makemore-manual-backprop.ipynb

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   "source": [
    "Manual Implementation of Backpropagation\n",
    "\n",
    "https://karpathy.medium.com/yes-you-should-understand-backprop-e2f06eab496b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn.functional as F\n",
    "import matplotlib.pyplot as plt # for making figures\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32033\n",
      "15\n",
      "['emma', 'olivia', 'ava', 'isabella', 'sophia', 'charlotte', 'mia', 'amelia']\n"
     ]
    }
   ],
   "source": [
    "# read in all the words\n",
    "words = open('names.txt', 'r').read().splitlines()\n",
    "print(len(words))\n",
    "print(max(len(w) for w in words))\n",
    "print(words[:8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 'a', 2: 'b', 3: 'c', 4: 'd', 5: 'e', 6: 'f', 7: 'g', 8: 'h', 9: 'i', 10: 'j', 11: 'k', 12: 'l', 13: 'm', 14: 'n', 15: 'o', 16: 'p', 17: 'q', 18: 'r', 19: 's', 20: 't', 21: 'u', 22: 'v', 23: 'w', 24: 'x', 25: 'y', 26: 'z', 0: '.'}\n",
      "27\n"
     ]
    }
   ],
   "source": [
    "# build the vocabulary of characters and mappings to/from integers\n",
    "chars = sorted(list(set(''.join(words))))\n",
    "stoi = {s:i+1 for i,s in enumerate(chars)}\n",
    "stoi['.'] = 0\n",
    "itos = {i:s for s,i in stoi.items()}\n",
    "vocab_size = len(itos)\n",
    "print(itos)\n",
    "print(vocab_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([182625, 3]) torch.Size([182625])\n",
      "torch.Size([22655, 3]) torch.Size([22655])\n",
      "torch.Size([22866, 3]) torch.Size([22866])\n"
     ]
    }
   ],
   "source": [
    "# build the dataset\n",
    "block_size = 3 # context length: how many characters do we take to predict the next one?\n",
    "\n",
    "def build_dataset(words):  \n",
    "  X, Y = [], []\n",
    "  \n",
    "  for w in words:\n",
    "    context = [0] * block_size\n",
    "    for ch in w + '.':\n",
    "      ix = stoi[ch]\n",
    "      X.append(context)\n",
    "      Y.append(ix)\n",
    "      context = context[1:] + [ix] # crop and append\n",
    "\n",
    "  X = torch.tensor(X)\n",
    "  Y = torch.tensor(Y)\n",
    "  print(X.shape, Y.shape)\n",
    "  return X, Y\n",
    "\n",
    "import random\n",
    "random.seed(42)\n",
    "random.shuffle(words)\n",
    "n1 = int(0.8*len(words))\n",
    "n2 = int(0.9*len(words))\n",
    "\n",
    "Xtr,  Ytr  = build_dataset(words[:n1])     # 80%\n",
    "Xdev, Ydev = build_dataset(words[n1:n2])   # 10%\n",
    "Xte,  Yte  = build_dataset(words[n2:])     # 10%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# utility function we will use later when comparing manual gradients to PyTorch gradients\n",
    "def cmp(s, dt, t):\n",
    "  ex = torch.all(dt == t.grad).item()\n",
    "  app = torch.allclose(dt, t.grad)\n",
    "  maxdiff = (dt - t.grad).abs().max().item()\n",
    "  print(f'{s:15s} | exact: {str(ex):5s} | approximate: {str(app):5s} | maxdiff: {maxdiff}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4137\n"
     ]
    }
   ],
   "source": [
    "n_embd = 10 # the dimensionality of the character embedding vectors\n",
    "n_hidden = 64 # the number of neurons in the hidden layer of the MLP\n",
    "\n",
    "g = torch.Generator().manual_seed(2147483647) # for reproducibility\n",
    "C  = torch.randn((vocab_size, n_embd),            generator=g)\n",
    "# Layer 1\n",
    "W1 = torch.randn((n_embd * block_size, n_hidden), generator=g) * (5/3)/((n_embd * block_size)**0.5)\n",
    "b1 = torch.randn(n_hidden,                        generator=g) * 0.1 # using b1 just for fun, it's useless because of BN\n",
    "# Layer 2\n",
    "W2 = torch.randn((n_hidden, vocab_size),          generator=g) * 0.1\n",
    "b2 = torch.randn(vocab_size,                      generator=g) * 0.1\n",
    "# BatchNorm parameters\n",
    "bngain = torch.randn((1, n_hidden))*0.1 + 1.0\n",
    "bnbias = torch.randn((1, n_hidden))*0.1\n",
    "\n",
    "# Note: I am initializating many of these parameters in non-standard ways\n",
    "# because sometimes initializating with e.g. all zeros could mask an incorrect\n",
    "# implementation of the backward pass.\n",
