rope_embedding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# RoPE 的基本实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mRunning cells with 'Python 3.8.2' requires the ipykernel package.\n",
      "\u001b[1;31mRun the following command to install 'ipykernel' into the Python environment. \n",
      "\u001b[1;31mCommand: '/usr/bin/python3 -m pip install ipykernel -U --user --force-reinstall'"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from einops import rearrange\n",
    "from torch import einsum, nn\n",
    "\n",
    "class RotaryEmbedding(nn.Module):\n",
    "    def __init__(self, dim, max_position_embeddings=2048, base=10000, device=None):\n",
    "        super().__init__()\n",
    "\n",
    "        self.dim = dim\n",
    "        self.max_position_embeddings = max_position_embeddings\n",
    "        self.base = base\n",
    "        inv_freq = 1.0 / (self.base ** (torch.arange(0, self.dim, 2).float().to(device) / self.dim))\n",
    "        self.register_buffer(\"inv_freq\", inv_freq, persistent=False)\n",
    "\n",
    "        # Build here to make `torch.jit.trace` work.\n",
    "        self._set_cos_sin_cache(\n",
    "            seq_len=max_position_embeddings, device=self.inv_freq.device, dtype=torch.get_default_dtype()\n",
    "        )\n",
    "        self.max_seq_len_cached = None\n",
    "\n",
    "\n",
    "    def _set_cos_sin_cache(self, seq_len, device, dtype):\n",
    "        self.max_seq_len_cached = seq_len\n",
    "        t = torch.arange(self.max_seq_len_cached, device=device, dtype=self.inv_freq.dtype)\n",
    "\n",
    "        freqs = torch.outer(t, self.inv_freq.to(t.device))\n",
    "        # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "        emb = torch.cat((freqs, freqs), dim=-1)\n",
    "        self.register_buffer(\"cos_cached\", emb.cos().to(dtype), persistent=False)\n",
    "        self.register_buffer(\"sin_cached\", emb.sin().to(dtype), persistent=False)\n",
    "\n",
    "    def forward(self, x, seq_len=None):\n",
    "        # x: [bs, num_attention_heads, seq_len, head_size]\n",
    "        if self.max_seq_len_cached is None or seq_len > self.max_seq_len_cached:\n",
    "            self._set_cos_sin_cache(seq_len=seq_len, device=x.device, dtype=x.dtype)\n",
    "\n",
    "        return (\n",
    "            self.cos_cached[:seq_len].to(dtype=x.dtype),\n",
    "            self.sin_cached[:seq_len].to(dtype=x.dtype),\n",
    "        )\n",
    "\n",
    "\n",
    "\n",
    "def rotate_half(x):\n",
    "    \"\"\"Rotates half the hidden dims of the input.\"\"\"\n",
    "    x1 = x[..., : x.shape[-1] // 2]\n",
    "    x2 = x[..., x.shape[-1] // 2 :]\n",
    "    return torch.cat((-x2, x1), dim=-1)\n",
    "\n",
    "\n",
    "def apply_rotary_pos_emb(q, k, cos, sin, position_ids, unsqueeze_dim=1):\n",
    "    cos = cos[position_ids].unsqueeze(unsqueeze_dim)\n",
    "    sin = sin[position_ids].unsqueeze(unsqueeze_dim)\n",
    "    q_embed = (q * cos) + (rotate_half(q) * sin)\n",
    "    k_embed = (k * cos) + (rotate_half(k) * sin)\n",
    "    return q_embed, k_embed\n",
    "\n",
    "\n",
    "\n",
    "# (bs, head, length, dim)\n",
    "q = torch.randn((2, 12, 10, 32))  # q=[q0, q1, .., qd-1]\n",
    "k = torch.randn((2, 12, 10, 32))\n",
    "v = torch.randn((2, 12, 10, 32))\n",
