Demonstration in PyTorch how convolutions can implemented using matrix multiplication

convolution_matrix_multiplication_equivalence.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "81e7ca94",
   "metadata": {},
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   "source": [
    "from torch import ops, nn\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "48f4402a",
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.manual_seed(42)\n",
    "n, k, m = 2, 3, 7\n",
    "x = torch.rand((n, k))\n",
    "w = torch.rand((k, m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "82f1f786",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.8491, 1.5473, 1.3366, 1.2461, 1.3900, 0.8708, 1.4785],\n",
       "        [0.6298, 1.3159, 1.2486, 0.9732, 1.1839, 0.8354, 1.2946]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "torch.matmul(x, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5f14b47b",
   "metadata": {},
   "outputs": [],
   "source": [
    "conv2d = torch.nn.Conv2d(in_channels=k, out_channels=m, kernel_size=1, stride=1, bias=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "58acf800",
   "metadata": {},
   "outputs": [],
   "source": [
    "conv2d.weight.data = w.T.reshape(m, k, 1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "66b90a65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.8491, 1.5473, 1.3366, 1.2461, 1.3900, 0.8708, 1.4785],\n",
       "        [0.6298, 1.3159, 1.2486, 0.9732, 1.1839, 0.8354, 1.2946]],\n",
       "       grad_fn=<PermuteBackward0>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conv2d(x.T.reshape(1, k, n, 1)).squeeze().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c737d72a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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