|
| 1 | +import numpy as np |
| 2 | + |
| 3 | + |
| 4 | +class Conv2D: |
| 5 | + def __init__(self, in_channels, out_channels, kernel_size=3, stride=1, padding=1): |
| 6 | + self.in_channels = in_channels |
| 7 | + self.out_channels = out_channels |
| 8 | + self.kernel_size = kernel_size |
| 9 | + self.stride = stride |
| 10 | + self.padding = padding |
| 11 | + |
| 12 | + # init kernels and biases |
| 13 | + self.kernels = ( |
| 14 | + np.random.randn(out_channels, in_channels, kernel_size, kernel_size) * 0.1 |
| 15 | + ) |
| 16 | + self.biases = np.zeros((out_channels, 1)) |
| 17 | + |
| 18 | + def _pad_input(self, X): |
| 19 | + if self.padding > 0: |
| 20 | + return np.pad( |
| 21 | + X, |
| 22 | + ( |
| 23 | + (0, 0), |
| 24 | + (0, 0), |
| 25 | + (self.padding, self.padding), |
| 26 | + (self.padding, self.padding), |
| 27 | + ), |
| 28 | + mode="constant", |
| 29 | + ) |
| 30 | + return X |
| 31 | + |
| 32 | + def forward(self, X): |
| 33 | + """ |
| 34 | + Perform forward propagation for convolutional layer. |
| 35 | +
|
| 36 | + Args: |
| 37 | + X: Input tensor of shape (batch_size, in_channels, height, width) |
| 38 | +
|
| 39 | + Returns: |
| 40 | + np.ndarray: Output tensor after convolution |
| 41 | + """ |
| 42 | + batch_size, in_channels, height, width = X.shape |
| 43 | + assert ( |
| 44 | + in_channels == self.in_channels |
| 45 | + ), "Input channels must match kernel channels." |
| 46 | + |
| 47 | + # calculate output dimensions |
| 48 | + out_height = (height + 2 * self.padding - self.kernel_size) // self.stride + 1 |
| 49 | + out_width = (width + 2 * self.padding - self.kernel_size) // self.stride + 1 |
| 50 | + |
| 51 | + # apply padding |
| 52 | + X_padded = self._pad_input(X) |
| 53 | + |
| 54 | + # allocate output tensor to store convolution results |
| 55 | + output = np.zeros((batch_size, self.out_channels, out_height, out_width)) |
| 56 | + |
| 57 | + # convolve |
| 58 | + for b in range(batch_size): # iterate over each sample in batch |
| 59 | + for o in range( |
| 60 | + self.out_channels |
| 61 | + ): # for each filter (each filter makes one feature map) |
| 62 | + for i in range( |
| 63 | + out_height |
| 64 | + ): # traverse over the locations of the feature map |
| 65 | + for j in range(out_width): |
| 66 | + # region of the input matrix that the kernel processes |
| 67 | + h_start = i * self.stride |
| 68 | + h_end = h_start + self.kernel_size |
| 69 | + w_start = j * self.stride |
| 70 | + w_end = w_start + self.kernel_size |
| 71 | + |
| 72 | + # extract the input region |
| 73 | + input_region = X_padded[b, :, h_start:h_end, w_start:w_end] |
| 74 | + |
| 75 | + # element-wise multiplication and summation |
| 76 | + output[b, o, i, j] = ( |
| 77 | + np.sum(input_region * self.kernels[o, :, :, :]) |
| 78 | + + self.biases[o] |
| 79 | + ) |
| 80 | + |
| 81 | + return output |
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