Summary from Alexander Jung
* The authors train a variant of AlexNet that has significantly fewer parameters than the original network, while keeping the network's accuracy stable.
* Advantages of this:
* More efficient distributed training, because less parameters have to be transferred.
* More efficient transfer via the internet, because the model's file size is smaller.
* Possibly less memory demand in production, because fewer parameters have to be kept in memory.
### How
* They define a Fire Module. A Fire Module contains of:
* Squeeze Module: A 1x1 convolution that reduces the number of channels (e.g. from 128x32x32 to 64x32x32).
* Expand Module: A 1x1 convolution and a 3x3 convolution, both applied to the output of the Squeeze Module. Their results are concatenated.
* Using many 1x1 convolutions is advantageous, because they need less parameters than 3x3s.
* They use ReLUs, only convolutions (no fully connected layers) and Dropout (50%, before the last convolution).
* They use late maxpooling. They argue that applying pooling late - rather than early - improves accuracy while not needing more parameters.
* They try residual connections:
* One network without any residual connections (performed the worst).
* One network with residual connections based on identity functions, but only between layers of same dimensionality (performed the best).
* One network with residual connections based on identity functions and other residual connections with 1x1 convs (where dimensionality changed) (performance between the other two).
* They use pruning from Deep Compression to reduce the parameters further. Pruning simply collects the 50% of all parameters of a layer that have the lowest values and sets them to zero. That creates a sparse matrix.
### Results
* 50x parameter reduction of AlexNet (1.2M parameters before pruning, 0.4M after pruning).
* 510x file size reduction of AlexNet (from 250mb to 0.47mb) when combined with Deep Compression.
* Top-1 accuracy remained stable.
* Pruning apparently can be used safely, even after the network parameters have already been reduced significantly.
* While pruning was generally safe, they found that two of their later layers reacted quite sensitive to it. Adding parameters to these (instead of removing them) actually significantly improved accuracy.
* Generally they found 1x1 convs to react more sensitive to pruning than 3x3s. Therefore they focused pruning on 3x3 convs.
* First pruning a network, then re-adding the pruned weights (initialized with 0s) and then retraining for some time significantly improved accuracy.
* The network was rather resilient to significant channel reduction in the Squeeze Modules. Reducing to 25-50% of the original channels (e.g. 128x32x32 to 64x32x32) seemed to be a good choice.
* The network was rather resilient to removing 3x3 convs and replacing them with 1x1 convs. A ratio of 2:1 to 1:1 (1x1 to 3x3) seemed to produce good results while mostly keeping the accuracy.
* Adding some residual connections between the Fire Modules improved the accuracy.
* Adding residual connections with identity functions *and also* residual connections with 1x1 convs (where dimensionality changed) improved the accuracy, but not as much as using *only* residual connections with identity functions (i.e. it's better to keep some modules without identity functions).
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### Rough chapter-wise notes
* (1) Introduction and Motivation
* Advantages from having less parameters:
* More efficient distributed training, because less data (parameters) have to be transfered.
* Less data to transfer to clients, e.g. when a model used by some app is updated.
* FPGAs often have hardly any memory, i.e. a model has to be small to be executed.
* Target here: Find a CNN architecture with less parameters than an existing one but comparable accuracy.
* (2) Related Work
* (2.1) Model Compression
* SVD-method: Just apply SVD to the parameters of an existing model.
* Network Pruning: Replace parameters below threshold with zeros (-> sparse matrix), then retrain a bit.
* Add quantization and huffman encoding to network pruning = Deep Compression.
* (2.2) CNN Microarchitecture
* The term "CNN Microarchitecture" refers to the "organization and dimensions of the individual modules" (so an Inception module would have a complex CNN microarchitecture).
* (2.3) CNN Macroarchitecture
* CNN Macroarchitecture = "big picture" / organization of many modules in a network / general characteristics of the network, like depth
* Adding connections between modules can help (e.g. residual networks)
* (2.4) Neural Network Design Space Exploration
* Approaches for Design Space Exporation (DSE):
* Bayesian Optimization, Simulated Annealing, Randomized Search, Genetic Algorithms
* (3) SqueezeNet: preserving accuracy with few parameters
* (3.1) Architectural Design Strategies
* A conv layer with N filters applied to CxHxW input (e.g. 3x128x128 for a possible first layer) with kernel size kHxkW (e.g. 3x3) has `N*C*kH*kW` parameters.
