  Vision transformers (ViTs) have demonstrated remarkable performance across
various visual tasks. However, ViT models suffer from substantial computational
and memory requirements, making it challenging to deploy them on
resource-constrained platforms. Quantization is a popular approach for reducing
model size, but most studies mainly focus on equal bit-width quantization for
the entire network, resulting in sub-optimal solutions. While there are few
works on mixed precision quantization (MPQ) for ViTs, they typically rely on
search space-based methods or employ mixed precision arbitrarily. In this
paper, we introduce LRP-QViT, an explainability-based method for assigning
mixed-precision bit allocations to different layers based on their importance
during classification. Specifically, to measure the contribution score of each
layer in predicting the target class, we employ the Layer-wise Relevance
Propagation (LRP) method. LRP assigns local relevance at the output layer and
propagates it through all layers, distributing the relevance until it reaches
the input layers. These relevance scores serve as indicators for computing the
layer contribution score. Additionally, we have introduced a clipped
channel-wise quantization aimed at eliminating outliers from post-LayerNorm
activations to alleviate severe inter-channel variations. To validate and
assess our approach, we employ LRP-QViT across ViT, DeiT, and Swin transformer
models on various datasets. Our experimental findings demonstrate that both our
fixed-bit and mixed-bit post-training quantization methods surpass existing
models in the context of 4-bit and 6-bit quantization.
