Improving SAM Requires Rethinking its Optimization Formulation

This is official code for Improving SAM Requires Rethinking its Optimization Formulation accepted at ICML 2024.

The lower-bound loss function for the maximizer defined in the paper is

$$ Q_{\phi, \mu}(w) = \frac{1}{n} \sum_{i=1}^n \frac{1}{\mu} \log \left(\sum_{j=1}^K e^{\mu \phi({F_{w}(x_i,y_i)_j})} \right) $$

Function $\phi(x)$ is the lower bound of 0-1 step function. We show 2 suggested lower bounds in the paper:

• For BiSAM (tanh), we set $\phi(x)=\tanh(\alpha x)$.
• For BiSAM (-log), we set $\phi(x) = -\log(1 + e^{(\gamma-x)}) + 1$ where $\gamma=\log(e-1)$.

The implementation of these 2 function can be found in loss_fnc.py

conda create -n bisam python=3.8
conda activate bisam

# On GPU
conda install pytorch torchvision torchaudio pytorch-cuda=12.1 -c pytorch -c nvidia

pip install -r requirements.txt
python train.py

1. This code contains SAM, BiSAM (-log), BiSAM (tanh) on CIFAR-10/CIFAR-100 listed in Table 1&2 in the paper. Use --opt bisam_log to modify it.

   --opt	sam	bisam_log	bisam_tanh
   optimizer	SAM	BiSAM (-log)	BiSAM (tanh)

2. Example scripts:

   python train.py --optim bisam_log --rho 0.05 --epochs 200 --learning_rate 0.1 --model resnet56 --dataset cifar10

@inproceedings{xie2024improving,
  title={Improving SAM Requires Rethinking its Optimization Formulation},
  author={Xie, Wanyun and Latorre, Fabian and Antonakopoulos, Kimon and Pethick, Thomas and Cevher, Volkan},
  booktitle={International Conference on Machine Learning (ICML)},
  year={2024}
}

[1] (Adaptive) SAM Optimizer