readme: # BERT-mini model finetuned with M-FAC
  
  This model is finetuned on SQuAD version 2 dataset with state-of-the-art second-order optimizer M-FAC.
  Check NeurIPS 2021 paper for more details on M-FAC: [https://arxiv.org/pdf/2107.03356.pdf](https://arxiv.org/pdf/2107.03356.pdf).
  
  ## Finetuning setup
  
  For fair comparison against default Adam baseline, we finetune the model in the same framework as described here [https://github.com/huggingface/transformers/tree/master/examples/pytorch/question-answering](https://github.com/huggingface/transformers/tree/master/examples/pytorch/question-answering) and just swap Adam optimizer with M-FAC.
  Hyperparameters used by M-FAC optimizer:
  
  ```bash
  learning rate = 1e-4
  number of gradients = 1024
  dampening = 1e-6
  ```
  
  ## Results
  
  We share the best model out of 5 runs with the following score on SQuAD version 2 validation set:
  
  ```bash
  exact_match = 58.38
  f1 = 61.65
  ```
  
  Mean and standard deviation for 5 runs on SQuAD version 2 validation set:
  
  | | Exact Match | F1  |
  |:----:|:-----------:|:----:|
  | Adam | 54.80 ± 0.47 | 58.13 ± 0.31 |
  | M-FAC | 58.02 ± 0.39 | 61.35 ± 0.24 |
  
  Results can be reproduced by adding M-FAC optimizer code in [https://github.com/huggingface/transformers/blob/master/examples/pytorch/question-answering/run_qa.py](https://github.com/huggingface/transformers/blob/master/examples/pytorch/question-answering/run_qa.py) and running the following bash script:
  
  ```bash
  CUDA_VISIBLE_DEVICES=0 python run_qa.py \
      --seed 8276 \
      --model_name_or_path prajjwal1/bert-mini \
      --dataset_name squad_v2 \
      --version_2_with_negative \
      --do_train \
      --do_eval \
      --per_device_train_batch_size 12 \
      --learning_rate 1e-4 \
      --num_train_epochs 2 \
      --max_seq_length 384 \
      --doc_stride 128 \
      --output_dir out_dir/ \
      --optim MFAC \
      --optim_args '{"lr": 1e-4, "num_grads": 1024, "damp": 1e-6}'
  ```
  
  We believe these results could be improved with modest tuning of hyperparameters: `per_device_train_batch_size`, `learning_rate`, `num_train_epochs`, `num_grads` and `damp`. For the sake of fair comparison  and a robust default setup we use the same hyperparameters across all models (`bert-tiny`, `bert-mini`) and all datasets (SQuAD version 2 and GLUE).
  
  Our code for M-FAC can be found here: [https://github.com/IST-DASLab/M-FAC](https://github.com/IST-DASLab/M-FAC).
  A step-by-step tutorial on how to integrate and use M-FAC with any repository can be found here: [https://github.com/IST-DASLab/M-FAC/tree/master/tutorials](https://github.com/IST-DASLab/M-FAC/tree/master/tutorials).
  
  ## BibTeX entry and citation info
  
  ```bibtex
  @article{frantar2021m,
    title={M-FAC: Efficient Matrix-Free Approximations of Second-Order Information},
    author={Frantar, Elias and Kurtic, Eldar and Alistarh, Dan},
    journal={Advances in Neural Information Processing Systems},
    volume={35},
    year={2021}
  }
  
  ```
  