Convolution

conv2d applies a 2-D cross-correlation between an input feature map and a set of learned filters, which is the core operation in convolutional neural networks. pad adds zero-padding around the spatial dimensions of a tensor before the convolution, allowing control over output size. Both operations are fully differentiable and support backpropagation through both input and kernel.

import simplegrad as sg

x = sg.normal((1, 3, 28, 28))                          # (N, C, H, W)
kernel = sg.normal((16, 3, 3, 3), requires_grad=True)  # (out_ch, in_ch, kH, kW)
out = sg.conv2d(x, kernel, stride=1, padding=1)

pad(x: Tensor, width: int | tuple[int, int, int, int], mode: str = 'constant', value: int = 0) -> Tensor

Pad a tensor along its spatial dimensions.

Parameters:

• x (Tensor) –

  Input tensor.

• width (int | tuple[int, int, int, int]) –

  Padding widths. An int or nested tuples as accepted by numpy.pad.

• mode (str, default: 'constant' ) –

  Padding mode (e.g. "constant", "reflect"). See numpy.pad docs.

• value (int, default: 0 ) –

  Fill value for "constant" mode.

conv2d(x: Tensor, weight: Tensor, bias: Tensor | None = None, stride: int | tuple[int, int] = 1, pad_width: int | tuple[int, int, int, int] = 0, pad_mode: str = 'constant', pad_value: int = 0) -> Tensor

Apply a 2D convolution over the input tensor.

Implements convolution as a single matrix multiplication (im2col). Supports batched inputs (4D) and single-sample inputs (3D).

Parameters:

• x (Tensor) –

  Input tensor of shape (batch, in_channels, H, W) or (in_channels, H, W).

• weight (Tensor) –

  Kernel tensor of shape (out_channels, in_channels, kH, kW).

• bias (Tensor | None, default: None ) –

  Optional bias of shape (out_channels,).

• stride (int | tuple[int, int], default: 1 ) –

  Convolution stride. Int or (height_stride, width_stride).

• pad_width (int | tuple[int, int, int, int], default: 0 ) –

  Padding to apply before convolution. Int (same on all sides) or (top, bottom, left, right).

• pad_mode (str, default: 'constant' ) –

  Padding mode passed to numpy.pad. Defaults to "constant".

• pad_value (int, default: 0 ) –

  Fill value for constant padding. Defaults to 0.