summaries: This work proposes a novel analytic framework exploited on a semantic segmentation model to visualize GANs at unit (feature map) level. The authors show that some GAN representations can be interpreted, correlate with the parsing result from the semantic segmentation model but as variables that have a causal effect on the synthesis of semantic objects in the output. This framework could allow to detect and remove the artifacts to improve the quality of the generated images. This paper provides a visualization framework to understand the generative neural network in GAN models. To achieve this, they first find a group of interpretable units and then quantify the causal effect of interpretable units. Finally, the contextual relationship between these units and their surrounding is examined by inserting the discovered object concepts into new images. Extensive experiments are presented and a video is provided.
abstractText: Generative Adversarial Networks (GANs) have recently achieved impressive results for many real-world applications, and many GAN variants have emerged with improvements in sample quality and training stability. However, they have not been well visualized or understood. How does a GAN represent our visual world internally? What causes the artifacts in GAN results? How do architectural choices affect GAN learning? Answering such questions could enable us to develop new insights and better models. In this work, we present an analytic framework to visualize and understand GANs at the unit-, object-, and scene-level. We first identify a group of interpretable units that are closely related to object concepts using a segmentation-based network dissection method. Then, we quantify the causal effect of interpretable units by measuring the ability of interventions to control objects in the output. We examine the contextual relationship between these units and their surroundings by inserting the discovered object concepts into new images. We show several practical applications enabled by our framework, from comparing internal representations across different layers, models, and datasets, to improving GANs by locating and removing artifact-causing units, to interactively manipulating objects in a scene. We provide open source interpretation tools to help researchers and practitioners better understand their GAN models.
authors.name: ADVERSARIAL NETWORKS
authors.name: David Bau
authors.name: Jun-Yan Zhu
authors.name: Hendrik Strobelt
authors.name: Bolei Zhou
authors.name: Joshua B. Tenenbaum
authors.name: William T. Freeman
authors.name: Antonio Torralba
references.authors: Sebastian Bach Alexander Binder Grégoire Montavon Frederick Klauschen Klaus-Robert Müller Wojciech Samek
references.title: On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation
references.venue: PloS one,
references.authors: David Bau Bolei Zhou Aditya Khosla Aude Oliva Antonio Torralba
references.title: Network dissection: Quantifying interpretability of deep visual representations
references.venue: In CVPR, 2017
references.authors: Ali Borji
references.title: Pros and cons of gan evaluation measures
references.venue: arXiv preprint arXiv:1802.03446,
references.authors: Jeffrey S Bowers Ivan I Vankov Markus F Damian Colin J Davis
references.title: Why do some neurons in cortex respond to information in a selective manner? insights
references.authors: Andrew Brock Theodore Lim James M Ritchie Nick Weston
references.title: Neural photo editing with introspective adversarial networks
references.venue: In ICLR,
references.authors: Sanjoy Dasgupta Timothy C Sheehan Charles F Stevens Saket Navlakha
references.title: A neural data structure for novelty detection
references.venue: Proceedings of the National Academy of Sciences,
references.authors: Emily L Denton Soumith Chintala Rob Fergus
references.title: Deep generative image models using a laplacian pyramid of adversarial networks
references.venue: In NIPS,
references.authors: Laurent Dinh Jascha Sohl-Dickstein Samy Bengio
references.title: Density estimation using real nvp
references.venue: In ICLR,
references.authors: Jeff Donahue Philipp Krähenbühl Trevor Darrell
references.title: Adversarial feature learning
references.venue: In ICLR,
references.authors: Alexey Dosovitskiy Thomas Brox
references.title: Generating images with perceptual similarity metrics based on deep networks
references.venue: In NIPS,
references.authors: Vincent Dumoulin Ishmael Belghazi Ben Poole Alex Lamb Martin Arjovsky Olivier Mastropietro Aaron Courville
references.title: Adversarially learned inference
references.venue: In ICLR,
references.authors: Ian Goodfellow Jean Pouget-Abadie Mehdi Mirza Bing Xu David Warde-Farley Sherjil Ozair Aaron Courville Yoshua Bengio
