  Some conventional transforms such as Discrete Walsh-Hadamard Transform (DWHT)
and Discrete Cosine Transform (DCT) have been widely used as feature extractors
in image processing but rarely applied in neural networks. However, we found
that these conventional transforms have the ability to capture the
cross-channel correlations without any learnable parameters in DNNs. This paper
firstly proposes to apply conventional transforms to pointwise convolution,
showing that such transforms significantly reduce the computational complexity
of neural networks without accuracy performance degradation. Especially for
DWHT, it requires no floating point multiplications but only additions and
subtractions, which can considerably reduce computation overheads. In addition,
its fast algorithm further reduces complexity of floating point addition from
$\mathcal{O}(n^2)$ to $\mathcal{O}(n\log n)$. These nice properties construct
extremely efficient networks in the number parameters and operations, enjoying
accuracy gain. Our proposed DWHT-based model gained 1.49\% accuracy increase
with 79.1\% reduced parameters and 48.4\% reduced FLOPs compared with its
baseline model (MoblieNet-V1) on the CIFAR 100 dataset.
