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EZCrop: Energy-Zoned Channels for Robust Output Pruning (Link)

Idea

Our key insight is that the energy distribution of feature maps generated by a fixed filter can reflect the filter's importance. The Supplementary Materials can be downloaded here.

Contributions

  • We analytically bridge the rank-based channel importance metric in the spatial domain to an energy perspective in the frequency domain, and for the first time explain the intereting constant-rank phenomenon in a channel matrix.
  • We propose a computationally efficient FFT-based metric for channel importance, which reduces the computational complexity from O(n^3) to O(n^2 logn).
  • The proposed EZCrop algorithm for channel pruning is simple, intuitive and robust. It outperforms other state-of-the-art pruning schemes and consistently delivers good performance, which is not a result of normal variations as confirmed through extensive experiments.

Citation

If you use EZCrop in your research, please kindly cite this work by

@article{lin2021ezcrop,
  title={EZCrop: Energy-Zoned Channels for Robust Output Pruning},
  author={Lin, Rui and Ran, Jie and Wang, Dongpeng and Chiu, King Hung and Wong, Ngai},
  journal={arXiv preprint arXiv:2105.03679},
  year={2021}
}

Runing Codes

To use EZCrop, the users are expected to generate the ratios first, then do the pruning and retrain the pruned model based on the evaluation results.

Energy Ratio Generation

python ratio_generation.py \
--ratio_path ratio_conv/ \
--EZCrop 1 \
--alpha [A number between 0 and 1] \
--conv_fm 1 \
--data_dir [Your path to the dataset] \
--dataset cifar10 \
--arch [Choose the model architecture] \
--pretrain_dir [Your path to Pretrained model] \
--limit 5 \
--batch_size 128 \
--gpu 0,1

Model Training

CIFAR-10

python evaluate_cifar.py \
--data_dir [Your path to the dataset] \
--arch [Choose the model architecture] \
--job_dir [Your path to save trained models] \
--pretrain_dir [Your path to Pretrained model] \
--ratio_conv_prefix [Ratio conv file folder] \
--compress_rate [Compress rate of each conv] \
--gpu 0,1 \

ImageNet

python evaluate.py \
--data_dir [Your path to the dataset] \
--arch [Choose the model architecture] \
--job_dir [Your path to save trained models] \
--pretrain_dir [Your path to Pretrained model] \
--ratio_conv_prefix [Ratio conv file folder] \
--compress_rate [Compress rate of each conv] \
--gpu 0,1 \

Core Codes

def torch_fftshift(real, imag):
    '''
    Input:
        - real: a matrix of size [h, w], which is the real number part of the feature map slice in frequency domain.
        - imag: a matrix of size [h, w], which is the imaginary number part of the feature map slice in frequency domain.
            
    Output:
        - real: a matrix of size [h, w], which is the real number part of the feature map slice in frequency domain 
        after shift operation.
        - imag: a matrix of size [h, w], which is the imaginary number part of the feature map slice in frequency domain
        after shift operation.
    '''
    for dim in range(0, len(real.size())):
        real = torch.roll(real, dims=dim, shifts=real.size(dim)//2)
        imag = torch.roll(imag, dims=dim, shifts=imag.size(dim)//2)
    return real, imag

def StepDecision(h, w, alpha):
    '''
    Input:
        - h: a scalar, which is the height of the given feature map slice.
        - w: a scalar, which is the width of the given feature map slice.
        - alpha: a scalar between 0 and 1, which determines the size of selcted area.
    
    Output:
        - step: a scalar, which decides the selected area of the given feature map in frequency domain.
    '''
    if h % 2 == 0 and w % 2 == 0:
        xc = h / 2
        yc = w / 2
    else:
        xc = (h - 1) / 2
        yc = (w - 1) / 2
    max_h = h - (xc + 1)
    max_w = w - (yc + 1)
    if xc - 1 == 0 or yc - 1 == 0:
        step = 0
    else:
        step = min(int(math.ceil(max_h * alpha)),int(math.ceil(max_w * alpha)))
    return step

def EnergyRatio(fm_slice, alpha=1/4):
    '''
    Input:
        - fm_slice: a matrix of size [h, w], which is a slice of a given feature map in spatial domain.
    
    Output:
        - ratio: a scalar, which is the ratio of the energy of the unselected area of the feature map 
        and the total energy of the feature map (both in frequency domain).
    '''
    FFT_fm_slice = torch.rfft(fm_slice, signal_ndim=2, onesided=False)
    shift_real, shift_imag = torch_fftshift(FFT_fm_slice[:,:,0], FFT_fm_slice[:,:,1])
    FFTshift_fm_slice = (shift_real**2 + shift_imag**2)**(1/2)
    FFTshift_fm_slice = torch.log(FFTshift_fm_slice+1)
    h, w = FFTshift_fm_slice.shape
    step = StepDecision(h, w, alpha)
    if h % 2 == 0 and w % 2 == 0:
        xc = h / 2
        yc = w / 2
    else:
        xc = (h - 1) / 2
        yc = (w - 1) / 2
    E = sum(sum(FFTshift_fm_slice))
    select_FFTshift_fm_slice = FFTshift_fm_slice[int(xc-step):int(xc+step+1), int(yc-step):int(yc+step+1)]
    select_E = sum(sum(select_FFTshift_fm_slice))
    ratio = 1 - select_E / E
    if ratio != ratio:
        ratio = torch.zeros(1)
    return ratio

Experimental Results

Time

Dataset Model HRank EZCrop (↓)
CIFAR-10 VGGNet 1505.54s 356.94s (76.29%)
CIFAR-10 ResNet-56 1247.51s 381.97s (69.38%)
CIFAR-10 DenseNet-40 473.17s 171.50s (63.76%)
ImageNet ResNet-50 7.96h 3.45h (56.60%)

VGGNet @ CIFAR-10

Params (↓) FLOPs (↓) Top-1%
2.76M (81.6%) 131.17M (58.1%) 94.01
2.50M (83.3%) 104.78M (66.6%) 93.70

ResNet-56 @ CIFAR-10

Params (↓) FLOPs (↓) Top-1%
0.56M (34.1%) 87.84M (30.0%) 94.18
0.48M (42.8%) 65.94M (47.4%) 93.80
0.24M (70.0%) 34.78M (74.1%) 92.52

DenseNet-40 @ CIFAR-10

Params (↓) FLOPs (↓) Top-1%
0.62M (40.1%) 173.39M (38.5%) 94.72
0.39M (61.9%) 113.08M (59.9%) 93.76

ResNet-50 @ ImageNet

Params FLOPs Top-1% Top-5%
15.09M 2.26B 75.68 92.70
11.05M 1.52B 92.00 74.33

Repetitive Pruning

#Pass (#epochs) FLOPs Params Top-1%
1 (300) 90.86M 0.63M 93.95
2 (300) 66.25M 0.46M 93.42
3 (300) 36.03M 0.22M 92.18

License

EZCrop is released under MIT License.

Acknowledgements

This code is implemented based on HRankPlus. We thanks for this open-source implementations.