Network Compression and Speedup SHUOCHAO YAO YIWEN XU
- Slides: 70
Network Compression and Speedup SHUOCHAO YAO, YIWEN XU, DANIEL CALZADA NETWORK COMPRESSION AND SPEEDUP 1
Source: http: //isca 2016. eecs. umich. edu/wp-content/uploads/2016/07/4 A-1. pdf NETWORK COMPRESSION AND SPEEDUP 2
Why smaller models? Operation Energy [p. J] Relative Cost 32 bit int ADD 0. 1 1 32 bit float ADD 0. 9 9 32 bit Register File 1 10 32 bit int MULT 3. 1 31 32 bit float MULT 3. 7 37 32 bit SRAM Cache 5 50 32 bit DRAM Memory 6400 Source: http: //isca 2016. eecs. umich. edu/wp-content/uploads/2016/07/4 A-1. pdf NETWORK COMPRESSION AND SPEEDUP 3
Matrix Factorization Weight Pruning Quantization method Outline Pruning + Quantization + Encoding Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 4
Matrix Factorization ◦ Singular Value Decomposition (SVD) ◦ Flattened Convolutions Outline Weight Pruning Quantization method Pruning + Quantization + Encoding Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 5
Fully Connected Layers: Singular Value Decomposition http: //www. alglib. net/matrixops/general/i/svd 1. gif NETWORK COMPRESSION AND SPEEDUP 6
Singular Value Decomposition http: //www. alglib. net/matrixops/general/i/svd 1. gif NETWORK COMPRESSION AND SPEEDUP 7
SVD: Compression Gong, Yunchao, et al. "Compressing deep convolutional networks using vector quantization. " ar. Xiv preprint ar. Xiv: 1412. 6115 (2014). NETWORK COMPRESSION AND SPEEDUP 8
SVD: Compression Results Trained on Image. Net 2012 database, then compressed 5 convolutional layers, 3 fully connected layers, softmax output layer Denton, Emily L. , et al. "Exploiting linear structure within convolutional networks for efficient evaluation. " Advances in Neural Information Processing Systems. 2014. NETWORK COMPRESSION AND SPEEDUP 9
SVD: Side Benefits Denton, Emily L. , et al. "Exploiting linear structure within convolutional networks for efficient evaluation. " Advances in Neural Information Processing Systems. 2014. NETWORK COMPRESSION AND SPEEDUP 10
Convolutions: Matrix Multiplication Most time is spent in the convolutional layers http: //stackoverflow. com/questions/15356153/how-do-convolution-matrices-work NETWORK COMPRESSION AND SPEEDUP 11
Flattened Convolutions Jin, Jonghoon, Aysegul Dundar, and Eugenio Culurciello. "Flattened convolutional neural networks for feedforward acceleration. " ar. Xiv preprint ar. Xiv: 1412. 5474 (2014). NETWORK COMPRESSION AND SPEEDUP 12
Flattened Convolutions Jin, Jonghoon, Aysegul Dundar, and Eugenio Culurciello. "Flattened convolutional neural networks for feedforward acceleration. " ar. Xiv preprint ar. Xiv: 1412. 5474 (2014). NETWORK COMPRESSION AND SPEEDUP 13
Flattening = MF Denton, Emily L. , et al. "Exploiting linear structure within convolutional networks for efficient evaluation. " Advances in Neural Information Processing Systems. 2014. NETWORK COMPRESSION AND SPEEDUP 14
Flattening: Speedup Results 3 convolutional layers (5 x 5 filters) with 96, 128, and 256 channels Used stacks of 2 rank-1 convolutions Jin, Jonghoon, Aysegul Dundar, and Eugenio Culurciello. "Flattened convolutional neural networks for feedforward acceleration. " ar. Xiv preprint ar. Xiv: 1412. 5474 (2014). NETWORK COMPRESSION AND SPEEDUP 15
Matrix Factorization Weight Pruning ◦ Magnitude-based method Outline ◦ Iterative pruning + Retraining ◦ Pruning with rehabilitation ◦ Hessian-based method Quantization method Pruning + Quantization + Encoding Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 16
Magnitude-based method: Iterative Pruning + Retraining Han, Song, et al. "Learning both weights and connections for efficient neural network. " NIPS. 2015. NETWORK COMPRESSION AND SPEEDUP 18
Magnitude-based method: Iterative Pruning + Retraining (Algorithm) Han, Song, et al. "Learning both weights and connections for efficient neural network. " NIPS. 2015. NETWORK COMPRESSION AND SPEEDUP 19
