Interpretable CNNs

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN), 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.

Divergence Triangle for Joint Training of Generator Model, Energy-based Model, and Inference Model

This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data. The divergence triangle is a robust training method that can learn from incomplete data.

Learning Dynamic Generator Model by Alternating Back-Propagation Through Time

This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a non-linear transformation of a latent state vector, where the non-linear transformation is parametrized by a top-down neural network. The sequence of latent state vectors follows a non-linear auto-regressive model, where the state vector of the next frame is a non-linear transformation of the state vector of the current frame as well as an independent noise vector that provides randomness in the transition. The non-linear transformation of this transition model can be parametrized by a feedforward neural network. We show that this model can be learned by an alternating back-propagation through time algorithm that iteratively samples the noise vectors and updates the parameters in the transition model and the generator model. We show that our training method can learn realistic models for dynamic textures and action patterns.

Explanatory Graphs for CNNs

This paper introduces a graphical model, namely an explanatory graph, which reveals the knowledge hierarchy hidden inside conv-layers of a pre-trained CNN. Each filter in a conv-layer of a CNN for object classification usually represents a mixture of object parts. We develop a simple yet effective method to disentangle object-part pattern components from each filter. We construct an explanatory graph to organize the mined part patterns, where a node represents a part pattern, and each edge encodes co-activation relationships and spatial relationships between patterns. More crucially, given a pre-trained CNN, the explanatory graph is learned without a need of annotating object parts. Experiments show that each graph node consistently represented the same object part through different images, which boosted the transferability of CNN features. We transferred part patterns in the explanatory graph to the task of part localization, and our method significantly outperformed other approaches.

Mining Interpretable AOG Representations from Convolutional Networks via Active Question Answering

In this paper, we present a method to mine object-part patterns from conv-layers of a pre-trained convolutional neural network (CNN). The mined object-part patterns are organized by an And-Or graph (AOG). This interpretable AOG representation consists of a four-layer semantic hierarchy, i.e., semantic parts, part templates, latent patterns, and neural units. The AOG associates each object part with certain neural units in feature maps of conv-layers. The AOG is constructed in a weakly-supervised manner, i.e., very few annotations (e.g., 3-20) of object parts are used to guide the learning of AOGs. We develop a question-answering (QA) method that uses active human-computer communications to mine patterns from a pre-trained CNN, in order to incrementally explain more features in conv-layers. During the learning process, our QA method uses the current AOG for part localization. The QA method actively identifies objects, whose feature maps cannot be explained by the AOG. Then, our method asks people to annotate parts on the unexplained objects, and uses answers to discover CNN patterns corresponding to the newly labeled parts. In this way, our method gradually grows new branches and refines existing branches on the AOG to semanticize CNN representations. In experiments, our method exhibited a high learning efficiency. Our method used about 1/6-1/3 of the part annotations for training, but achieved similar or better part-localization performance than fast-RCNN methods.

Cooperative Holistic Scene Understanding: Unifying 3D Object, Layout, and Camera Pose Estimation

Holistic 3D indoor scene understanding refers to jointly recovering the i) object bounding boxes, ii) room layout, and iii) camera pose, all in 3D. The existing methods either are ineffective or only tackle the problem partially. In this paper, we propose an end-to-end model that simultaneously solves all three tasks in real-time given only a single RGB image. The essence of the proposed method is to improve the prediction by i) parametrizing the targets (\eg, 3D boxes) instead of directly estimating the targets, and ii) cooperative training across different modules in contrast to training these modules individually. Specifically, we parametrize the 3D object bounding boxes by the predictions from several modules, \ie, 3D camera pose and object attributes. The proposed method provides two major advantages: i) The parametrization helps maintain the consistency between the 2D image and the 3D world, thus largely reducing the prediction variances in 3D coordinates. ii) Constraints can be imposed on the parametrization to train different modules simultaneously. We call these constraints "cooperative losses" as they enable the joint training and inference. We employ three cooperative losses for 3D bounding boxes, 2D projections, and physical constraints to estimate a geometrically consistent and physically plausible 3D scene. Experiments on the SUN RGB-D dataset shows that the proposed method significantly outperforms prior approaches on 3D object detection, 3D layout estimation, 3D camera pose estimation, and holistic scene understanding.

