I knew the concept from ML coursework but writing the actual nested loop logic under pressure is a different thing.
Start by clarifying the input dimensions, filter size, stride, padding, and whether it's a single-channel or multi-channel convolution. Then, outline a naive implementation using nested loops, and discuss how to optimize it with vectorization or im2col. Finally, analyze the time and space complexity and mention trade-offs between different implementations.
Pro tip: Demonstrate awareness of edge cases like non-square inputs, even-sized filters, and padding modes; also mention how frameworks like PyTorch implement convolution using im2col and GEMM for efficiency.
Ask about input dimensions, filter size, stride, padding, number of channels, and output requirements to ensure you understand the problem scope.
Describe a straightforward nested-loop approach: iterate over output positions, compute the sum of element-wise products between the filter and the input patch.
Explain how to use im2col to transform the input into a matrix, then perform matrix multiplication (GEMM) for efficiency, leveraging optimized BLAS libraries.
Discuss time complexity (O(output_height * output_width * filter_height * filter_width * channels)) and space complexity, and compare naive vs. im2col in terms of memory and speed.
Mention handling of padding, stride, dilation, and multi-channel inputs; also briefly discuss backpropagation for training if relevant.
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