Filter pruning

Scroll down for the examples of the JSON configuration files that can be used to apply this algorithm.

Filter pruning algorithm zeros output filters in Convolutional layers based on some filter importance criterion (filters with smaller importance are pruned). The framework contains three filter importance criteria: L1, L2 norm, and Geometric Median. Also, different schemes of pruning application are presented by different schedulers. Not all Convolution layers in the model can be pruned. Such layers are determined by the model architecture automatically as well as cross-layer dependencies that impose constraints on pruning filters.

Filter importance criteria L1, L2

L1, L2 filter importance criteria are based on the following assumption:

Convolutional filters with small $l_p$ norms do not significantly contribute to output activation values, and thus have a small impact on the final predictions of CNN models. In the above, the $l_p$ norm for filter F is:

$||F||_p = \sqrt[p]{\sum\limits_{c, k_1, k_2 = 1}^{C, K, K} |F(c, k_1, k_2)|^p}$

During the pruning procedure filters with smaller L1 or L2 norm will be pruned first.

Geometric Median

Usage of the geometric median filter importance criterion is based on the following assumptions:

Let ${F_i, \dots , F_j}$ be the set of N filters in a convolutional layer that are closest to the geometric median of all the filters in that layer. As it was shown, each of those filters can be decomposed into a linear combination of the rest of the filters further from the geometric median with a small error. Hence, these filters can be pruned without much impact on network accuracy. Since we have only fixed number of filters in each layer and the task of calculation of geometric median is a non-trivial problem in computational geometry, we can instead find which filters minimize the summation of the distance with other filters.

Then Geometric Median importance of $F_i$ filter from $L_j$ layer is: $G(F_i) = \sum_{F_j \in {F_1, \dots F_m}, j\neq i} ||F_i - F_j||_2$ Where $L_j$ is j-th convolutional layer in model. ${F_1, \dots F_m} \in L_j$ - set of all output filters in $L_j$ layer.

Then during pruning filters with smaller $G(F_i)$ importance function will be pruned first.

Schedulers

Baseline Scheduler

Firstly, during num_init_steps epochs the model is trained without pruning. Secondly, the pruning algorithm calculates filter importances and prunes a pruning_target part of the filters with the smallest importance in each prunable convolution. The zeroed filters are frozen afterwards and the remaining model parameters are fine-tuned.

Parameters of the scheduler:

• num_init_steps - number of epochs for model pretraining before pruning.
• pruning_target - pruning level target. For example, the value 0.5 means that right after pretraining, convolutions that can be pruned will have 50% of their filters set to zero.

Exponential scheduler

Similar to the Baseline scheduler, during num_init_steps epochs model is pretrained without pruning. During the next pruning steps epochs Exponential scheduler gradually increasing pruning level from pruning_init to pruning_target. After each pruning training epoch pruning algorithm calculates filter importances for all convolutional filters and prune (setting to zero) current_pruning_level part of filters with the smallest importance in each Convolution. After num_init_steps + pruning_steps epochs algorithm with zeroed filters is frozen and remaining model parameters only fine-tunes.

Current pruning level $P_{i}$ (on i-th epoch) during training calculates by equation: $P_i = a * e^{- k * i}$ Where $a, k$ - parameters.

Parameters of scheduler:

• num_init_steps - number of epochs for model pretraining before pruning.
• pruning_steps - the number of epochs during which the pruning level target is increased from pruning_init to pruning_target value.
• pruning_init - initial pruning level target. For example, value 0.1 means that at the begging of training, convolutions that can be pruned will have 10% of their filters set to zero.
• pruning_target - pruning level target at the end of the schedule. For example, the value 0.5 means that at the epoch with the number of num_init_steps + pruning_steps, convolutions that can be pruned will have 50% of their filters set to zero.

Exponential with bias scheduler

Similar to the Exponential scheduler, but current pruning level $P_{i}$ (on i-th epoch) during training calculates by equation: $P_i = a * e^{- k * i} + b$ Where $a, k, b$ - parameters.

NOTE: Baseline scheduler prunes filters only ONCE and after it just fine-tunes remaining parameters while exponential (and exponential with bias) schedulers choose and prune different filters subsets at each pruning epoch.