Magnitude-based method: Iterative Pruning + Retraining (Experiment: Alex. Net) Layer Weights FLOP Act% Weights% FLOP% conv 1 35 K 211 M 88% 84% conv 2 307 K 448 M 52% 38% 33% conv 3 885 K 299 M 37% 35% 18% conv 4 663 K 224 M 40% 37% 14% conv 5 442 K 150 M 34% 37% 14% fc 1 38 M 75 M 36% 9% 3% fc 2 17 M 34 M 40% 9% 3% fc 3 4 M 8 M 100% 25% 10 Total 61 M 1. 5 B 54% 11% 30% Han, Song, et al. "Learning both weights and connections for efficient neural network. " NIPS. 2015. NETWORK COMPRESSION AND SPEEDUP 22
Magnitude-based method: Iterative Pruning + Retraining (Experiment: Tradeoff) Han, Song, et al. "Learning both weights and connections for efficient neural network. " NIPS. 2015. NETWORK COMPRESSION AND SPEEDUP 23
Pruning with rehabilitation: Dynamic Network Surgery (Motivation) Pruned connections have no chance to come back. Incorrect pruning may cause severe accuracy loss. Avoid the risk of irretrievable network damage. Improve the learning efficiency. Guo, Yiwen, et al. "Dynamic Network Surgery for Efficient DNNs. " NIPS. 2016. NETWORK COMPRESSION AND SPEEDUP 24
Pruning with rehabilitation: Dynamic Network Surgery (Formulation) Guo, Yiwen, et al. "Dynamic Network Surgery for Efficient DNNs. " NIPS. 2016. NETWORK COMPRESSION AND SPEEDUP 25
Pruning with rehabilitation: Dynamic Network Surgery (Algorithm) Guo, Yiwen, et al. "Dynamic Network Surgery for Efficient DNNs. " NIPS. 2016. NETWORK COMPRESSION AND SPEEDUP 26
Pruning with rehabilitation: Dynamic Network Surgery (Experiment on Alex. Net) Layer Parameters (Han et al. 2015) Parameters (DNS) conv 1 35 K 84% 53. 8% conv 2 307 K 38% 40. 6% conv 3 885 K 35% 29. 0% conv 4 664 K 37% 32. 3% conv 5 443 K 37% 32. 5% fc 1 38 M 9% 3. 7% fc 2 17 M 9% 6. 6% fc 3 4 M 25% 4. 6% Total 61 M 11% 5. 7% Guo, Yiwen, et al. "Dynamic Network Surgery for Efficient DNNs. " NIPS. 2016. NETWORK COMPRESSION AND SPEEDUP 28
Matrix Factorization Weight Pruning ◦ Magnitude-based method ◦ Hessian-based method Outline ◦ Diagonal Hessian-based method ◦ Full Hessian-based method Quantization method Pruning + Quantization + Encoding Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 29
Diagonal Hessian-based method: Optimal Brain Damage The idea of model compression & speed up: traced by to 1990. Actually theoretically more “optimal” compared with the current state of the art, but much more computational inefficient. Delete parameters with small “saliency”. ◦ Saliency: effect on the training error Propose a theoretically justified saliency measure. NETWORK COMPRESSION AND SPEEDUP 30
Diagonal Hessian-based method: Optimal Brain Damage (Formulation) Le. Cun, Yann, et al. "Optimal brain damage. " NIPs. Vol. 2. 1989. NETWORK COMPRESSION AND SPEEDUP 31
Diagonal Hessian-based method: Optimal Brain Damage (Algorithm) Le. Cun, Yann, et al. "Optimal brain damage. " NIPs. Vol. 2. 1989. NETWORK COMPRESSION AND SPEEDUP 32
Diagonal Hessian-based method: Optimal Brain Damage (Experiment: OBD vs. Magnitude) OBD vs. Magnitude Deletion based on saliency performs better Le. Cun, Yann, et al. "Optimal brain damage. " NIPs. Vol. 2. 1989. NETWORK COMPRESSION AND SPEEDUP 33
Diagonal Hessian-based method: Optimal Brain Damage (Experiment: Retraining) How retraining helps? Without retraining Retraining Le. Cun, Yann, et al. "Optimal brain damage. " NIPs. Vol. 2. 1989. NETWORK COMPRESSION AND SPEEDUP 34
Full Hessian-based method: Optimal Brain Surgeon Motivation: ◦ A more accurate estimation of saliency. ◦ Optimal weight updates. Advantage: ◦ More accuracy estimation with saliency. ◦ Directly provide the weight updates, which minimize the change of objective function. Disadvantage ◦ More computation compared with OBD. ◦ Weight updates are not based on minimizing the objective function. Hassibi, Babak, and David G. Stork. "Second order derivatives for network pruning: Optimal brain surgeon. ” NIPS, 1993 NETWORK COMPRESSION AND SPEEDUP 35
Full Hessian-based method: Optimal Brain Surgeon (Formulation) Hassibi, Babak, and David G. Stork. "Second order derivatives for network pruning: Optimal brain surgeon. ” NIPS, 1993 NETWORK COMPRESSION AND SPEEDUP 36
