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Distributed Code or Grandmother Cells: Insights From Convolutional Neural Networks

In Computer Vision, deep learning, Machine Learning, Neural Science, Sparse Coding on January 23, 2016 at 1:31 pm

by Li Yang Ku (Gooly)

grandmother-cell

Convolutional Neural Network (CNN)-based features will likely replace engineered representations such as SIFT and HOG, yet we know little on what it represents. In this post I will go through a few papers that dive deeper into CNN-based features and discuss whether CNN feature vectors tend to be more like grandmother cells, where most information resides in a small set of filter responses, or distributed code, where most filter responses carry information equally. The content of this post is mostly taken from the following three papers:

  1. Agrawal, Pulkit, Ross Girshick, and Jitendra Malik. “Analyzing the performance of multilayer neural networks for object recognition.” Computer Vision–ECCV 2014. Springer International Publishing, 2014. 329-344.
  2. Hinton, Geoffrey, Oriol Vinyals, and Jeff Dean. “Distilling the knowledge in a neural network.” arXiv preprint arXiv:1503.02531 (2015).
  3. Dosovitskiy, Alexey, and Thomas Brox. “Inverting convolutional networks with convolutional networks.” arXiv preprint arXiv:1506.02753 (2015).

So why do we want to take insights from convolutional neural networks (CNN)? Like what I talked about in my previous postIn 2012, University of Toronto’s CNN implementation won the ImageNet challenge by a large margin, 15.3% and 26.6% in classification and detection by the nearest competitor. Since then CNN approaches have been leaders in most computer vision benchmarks. Although CNN doesn’t work like the brain, the characteristic that makes it work well might be also true in the brain.

faceselectiv

The grandmother cell is a hypothetical neuron that represents a complex but specific concept or object proposed by cognitive scientist Jerry Letvin in 1969. Although it is mostly agreed that the original concept of grandmother cell which suggests that each person or object one recognizes is associated with a single cell is biological implausible (see here for more discussion), the less extreme idea of grandmother cell is now explained as sparse coding.

Deformable Part Model

Before diving into CNN features we look into existing computer vision algorithms and see which camp they belong to. Traditional object recognition algorithms either are part-based approaches that use mid-level patches or use a bag of local descriptors such as SIFT. One of the well know part-based approaches is the deformable part model which uses HOG to model parts and a score on respective location and deformation to model their spatial relationship. Each part is a mid-level patch that can be seen as a feature that fires to specific visual patterns and mid-level patch discovery can be viewed as the search for a set of grandmother cell templates.

SIFT

On the other hand, unlike mid-level patches, SIFT like features represent low level edges and corners. This bag of descriptors approach uses a distributed code; a single feature by itself is not discriminative, but a group of features taken together is.

There were many attempts to understand CNN more. One of the early work done by Zeiler and Fergus find locally optimal visual inputs for individual filters. However this does not characterize the distribution of images that cause a filter to activate. Agrawal et al. claimed that a grandmother cell can be seen as a filter with high precision and recall. Therefore for each conv-5 filter in the CNN trained on ImageNet they calculate the average precision for classifying images. They showed that grandmother cell like filters exist for only a few classes, such as bicycle, person, cars, and cats. The number of filters required to recognize objects of a class is also measured. For classes such as persons, cars, and cats few filters are required, but most classes require 30 to 40 filters.

convolutional-neural-networks-top-9-layer-4-5

In the work done by Hinton et al. a concept called distillation is introduced. Distillation transfers the knowledge of a cumbersome model to a small model. For a cumbersome model, the training objective is to maximize the probability of the correct answer. A side effect is that it also assigns probabilities to incorrect answers. Instead of training on the correct answer, distillation train on soft targets, which is the probabilities of all answers generated from the cumbersome model. They showed that the small model performs better when trained on these soft targets versus when trained on the correct answer. This result suggests that the relative probabilities of incorrect answers tell us a lot about how the cumbersome model tends to generalize.