    "position_ids = torch.tensor(list(range(0, 10))).unsqueeze(0).repeat(2, 1)\n",
    "print('q:', q[0][0][0])\n",
    "print('k:', k[0][0][0])\n",
    "rotary_emb = RotaryEmbedding(dim=32,max_position_embeddings=10)\n",
    "cos, sin = rotary_emb(v, seq_len=10)\n",
    "q_new, k_new = apply_rotary_pos_emb(q, k, cos, sin, position_ids)\n",
    "print('q_new: ', q_new[0][0][0])\n",
    "print('k_new: ', k_new[0][0][0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RoPE 的远程衰减\n",
    "\n",
    "- 除了 base=1 外，均有明显的远程衰减特性\n",
    "- base 越小，衰减得越快且幅度也更大\n",
    "- base 越大，衰减得越慢且幅度也越小"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/fromeast/anaconda3/lib/python3.11/site-packages/scipy/integrate/_quadpack_py.py:577: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return _quadpack._qagse(func,a,b,args,full_output,epsabs,epsrel,limit)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def integrand(t, dis, base=10000):\n",
    "    return np.exp(1j * dis * base**(-t))\n",
    "\n",
    "def plot():\n",
    "    x = np.arange(0, 100, 0.1)\n",
    "    base_list = [1, 100, 1000, 10000, 100000]\n",
    "    y = np.zeros((len(base_list),len(x)))\n",
    "    for b in range(len(base_list)):\n",
    "        n = base_list[b]\n",
    "        for i in range(len(x)):\n",
    "            res, err=quad(integrand, 0, 1, args=(x[i],n))\n",
    "            y[b][i]=res\n",
    "            \n",
    "    plt.plot(x, y[0], 'g', label='base='+str(base_list[0]))\n",
    "    plt.plot(x, y[1], 'r', label='base='+str(base_list[1]))\n",
    "    plt.plot(x, y[2], 'b', label='base='+str(base_list[2]))\n",
    "    plt.plot(x, y[3], 'k', label='base='+str(base_list[3]))\n",
    "    plt.plot(x, y[4], 'c', label='base='+str(base_list[4]))\n",
    "    \n",
    "    plt.xlabel('Distance')\n",
    "    plt.ylabel('Value')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 线性插值的实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q: tensor([-0.7386,  0.3126, -0.6404, -1.1976,  0.1745,  0.8204,  1.9868, -2.1083,\n",
      "         1.7011,  0.8929,  0.0727,  0.2456,  0.3690,  1.4194,  0.9576, -1.9760,\n",
      "        -0.2564,  0.9356,  1.2557,  0.6416,  1.2461,  0.4018,  0.1794,  0.1308,\n",
      "        -0.0078,  0.8118,  1.4571,  0.1142,  1.2326, -0.7917, -2.3047, -0.0602])\n",
      "k: tensor([-0.6328,  0.1178, -1.1089,  1.5455,  0.9656, -0.1420,  0.4648, -1.4591,\n",
      "        -0.9455,  0.3302, -0.5119, -1.4733, -1.2549, -0.1893,  0.7730, -0.3901,\n",
      "         0.0137,  0.3142, -0.6838,  0.4591,  0.5648, -0.1194,  0.8176, -1.2282,\n",
      "         0.1147, -0.3555,  0.0753,  0.1046, -0.5155, -1.0724, -0.0387, -0.7406])\n",
      "q_new:  tensor([-0.7386,  0.3126, -0.6404, -1.1976,  0.1745,  0.8204,  1.9868, -2.1083,\n",
      "         1.7011,  0.8929,  0.0727,  0.2456,  0.3690,  1.4194,  0.9576, -1.9760,\n",
      "        -0.2564,  0.9356,  1.2557,  0.6416,  1.2461,  0.4018,  0.1794,  0.1308,\n",
      "        -0.0078,  0.8118,  1.4571,  0.1142,  1.2326, -0.7917, -2.3047, -0.0602])\n",
      "k_new:  tensor([-0.6328,  0.1178, -1.1089,  1.5455,  0.9656, -0.1420,  0.4648, -1.4591,\n",
      "        -0.9455,  0.3302, -0.5119, -1.4733, -1.2549, -0.1893,  0.7730, -0.3901,\n",
      "         0.0137,  0.3142, -0.6838,  0.4591,  0.5648, -0.1194,  0.8176, -1.2282,\n",
      "         0.1147, -0.3555,  0.0753,  0.1046, -0.5155, -1.0724, -0.0387, -0.7406])\n"
