Codes/ch03/01_main-chapter-code/exercise-solutions.ipynb

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   "cell_type": "markdown",
   "id": "51c9672d-8d0c-470d-ac2d-1271f8ec3f14",
   "metadata": {},
   "source": [
    "# Chapter 3 习题解答"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33dfa199-9aee-41d4-a64b-7e3811b9a616",
   "metadata": {},
   "source": [
    "# 3.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5fee2cf5-61c3-4167-81b5-44ea155bbaf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "\n",
    "inputs = torch.tensor(\n",
    "  [[0.43, 0.15, 0.89], # Your     (x^1)\n",
    "   [0.55, 0.87, 0.66], # journey  (x^2)\n",
    "   [0.57, 0.85, 0.64], # starts   (x^3)\n",
    "   [0.22, 0.58, 0.33], # with     (x^4)\n",
    "   [0.77, 0.25, 0.10], # one      (x^5)\n",
    "   [0.05, 0.80, 0.55]] # step     (x^6)\n",
    ")\n",
    "\n",
    "d_in, d_out = 3, 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "62ea289c-41cd-4416-89dd-dde6383a6f70",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "\n",
    "class SelfAttention_v1(nn.Module):\n",
    "\n",
    "    def __init__(self, d_in, d_out):\n",
    "        super().__init__()\n",
    "        self.d_out = d_out\n",
    "        self.W_query = nn.Parameter(torch.rand(d_in, d_out))\n",
    "        self.W_key   = nn.Parameter(torch.rand(d_in, d_out))\n",
    "        self.W_value = nn.Parameter(torch.rand(d_in, d_out))\n",
    "\n",
    "    def forward(self, x):\n",
    "        keys = x @ self.W_key\n",
    "        queries = x @ self.W_query\n",
    "        values = x @ self.W_value\n",
    "        \n",
    "        attn_scores = queries @ keys.T # omega\n",
    "        attn_weights = torch.softmax(attn_scores / keys.shape[-1]**0.5, dim=-1)\n",
    "\n",
    "        context_vec = attn_weights @ values\n",
    "        return context_vec\n",
    "\n",
    "torch.manual_seed(123)\n",
    "sa_v1 = SelfAttention_v1(d_in, d_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7b035143-f4e8-45fb-b398-dec1bd5153d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SelfAttention_v2(nn.Module):\n",
    "\n",
    "    def __init__(self, d_in, d_out):\n",
    "        super().__init__()\n",
    "        self.d_out = d_out\n",
    "        self.W_query = nn.Linear(d_in, d_out, bias=False)\n",
    "        self.W_key   = nn.Linear(d_in, d_out, bias=False)\n",
    "        self.W_value = nn.Linear(d_in, d_out, bias=False)\n",
    "\n",
    "    def forward(self, x):\n",
    "        keys = self.W_key(x)\n",
    "        queries = self.W_query(x)\n",
    "        values = self.W_value(x)\n",
    "        \n",
    "        attn_scores = queries @ keys.T\n",
    "        attn_weights = torch.softmax(attn_scores / keys.shape[-1]**0.5, dim=1)\n",
    "\n",
    "        context_vec = attn_weights @ values\n",
    "        return context_vec\n",
    "\n",
    "torch.manual_seed(123)\n",
    "sa_v2 = SelfAttention_v2(d_in, d_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7591d79c-c30e-406d-adfd-20c12eb448f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "sa_v1.W_query = torch.nn.Parameter(sa_v2.W_query.weight.T)\n",
    "sa_v1.W_key = torch.nn.Parameter(sa_v2.W_key.weight.T)\n",
    "sa_v1.W_value = torch.nn.Parameter(sa_v2.W_value.weight.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ddd0f54f-6bce-46cc-a428-17c2a56557d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.5337, -0.1051],\n",
       "        [-0.5323, -0.1080],\n",
       "        [-0.5323, -0.1079],\n",
       "        [-0.5297, -0.1076],\n",
       "        [-0.5311, -0.1066],\n",
       "        [-0.5299, -0.1081]], grad_fn=<MmBackward0>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sa_v1(inputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "340908f8-1144-4ddd-a9e1-a1c5c3d592f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.5337, -0.1051],\n",
       "        [-0.5323, -0.1080],\n",
       "        [-0.5323, -0.1079],\n",
       "        [-0.5297, -0.1076],\n",
       "        [-0.5311, -0.1066],\n",
       "        [-0.5299, -0.1081]], grad_fn=<MmBackward0>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sa_v2(inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33543edb-46b5-4b01-8704-f7f101230544",
   "metadata": {},
   "source": [
    "# 3.2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fc1a301",
   "metadata": {},
   "source": [
    "如果我们想要多头注意力机制的输出和之前单头注意力机制一样为 2，我们可以将输出维度 `d_out` 设置为 1："
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18e748ef-3106-4e11-a781-b230b74a0cef",
   "metadata": {},
   "source": [
    "```python\n",
    "torch.manual_seed(123)\n",
    "\n",
    "d_out = 1\n",
    "mha = MultiHeadAttentionWrapper(d_in, d_out, block_size, 0.0, num_heads=2)\n",
    "\n",
    "context_vecs = mha(batch)\n",
    "\n",
    "print(context_vecs)\n",
    "print(\"context_vecs.shape:\", context_vecs.shape)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78234544-d989-4f71-ac28-85a7ec1e6b7b",
   "metadata": {},
   "source": [
    "```\n",
    "tensor([[[-9.1476e-02,  3.4164e-02],\n",
    "         [-2.6796e-01, -1.3427e-03],\n",
    "         [-4.8421e-01, -4.8909e-02],\n",
    "         [-6.4808e-01, -1.0625e-01],\n",
    "         [-8.8380e-01, -1.7140e-01],\n",
    "         [-1.4744e+00, -3.4327e-01]],\n",
    "\n",
    "        [[-9.1476e-02,  3.4164e-02],\n",
    "         [-2.6796e-01, -1.3427e-03],\n",
    "         [-4.8421e-01, -4.8909e-02],\n",
    "         [-6.4808e-01, -1.0625e-01],\n",
    "         [-8.8380e-01, -1.7140e-01],\n",
    "         [-1.4744e+00, -3.4327e-01]]], grad_fn=<CatBackward0>)\n",
    "context_vecs.shape: torch.Size([2, 6, 2])\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92bdabcb-06cf-4576-b810-d883bbd313ba",
   "metadata": {},
   "source": [
    "# 3.3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84c9b963-d01f-46e6-96bf-8eb2a54c5e42",
   "metadata": {},
   "source": [
    "```python\n",
    "block_size = 1024\n",
    "d_in, d_out = 768, 768\n",
    "num_heads = 12\n",
    "\n",
    "mha = MultiHeadAttention(d_in, d_out, block_size, 0.0, num_heads)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "375d5290-8e8b-4149-958e-1efb58a69191",
   "metadata": {},
   "source": [
    "上述实现的参数量为:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d7e603c-1658-4da9-9c0b-ef4bc72832b4",
   "metadata": {},
   "source": [
    "```python\n",
    "def count_parameters(model):\n",
    "    return sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
    "\n",
    "count_parameters(mha)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51ba00bd-feb0-4424-84cb-7c2b1f908779",
   "metadata": {},
   "source": [
    "```\n",
    "2360064  # (2.36 M)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a56c1d47-9b95-4bd1-a517-580a6f779c52",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "GPT-2 模型有 117M 的参数，但正如我们所见，绝大部分参数其实都不是来源于多头注意力机制（而是线性层）。"
   ]
  }
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