Deep Learning for Computer Vision: Memory usage and computational considerations (UPC 2016)
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The document discusses estimating memory usage and computational requirements for designing deep neural networks, focusing on factors like network size, mini-batch sizes, and effective aperture sizes. It covers methods for calculating memory and computational complexity, providing insights into the architecture and training considerations of convolutional networks. Additionally, strategies for improving accuracy through increased network depth and width are highlighted, along with the implications for memory constraints on modern GPUs.
![[course site]
Memory usage and
computational
considerations
Day 2 Lecture 1
Kevin McGuinness
kevin.mcguinness@dcu.ie
Research Fellow
Insight Centre for Data Analytics
Dublin City University](https://image.slidesharecdn.com/dlcvd2l1memory-160802094314/85/Deep-Learning-for-Computer-Vision-Memory-usage-and-computational-considerations-UPC-2016-1-320.jpg)
![Memory for convolutions
Several libraries implement convolutions as matrix multiplications (e.g. caffe). Approach known as
convolution lowering
Fast (use optimized BLAS implementations) but can use a lot of memory, esp. for larger kernel sizes
and deep conv layers
5
5
…
25
224
224
224x224
[50716 x 25] [25 x 1]
Kernel
cuDNN uses a more
memory efficient
method!
https://arxiv.org/pdf/1
410.0759.pdf
18](https://image.slidesharecdn.com/dlcvd2l1memory-160802094314/85/Deep-Learning-for-Computer-Vision-Memory-usage-and-computational-considerations-UPC-2016-18-320.jpg)
Deep Learning for Computer Vision: Memory usage and computational considerations (UPC 2016)
- 1. [course site] Memory usage and computational considerations Day 2 Lecture 1 Kevin McGuinness [email protected] Research Fellow Insight Centre for Data Analytics Dublin City University
- 2. Introduction Useful when designing deep neural network architectures to be able to estimate memory and computational requirements on the “back of an envelope” This lecture will cover: ● Estimating neural network memory consumption ● Mini-batch sizes and gradient splitting trick ● Estimating neural network computation (FLOP/s) ● Calculating effective aperture sizes 2
- 3. Improving convnet accuracy A common strategy for improving convnet accuracy is to make it bigger ● Add more layers ● Made layers wider, increase depth ● Increase kernel sizes* Works if you have sufficient data and strong regularization (dropout, maxout, etc.) Especially true in light of recent advances: ● ResNets: 50-1000 layers ● Batch normalization: reduce covariate shift network year layers top-5 Alexnet 2012 7 17.0 VGG-19 2014 19 9.35 GoogleNet 2014 22 9.15 Resnet-50 2015 50 6.71 Resnet-152 2015 152 5.71 Without ensembles 3
- 4. Increasing network size Increasing network size means using more memory Train time: ● Memory to store outputs of intermediate layers (forward pass) ● Memory to store parameters ● Memory to store error signal at each neuron ● Memory to store gradient of parameters ● Any extra memory needed by optimizer (e.g. for momentum) Test time: ● Memory to store outputs of intermediate layers (forward pass) ● Memory to store parameters Modern GPUs are still relatively memory constrained: ● GTX Titan X: 12GB ● GTX 980: 4GB ● Tesla K40: 12GB ● Tesla K20: 5GB 4
- 5. Calculating memory requirements Often the size of the network will be practically bound by available memory Useful to be able to estimate memory requirements of network True memory usage depends on the implementation 5
- 6. Calculating the model size Conv layers: Num weights on conv layers does not depend on input size (weight sharing) Depends only on depth, kernel size, and depth of previous layer 6
- 7. Calculating the model size parameters weights: depthn x (kernelw x kernelh ) x depth(n-1) biases: depthn 7
- 8. Calculating the model size parameters weights: 32 x (3 x 3) x 1 = 288 biases: 32 8
- 9. Calculating the model size parameters weights: 32 x (3 x 3) x 32 = 9216 biases: 32 Pooling layers are parameter-free 9