Full Hessian-based method: Optimal Brain Surgeon (Algorithm) Hassibi, Babak, and David G. Stork. "Second order derivatives for network pruning: Optimal brain surgeon. ” NIPS, 1993 NETWORK COMPRESSION AND SPEEDUP 37
Full Hessian-based method: Optimal Brain Surgeon Hassibi, Babak, and David G. Stork. "Second order derivatives for network pruning: Optimal brain surgeon. ” NIPS, 1993 NETWORK COMPRESSION AND SPEEDUP 38
Matrix Factorization Weight Pruning Quantization method Outline ◦ Full Quantization ◦ Fixed-point format ◦ Code book ◦ Quantization with full-precision copy Pruning + Quantization + Encoding Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 39
Full Quantization : Fixed-point format Gupta, Suyog, et al. "Deep Learning with Limited Numerical Precision. " ICML. 2015. NETWORK COMPRESSION AND SPEEDUP 40
Full Quantization : Fixed-point format (Rounding Modes) Gupta, Suyog, et al. "Deep Learning with Limited Numerical Precision. " ICML. 2015. NETWORK COMPRESSION AND SPEEDUP 41
Multiply and accumulate (MACC) operation Gupta, Suyog, et al. "Deep Learning with Limited Numerical Precision. " ICML. 2015. NETWORK COMPRESSION AND SPEEDUP 42
Full Quantization: Fixed-point format (Experiment on MNIST with CNNs) Gupta, Suyog, et al. "Deep Learning with Limited Numerical Precision. " ICML. 2015. NETWORK COMPRESSION AND SPEEDUP 44
Full Quantization: Fixed-point format (Experiment on CIFAR 10 with fully connected DNNs) Gupta, Suyog, et al. "Deep Learning with Limited Numerical Precision. " ICML. 2015. NETWORK COMPRESSION AND SPEEDUP 45
Full Quantization: Code book Gong, Yunchao, et al. "Compressing deep convolutional networks using vector quantization. " ar. Xiv preprint ar. Xiv: 1412. 6115 (2014). NETWORK COMPRESSION AND SPEEDUP 46
Full Quantization: Code book (Experiment on PQ) NETWORK COMPRESSION AND SPEEDUP 47
Full Quantization: Code book Gong, Yunchao, et al. "Compressing deep convolutional networks using vector quantization. " ar. Xiv preprint ar. Xiv: 1412. 6115 (2014). NETWORK COMPRESSION AND SPEEDUP 48
Matrix Factorization Weight Pruning Quantization method Outline ◦ Full quantization ◦ Quantization with full-precision copy ◦ Binnaryconnect ◦ BNN Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 49
Quantization with full-precision copy: Binaryconnect (Motivation) Use only two possible value (e. g. +1 or -1) for weights. Replace many multiply-accumulate operations by simple accumulations. Fixed-point adders are much less expensive both in terms of area and energy than fixed-point multiply-accumulators. Courbariaux, et al. "Binaryconnect: Training deep neural networks with binary weights during propagations. " NIPS. 2015 NETWORK COMPRESSION AND SPEEDUP 50
Quantization with full-precision copy: Binaryconnect (Binarization) Courbariaux, et al. "Binaryconnect: Training deep neural networks with binary weights during propagations. " NIPS. 2015 NETWORK COMPRESSION AND SPEEDUP 51
Quantization with full-precision copy: Binaryconnect 1. Given the DNN input, compute the unit activations layer by layer, leading to the top layer which is the output of the DNN, given its input. This step is referred as the forward propagation. 2. Given the DNN target, compute the training objective’s gradient w. r. t. each layer’s activations, starting from the top layer and going down layer by layer until the first hidden layer. This step is referred to as the backward propagation or backward phase of back-propagation. 3. Compute the gradient w. r. t. each layer’s parameters and then update the parameters using their computed gradients and their previous values. This step is referred to as the parameter update. Courbariaux, et al. "Binaryconnect: Training deep neural networks with binary weights during propagations. " NIPS. 2015 NETWORK COMPRESSION AND SPEEDUP 52