Cooperative Training of Descriptor and Generator Networks

This paper studies the cooperative training of two generative models for image modeling and synthesis. Both models are parametrized by convolutional neural networks (ConvNets). The first model is a deep energy-based model, whose energy function is defined by a bottom-up ConvNet, which maps the observed image to the energy. We call it the descriptor network. The second model is a generator network, which is a non-linear version of factor analysis. It is defined by a top-down ConvNet, which maps the latent factors to the observed image. The maximum likelihood learning algorithms of both models involve MCMC sampling such as Langevin dynamics. We observe that the two learning algorithms can be seamlessly interwoven into a cooperative learning algorithm that can train both models simultaneously. Specifically, within each iteration of the cooperative learning algorithm, the generator model generates initial synthesized examples to initialize a finite-step MCMC that samples and trains the energy-based descriptor model. After that, the generator model learns from how the MCMC changes its synthesized examples. That is, the descriptor model teaches the generator model by MCMC, so that the generator model accumulates the MCMC transitions and reproduces them by direct ancestral sampling. We call this scheme MCMC teaching. We show that the cooperative algorithm can learn highly realistic generative models.

Learning Grid-like Units with Vector Representation of Self-Position and Matrix Representation of Self-Motion

This paper proposes a model for learning grid-like units for spatial awareness and navigation. In this model, the self-position of the agent is represented by a vector, and the self-motion of the agent is represented by a block-diagonal matrix. Each component of the vector is a unit (or a cell). The model consists of the following two sub-models. (1) Motion sub-model. The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., multiplying the matrix representation of the motion to the current vector representation of the position in order to obtain the vector representation of the next position. (2) Localization sub-model. The adjacency between any two positions is a monotone decreasing function of their Euclidean distance, and the adjacency is modeled by the inner product between the vector representations of the two positions. Both sub-models can be implemented by neural networks. The motion sub-model is a recurrent network with dynamic weight matrix, and the localization sub-model is a feedforward network. The model can be learned by minimizing a loss function that combines the loss functions of the two sub-models. The learned units exhibit grid-like patterns (as well as stripe patterns) in all 1D, 2D and 3D environments. The learned model can be used for path integral and path planning. Moreover, the learned representation is capable of error correction.

A Tale of Three Probabilistic Families: Discriminative, Descriptive and Generative Models

The pattern theory of Grenander is a mathematical framework where the patterns are represented by probability models on random variables of algebraic structures. In this paper, we review three families of probability models, namely, the discriminative models, the descriptive models, and the generative models. A discriminative model is in the form of a classifier. It specifies the conditional probability of the class label given the input signal. The descriptive model specifies the probability distribution of the signal, based on an energy function defined on the signal. A generative model assumes that the signal is generated by some latent variables via a transformation. We shall review these models within a common framework and explore their connections. We shall also review the recent developments that take advantage of the high approximation capacities of deep neural networks.

Mining a Deep And-OR Object Semantics from Web Images via Cost-Sensitive Question-Answer-Based Active Annotations

This paper presents a cost-sensitive active Question-Answering (QA) framework for learning a nine-layer And-Or graph (AOG) from web images. The AOG explicitly represents object categories, poses/viewpoints, parts, and detailed structures within the parts in a compositional hierarchy. The QA framework is designed to minimize an overall risk, which trades off the loss and query costs. The loss is defined for nodes in all layers of the AOG, including the generative loss (measuring the likelihood of the images) and the discriminative loss (measuring the fitness to human answers). The cost comprises both the human labor of answering questions and the computational cost of model learning. The cost-sensitive QA framework iteratively selects different storylines of questions to update different nodes in the AOG. Experiments showed that our method required much less human supervision (e.g., labeling parts on 3--10 training objects for each category) and achieved better performance than baseline methods.