This repository is the official PyTorch implementation of the paper White-Box Transformers via Sparse Rate Reduction (2023)

by Yaodong Yu (UC Berkeley), Sam Buchanan (TTIC), Druv Pai (UC Berkeley), Tianzhe Chu (UC Berkeley), Ziyang Wu (UC Berkeley), Shengbang Tong (UC Berkeley), Benjamin D Haeffele (Johns Hopkins University), and Yi Ma (UC Berkeley).

CRATE (Coding RAte reduction TransformEr) is a white-box (mathematically interpretable) transformer architecture, where each layer performs a single step of an alternating minimization algorithm to optimize the sparse rate reduction objective

where the $\ell^{0}$-norm promotes the sparsity of the final token representations $\mathbf{Z} = f(\mathbf{X})$. The function $f$ is defined as $$f=f^{L} \circ f^{L-1} \circ \cdots \circ f^{1} \circ f^{0},$$ $f^0$ is the pre-processing mapping, and $f^{\ell}$ is the $\ell$-th layer forward mapping that transforms the token distribution to optimize the above sparse rate reduction objective incrementally. More specifically, $f^{\ell}$ transforms the $\ell$-th layer token representations $\mathbf{Z}^{\ell}$ to $\mathbf{Z}^{\ell+1}$ via the $\texttt{MSSA}$ (Multi-Head Subspace Self-Attention) block and the $\texttt{ISTA}$ (Iterative Shrinkage-Thresholding Algorithms) block, i.e., $$\mathbf{Z}^{\ell+1} = f^{\ell}(\mathbf{Z}^{\ell}) = \texttt{ISTA}(\texttt{MSSA}(\mathbf{Z}^{\ell})).$$ Figure 1 presents an overview of the pipeline for our proposed CRATE architecture:

Figure 2 shows the overall architecture of one block of CRATE:

In Figure 3, we measure the compression term [ $R^{c}$ ($\mathbf{Z}^{\ell+1/2}$) ] and the sparsity term [ $||\mathbf{Z}^{\ell+1}||_0$ ] defined in the sparse rate reduction objective, and we find that each layer of CRATE indeed optimizes the targeted objectives:

A CRATE model can be defined using the following code, (the below parameters are specified for CRATE-Tiny)

from model.crate import CRATE
dim = 384
n_heads = 6
depth = 12
model = CRATE(image_size=224,
              patch_size=16,
              num_classes=1000,
              dim=dim,
              depth=depth,
              heads=n_heads,
              dim_head=dim // n_heads)

To train a CRATE model on ImageNet-1K, run the following script (training CRATE-tiny)

As an example, we use the following command for training CRATE-tiny on ImageNet-1K:

python main.py 
  --arch CRATE_tiny 
  --batch-size 512 
  --epochs 200 
  --optimizer Lion 
  --lr 0.0002 
  --weight-decay 0.05 
  --print-freq 25 
  --data DATA_DIR

and replace DATA_DIR with [imagenet-folder with train and val folders].

python finetune.py 
  --bs 256 
  --net CRATE_tiny 
  --opt adamW  
  --lr 5e-5 
  --n_epochs 200 
  --randomaug 1 
  --data cifar10 
  --ckpt_dir CKPT_DIR 
  --data_dir DATA_DIR

Replace CKPT_DIR with the path for the pretrained CRATE weight, and replace DATA_DIR with the path for the CIFAR10 dataset. If CKPT_DIR is None, then this script is for training CRATE from random initialization on CIFAR10.

For technical details and full experimental results, please check the paper. Please consider citing our work if you find it helpful to yours:

@misc{yu2023whitebox,
      title={White-Box Transformers via Sparse Rate Reduction}, 
      author={Yaodong Yu and Sam Buchanan and Druv Pai and Tianzhe Chu and Ziyang Wu and Shengbang Tong and Benjamin D. Haeffele and Yi Ma},
      year={2023},
      eprint={2306.01129},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}