NumPy で畳込み層

# Copyright 2021 Seiya Tokui
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
import numpy


def conv2d(x, w, bias=None, stride=1, padding=0, dilation=1, groups=1):
    """PyTorch-compatible simple implementation of conv2d in pure NumPy.

    NOTE: This code prioritizes simplicity, sacrificing the performance.
    It is much faster to use matmul instead of einsum (at least with NumPy 1.19.1).

    MIT License.

    """
    sY, sX = stride if isinstance(stride, (list, tuple)) else (stride, stride)
    pY, pX = padding if isinstance(padding, (list, tuple)) else (padding, padding)
    dY, dX = dilation if isinstance(dilation, (list, tuple)) else (dilation, dilation)
    N, iC, iH, iW = x.shape
    oC, iCg, kH, kW = w.shape
    pY_ex = (sY - (iH + pY * 2 - (kH - 1) * dY) % sY) % sY
    pX_ex = (sX - (iW + pX * 2 - (kW - 1) * dX) % sX) % sX
    oH = (iH + pY * 2 + pY_ex - (kH - 1) * dY) // sY
    oW = (iW + pX * 2 + pX_ex - (kW - 1) * dX) // sX

    x = numpy.pad(x, ((0, 0), (0, 0), (pY, pY + pY_ex), (pX, pX + pX_ex)))
    sN, sC, sH, sW = x.strides
    col = numpy.lib.stride_tricks.as_strided(
        x, shape=(N, groups, iCg, oH, oW, kH, kW),
        strides=(sN, sC * iCg, sC, sH * sY, sW * sX, sH * dY, sW * dX),
    )
    w = w.reshape(groups, oC // groups, iCg, kH, kW)
    y = numpy.einsum('ngihwkl,goikl->ngohw', col, w).reshape(N, oC, oH, oW)
    if bias is not None:
        y += bias[:, None, None]
    return y