references.title: Generative adversarial nets
references.venue: In NIPS,
references.authors: Ishaan Gulrajani Faruk Ahmed Martin Arjovsky Vincent Dumoulin Aaron C Courville
references.title: Improved training of wasserstein gans
references.venue: In NIPS,
references.authors: Martin Heusel Hubert Ramsauer Thomas Unterthiner Bernhard Nessler Sepp Hochreiter
references.title: Gans trained by a two time-scale update rule converge to a local nash equilibrium
references.venue: In NIPS,
references.authors: Judy Hoffman Eric Tzeng Taesung Park Jun-Yan Zhu Phillip Isola Kate Saenko Alexei A Efros Trevor Darrell
references.title: Cycada: Cycle-consistent adversarial domain adaptation
references.venue: In ICML,
references.authors: Paul W Holland
references.title: Causal inference, path analysis and recursive structural equations models
references.venue: ETS Research Report Series,
references.authors: Phillip Isola Jun-Yan Zhu Tinghui Zhou Alexei A Efros
references.title: Image-to-image translation with conditional adversarial networks
references.venue: In CVPR,
references.authors: Andrej Karpathy Justin Johnson Li Fei-Fei
references.title: Visualizing and understanding recurrent networks
references.venue: In ICLR,
references.authors: Tero Karras Timo Aila Samuli Laine Jaakko Lehtinen
references.title: Progressive growing of gans for improved quality, stability, and variation
references.venue: In ICLR,
references.authors: Been Kim Justin Gilmer Fernanda Viegas Ulfar Erlingsson Martin Wattenberg
references.title: Tcav: Relative concept importance testing with linear concept activation vectors
references.venue: arXiv preprint arXiv:1711.11279,
references.authors: Diederik P Kingma Max Welling
references.title: Auto-encoding variational bayes
references.venue: ICLR,
references.authors: Scott M Lundberg Su-In Lee
references.title: A unified approach to interpreting model predictions
references.venue: In NIPS,
references.authors: Aravindh Mahendran Andrea Vedaldi
references.title: Understanding deep image representations by inverting them
references.venue: In CVPR,
references.authors: Michael Mathieu Camille Couprie Yann LeCun
references.title: Deep multi-scale video prediction beyond mean square error
references.venue: In ICLR,
references.authors: Takeru Miyato Toshiki Kataoka Masanori Koyama Yuichi Yoshida
references.title: Spectral normalization for generative adversarial networks
references.venue: In ICLR,
references.authors: Ari S Morcos David GT Barrett Neil C Rabinowitz Matthew Botvinick
references.title: On the importance of single directions for generalization
references.venue: arXiv preprint arXiv:1803.06959,
references.authors: Chris Olah Arvind Satyanarayan Ian Johnson Shan Carter Ludwig Schubert Katherine Ye Alexander Mordvintsev
references.title: The building blocks of interpretability
references.venue: Distill, 3(3):e10,
references.authors: Rodrigo Quian Quiroga
references.title: Concept cells: the building blocks of declarative memory functions
references.venue: Nature Reviews Neuroscience,
references.authors: Alec Radford Luke Metz Soumith Chintala
references.title: Unsupervised representation learning with deep convolutional generative adversarial networks
references.venue: In ICLR,
references.authors: Ramprasaath R Selvaraju Michael Cogswell Abhishek Das Ramakrishna Vedantam Devi Parikh Dhruv Batra
references.title: Grad-cam: Visual explanations from deep networks via gradient-based localization
references.venue: In ICCV,
references.authors: Karen Simonyan Andrea Vedaldi Andrew Zisserman
references.title: Deep inside convolutional networks: Visualising image classification models and saliency maps
references.venue: In ICLR Workshop,
references.authors: Hendrik Strobelt Sebastian Gehrmann Hanspeter Pfister Alexander M. Rush
references.title: LSTMVis: A tool for visual analysis of hidden state dynamics in recurrent neural networks
references.venue: IEEE TVCG,
references.authors: Mukund Sundararajan Ankur Taly Qiqi Yan
references.title: Axiomatic attribution for deep networks
references.venue: In PMLR,
references.authors: Ting-Chun Wang Ming-Yu Liu Jun-Yan Zhu Guilin Liu Andrew Tao Jan Kautz Bryan Catanzaro
references.title: Video-to-video synthesis
references.venue: In NIPS,
references.authors: Xiaolong Wang Abhinav Shrivastava Abhinav Gupta
references.title: A-fast-rcnn: Hard positive generation via adversary for object detection
references.venue: In CVPR,
references.authors: Dedy Rahman Wijaya Riyanarto Sarno Enny Zulaika
references.title: Information quality ratio as a novel metric for mother wavelet selection
references.venue: Chemometrics and Intelligent Laboratory Systems,
references.authors: Tete Xiao Yingcheng Liu Bolei Zhou Yuning Jiang Jian Sun