- 10. Calculating the model size Fully connected layers ● #weights = #outputs x #inputs ● #biases = #outputs If previous layer has spatial extent (e.g. pooling or convolutional), then #inputs is size of flattened layer. 10
- 11. Calculating the model size parameters weights: #outputs x #inputs biases: #inputs 11
- 12. Calculating the model size parameters weights: 128 x (14 x 14 x 32) = 802816 biases: 128 12
- 13. Calculating the model size parameters weights: 10 x 128 = 1280 biases: 10 13
- 14. Total model size parameters weights: 10 x 128 = 1280 biases: 10 parameters weights: 128 x (14 x 14 x 32) = 802816 biases: 128 parameters weights: 32 x (3 x 3) x 32 = 9216 biases: 32 parameters weights: 32 x (3 x 3) x 1 = 288 biases: 32 Total: 813,802 ~ 3.1 MB (32-bit floats) 14
- 15. Layer blob sizes Easy… Conv layers: width x height x depth FC layers: #outputs 32 x (14 x 14) = 6,272 32 x (28 x 28) = 25,088 15
- 16. Total memory requirements (train time) Memory for layer error Memory for parameters Memory for param gradients Depends on implementation and optimizer Memory for momentum Memory for layer outputs Implementation overhead (memory for convolutions, etc.) 16
- 17. Total memory requirements (test time) Memory for layer error Memory for parameters Memory for param gradients Depends on implementation and optimizer Memory for momentum Memory for layer outputs Implementation overhead (memory for convolutions, etc.) 17
- 18. Memory for convolutions Several libraries implement convolutions as matrix multiplications (e.g. caffe). Approach known as convolution lowering Fast (use optimized BLAS implementations) but can use a lot of memory, esp. for larger kernel sizes and deep conv layers 5 5 … 25 224 224 224x224 [50716 x 25] [25 x 1] Kernel cuDNN uses a more memory efficient method! https://arxiv.org/pdf/1 410.0759.pdf 18
- 19. Mini-batch sizes Total memory in previous slides is for a single example. In practice, we want to do mini-batch SGD: ● More stable gradient estimates ● Faster training on modern hardware Size of batch is limited by model architecture, model size, and hardware memory. May need to reduce batch size for training larger models. This may affect convergence if gradients are too noisy. 19
- 20. Gradient splitting trick Mini-batch 1 Network ΔW Loss 1 Loss 1 Mini-batch 2 Loss 2 ΔW Loss 2 Mini-batch 3 Loss 3 ΔW Loss 3 Loss on batch n 20
- 21. Estimating computational complexity Useful to be able to estimate computational complexity of an architecture when designing it Computation in deep NN is dominated by multiply-adds in FC and conv layers. Typically we estimate the number of FLOPs (multiply-adds) in the forward pass Ignore non-linearities, dropout, and normalization layers (negligible cost). 21
- 22. Estimating computational complexity Fully connected layer FLOPs Easy: equal to the number of weights (ignoring biases) = #num_inputs x #num_outputs Convolution layer FLOPs Product of: ● Spatial width of the map ● Spatial height of the map ● Previous layer depth ● Current layer deptjh ● Kernel width ● Kernel height 22
- 23. Example: VGG-16 Layer H W kernel H kernel W depth repeats FLOP/s input 224 224 1 1 3 1 0.00E+00 conv1 224 224 3 3 64 2 1.94E+09 conv2 112 112 3 3 128 2 2.77E+09 conv3 56 56 3 3 256 3 4.62E+09 conv4 28 28 3 3 512 3 4.62E+09 conv5 14 14 3 3 512 3 1.39E+09 flatten 1 1 0 0 100352 1 0.00E+00 fc6 1 1 1 1 4096 1 4.11E+08 fc7 1 1 1 1 4096 1 1.68E+07 fc8 1 1 1 1 100 1 4.10E+05 1.58E+10 Bulk of computation is here 23
- 24. Effective aperture size Useful to be able to compute how far a convolutional node in a convnet sees: ● Size of the input pixel patch that affects a node’s output ● Known as the effective aperture size, coverage, or receptive field size Depends on kernel size and strides from previous layers ● 7x7 kernel can see a 7x7 patch of the layer below ● Stride of 2 doubles what all layers after can see Calculate recursively 24
- 25. Summary Shown how to estimate memory and computational requirements of a deep neural network model Very useful to be able to quickly estimate these when designing a deep NN Effective aperture size tells us how much a conv node can see. Easy to calculate recursively 25