     ]
    }
   ],
   "source": [
    "class LinearScaledRotaryEmbedding(torch.nn.Module):\n",
    "    def __init__(self, dim, max_position_embeddings=2048, base=10000, scale=1, device=None):\n",
    "        super().__init__()\n",
    "        # 相比RoPE增加scale参数\n",
    "        self.scale = scale\n",
    "        # inv_freq为基值向量\n",
    "        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float().to(device) / dim))\n",
    "        self.register_buffer(\"inv_freq\", inv_freq)\n",
    "\n",
    "        # Build here to make `torch.jit.trace` work.\n",
    "        self.max_seq_len_cached = max_position_embeddings\n",
    "        # 构建max_seq_len_cached大小的张量t\n",
    "        t = torch.arange(self.max_seq_len_cached, device=self.inv_freq.device, dtype=self.inv_freq.dtype)\n",
    "        # 张量t归一化，RoPE没有这一步\n",
    "        t /= self.scale\n",
    "        # einsum计算频率矩阵\n",
    "        # 'i, j->i j’表示分别输入尺寸为[i]、[j]的向量，做笛卡尔运算得到尺寸为[i, j]的矩阵。\n",
    "        freqs = torch.einsum(\"i,j->ij\", t, self.inv_freq)\n",
    "        # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "        # 在-1维做一次拷贝、拼接\n",
    "        emb = torch.cat((freqs, freqs), dim=-1)\n",
    "        dtype = torch.get_default_dtype()\n",
    "        # 注册为模型的缓冲区cos_cached和sin_cached\n",
    "        self.register_buffer(\"cos_cached\", emb.cos().to(dtype), persistent=False)\n",
    "        self.register_buffer(\"sin_cached\", emb.sin().to(dtype), persistent=False)\n",
    "\n",
    "    def forward(self, x, seq_len=None):\n",
    "        # x: [bs, num_attention_heads, seq_len, head_size]\n",
    "        # This `if` block is unlikely to be run after we build sin/cos in `__init__`. Keep the logic here just in case.\n",
    "        # seq_len为序列长度，seq_len大于max_seq_len_cached，则重新计算频率矩阵，并更新cos_cached和sin_cached的缓冲区\n",
    "        if seq_len > self.max_seq_len_cached:\n",
    "            self.max_seq_len_cached = seq_len\n",
    "            t = torch.arange(self.max_seq_len_cached, device=x.device, dtype=self.inv_freq.dtype)\n",
    "            t /= self.scale\n",
    "            freqs = torch.einsum(\"i,j->ij\", t, self.inv_freq)\n",
    "            # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "            emb = torch.cat((freqs, freqs), dim=-1).to(x.device)\n",
    "            self.register_buffer(\"cos_cached\", emb.cos().to(x.dtype), persistent=False)\n",
    "            self.register_buffer(\"sin_cached\", emb.sin().to(x.dtype), persistent=False)\n",
    "        # 长度裁剪：返回cos_cached和sin_cached中与seq_len（序列长度）\n",
    "        return (\n",
    "            self.cos_cached[:seq_len].to(dtype=x.dtype),\n",
    "            self.sin_cached[:seq_len].to(dtype=x.dtype),\n",
    "        )\n",
    "    \n",
    "# (bs, head, length, dim)\n",
    "q = torch.randn((2, 12, 10, 32))  # q=[q0, q1, .., qd-1]\n",
    "k = torch.randn((2, 12, 10, 32))\n",
    "v = torch.randn((2, 12, 10, 32))\n",
    "position_ids = torch.tensor(list(range(0, 10))).unsqueeze(0).repeat(2, 1)\n",
    "print('q:', q[0][0][0])\n",
    "print('k:', k[0][0][0])\n",
    "rotary_emb = LinearScaledRotaryEmbedding(dim=32, max_position_embeddings=10, scale=2)\n",
    "cos, sin = rotary_emb(v, seq_len=20)\n",
    "\n",
    "q_new, k_new = apply_rotary_pos_emb(q, k, cos, sin, position_ids)\n",