Batch-norm statistics adaptation

After the compression-related changes in the model have been committed, the statistics of the batchnorm layers (per-channel rolling means and variances of activation tensors) can be updated by passing several batches of data through the model before the fine-tuning starts. This allows to correct the compression-induced bias in the model and reduce the corresponding accuracy drop even before model training. This option is common for quantization, magnitude sparsity and filter pruning algorithms. It can be enabled by setting a non-zero value of num_bn_adaptation_samples in the batchnorm_adaptation section of the initializer configuration (see example below).

Interlayer ranking types

Interlayer ranking type can be one of unweighted_ranking or learned_ranking.

• In case of unweighted_ranking and with all_weights=True all filter norms will be collected together and sorted to choose the least important ones. But this approach may not be optimal because filter norms are a good measure of filter importance inside a layer, but not across layers.
• In the case of learned_ranking that uses re-implementation of Learned Global Ranking method (LeGR), a set of ranking coefficients will be learned for comparing filters across different layers. The $(a_i, b_i)$ pair of scalars will be learned for each ( $i$ layer and used to transform norms of $i$-th layer filters before sorting all filter norms together as $a_i * N_i + b_i$ , where $N_i$ - is vector of filter norma of $i$-th layer, $(a_i, b_i)$ is ranking coefficients for $i$-th layer. This approach allows pruning the model taking into account layer-specific sensitivity to weight perturbations and get pruned models with higher accuracy.

NOTE: In all our pruning experiments we used SGD optimizer.

Filter pruning statistics

A model compression can be measured by two main metrics: filter pruning level and FLOPs pruning level. While filter pruning level shows the ratio of removed filters to the total number of filters in the model, FLOPs pruning level indicates how the removed filters affect the number of floating point operations required to run a model.

During the algorithm execution several compression statistics are available. See the example below.

Statistics by pruned layers:
+----------------------+------------------+--------------+---------------------+
|     Layer's name     |  Weight's shape  | Mask's shape |   Filter pruning    |
|                      |                  |              |        level        |
+======================+==================+==============+=====================+
| ConvBlock[conv1]/NNC | [192, 32, 1, 1]  | [192]        | 0.500               |
| FConv2d[conv]        |                  |              |                     |
+----------------------+------------------+--------------+---------------------+
| ConvBlock[conv2]/NNC | [384, 64, 1, 1]  | [384]        | 0.500               |
| FConv2d[conv]        |                  |              |                     |
+----------------------+------------------+--------------+---------------------+
Statistics of the pruned model:
+---------+-------+---------+---------------+
|    #    | Full  | Current | Pruning level |
+=========+=======+=========+===============+
| GFLOPS  | 0.602 | 0.241   | 0.599         |
+---------+-------+---------+---------------+
| MParams | 3.470 | 1.997   | 0.424         |
+---------+-------+---------+---------------+
| Filters | 17056 | 10216   | 0.401         |
+---------+-------+---------+---------------+
Prompt: statistic pruning level = 1 - statistic current / statistic full.
Statistics of the filter pruning algorithm:
+---------------------------------------+-------+
|           Statistic's name            | Value |
+=======================================+=======+
| Filter pruning level in current epoch | 0.500 |
+---------------------------------------+-------+
| Target filter pruning level           | 0.800 |
+---------------------------------------+-------+

Layer statistics

Statistics by pruned layers section lists names of all layers that will be pruned, shapes of their weight tensors, shapes of pruning masks applied to respective weights and percentage of zeros in those masks.

Model statistics

The columns Full and Current represent the values of the corresponding statistics in the original model and compressed one in the current state, respectively.

The Pruning level column indicates the ratio between the values of the full and current statistics in the corresponding rows, defined by the formula:

$Statistic\\:pruning\\:level = 1 - statistic\\:current / statistic\\:full$

Filter pruning level - percentage of filters removed from the model.

GFLOPs pruning level - an estimated reduction in the number of floating point operations of the model. The number of FLOPs for a single convolutional layer can be calculated as:

$FLOPs = 2 * input\\:channels * kernel\\:size ^2 * W * H * filters$

NOTE: One GFLOP is one billion (1e9) FLOPs.

Each removed filter contributes to FLOPs reduction in two convolutional layers as it affects the number of filters in one and the number of input channels of the next layer. Thus, it is expected that this number may differ significantly from the filter pruning level.

