MLP-Mixer as a Wide and Sparse MLP
Tomohiro Hayase Ryo Karakida
Multi-layer perceptron (MLP) is a fundamental component of deep learning that
has been extensively employed for various problems. However, recent empirical
successes in MLP-based architectures, particularly the progress of the
MLP-Mixer, have revealed that there is still hidden potential in improving MLPs
to achieve better performance. In this study, we reveal that the MLP-Mixer
works effectively as a wide MLP with certain sparse weights. Initially, we
clarify that the mixing layer of the Mixer has an effective expression as a
wider MLP whose weights are sparse and represented by the Kronecker product.
This expression naturally defines a permuted-Kronecker (PK) family, which can
be regarded as a general class of mixing layers and is also regarded as an
approximation of Monarch matrices. Subsequently, because the PK family
effectively constitutes a wide MLP with sparse weights, one can apply the
hypothesis proposed by Golubeva, Neyshabur and Gur-Ari (2021) that the
prediction performance improves as the width (sparsity) increases when the
number of weights is fixed. We empirically verify this hypothesis by maximizing
the effective width of the MLP-Mixer, which enables us to determine the
appropriate size of the mixing layers quantitatively.