* So one way to reduce the parameters is to decrease kH and kW, e.g. from 3x3 to 1x1 (reduces parameters by a factor of 9).
* A second way is to reduce the number of channels (C), e.g. by using 1x1 convs before the 3x3 ones.
* They think that accuracy can be improved by performing downsampling later in the network (if parameter count is kept constant).
* (3.2) The Fire Module
* The Fire Module has two components:
* Squeeze Module:
* One layer of 1x1 convs
* Expand Module:
* Concat the results of:
* One layer of 1x1 convs
* One layer of 3x3 convs
* The Squeeze Module decreases the number of input channels significantly.
* The Expand Module then increases the number of input channels again.
* (3.3) The SqueezeNet architecture
* One standalone conv, then several fire modules, then a standalone conv, then global average pooling, then softmax.
* Three late max pooling laters.
* Gradual increase of filter numbers.
* (3.3.1) Other SqueezeNet details
* ReLU activations
* Dropout before the last conv layer.
* No linear layers.
* (4) Evaluation of SqueezeNet
* Results of competing methods:
* SVD: 5x compression, 56% top-1 accuracy
* Pruning: 9x compression, 57.2% top-1 accuracy
* Deep Compression: 35x compression, ~57% top-1 accuracy
* SqueezeNet: 50x compression, ~57% top-1 accuracy
* SqueezeNet combines low parameter counts with Deep Compression.
* The accuracy does not go down because of that, i.e. apparently Deep Compression can even be applied to small models without giving up on performance.
* (5) CNN Microarchitecture Design Space Exploration
* (5.1) CNN Microarchitecture metaparameters
* blabla we test various values for this and that parameter
* (5.2) Squeeze Ratio
* In a Fire Module there is first a Squeeze Module and then an Expand Module. The Squeeze Module decreases the number of input channels to which 1x1 and 3x3 both are applied (at the same time).
* They analyzed how far you can go down with the Sqeeze Module by training multiple networks and calculating the top-5 accuracy for each of them.
* The accuracy by Squeeze Ratio (percentage of input channels kept in 1x1 squeeze, i.e. 50% = reduced by half, e.g. from 128 to 64):
* 12%: ~80% top-5 accuracy
* 25%: ~82% top-5 accuracy
* 50%: ~85% top-5 accuracy
* 75%: ~86% top-5 accuracy
* 100%: ~86% top-5 accuracy
* (5.3) Trading off 1x1 and 3x3 filters
* Similar to the Squeeze Ratio, they analyze the optimal ratio of 1x1 filters to 3x3 filters.
* E.g. 50% would mean that half of all filters in each Fire Module are 1x1 filters.
* Results:
* 01%: ~76% top-5 accuracy
* 12%: ~80% top-5 accuracy
* 25%: ~82% top-5 accuracy
* 50%: ~85% top-5 accuracy
* 75%: ~85% top-5 accuracy
* 99%: ~85% top-5 accuracy
* (6) CNN Macroarchitecture Design Space Exploration
* They compare the following networks:
* (1) Without residual connections
* (2) With residual connections between modules of same dimensionality
* (3) With residual connections between all modules (except pooling layers) using 1x1 convs (instead of identity functions) where needed
* Adding residual connections (2) improved top-1 accuracy from 57.5% to 60.4% without any new parameters.
* Adding complex residual connections (3) worsed top-1 accuracy again to 58.8%, while adding new parameters.
* (7) Model Compression Design Space Exploration
* (7.1) Sensitivity Analysis: Where to Prune or Add parameters
* They went through all layers (including each one in the Fire Modules).
* In each layer they set the 50% smallest weights to zero (pruning) and measured the effect on the top-5 accuracy.
* It turns out that doing that has basically no influence on the top-5 accuracy in most layers.
* Two layers towards the end however had significant influence (accuracy went down by 5-10%).
* Adding parameters to these layers improved top-1 accuracy from 57.5% to 59.5%.
* Generally they found 1x1 layers to be more sensitive than 3x3 layers so they pruned them less aggressively.
* (7.2) Improving Accuracy by Densifying Sparse Models
* They found that first pruning a model and then retraining it again (initializing the pruned weights to 0) leads to higher accuracy.
* They could improve top-1 accuracy by 4.3% in this way.
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