt.size(1)\n",
    "pts = i_seq_pt[:i.ptslen[0,idx],idx].cpu()\n",
    "pts_len = i.ptslen[0,idx]\n",
    "mean_y = d['mean_y'][0].view(-1,this_batch_size, d['mean_y'][0].size(1))[:pts_len,idx]*train_ds.coord_std[1]+train_ds.coord_mean[1]\n",
    "mean_x = d['mean_x'][0].view(-1,this_batch_size, d['mean_x'][0].size(1))[:pts_len,idx]*train_ds.coord_std[0]+train_ds.coord_mean[0]\n",
    "pi   = d['pi'][0].view(-1,this_batch_size, d['pi'][0].size(1))[:pts_len,idx]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The weights of the probabilities look reasonably similar to Graves Figure 14 in that we movements within strokes and in between being sampled from different mixture components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'natural story-telling skill, it is'"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbe0b4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbe9bf860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(15,5))\n",
    "pyplot.imshow(pi.t(), aspect='auto')\n",
    "#pts = torch.stack([i.xs,i.ys,i.pen.float()],dim=-1)\n",
    "pyplot.figure(figsize=(15,5))\n",
    "show_stroke(pts)\n",
    "txt = train_ds.tensor_to_str(i.txt[:i.txtlen[0,idx],idx])\n",
    "txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we want to visualize the probability distributions for the points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cd99924a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def show_mixture_of_normals(x, y, sx, sy, rho, weights):\n",
    "    x = x.view(1,1,-1)\n",
    "    y = y.view(1,1,-1)\n",
    "    sx = sx.view(1,1,-1)\n",
    "    sy = sy.view(1,1,-1)\n",
    "    rho = rho.view(1,1,-1)\n",
    "    weights = weights.view(1,1,-1)\n",
    "    xmin, ymin = x.min(), y.min()\n",
    "    xmax, ymax = x.max(), y.max()\n",
    "    NX, NY = 1000, 70\n",
    "    xx = torch.arange(0., NX).view(1,-1,1)*(xmax-xmin)/NX+xmin\n",
    "    yy = torch.arange(0., NY).view(-1,1,1)*(ymax-ymin)/NY+ymin\n",
    "    x_s = (x-xx)/sx\n",
    "    y_s = (y-yy)/sy\n",
    "    tmp = 1-rho**2\n",
    "    log_dens = -(x_s**2+y_s**2-2*rho*x_s*y_s)/(2*tmp)-numpy.log(2*numpy.pi)-torch.log(sx)- torch.log(sy) - 0.5*torch.log(tmp)\n",
    "    dens = (weights*torch.exp(log_dens)).sum(-1)\n",
    "    pyplot.imshow(dens**0.25, aspect='auto') # note: the **0.25 is only for the color mapping\n",
    "\n",
    "\n",
    "idx=1\n",
    "this_batch_size = i_seq_pt.size(1)\n",
    "pts = i_seq_pt[:i.ptslen[0,idx],idx].cpu()\n",
    "pts_len = i.ptslen[0,idx]\n",
    "cut_pts_len = min(pts_len, 100)\n",
    "mean_x = d['mean_x'][0].view(-1,this_batch_size, d['mean_x'][0].size(1))[:cut_pts_len,idx]*train_ds.coord_std[0]+train_ds.coord_mean[0]\n",
    "mean_y = d['mean_y'][0].view(-1,this_batch_size, d['mean_y'][0].size(1))[:cut_pts_len,idx]*train_ds.coord_std[1]+train_ds.coord_mean[1]\n",
    "std_x  = d['std_x'][0].view(-1,this_batch_size,  d['std_x'][0].size(1))[:cut_pts_len,idx]*train_ds.coord_std[0]\n",
    "std_y  = d['std_y'][0].view(-1,this_batch_size,  d['std_y'][0].size(1))[:cut_pts_len,idx]*train_ds.coord_std[1]\n",
    "pi     = d['pi'][0].view(-1,this_batch_size,  d['pi'][0].size(1))[:cut_pts_len,idx].contiguous()\n",
    "rho    = d['rho'][0].view(-1,this_batch_size, d['rho'][0].size(1))[:cut_pts_len,idx].contiguous()\n",
    "_,maxidx = pi.max(1)\n",
    "offset_x = torch.cat([torch.zeros(1),mean_x[torch.arange(0,len(mean_x), out=torch.LongTensor()), maxidx].cumsum(0)[:-1]],0)\n",
    "offset_y = torch.cat([torch.zeros(1),mean_y[torch.arange(0,len(mean_y), out=torch.LongTensor()), maxidx].cumsum(0)[:-1]],0)\n",
    "\n",
    "if 0:\n",
    "    NP = 10\n",
    "    x = torch.randn(NP)\n",
    "    y = torch.randn(NP)\n",
    "    sx = torch.exp(-1.5+0.5*torch.randn(NP))\n",
    "    sy = torch.exp(-1.5+0.5*torch.randn(NP))\n",
    "    rho = torch.zeros(NP)\n",
    "    weights = torch.ones(NP)\n",
    "pyplot.figure(figsize=(15,5))\n",
    "show_mixture_of_normals(mean_x+offset_x.unsqueeze(1), mean_y+offset_y.unsqueeze(1), std_x, std_y, rho, pi)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast to Figure 14 in Graves, we do not see that much of the increased uncertainty (but note with Graves that in Figure 14 the uncertainty is much smaller for the moves to a new stroke than in the non-conditioned output of Figure 10). This may mean our model is overfitting more than his. Graves uses regularisation with adaptive weighted noise which - to the best of my understanding - is very similar to the recently more popular Bayesian Variational Inference scheme.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also recreate figure 13. To illustrate which character is dominant in the attention mechanism, we color the strokes accordingly. (I first saw colored strokes at [David Ha aka Hardmaru's blog](http://blog.otoro.net/2015/12/12/handwriting-generation-demo-in-tensorflow/), but at first glance he seems to color strokes, but we colorcode the attentention on chars.) It seems that the model looks at the next character quite early."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8e00a6ff98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8cbfb3dd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seq_phi  = d['seq_phi'][0][:pts_len,:, idx]\n",
    "pyplot.figure(figsize=(15,5))\n",
    "pyplot.imshow(d['seq_phi'][0][:pts_len,:, idx].t(), aspect=\"auto\")\n",
    "ax = pyplot.gca()\n",
    "ax.set_yticks(range(i.txtlen[0,idx].item()))\n",
    "ax.set_yticklabels(list(txt))\n",
    "pyplot.figure(figsize=(15,2))\n",
    "colorlist = [pyplot.cm.jet(int(5*i/(seq_phi.size(1)-1)*(pyplot.cm.jet.N-1))%256) for i in range(seq_phi.size(1))]\n",
    "colors = [colorlist[c] for c in seq_phi.max(1)[1].tolist()]\n",
    "show_stroke(pts, colors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I hope you enjoyed the exploration of Graves' classic model as much as I did writing it.\n",
    "\n",
    "Feedback and corrections are always welcome at <tv@lernapparat.de>, I read and appreciate every mail.\n",
    "\n",
    "*Thomas Viehmann*"
   ]
  },
  {
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}