    "\n",
    "parameters = [C, W1, b1, W2, b2, bngain, bnbias]\n",
    "print(sum(p.nelement() for p in parameters)) # number of parameters in total\n",
    "for p in parameters:\n",
    "  p.requires_grad = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 32\n",
    "n = batch_size # a shorter variable also, for convenience\n",
    "# construct a minibatch\n",
    "ix = torch.randint(0, Xtr.shape[0], (batch_size,), generator=g)\n",
    "Xb, Yb = Xtr[ix], Ytr[ix] # batch X,Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(3.3405, grad_fn=<NegBackward0>)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# forward pass, \"chunkated\" into smaller steps that are possible to backward one at a time\n",
    "\n",
    "emb = C[Xb] # embed the characters into vectors\n",
    "embcat = emb.view(emb.shape[0], -1) # concatenate the vectors\n",
    "# Linear layer 1\n",
    "hprebn = embcat @ W1 + b1 # hidden layer pre-activation\n",
    "# BatchNorm layer\n",
    "bnmeani = 1/n*hprebn.sum(0, keepdim=True)\n",
    "bndiff = hprebn - bnmeani\n",
    "bndiff2 = bndiff**2\n",
    "bnvar = 1/(n-1)*(bndiff2).sum(0, keepdim=True) # note: Bessel's correction (dividing by n-1, not n)\n",
    "bnvar_inv = (bnvar + 1e-5)**-0.5\n",
    "bnraw = bndiff * bnvar_inv\n",
    "hpreact = bngain * bnraw + bnbias\n",
    "# Non-linearity\n",
    "h = torch.tanh(hpreact) # hidden layer\n",
    "# Linear layer 2\n",
    "logits = h @ W2 + b2 # output layer\n",
    "# cross entropy loss (same as F.cross_entropy(logits, Yb))\n",
    "logit_maxes = logits.max(1, keepdim=True).values\n",
    "norm_logits = logits - logit_maxes # subtract max for numerical stability\n",
    "counts = norm_logits.exp()\n",
    "counts_sum = counts.sum(1, keepdims=True)\n",
    "counts_sum_inv = counts_sum**-1 # if I use (1.0 / counts_sum) instead then I can't get backprop to be bit exact...\n",
    "probs = counts * counts_sum_inv\n",
    "logprobs = probs.log()\n",
    "loss = -logprobs[range(n), Yb].mean()\n",
    "\n",
    "# PyTorch backward pass\n",
    "for p in parameters:\n",
    "  p.grad = None\n",
    "for t in [logprobs, probs, counts, counts_sum, counts_sum_inv, # afaik there is no cleaner way\n",
    "          norm_logits, logit_maxes, logits, h, hpreact, bnraw,\n",
    "         bnvar_inv, bnvar, bndiff2, bndiff, hprebn, bnmeani,\n",
    "         embcat, emb]:\n",
    "  t.retain_grad()\n",
    "loss.backward()\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([32, 1]), torch.Size([32, 27]), torch.Size([32, 27]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logit_maxes.shape, logits.shape, norm_logits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "logprobs        | exact: True  | approximate: True  | maxdiff: 0.0\n",
      "probs           | exact: True  | approximate: True  | maxdiff: 0.0\n",
      "counts_sum_inv  | exact: True  | approximate: True  | maxdiff: 0.0\n",
      "counts_sum      | exact: True  | approximate: True  | maxdiff: 0.0\n",
      "counts          | exact: True  | approximate: True  | maxdiff: 0.0\n",
      "norm_logits     | exact: True  | approximate: True  | maxdiff: 0.0\n"
     ]
    }
   ],
   "source": [
    "# Manual Backpropagation\n",
    "\n",
    "dlogprobs = torch.zeros_like(logprobs)\n",
    "dlogprobs[range(n), Yb] = -1.0/n\n",
    "dprobs = (1.0 / probs) * dlogprobs\n",
    "dcounts_sum_inv = (counts * dprobs).sum(1, keepdims=True)\n",
    "dcounts = (counts_sum_inv * dprobs)\n",
    "dcounts_sum = (-counts_sum**-2) * dcounts_sum_inv\n",
    "dcounts += torch.ones_like(counts) * dcounts_sum\n",
    "dnorm_logits = counts * dcounts\n",
    "dlogits = dnorm_logits.clone()\n",
    "dlogits_max = (-dnorm_logits).sum(1, keepdims=True)\n",
    "\n",
    "cmp(\"logprobs\", dlogprobs, logprobs)\n",
    "cmp(\"probs\", dprobs, probs)\n",
    "cmp(\"counts_sum_inv\", dcounts_sum_inv, counts_sum_inv)\n",
    "cmp(\"counts_sum\", dcounts_sum, counts_sum)\n",
    "cmp(\"counts\", dcounts, counts)\n",
    "cmp(\"norm_logits\", dnorm_logits, norm_logits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 38:33"
   ]
  }
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