Convolution Shape and Parameter Calculator

Shape mismatches are the most common deep learning bug. Implement PyTorch's formulas:

• conv_out(n, k, stride=1, padding=0, dilation=1): $\left\lfloor\frac{n + 2p - d(k-1) - 1}{s}\right\rfloor + 1$
• conv_transpose_out(n, k, stride=1, padding=0, dilation=1, output_padding=0): $(n-1)s - 2p + d(k-1) + \text{output\_padding} + 1$
• same_padding(k, dilation=1): the padding that keeps the size unchanged at stride 1, for odd effective kernel sizes: $d(k-1)/2$
• conv_params(c_in, c_out, k, groups=1, bias=True): weights $c_{out} \cdot \frac{c_{in}}{groups} \cdot k^2$, plus $c_{out}$ biases
• separable_params(c_in, c_out, k): a depthwise k×k convolution (groups = c_in, with bias) followed by a pointwise 1×1 convolution (with bias)
• trace_shapes(n, layers): apply a list of (k, stride, padding) conv layers to a size n and return the list of sizes after each layer