    "print('q_new: ', q_new[0][0][0])\n",
    "print('k_new: ', k_new[0][0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NTK aware 外推的实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q: tensor([-2.0356,  0.5335, -0.2943,  2.2030, -0.5060,  0.3836,  0.8608,  0.5533,\n",
      "         0.6158,  0.9927, -0.7878, -0.3978,  0.3661,  1.1224, -1.8043, -0.7314,\n",
      "        -1.3826, -1.5953,  0.4749, -0.7502,  0.8913, -1.2234, -0.1037,  0.2985,\n",
      "        -0.5934,  1.3392, -0.2031, -1.2564, -0.6747, -0.9470, -0.7968, -0.1576])\n",
      "k: tensor([ 0.2242,  0.7023, -0.5397, -1.2178,  0.9707,  0.7650, -1.0225, -0.8561,\n",
      "        -1.3768, -1.4814,  0.9796, -0.2181, -1.2774,  1.9119,  1.5775,  0.5692,\n",
      "        -0.7546, -2.0346, -0.6144, -0.1261,  2.2313, -0.1916,  2.5680,  0.5018,\n",
      "        -0.0589, -1.0014, -0.6470,  0.1474, -1.3001,  0.2115, -0.7482,  0.3008])\n",
      "q_new:  tensor([-2.0356,  0.5335, -0.2943,  2.2030, -0.5060,  0.3836,  0.8608,  0.5533,\n",
      "         0.6158,  0.9927, -0.7878, -0.3978,  0.3661,  1.1224, -1.8043, -0.7314,\n",
      "        -1.3826, -1.5953,  0.4749, -0.7502,  0.8913, -1.2234, -0.1037,  0.2985,\n",
      "        -0.5934,  1.3392, -0.2031, -1.2564, -0.6747, -0.9470, -0.7968, -0.1576])\n",
      "k_new:  tensor([ 0.2242,  0.7023, -0.5397, -1.2178,  0.9707,  0.7650, -1.0225, -0.8561,\n",
      "        -1.3768, -1.4814,  0.9796, -0.2181, -1.2774,  1.9119,  1.5775,  0.5692,\n",
      "        -0.7546, -2.0346, -0.6144, -0.1261,  2.2313, -0.1916,  2.5680,  0.5018,\n",
      "        -0.0589, -1.0014, -0.6470,  0.1474, -1.3001,  0.2115, -0.7482,  0.3008])\n"
     ]
    }
   ],
   "source": [
    "class NTKScaledRotaryEmbedding(torch.nn.Module):\n",
    "    def __init__(self, dim, max_position_embeddings=2048, base=10000, alpha=1, device=None):\n",
    "        super().__init__()\n",
    "        # 与线性插值法相比，实现更简单，alpha仅用来改变base\n",
    "        base = base * alpha ** (dim / (dim-2))\n",
    "        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float().to(device) / dim))\n",
    "        self.register_buffer(\"inv_freq\", inv_freq)\n",
    "\n",
    "        # Build here to make `torch.jit.trace` work.\n",
    "        self.max_seq_len_cached = max_position_embeddings\n",
    "        t = torch.arange(self.max_seq_len_cached, device=self.inv_freq.device, dtype=self.inv_freq.dtype)\n",
    "        freqs = torch.einsum(\"i,j->ij\", t, self.inv_freq)\n",
    "        # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "        emb = torch.cat((freqs, freqs), dim=-1)\n",
    "        dtype = torch.get_default_dtype()\n",
    "        self.register_buffer(\"cos_cached\", emb.cos().to(dtype), persistent=False)\n",
    "        self.register_buffer(\"sin_cached\", emb.sin().to(dtype), persistent=False)\n",
    "\n",
    "    def forward(self, x, seq_len=None):\n",
    "        # x: [bs, num_attention_heads, seq_len, head_size]\n",
    "        # This `if` block is unlikely to be run after we build sin/cos in `__init__`. Keep the logic here just in case.\n",
    "        if seq_len > self.max_seq_len_cached:\n",
    "            self.max_seq_len_cached = seq_len\n",
    "            t = torch.arange(self.max_seq_len_cached, device=x.device, dtype=self.inv_freq.dtype)\n",
    "            freqs = torch.einsum(\"i,j->ij\", t, self.inv_freq)\n",