Quantization with full-precision copy: Binaryconnect Binary. Connect only binarize the weights during the forward and backward propagations (steps 1 and 2) but not during the parameter update (step 3). Courbariaux, et al. "Binaryconnect: Training deep neural networks with binary weights during propagations. " NIPS. 2015 NETWORK COMPRESSION AND SPEEDUP 53
Quantization with full-precision copy: Binaryconnect 1. Binarize weights and perform forward pass. 2. Back propagate gradient based on binarized weights. 3. Update the full-precision weights. 4. Iterate to step 1. Courbariaux, et al. "Binaryconnect: Training deep neural networks with binary weights during propagations. " NIPS. 2015 NETWORK COMPRESSION AND SPEEDUP 54
Quantization with full-precision copy: Binaryconnect Courbariaux, et al. "Binaryconnect: Training deep neural networks with binary weights during propagations. " NIPS. 2015 NETWORK COMPRESSION AND SPEEDUP 56
Quantization with full-precision copy: Binarized Neural Networks (Motivation) Neural networks with both binary weights and activations at run-time and when computing the parameters’ gradient at train time. Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or 1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). NETWORK COMPRESSION AND SPEEDUP 57
Quantization with full-precision copy: Binarized Neural Networks Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or 1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). NETWORK COMPRESSION AND SPEEDUP 58
Quantization with full-precision copy: Binarized Neural Networks Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or 1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). NETWORK COMPRESSION AND SPEEDUP 59
Quantization with full-precision copy: Binarized Neural Networks Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or 1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). NETWORK COMPRESSION AND SPEEDUP 61
Matrix Factorization Weight Pruning Quantization method Outline Pruning + Quantization + Encoding ◦ Deep Compression Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 62
Pruning + Quantization + Encoding: Deep Compression Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or 1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). NETWORK COMPRESSION AND SPEEDUP 63
Pruning + Quantization + Encoding: Deep Compression 1. Choose a neural network architecture. 2. Train the network until a reasonable solution is obtained. 3. Prune the network with magnitude-based method until a reasonable solution is obtained. 4. Quantize the network with k-means based method until a reasonable solution is obtained. 5. Further compress the network with Huffman coding. Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or 1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). NETWORK COMPRESSION AND SPEEDUP 64
Pruning + Quantization + Encoding: Deep Compression NETWORK COMPRESSION AND SPEEDUP 66
Matrix Factorization Weight Pruning Quantization method Outline Pruning + Quantization + Encoding Design small architecture: Squeeze. Net NETWORK COMPRESSION AND SPEEDUP 67
Design small architecture: Squeeze. Net Compression scheme on pre-trained model VS Design small CNN architecture from scratch (also preserve accuracy? ) NETWORK COMPRESSION AND SPEEDUP 68
Squeeze. Net Design Strategies Strategy 1. Replace 3 x 3 filters with 1 x 1 filters ◦ Parameters per filter: (3 x 3 filter) = 9 * (1 x 1 filter) Strategy 2. Decrease the number of input channels to 3 x 3 filters ◦ Total # of parameters: (# of input channels) * (# of filters) * ( # of parameters per filter) Strategy 3. Downsample late in the network so that convolution layers have large activation maps ◦ Size of activation maps: the size of input data, the choice of layers in which to downsample in the CNN architecture Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 69
Microarchitecture – Fire Module Fire module is consist of: ◦ A squeeze convolution layer ◦ full of s 1 x 1 # of 1 x 1 filters ◦ An expand layer ◦ mixture of e 1 x 1 # of 1 x 1 and e 3 x 3 # of 3 x 3 filters Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 70