references.title: Unified perceptual parsing for scene understanding
references.venue: In ECCV,
references.authors: Fisher Yu Ari Seff Yinda Zhang Shuran Song Thomas Funkhouser Jianxiong Xiao
references.title: Lsun: Construction of a large-scale image dataset using deep learning with humans in the loop
references.venue: arXiv preprint arXiv:1506.03365,
references.authors: Rafael Yuste
references.title: From the neuron doctrine to neural networks
references.venue: Nature reviews neuroscience,
references.authors: Matthew D Zeiler Rob Fergus
references.title: Visualizing and understanding convolutional networks
references.venue: In ECCV,
references.authors: Han Zhang Ian Goodfellow Dimitris Metaxas Augustus Odena
references.title: Self-attention generative adversarial networks
references.venue: arXiv preprint arXiv:1805.08318,
references.authors: Quanshi Zhang Ying Nian Wu Song-Chun Zhu
references.title: Interpretable convolutional neural networks
references.venue: In CVPR,
references.authors: Bolei Zhou Aditya Khosla Agata Lapedriza Aude Oliva Antonio Torralba
references.title: Object detectors emerge in deep scene cnns
references.venue: In ICLR,
references.authors: Bolei Zhou Hang Zhao Xavier Puig Sanja Fidler Adela Barriuso Antonio Torralba
references.title: Scene parsing through ade20k dataset
references.venue: In CVPR,
references.authors: Bolei Zhou David Bau Aude Oliva Antonio Torralba
references.title: Interpreting deep visual representations via network dissection
references.venue: PAMI, 2018a
references.authors: Bolei Zhou Yiyou Sun David Bau Antonio Torralba
references.title: Interpretable basis decomposition for visual explanation
references.venue: In ECCV, pp
references.authors: Tinghui Zhou Philipp Krahenbuhl Mathieu Aubry Qixing Huang Alexei A Efros
references.title: Learning dense correspondence via 3d-guided cycle consistency
references.venue: In CVPR,
references.authors: Jun-Yan Zhu Philipp Krähenbühl Eli Shechtman Alexei A. Efros
references.title: Generative visual manipulation on the natural image manifold
references.venue: In ECCV,
references.authors: Jun-Yan Zhu Taesung Park Phillip Isola Alexei A Efros
references.title: Unpaired image-to-image translation using cycle-consistent adversarial networks
references.venue: In ICCV,
references.authors: Karras
references.title: Our method relies on having a segmentation function sc(x) that identifies pixels of class c in the output x. However, the segmentation model sc can perform poorly in the cases where x does not resemble the original training set of sc. This phenomenon is visible when analyzing earlier GAN models. For example, Figure 15 visualizes two units from a WGAN-GP model (Gulrajani et al., 2017) for LSUN bedrooms
sections.text: Generative Adversarial Networks (GANs) have recently achieved impressive results for many real-world applications, and many GAN variants have emerged with improvements in sample quality and training stability. However, they have not been well visualized or understood. How does a GAN represent our visual world internally? What causes the artifacts in GAN results? How do architectural choices affect GAN learning? Answering such questions could enable us to develop new insights and better models.
  In this work, we present an analytic framework to visualize and understand GANs at the unit-, object-, and scene-level. We first identify a group of interpretable units that are closely related to object concepts using a segmentation-based network dissection method. Then, we quantify the causal effect of interpretable units by measuring the ability of interventions to control objects in the output. We examine the contextual relationship between these units and their surroundings by inserting the discovered object concepts into new images. We show several practical applications enabled by our framework, from comparing internal representations across different layers, models, and datasets, to improving GANs by locating and removing artifact-causing units, to interactively manipulating objects in a scene. We provide open source interpretation tools to help researchers and practitioners better understand their GAN models.
sections.heading: 1 INTRODUCTION
sections.text: Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) have been able to produce photorealistic images, often indistinguishable from real images. This remarkable ability has powered many real-world applications ranging from visual recognition (Wang et al., 2017), to image manipulation (Isola et al., 2017; Zhu et al., 2017), to video prediction (Mathieu et al., 2016). Since their invention in 2014, many GAN variants have been proposed (Radford et al., 2016; Zhang et al., 2018a), often producing more realistic and diverse samples with better training stability.
