The model parameters of convolutional neural networks (CNNs) are determined by backpropagation (BP). In this work, we propose an interpretable feedforward (FF) design without any BP as a reference. The FF design adopts a data-centric approach. It derives network parameters of the current layer based on data statistics from the output of the previous layer in a one-pass manner. To construct convolutional layers, we develop a new signal transform, called the Saab (Subspace Approximation with Adjusted Bias) transform. It is a variant of the principal component analysis (PCA) with an added bias vector to annihilate activation's nonlinearity. Multiple Saab transforms in cascade yield multiple convolutional layers. As to fully-connected (FC) layers, we construct them using a cascade of multi-stage linear least squared regressors (LSRs). The classification and robustness (against adversarial attacks) performances of BP- and FF-designed CNNs applied to the MNIST and the CIFAR-10 datasets are compared. Finally, we comment on the relationship between BP and FF designs.

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在数学(特别是功能分析)中,卷积是对两个函数(f和g)的数学运算,产生三个函数,表示第一个函数的形状如何被另一个函数修改。 卷积一词既指结果函数,又指计算结果的过程。 它定义为两个函数的乘积在一个函数反转和移位后的积分。 并针对所有shift值评估积分,从而生成卷积函数。

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method does not require additional annotations of object parts or textures for supervision. Instead, we use the same training data as traditional CNNs. Our method automatically assigns each interpretable filter in a high conv-layer with an object part of a certain category during the learning process. Such explicit knowledge representations in conv-layers of CNN help people clarify the logic encoded in the CNN, i.e., answering what patterns the CNN extracts from an input image and uses for prediction. We have tested our method using different benchmark CNNs with various structures to demonstrate the broad applicability of our method. Experiments have shown that our interpretable filters are much more semantically meaningful than traditional filters.

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During the last decade, Convolutional Neural Networks (CNNs) have become the de facto standard for various Computer Vision and Machine Learning operations. CNNs are feed-forward Artificial Neural Networks (ANNs) with alternating convolutional and subsampling layers. Deep 2D CNNs with many hidden layers and millions of parameters have the ability to learn complex objects and patterns providing that they can be trained on a massive size visual database with ground-truth labels. With a proper training, this unique ability makes them the primary tool for various engineering applications for 2D signals such as images and video frames. Yet, this may not be a viable option in numerous applications over 1D signals especially when the training data is scarce or application-specific. To address this issue, 1D CNNs have recently been proposed and immediately achieved the state-of-the-art performance levels in several applications such as personalized biomedical data classification and early diagnosis, structural health monitoring, anomaly detection and identification in power electronics and motor-fault detection. Another major advantage is that a real-time and low-cost hardware implementation is feasible due to the simple and compact configuration of 1D CNNs that perform only 1D convolutions (scalar multiplications and additions). This paper presents a comprehensive review of the general architecture and principals of 1D CNNs along with their major engineering applications, especially focused on the recent progress in this field. Their state-of-the-art performance is highlighted concluding with their unique properties. The benchmark datasets and the principal 1D CNN software used in those applications are also publically shared in a dedicated website.

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Convolutional neural networks (CNNs) can model complicated non-linear relations between images. However, they are notoriously sensitive to small changes in the input. Most CNNs trained to describe image-to-image mappings generate temporally unstable results when applied to video sequences, leading to flickering artifacts and other inconsistencies over time. In order to use CNNs for video material, previous methods have relied on estimating dense frame-to-frame motion information (optical flow) in the training and/or the inference phase, or by exploring recurrent learning structures. We take a different approach to the problem, posing temporal stability as a regularization of the cost function. The regularization is formulated to account for different types of motion that can occur between frames, so that temporally stable CNNs can be trained without the need for video material or expensive motion estimation. The training can be performed as a fine-tuning operation, without architectural modifications of the CNN. Our evaluation shows that the training strategy leads to large improvements in temporal smoothness. Moreover, in situations where the quantity of training data is limited, the regularization can help in boosting the generalization performance to a much larger extent than what is possible with na\"ive augmentation strategies.

