Deep learning on 3D geometries. Hope Yao Design Informatics Lab Department of Mechanical and Aerospace Engineering
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1 Deep learning on 3D geometries Hope Yao Design Informatics Lab Department of Mechanical and Aerospace Engineering
2 Overview Background Methods Numerical Result Future improvements Conclusion
3 Background machine learning Terms: Classification Is the problem of identifying to which of a set of class a new observation belongs, on the basis of a training set of data containing observations whose class membership is known Label Cross or dots in the figure Training Draw boundary Prediction Which category is the triangle?
4 Background ImageNet(2010) Image search Facial recognition Pose estimation Navigation
5 Background ImageNet(2010) International Large Scale Visual Recognition Challenge Image search Facial recognition Pose estimation Navigation
6 Background ModelNet(2015) Robot manipulation Product design 3D printing VR/AR
7 Background ModelNet(2015) Robot manipulation Product design 3D printing VR/AR
8 Methods Perceptron Perceptron training is an optimization problem w = argmin * (Y- Y(X; w)) X is features, w is weights, f is a nonlinear function Y- is ground truth, Y is network prediction
9 Methods Neural Network Network training is an optimization problem w = argmin * (Y- Y(X; w)) X is features, w is weights, f is a nonlinear function Y- is ground truth, Y is network prediction
10 Methods Convolutional NN
11 Methods Convolutional NN From google Benefits: 1. Capture spatial relations 2. Reduce number of unknown parameters
12 Methods Convolutional NN From google Benefits: 1. Capture spatial relations 2. Reduce number of unknown parameters Wu, Z., & Song, S. et. (2015).
13 Methods - computation difficulties High resolution data will bring exponentially higher computation High data dimension will also increase computation cost exponentially Parameters in network Operations per forward pass ModelNet ImageNet ModelNet ImageNet MNIST MNIST
14 Methods - Fourier convolution theorem f d-dimensional tensor g d-dimensional tensor * Convolution 8 Dot product C Fourier transform IFT Inverse FT n Size of f k Size of g f6 g = f7 8 g9 f g = IFT(f7 8 g9) Complexity of direct computation O(n > k > ) Complexity of Fast Fourier convolution O(dn > logn+dk > logk)
15 Numerical Results Network Accuracy ch=16 ch=24 ch=24 N=100 N=10 ch=16 conv sub conv sub Trad nn
16 Numerical Results Network Accuracy ch=16 ch=24 ch=24 N=100 N=10 ch=16 conv sub conv sub Trad nn Achieved 91.5% accuracy, comparable to the best result in (VoxNet,
17 Numerical Results 3D Convolution Time run for 100 times k = 5, n = 64 d = 3, ch = 16 run for 100 times k = 64, n = 64 d = 3, ch = 16 seconds seconds runs runs
18 Future improvements - XNOR Only binary variable is needed to represent the geometry A and B is binary version of W and X α and β are real coefficients W X = α A β B α β A B = argmin( W X α A β B ) I,K,L,M
19 Future improvements - XNOR Only binary variable is needed to represent the geometry A and B is binary version of W and X α and β are real coefficients W X = α A β B α β A B = argmin( W X α A β B ) I,K,L,M Rastegari, M. et al. (2016).
20 Future improvements X-ray style filters to reduce dimension Qi, C. R. et al(2016)
21 Future improvements Determine where to look at based on previous information Focus on only salient regions using Recurrent Neural Network Mnih, V. et al. (2014). Nips, arxiv:
22 Future improvements Determine where to look at based on previous information Focus on only salient regions using Recurrent Neural Network Mnih, V. et al. (2014). Nips, arxiv:
23 conclusion 3D Deep Learning is very promising Obtained high classification accuracy Some issue in speed up convolution There are lot left to be done
24 Acknowledgement to Dr. Toby Sanders Dr. John Stufken And all other RTG course faculties
25 Thank you! What questions do you have?
26 Background MNIST(1998) 70k digits 28x28 pixels Post office Bank Library
27 Background MNIST(1998) 70k digits 28x28 pixels year method Error rate 1998 Linear 8.0% 2002 SVM 0.56% 2007 KNN 0.52% 2010 Neural Net 0.35% 2012 Conv NN 0.23% Post office Bank Library
28 Methods - Parallelization Graphical Processing Unit From Nvidia
29 Methods - Parallelization Graphical Processing Unit From Nvidia
30 Methods - Parallelization Graphical Processing Unit Dual E v2: 2.1*6*2*16=0.4TFlops Single Titan X Pascal: 1.5*3584*2 = 11TFlops From Nvidia
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