  Despite this tremendous success, many questions remain to be answered. For example, to produce a church image (Figure 1a), what knowledge does a GAN need to learn? Alternatively, when a GAN sometimes produces terribly unrealistic images (Figure 1f), what causes the mistakes? Why does one GAN variant work better than another? What fundamental differences are encoded in their weights?
  In this work, we study the internal representations of GANs. To a human observer, a well-trained GAN appears to have learned facts about the objects in the image: for example, a door can appear on a building but not on a tree. We wish to understand how a GAN represents such structure. Do the objects emerge as pure pixel patterns without any explicit representation of objects such as doors and trees, or does the GAN contain internal variables that correspond to the objects that humans perceive? If the GAN does contain variables for doors and trees, do those variables cause the generation of those objects, or do they merely correlate? How are relationships between objects represented?
  We present a general method for visualizing and understanding GANs at different levels of abstraction, from each neuron, to each object, to the contextual relationship between different objects. We first identify a group of interpretable units that are related to object concepts (Figure 1b). These units’ featuremaps closely match the semantic segmentation of a particular object class (e.g., trees). Second, we directly intervene within the network to identify sets of units that cause a type of objects to disappear (Figure 1c) or appear (Figure 1d). We quantify the causal effect of these units using a standard causality metric. Finally, we examine the contextual relationship between these causal object units and the background. We study where we can insert object concepts in new images and how this intervention interacts with other objects in the image (Figure 1d). To our knowledge, our work provides the first systematic analysis for understanding the internal representations of GANs.
  Finally, we show several practical applications enabled by this analytic framework, from comparing internal representations across different layers, GAN variants and datasets; to debugging and improving GANs by locating and ablating “artifact” units (Figure 1e); to understanding contextual relationships between objects in scenes; to manipulating images with interactive object-level control.
sections.heading: 2 RELATED WORK
sections.text: Generative Adversarial Networks. The quality and diversity of results from GANs (Goodfellow et al., 2014) has continued to improve, from generating simple digits and faces (Goodfellow et al., 2014), to synthesizing natural scene images (Radford et al., 2016; Denton et al., 2015), to generating 1k photorealistic portraits (Karras et al., 2018), to producing one thousand object classes (Miyato et al., 2018; Zhang et al., 2018a). GANs have also enabled applications such as visual recognition (Wang et al., 2017; Hoffman et al., 2018), image manipulation (Isola et al., 2017; Zhu et al., 2017), and video generation (Mathieu et al., 2016; Wang et al., 2018). Despite the successes, little work has been done to visualize what GANs have learned. Prior work (Radford et al., 2016; Zhu et al., 2016; Brock et al., 2017) manipulates latent vectors and observes how the results change accordingly.
  Visualizing deep neural networks. A CNN can be visualized by reconstructing salient image features (Simonyan et al., 2014; Mahendran & Vedaldi, 2015) or by mining patches that maximize hidden layers’ activations (Zeiler & Fergus, 2014); or we can synthesize input images to invert a feature layer (Dosovitskiy & Brox, 2016). Alternately, we can identify the semantics of each unit (Zhou et al., 2015; Bau et al., 2017; Zhou et al., 2018a) by measuring agreement between unit activations and object segmentation masks, or by training a network to increase interpretability of such units (Zhang et al., 2018b). Visualization of an RNN has also revealed interpretable units that track long-range dependencies (Karpathy et al., 2016; Strobelt et al., 2018). Most previous work on network visualization has focused on networks trained for classification; our work explores deep generative models trained for image generation.
  Understanding neural representation in biology. Studies of biological neural networks find evidence of both local representations in which individual neurons are selective for meaningful concepts (Quiroga, 2012), as well as distributed representations in which individual neurons are essentially meaningless (Yuste, 2015). Computational models of biological learning (Bowers et al., 2016; Dasgupta et al., 2018) find sparse and local representations can aid generalization to novel stimuli.
  Explaining the decisions of deep neural networks. Individual network decisions can be explained using informative heatmaps (Zhou et al., 2018b; 2016; Selvaraju et al., 2017) or by scoring salience (Simonyan et al., 2014; Bach et al., 2015; Sundararajan et al., 2017; Lundberg & Lee, 2017). Such analyses reveals which inputs contribute most to a categorical prediction by a network. Recent work has also studied the contribution of feature vectors (Kim et al., 2017; Zhou et al., 2018b) or individual channels (Olah et al., 2018) to a final prediction, and Morcos et al. (2018) has examined the effect of individual units by ablating them. Those methods explain discriminative classifiers. Our method aims to explain how an image can be generated by a network, which is much less explored.
sections.heading: 3 METHOD
sections.text: Our goal is to analyze how objects such as trees are encoded by the internal representations of a GAN generator G : z→ x. Here z ∈ R|z| denotes a latent vector sampled from a low-dimensional distribution, and x ∈ RH×W×3 denotes an H ×W generated image. We use representation to
  describe the tensor r output from a particular layer of the generator G, where the generator creates an image x from random z through a composition of layers: r = h(z) and x = f(r) = f(h(z)) = G(z).