    "            # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "            emb = torch.cat((freqs, freqs), dim=-1).to(x.device)\n",
    "            self.register_buffer(\"cos_cached\", emb.cos().to(x.dtype), persistent=False)\n",
    "            self.register_buffer(\"sin_cached\", emb.sin().to(x.dtype), persistent=False)\n",
    "        return (\n",
    "            self.cos_cached[:seq_len].to(dtype=x.dtype),\n",
    "            self.sin_cached[:seq_len].to(dtype=x.dtype),\n",
    "        )\n",
    "    \n",
    "# (bs, head, length, dim)\n",
    "q = torch.randn((2, 12, 10, 32))  # q=[q0, q1, .., qd-1]\n",
    "k = torch.randn((2, 12, 10, 32))\n",
    "v = torch.randn((2, 12, 10, 32))\n",
    "position_ids = torch.tensor(list(range(0, 10))).unsqueeze(0).repeat(2, 1)\n",
    "print('q:', q[0][0][0])\n",
    "print('k:', k[0][0][0])\n",
    "rotary_emb = NTKScaledRotaryEmbedding(dim=32, max_position_embeddings=10, alpha=10)\n",
    "cos, sin = rotary_emb(v, seq_len=20)\n",
    "\n",
    "q_new, k_new = apply_rotary_pos_emb(q, k, cos, sin, position_ids)\n",
    "print('q_new: ', q_new[0][0][0])\n",
    "print('k_new: ', k_new[0][0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynaimic NTK 外推的实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q: tensor([-1.0314,  0.3475,  0.6054,  0.4758,  0.2080, -0.1064, -0.2559, -1.2432,\n",
      "        -1.2669, -0.8704, -1.3891,  0.5940, -0.5314, -1.0073,  0.5326, -0.9410,\n",
      "         0.6888, -0.2143, -0.8900, -0.5465, -0.8815,  0.8723, -0.0125, -1.6313,\n",
      "         0.1018,  0.7021, -0.5169, -0.1331, -1.0006,  0.1864,  0.2876, -0.9891])\n",
      "k: tensor([ 1.5224, -1.2986, -0.5644, -0.5807,  2.1788, -0.2760, -0.6890,  0.4139,\n",
      "        -0.0151, -1.4198,  0.6517,  0.2883, -0.7820, -0.2261, -0.7961, -1.7140,\n",
      "        -0.9996,  0.2228, -0.5026, -1.3464, -0.1856,  2.9333,  1.4121,  0.6357,\n",
      "         0.4330, -2.9884,  1.1371,  0.5648,  1.5028,  0.8673,  0.1810,  0.6892])\n",
      "q_new:  tensor([-1.0314,  0.3475,  0.6054,  0.4758,  0.2080, -0.1064, -0.2559, -1.2432,\n",
      "        -1.2669, -0.8704, -1.3891,  0.5940, -0.5314, -1.0073,  0.5326, -0.9410,\n",
      "         0.6888, -0.2143, -0.8900, -0.5465, -0.8815,  0.8723, -0.0125, -1.6313,\n",
      "         0.1018,  0.7021, -0.5169, -0.1331, -1.0006,  0.1864,  0.2876, -0.9891])\n",
      "k_new:  tensor([ 1.5224, -1.2986, -0.5644, -0.5807,  2.1788, -0.2760, -0.6890,  0.4139,\n",
      "        -0.0151, -1.4198,  0.6517,  0.2883, -0.7820, -0.2261, -0.7961, -1.7140,\n",
      "        -0.9996,  0.2228, -0.5026, -1.3464, -0.1856,  2.9333,  1.4121,  0.6357,\n",
      "         0.4330, -2.9884,  1.1371,  0.5648,  1.5028,  0.8673,  0.1810,  0.6892])\n"
     ]
    }
   ],
   "source": [
    "class DynamicScaledRotaryEmbedding(torch.nn.Module):\n",
    "    def __init__(self, dim, max_position_embeddings=2048, base=10000, ntk=False, device=None):\n",
    "        super().__init__()\n",
    "        # 是否开启NTK（Neural Tangent Kernel）\n",
    "        self.ntk = ntk\n",
    "        self.base = base\n",
    "        self.dim = dim\n",
    "        self.max_position_embeddings = max_position_embeddings\n",
    "        # inv_freq为基值向量\n",
    "        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float().to(device) / dim))\n",