Microarchitecture – Fire Module Strategy 2. Decrease the number of input channels to 3 x 3 filters Total # of parameters: (# of input channels) * (# of filters) * ( # of parameters per filter) Squeeze Layer How much can we limit s 1 x 1? Set s 1 x 1 < (e 1 x 1 + e 3 x 3), limits the # of input channels to 3*3 filters Strategy 1. Replace 3*3 filters with 1*1 filters Parameters per filter: (3*3 filter) = 9 * (1*1 filter) How much can we replace 3*3 with 1*1? (e 1 x 1 vs e 3 x 3 )? Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 71
Parameters in Fire Module The # of expanded filter(ei) ei = ei, 1 x 1 + ei, 3 x 3 The % of 3 x 3 filter in expanded layer(pct 3 x 3) ei, 3 x 3 = pct 3 x 3 * ei The Squeeze Ratio(SR) si, 1 x 1 = SR *ei Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 72
Macroarchitecture Strategy 3. Downsample late in the network so that convolution layers have large activation maps Size of activation maps: the size of input data, the choice of layers in which to downsample in the CNN architecture These relative late placements of pooling concentrates activation maps at later phase to preserve higher accuracy Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 73
Macroarchitecture Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 74
Evaluation of Results Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 75
Further Compression on 4. 8 M? Further Compression ◦ Deep Compression + Quantization Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " NETWORK COMPRESSION AND SPEEDUP 76
Compress Pre-trained Networks • On Single Layer: Takeaway Points • Fully connected layer: SVD • Convolutional layer: Flattened Convolutions • Weight Pruning: • Magnitude-based pruning method is simple and effective, which is the first choice for weight pruning. • Retraining is important for model compression. • Weight quantization with the full-precision copy can prevent gradient vanishing. • Weight pruning, quantization, and encoding are independent. We can use all three methods together for better compression ratio. Design a smaller CNN architecture • Example: Squeeze. Net • Use of Fire module, delay pooling at later stage NETWORK COMPRESSION AND SPEEDUP 77
Reading List • Denton, Emily L. , et al. "Exploiting linear structure within convolutional networks for efficient evaluation. " Advances in Neural Information Processing Systems. 2014. • Jin, Jonghoon, Aysegul Dundar, and Eugenio Culurciello. "Flattened convolutional neural networks for feedforward acceleration. " ar. Xiv preprint ar. Xiv: 1412. 5474 (2014). • Gong, Yunchao, et al. "Compressing deep convolutional networks using vector quantization. " ar. Xiv preprint ar. Xiv: 1412. 6115 (2014). • Han, Song, et al. "Learning both weights and connections for efficient neural network. " Advances in Neural Information Processing Systems. 2015. • Guo, Yiwen, Anbang Yao, and Yurong Chen. "Dynamic Network Surgery for Efficient DNNs. " Advances In Neural Information Processing Systems. 2016. • Gupta, Suyog, et al. "Deep Learning with Limited Numerical Precision. " ICML. 2015. • Courbariaux, Matthieu, Yoshua Bengio, and Jean-Pierre David. "Binaryconnect: Training deep neural networks with binary weights during propagations. " Advances in Neural Information Processing Systems. 2015. • Courbariaux, Matthieu, et al. "Binarized neural networks: Training deep neural networks with weights and activations constrained to+ 1 or-1. " ar. Xiv preprint ar. Xiv: 1602. 02830 (2016). • Han, Song, Huizi Mao, and William J. Dally. "Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. " ar. Xiv preprint ar. Xiv: 1510. 00149 (2015). • Iandola, Forrest N. , et al. "Squeeze. Net: Alex. Net-level accuracy with 50 x fewer parameters and< 0. 5 MB model size. " ar. Xiv preprint ar. Xiv: 1602. 07360 (2016). NETWORK COMPRESSION AND SPEEDUP 78
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