What is the Best Multi-Stage Architecture for Object Recognition Kevin Jarrett, Koray Kavukcuoglu, Marc’ Aurelio Ranzato and Yann LeCun Presented by Lingbo Li ECE, Duke University Dec. 13rd, 2010

Outline Introduction Model Architecture Training Protocol Experiments  Caltech 101 Dataset  NORB Dataset  MNIST Dataset Conclusions

Introduction (I) Feature extraction stages:  A filter bank  A non-linear operation  A pooling operation Recognition architectures: Single stage of features + supervised classifier: SIFT, HoG, etc. Two or more successive stages of feature extractors + supervised classifier: convolutional networks

Introduction (II) Q1: How do the non-linearities that follow the filter banks influence the recognition accuracy? Q2: Is there any advantage to using an architecture with two successive stages of features extraction, rather than with a single stage? Q3: Does learning the filter banks in an unsupervised or supervised manner improve the performance over hard- wired filters or even random filters?

Model Architecture (I) Input: Output : Filter : A filter bank layer with 64 filters of size 9x9 : is the j-th feature map

Model Architecture (II)  Subtractive normalization operation  Divisive normalization operation

Model Architecture (III) An average pooling layer with 4x4 down-sampling: A max-pooling layer with 4x4 down-sampling:

Model Architecture (IV) Combining Modules into a Hierarchy

Training Protocol (I) Optimal sparse coding: Under sparse condition, this problem can be written as an optimization problem: Given training samples, learning proceeds: 1)Minimize the loss function 2)Find by running a rather expensive optimization algorithm.

Training Protocol (II) Predictive Sparse Decomposition (PSD) PSD trains a regressor to approximate the sparse solution for all training samples, where Learning proceeds by minimizing the loss function where Thus, (dictionary) and (filters) are simultaneously optimized.

Training Protocol (III) A single letter: an architecture with a single stage of feature extraction followed by a classifier; A double letter: an architecture with two stages if feature extraction followed by a classifier.  Filters are set to random values and kept fixed. Classifiers are trained in supervised mode.  Filters are trained using unsupervised PSD algorithm, and kept fixed. Classifiers are trained in supervised model.  Filters are initialized with random values. The entire system (Feature stages + classifiers) is trained in supervised mode with gradient descent.  Filters are initialized with the PSD unsupervised learning algorithm. The entire system (feature stages + classifiers) is trained in supervised mode by gradient descent.

Experiments (I) – Caltech 101 Data pre-processing: 1)Convert to gray-scale and resize to 151x151 pixels; 2)Subtract the image mean and divide by the image standard deviation; 3)Apply subtractive/divisive normalization (N layer with c=1); 4)Zero-padding the shorter side to 143 pixels. Recognition rates are averaged over 5 drawings of the training set (30 images per class). Hyper-parameters are selected to maximize the performance on the validation set of 5 samples per class taken out of the training sets.

Experiments (I) – Caltech 101 Using a Single Stage of Feature Extraction: Using Two Stages of Feature Extraction: Multinomial logistic regression PMK-SVM 64 26x26 feature maps Multinomial logistic regression PMK-SVM 256 4x4 feature maps 64 26x26 feature maps

Experiments (I) – Caltech 101

Random filters and no filter learning whatsoever with can achieve decent performance; Supervised fine tuning improves the performance; Two-stage systems are better than their single-stage counterparts; With rectification and normalization, unsupervised training does not improve the performance; abs rectification is a crucial component for good performance; Single-stage system with PMK-SVM reaches the same performance with a two-stage with logistic regression;

Experiments (II) – NORB Dataset NORB dataset has 5 object categories; training samples and test samples (4860 per class); Each image is gray-scale with 96x96 pixels; Only consider the protocols; 1)Random filters do not perform as well as learned filters with more labels samples. 2)The use of abs and normalization makes a big difference.

Experiments (II) – NORB Dataset Use gradient descent to find the optimal input patterns in a architecture. In the left figure: (1-a) random stage-1 filters; (1-b) corresponding optimal inputs; (2-a) PSD filters; (2-b) Optimal input patterns; (3) subset of stage-2 filters after PSD and supervised refinement on Caltech-101. (3) (1-a) (2-b) (2-a) (1-b)

Experiments (III) – MNIST Dataset 60,000 gray-scale 28x28 pixel images for training and 10,000 images for testing; 2-stage of feature extraction: convolution 50 7x7 filters Max-pooling 2*2 windows 50 28x28 feature maps 50 14x14 feature maps Input Image 34x3 4 convolution x5filters 64 10x10 feature maps Max-pooling 2x2 windows 64 5x5 feature maps the first stage the second stage 10-way multinomial logistic regression

Experiments (III) – MNIST Dataset Parameters are trained with PSD: the only hyper- parameter is tuned with a validation set of 10,000 training samples. The classifier is randomly initialized; The whole system is tuned in supervised mode. A test error rate of 0.53% was obtained.

Conclusions (I) Q1: How do the non-linearities that follow the filter banks influence the recognition accuracy? 1) A rectifying non-linearity is the single most important factor. 2) A local normalization layer can also improve the performance. Q2: Is there any advantage to using an architecture with two successive stages of feature extraction, rather than with a single stage? 1) Two stages are better than one. 2) The performance of two-stage system is similar to that of the best single-stage systems based on SIFT and PMK-SVM.

Conclusions (II) Q3: Does learning the filter banks in an unsupervised or supervised manner improve the performance over hard-wired filters or even random filters? 1) Random filters yield good performance only in the case of small training set. 2) The optimal input patterns for a randomly initialized stage are similar to the optimal inputs for a stage that use learned filters. 3) The global supervised learning of filters yields good recognition rate if with the proper non-linearites. 4) Unsupervised pre-training followed by supervised refinement yields the best overall accuracy.