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With the widespread applications of deep convolutional neural networks (DCNNs), it becomes increasingly important for DCNNs not only to make accurate predictions but also to explain how they make their decisions. In this work, we propose a CHannel-wise disentangled InterPretation (CHIP) model to give the visual interpretation to the predictions of DCNNs. The proposed model distills the class-discriminative importance of channels in networks by utilizing the sparse regularization. Here, we first introduce the network perturbation technique to learn the model. The proposed model is capable to not only distill the global perspective knowledge from networks but also present the class-discriminative visual interpretation for specific predictions of networks. It is noteworthy that the proposed model is able to interpret different layers of networks without re-training. By combining the distilled interpretation knowledge in different layers, we further propose the Refined CHIP visual interpretation that is both high-resolution and class-discriminative. Experimental results on the standard dataset demonstrate that the proposed model provides promising visual interpretation for the predictions of networks in image classification task compared with existing visual interpretation methods. Besides, the proposed method outperforms related approaches in the application of ILSVRC 2015 weakly-supervised localization task.

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We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike "deep kernels", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass through the original CNN with only one filter per layer. The kernel equivalent to a 32-layer ResNet obtains 0.84% classification error on MNIST, a new record for GPs with a comparable number of parameters.

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We propose a Bayesian convolutional neural network built upon Bayes by Backprop and elaborate how this known method can serve as the fundamental construct of our novel, reliable variational inference method for convolutional neural networks. First, we show how Bayes by Backprop can be applied to convolutional layers where weights in filters have probability distributions instead of point-estimates; and second, how our proposed framework leads with various network architectures to performances comparable to convolutional neural networks with point-estimates weights. In the past, Bayes by Backprop has been successfully utilised in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of the group of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.

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Current visualization based network interpretation methodssuffer from lacking semantic-level information. In this paper, we introduce the novel task of interpreting classification models using fine grained textual summarization. Along with the label prediction, the network will generate a sentence explaining its decision. Constructing a fully annotated dataset of filter|text pairs is unrealistic because of image to filter response function complexity. We instead propose a weakly-supervised learning algorithm leveraging off-the-shelf image caption annotations. Central to our algorithm is the filter-level attribute probability density function (PDF), learned as a conditional probability through Bayesian inference with the input image and its feature map as latent variables. We show our algorithm faithfully reflects the features learned by the model using rigorous applications like attribute based image retrieval and unsupervised text grounding. We further show that the textual summarization process can help in understanding network failure patterns and can provide clues for further improvements.

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This paper proposes a method to modify traditional convolutional neural networks (CNNs) into interpretable CNNs, in order to clarify knowledge representations in high conv-layers of CNNs. In an interpretable CNN, each filter in a high conv-layer represents a certain object part. We do not need any annotations of object parts or textures to supervise the learning process. Instead, the interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. Our method can be applied to different types of CNNs with different structures. The clear knowledge representation in an interpretable CNN can help people understand the logics inside a CNN, i.e., based on which patterns the CNN makes the decision. Experiments showed that filters in an interpretable CNN were more semantically meaningful than those in traditional CNNs.

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This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance in various tasks, the interpretability is always the Achilles' heel of deep neural networks. At present, deep neural networks obtain high discrimination power at the cost of low interpretability of their black-box representations. We believe that high model interpretability may help people to break several bottlenecks of deep learning, e.g., learning from very few annotations, learning via human-computer communications at the semantic level, and semantically debugging network representations. We focus on convolutional neural networks (CNNs), and we revisit the visualization of CNN representations, methods of diagnosing representations of pre-trained CNNs, approaches for disentangling pre-trained CNN representations, learning of CNNs with disentangled representations, and middle-to-end learning based on model interpretability. Finally, we discuss prospective trends in explainable artificial intelligence.

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Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for each graph data while training. To efficiently learn the graph, a distance metric learning is proposed. Extensive experiments on nine graph-structured datasets have demonstrated the superior performance improvement on both convergence speed and predictive accuracy.

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