Posted Content•
Sampling the "Inverse Set" of a Neuron: An Approach to Understanding Neural Nets.
TL;DR: The approach in this paper is to characterize the region of input space that excites a given neuron to a certain level; this inverse set is a complicated high dimensional object that is explored by an optimization-based sampling approach.
Abstract: With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or express in simple terms. The approach we propose in this paper is to characterize the region of input space that excites a given neuron to a certain level; we call this the inverse set. This inverse set is a complicated high dimensional object that we explore by an optimization-based sampling approach. Inspection of samples of this set by a human can reveal regularities that help to understand the neuron. This goes beyond approaches which were limited to finding an image which maximally activates the neuron or using Markov chain Monte Carlo to sample images, but this is very slow, generates samples with little diversity and lacks control over the activation value of the generated samples. Our approach also allows us to explore the intersection of inverse sets of several neurons and other variations.
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19 Sep 2021
TL;DR: The approach in this paper is to characterize the region of input space that excites a given neuron to a certain level; this inverse set is a complicated high dimensional object that is explored by an optimization-based sampling approach.
Abstract: With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or express in simple terms. The approach we propose in this paper is to characterize the region of input space that excites a given neuron to a certain level; we call this the inverse set. This inverse set is a complicated high dimensional object that we explore by an optimization-based sampling approach. Inspection of samples of this set by a human can reveal regularities that help to understand the neuron. This goes beyond approaches which were limited to finding an image which maximally activates the neuron [1] or using Markov chain Monte Carlo to sample images [2], but this is very slow, generates samples with little diversity and lacks control over the activation value of the generated samples. Our approach also allows us to explore the intersection of inverse sets of several neurons and other variations.
4 citations
19 Sep 2021
TL;DR: This work mimicking part of the net with a decision tree having sparse weight vectors at the nodes is able to learn trees that are both highly accurate and interpretable, so they can provide insights into the deep net black box.
Abstract: The widespread deployment of deep nets in practical applications has lead to a growing desire to understand how and why such blackbox methods perform prediction. Much work has focused on understanding what part of the input pattern (an image, say) is responsible for a particular class being predicted, and how the input may be manipulated to predict a different class. We focus instead on understanding what internal features computed by the neural net are responsible for a particular class. We achieve this by mimicking part of the net with a decision tree having sparse weight vectors at the nodes. We are able to learn trees that are both highly accurate and interpretable, so they can provide insights into the deep net black box. Further, we show we can easily manipulate the neural net features in order to make the net predict, or not predict, a given class, thus showing that it is possible to carry out adversarial attacks at the level of the features. We demonstrate this robustly in MNIST and ImageNet with LeNet5 and VGG networks.
4 citations
Posted Content•
TL;DR: The authors consider counterfactual explanations, the problem of minimally adjusting features in a source input instance so that it is classified as a target class under a given classifier, which is formally equivalent to finding adversarial examples.
Abstract: We consider counterfactual explanations, the problem of minimally adjusting features in a source input instance so that it is classified as a target class under a given classifier. This has become a topic of recent interest as a way to query a trained model and suggest possible actions to overturn its decision. Mathematically, the problem is formally equivalent to that of finding adversarial examples, which also has attracted significant attention recently. Most work on either counterfactual explanations or adversarial examples has focused on differentiable classifiers, such as neural nets. We focus on classification trees, both axis-aligned and oblique (having hyperplane splits). Although here the counterfactual optimization problem is nonconvex and nondifferentiable, we show that an exact solution can be computed very efficiently, even with high-dimensional feature vectors and with both continuous and categorical features, and demonstrate it in different datasets and settings. The results are particularly relevant for finance, medicine or legal applications, where interpretability and counterfactual explanations are particularly important.
4 citations
Posted Content•
TL;DR: The authors mimicking part of the neural network with an oblique decision tree having sparse weight vectors at the decision nodes, and using the recently proposed Tree Alternating Optimization (TAO) algorithm, they are able to learn trees that are both highly accurate and interpretable.
Abstract: The widespread deployment of deep nets in practical applications has lead to a growing desire to understand how and why such black-box methods perform prediction. Much work has focused on understanding what part of the input pattern (an image, say) is responsible for a particular class being predicted, and how the input may be manipulated to predict a different class. We focus instead on understanding which of the internal features computed by the neural net are responsible for a particular class. We achieve this by mimicking part of the neural net with an oblique decision tree having sparse weight vectors at the decision nodes. Using the recently proposed Tree Alternating Optimization (TAO) algorithm, we are able to learn trees that are both highly accurate and interpretable. Such trees can faithfully mimic the part of the neural net they replaced, and hence they can provide insights into the deep net black box. Further, we show we can easily manipulate the neural net features in order to make the net predict, or not predict, a given class, thus showing that it is possible to carry out adversarial attacks at the level of the features. These insights and manipulations apply globally to the entire training and test set, not just at a local (single-instance) level. We demonstrate this robustly in the MNIST and ImageNet datasets with LeNet5 and VGG networks.