Inverting CNN Features

On the other hand, Dosovitskiy et al. tried to understand CNN features through inverting the CNN. They claim that inverting CNN features allows us to see which information of the input image is preserved in the features. Applying inverse to a perturbed feature vector yields further insight into the structure of the feature space. Interestingly, when they discard features in the FC8 layer they found most information is contained in small probabilities of those classes instead of the top-5 activation. This result is consistent with the result of the distillation experiment mentioned previously.

Top-5 vs rest feature in FC8

These findings suggest that a combination of distributed code and some grandmother like cells may be closer to how CNN features work and might also be how our brain encodes visual inputs.

 

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Sparse Coding in a Nutshell

In Computer Vision, Neural Science, Sparse Coding on May 24, 2014 at 7:24 pm

by Li Yang Ku (Gooly)

nutshell

I’ve been reading some of Dieter Fox’s publications recently and a series of work on Hierarchical Matching Pursuit (HMP) caught my eye. There are three papers that is based on HMP, “Hierarchical Matching Pursuit for Image Classification: Architecture and Fast Algorithms”, “Unsupervised feature learning for RGB-D based object recognition” and “Unsupervised Feature Learning for 3D Scene Labeling”. In all 3 of these publications, the HMP algorithm is what it is all about. The first paper, published in 2011, deals with scene classification and object recognition on gray scale images; the second paper, published in 2012, takes RGBD image as input for object recognition; while the third paper, published in 2014, further extends the application to scene recognition using point cloud input. The 3 figures below are the feature dictionaries used in these 3 papers in chronicle order.

hmp

One of the center concept of HMP is to learn low level and mid level features instead of using hand craft features like SIFT feature. In fact the first paper claims that it is the first work to show that learning features from the pixel level significantly outperforms those approaches built on top of SIFT. Explaining it in a sentence, HMP is an algorithm that builds up a sparse dictionary and encodes it hierarchically such that meaningful features preserves. The final classifier is simply a linear support vector machine, so the magic is mostly in sparse coding. To fully understand why sparse coding might be a good idea we have to go back in time.

Back in the 50’s, Hubel and Wiesel’s work on discovering Gabor filter like neurons in the cat brain really inspired a lot of people. However, the community thought the Gabor like filters are some sort of edge detectors. This discovery leads to a series of work done on edge detection in the 80’s when digital image processing became possible on computers. Edge detectors such as Canny, Harris, Sobel, Prewitt, etc are all based on the concept of detecting edges before recognizing objects. More recent algorithms such as Histogram of Oriented Gradient (HOG) are an extension of these edge detectors. An example of HOG is the quite successful paper on pedestrian detection “Histograms of oriented gradients for human detection” (See figure below).

hog and sift

If we move on to the 90’s and 2000’s, SIFT like features seems to have dominated a large part of the Computer Vision world. These hand-craft features works surprisingly well and lead to many real applications. These type of algorithms usually consist of two steps, 1) detect interesting feature points (yellow circles in the figure above) , 2) generate an invariant descriptor around it (green check boards in the figure above). One of the reasons it works well is that SIFT only cares interest points, therefore lowering the dimension of the feature significantly. This allows classifiers to require less training samples before it can make reasonable predictions. However, throwing away all those geometry and texture information is unlikely how we humans see the world and will fail in texture-less scenarios.

In 1996, Olshausen showed that by adding a sparse constraint, gabor like filters are the codes that best describe natural images. What this might suggest is that Filters in V1 (Gabor filters) are not just edge detectors, but statistically the best coding for natural images under the sparse constraint. I regard this as the most important proof that our brain uses sparse coding and the reason it works better in many new algorithms that uses sparse coding such as the HMP. If you are interested in why evolution picked sparse coding, Jeff Hawkins has a great explanation in one of his talks (at 17:33); besides saving energy, it also helps generalizing and makes comparing features easy. Andrew Ng also has a paper “The importance of encoding versus training with sparse coding and vector quantization” on analyzing which part of sparse coding leads to better result.