In addition, the decrease in GFLOPs is estimated by calculating the number of FLOPs of convolutional and fully connected layers. As a result, these estimates may differ slightly from the actual number of FLOPs in the compressed model.

MParams pruning level - calculated reduction in the number of parameters in the model in millions. Typically convolutional layer weights have the shape of $(kernel\\:size,\\:kernel\\:size,\\:input\\:channels,\\:filter\\:num)$.

Thus, each removed filter affects the number of parameters in two convolutional layers as it affects the number of filters in one and the number of input channels of the next layer. It is expected that this number may differ significantly from the filter pruning level.

Algorithm statistics

Filter (or FLOPs) pruning level in current epoch - a pruning level calculated by the algorithm scheduler to be applied in the current training epoch.

NOTE: In case of Filter pruning level in current epoch this metric does not indicate the whole model filter pruning level, as it does not take into account the number of filters in layers that cannot be pruned.

Target filter (or FLOPs) pruning level - a pruning level that is expected to be achieved at the end of the algorithm execution.

NOTE: In case of Target filter pruning level this number indicates what percentage of filters will be removed from only those layers that can be pruned.

It is important to note that pruning levels mentioned in the statistics of the filter pruning algorithm are the goals the algorithm aims to achieve. It is not always possible to achieve these levels of pruning due to cross-layer and inference constraints. Therefore, it is expected that these numbers may differ from the calculated statistics in the statistics of the pruned model section.

Example configuration files

For the full list of the algorithm configuration parameters via config file, see the corresponding section in the NNCF config schema.

• Prune a model with default parameters (from 0 to 0.5 filter pruning level across 100 epochs with exponential schedule)

  {
      "input_info": { "sample_size": [1, 3, 224, 224] },
      "compression":
      {
          "algorithm": "filter_pruning"
      }
  }

• Same as above, but filter importance is considered globally across all eligible weighted operations:

  {
      "input_info": { "sample_size": [1, 3, 224, 224] },
      "compression":
      {
          "algorithm": "filter_pruning",
          "all_weights": true
      }
  }

• Prune a model, immediately setting filter pruning level to 10%, applying batchnorm adaptation and reaching 60% within 20 epochs using exponential schedule, enabling pruning of first convolutional layers and downsampling convolutional layers:

  {
      "input_info": { "sample_size": [1, 3, 224, 224] },
      "compression":
      {
          "algorithm": "filter_pruning",
          "pruning_init": 0.1,
          "params": {
              "pruning_target": 0.6,
              "pruning_steps": 20,
              "schedule": "exponential",
              "prune_first_conv": true,
              "prune_downsample_convs": true
          }
      }
  }

• Prune a model using geometric median filter importance and reaching 30% filter pruning level within 10 epochs using exponential schedule, postponing application of pruning for 10 epochs:

  {
      "input_info": { "sample_size": [1, 3, 224, 224] },
      "compression":
      {
          "algorithm": "filter_pruning",
          "params": {
              "filter_importance": "geometric_median",
              "pruning_target": 0.3,
              "pruning_steps": 10,
              "schedule": "exponential",
              "num_init_steps": 10
          }
      }
  }

• Prune and quantize a model at the same time using a FLOPS target for pruning and defaults for the rest of parameters:

  {
      "input_info": { "sample_size": [1, 3, 224, 224] },
      "compression":
      [
          {
              "algorithm": "filter_pruning",
              "params": {
                  "pruning_flops_target": 0.6
              }
          },
          {
              "algorithm": "quantization"
          }
      ]
  }

• Prune a model with default parameters, estimate filter ranking by Learned Global Ranking method before finetuning. LEGR algorithm will be using 200 generations for the evolution algorithm, 20 train steps to estimate pruned model accuracy on each generation and target maximal filter pruning level equal to 50%:

  {
      "input_info": { "sample_size": [1, 3, 224, 224] },
      "compression":
      [
          {
              "algorithm": "filter_pruning",
              "params":
              {
                  "interlayer_ranking_type": "learned_ranking",
                  "legr_params":
                  {
                      "generations": 200,
                      "train_steps": 20,
                      "max_pruning": 0.5
                  }
              }
          }
      ]
  }