1 citations
23 May 2022
TL;DR: In this article , the authors use sparse oblique trees as a tool to select features from the dataset, which helps to visualize the underlying patterns in the dataset and determine what set of features differentiate between classes or groups of classes.
Abstract: Interpreting the image datasets is a difficult task, as each image contains a lot of irrelevant data. This paper presents a simple yet effective method to interpret the image datasets. We achieve this by using sparse oblique trees as a tool to select features from the dataset. These trees are not only accurate but also very interpretable. The hierarchical structure of the tree helps to visualize the underlying patterns in the dataset. By studying the weights of the nodes, we can determine what set of features differentiate between classes or groups of classes. We effectively demonstrate our results in multiple image datasets.
1 citations
References
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Proceedings Article•
03 Dec 2012TL;DR: The state-of-the-art performance of CNNs was achieved by Deep Convolutional Neural Networks (DCNNs) as discussed by the authors, which consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax.
Abstract: We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overriding in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.
73,978 citations
20 Jun 2009
TL;DR: A new database called “ImageNet” is introduced, a large-scale ontology of images built upon the backbone of the WordNet structure, much larger in scale and diversity and much more accurate than the current image datasets.
Abstract: The explosion of image data on the Internet has the potential to foster more sophisticated and robust models and algorithms to index, retrieve, organize and interact with images and multimedia data. But exactly how such data can be harnessed and organized remains a critical problem. We introduce here a new database called “ImageNet”, a large-scale ontology of images built upon the backbone of the WordNet structure. ImageNet aims to populate the majority of the 80,000 synsets of WordNet with an average of 500-1000 clean and full resolution images. This will result in tens of millions of annotated images organized by the semantic hierarchy of WordNet. This paper offers a detailed analysis of ImageNet in its current state: 12 subtrees with 5247 synsets and 3.2 million images in total. We show that ImageNet is much larger in scale and diversity and much more accurate than the current image datasets. Constructing such a large-scale database is a challenging task. We describe the data collection scheme with Amazon Mechanical Turk. Lastly, we illustrate the usefulness of ImageNet through three simple applications in object recognition, image classification and automatic object clustering. We hope that the scale, accuracy, diversity and hierarchical structure of ImageNet can offer unparalleled opportunities to researchers in the computer vision community and beyond.
49,639 citations
"Sampling the "Inverse Set" of a Neu..." refers methods in this paper
...So, we also used a pre-trained CaffeNet (Jia et al., 2014) for our experiments, which had been trained on ImageNet dataset (Deng et al., 2009)....
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..., 2014) for our experiments, which had been trained on ImageNet dataset (Deng et al., 2009)....
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08 Dec 2014
TL;DR: A new framework for estimating generative models via an adversarial process, in which two models are simultaneously train: a generative model G that captures the data distribution and a discriminative model D that estimates the probability that a sample came from the training data rather than G.
Abstract: We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
38,211 citations
"Sampling the "Inverse Set" of a Neu..." refers background or methods in this paper
...Recently, Dosovitskiy and Brox (2016b) trained a neural network using GAN (Goodfellow et al., 2014) to generate realistic images from a feature vector, which is later used by Nguyen et al....
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...Recently, Dosovitskiy and Brox (2016b) trained a neural network using GAN (Goodfellow et al., 2014) to generate realistic images from a feature vector, which is later used by Nguyen et al. (2016) to generate realistic images for activation maximization....
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Book•
01 Nov 2008TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
17,420 citations
06 Sep 2014
TL;DR: A novel visualization technique is introduced that gives insight into the function of intermediate feature layers and the operation of the classifier in large Convolutional Network models, used in a diagnostic role to find model architectures that outperform Krizhevsky et al on the ImageNet classification benchmark.
Abstract: Large Convolutional Network models have recently demonstrated impressive classification performance on the ImageNet benchmark Krizhevsky et al. [18]. However there is no clear understanding of why they perform so well, or how they might be improved. In this paper we explore both issues. We introduce a novel visualization technique that gives insight into the function of intermediate feature layers and the operation of the classifier. Used in a diagnostic role, these visualizations allow us to find model architectures that outperform Krizhevsky et al on the ImageNet classification benchmark. We also perform an ablation study to discover the performance contribution from different model layers. We show our ImageNet model generalizes well to other datasets: when the softmax classifier is retrained, it convincingly beats the current state-of-the-art results on Caltech-101 and Caltech-256 datasets.
12,783 citations
"Sampling the "Inverse Set" of a Neu..." refers methods in this paper
...This is done by back propagation, gradient descent or training a neural network (Mahendran and Vedaldi, 2015; Wei et al., 2015; Zeiler and Fergus, 2014; Dosovitskiy and Brox, 2016a)....
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