Convconvf

Convconvf is a theoretical concept in neural network optimization that refers to the fusion of two consecutive convolution operations into a single computational step by combining their kernels. The idea is to reduce computational overhead and memory bandwidth by replacing a pair of convolutions with an equivalent, larger convolution. The term appears in discussions of graph-level optimizations and compiler-based approaches to deep learning.

The mathematical basis is straightforward when there is no nonlinearity between the layers. If Y = X convolved with K1 and Z = Y convolved with K2, then Z is equivalent to X convolved with a composite kernel Kcomp, formed by the convolution of K1 and K2, provided stride and padding are chosen to preserve spatial dimensions. In such cases, convconvf aims to replace the two-layer sequence with a single convolution using the composite kernel Kcomp = K2 convolved with K1, with order reflecting the original convolution sequence.

Applicability requires a linear sequence of operations: no intervening nonlinear activation, and compatible strides and padding to maintain output size. The approach also needs proper channel alignment so that the fused kernel maps input and output channels correctly, which can be straightforward for single-path layers but more complex for multi-branch architectures.

Implementation and tooling often involve kernel fusion in deep learning compilers and graph optimizers. Real-world support depends on hardware capabilities and library implementations; fused kernels must be efficient to beat the cost of computing the larger, single convolution.

Limitations include potential growth in effective kernel size and parameter count, which can offset gains. Benefits may be reduced or negated when nonlinearities, skip connections, or irregular architectures are present. See also kernel fusion, operator fusion, and convolution in neural networks.