    "        self.register_buffer(\"inv_freq\", inv_freq)\n",
    "\n",
    "        # Build here to make `torch.jit.trace` work.\n",
    "        self.max_seq_len_cached = max_position_embeddings\n",
    "        t = torch.arange(self.max_seq_len_cached, device=self.inv_freq.device, dtype=self.inv_freq.dtype)\n",
    "        freqs = torch.einsum(\"i,j->ij\", t, self.inv_freq)\n",
    "        # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "        # emb：[max_seq_len_cached, dim]\n",
    "        emb = torch.cat((freqs, freqs), dim=-1)\n",
    "        dtype = torch.get_default_dtype()\n",
    "        self.register_buffer(\"cos_cached\", emb.cos().to(dtype), persistent=False)\n",
    "        self.register_buffer(\"sin_cached\", emb.sin().to(dtype), persistent=False)\n",
    "\n",
    "    def forward(self, x, seq_len=None):\n",
    "        # x: [bs, num_attention_heads, seq_len, head_size]\n",
    "        # This `if` block is unlikely to be run after we build sin/cos in `__init__`. Keep the logic here just in case.\n",
    "        if seq_len > self.max_seq_len_cached:\n",
    "            self.max_seq_len_cached = seq_len\n",
    "            if self.ntk:\n",
    "                base = self.base * ((self.ntk * seq_len / self.max_position_embeddings) - (self.ntk - 1)) ** (self.dim / (self.dim-2))\n",
    "                # 计算新的inv_freq\n",
    "                inv_freq = 1.0 / (base ** (torch.arange(0, self.dim, 2).float().to(x.device) / self.dim))\n",
    "                self.register_buffer(\"inv_freq\", inv_freq)\n",
    "            t = torch.arange(self.max_seq_len_cached, device=x.device, dtype=self.inv_freq.dtype)\n",
    "            if not self.ntk:\n",
    "                # 缩放\n",
    "                t *= self.max_position_embeddings / seq_len\n",
    "            # 得到新的频率矩阵freqs\n",
    "            freqs = torch.einsum(\"i,j->ij\", t, self.inv_freq)\n",
    "            # Different from paper, but it uses a different permutation in order to obtain the same calculation\n",
    "            # freqs与自身拼接得到新的emb\n",
    "            emb = torch.cat((freqs, freqs), dim=-1).to(x.device)\n",
    "            # 注册为模型的缓冲区cos_cached和sin_cached\n",
    "            self.register_buffer(\"cos_cached\", emb.cos().to(x.dtype), persistent=False)\n",
    "            self.register_buffer(\"sin_cached\", emb.sin().to(x.dtype), persistent=False)\n",
    "\n",
    "        # 长度裁剪\n",
    "        return (\n",
    "            self.cos_cached[:seq_len].to(dtype=x.dtype),\n",
    "            self.sin_cached[:seq_len].to(dtype=x.dtype),\n",
    "        )\n",
    "    \n",
    "# (bs, head, length, dim)\n",
    "q = torch.randn((2, 12, 10, 32))  # q=[q0, q1, .., qd-1]\n",
    "k = torch.randn((2, 12, 10, 32))\n",
    "v = torch.randn((2, 12, 10, 32))\n",
    "position_ids = torch.tensor(list(range(0, 10))).unsqueeze(0).repeat(2, 1)\n",
    "print('q:', q[0][0][0])\n",
    "print('k:', k[0][0][0])\n",
    "rotary_emb = DynamicScaledRotaryEmbedding(dim=32, max_position_embeddings=10, ntk=True)\n",
    "cos, sin = rotary_emb(v, seq_len=20)\n",
    "\n",
    "q_new, k_new = apply_rotary_pos_emb(q, k, cos, sin, position_ids)\n",
    "print('q_new: ', q_new[0][0][0])\n",
    "print('k_new: ', k_new[0][0][0])"
   ]
  }
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