  Since r has all the data necessary to produce the image x = f(r), r certainly contains the information to deduce the presence of any visible class c in the image. Therefore the question we ask is not whether information about c is present in r — it is — but how such information is encoded in r. In particular, for any class from a universe of concepts c ∈ C, we seek to understand whether r explicitly represents c in some way where it is possible to factor r at locations P into two components
  rU,P = (rU,P, rU,P), (1)
  where the generation of the object c at locations P depends mainly on the units rU,P, and is insensitive to the other units rU,P. Here we refer to each channel of the featuremap as a unit: U denotes the set of unit indices of interest and U is its complement; we will write U and P to refer to the entire set of units and featuremap pixels in r. We study the structure of r in two phases:
  • Dissection: starting with a large dictionary of object classes, we identify the classes that have an explicit representation in r by measuring the agreement between individual units of r and every class c (Figure 1b). • Intervention: for the represented classes identified through dissection, we identify causal
  sets of units and measure causal effects between units and object classes by forcing sets of units on and off (Figure 1c,d).
sections.heading: 3.1 CHARACTERIZING UNITS BY DISSECTION
sections.text: We first focus on individual units of the representation. Recall that ru,P is the one-channel h × w featuremap of unit u in a convolutional generator, where h× w is typically smaller than the image size. We want to know if a specific unit ru,P encodes a semantic class such as a “tree”. For image classification networks, Bau et al. (2017) has observed that many units can approximately locate emergent object classes when the units are upsampled and thresholded. In that spirit, we select a universe of concepts c ∈ C for which we have a semantic segmentation sc(x) for each class. Then we quantify the spatial agreement between the unit u’s thresholded featuremap and a concept c’s segmentation with the following intersection-over-union (IoU) measure:
  IoUu,c ≡ Ez ∣∣∣(r↑u,P > tu,c) ∧ sc(x)∣∣∣ Ez ∣∣∣(r↑u,P > tu,c) ∨ sc(x)∣∣∣ ,where tu,c = argmaxt I(r↑u,P > t; sc(x)) H(r↑u,P > t, sc(x)) , (2)
  where ∧ and ∨ denote intersection and union operations, and x = G(z) denotes the image generated from z. The one-channel feature map ru,P slices the entire featuremap r = h(z) at unit u. As shown in Figure 2a, we upsample ru,P to the output image resolution as r ↑ u,P. (r ↑ u,P > tu,c) produces a binary mask by thresholding the r↑u,P at a fixed level tu,c. sc(x) is a binary mask where each pixel indicates the presence of class c in the generated image x. The threshold tu,c is chosen to be informative as possible by maximizing the information quality ratio I/H (using a separate validation set), that is, it maximizes the portion of the joint entropy H which is mutual information I (Wijaya et al., 2017).
  We can use IoUu,c to rank the concepts related to each unit and label each unit with the concept that matches it best. Figure 3 shows examples of interpretable units with high IoUu,c. They are not the
  only units to match tables and sofas: layer3 of the dining room generator has 31 units (of 512) that match tables and table parts, and layer4 of the living room generator has 65 (of 512) sofa units.
  Once we have identified an object class that a set of units match closely, we next ask: which units are responsible for triggering the rendering of that object? A unit that correlates highly with an output object might not actually cause that output. Furthermore, any output will jointly depend on several parts of the representation. We need a way to identify combinations of units that cause an object.
sections.heading: 3.2 MEASURING CAUSAL RELATIONSHIPS USING INTERVENTION
sections.text: To answer the above question about causality, we probe the network using interventions: we test whether a set of units U in r cause the generation of c by forcing the units of U on and off.
  Recall that rU,P denotes the featuremap r at units U and locations P. We ablate those units by forcing rU,P = 0. Similarly, we insert those units by forcing rU,P = k, where k is a per-class constant, as described in Section S-6.4. We decompose the featuremap r into two parts (rU,P, rU,P), where rU,P are unforced components of r:
  Original image : x = G(z) ≡ f(r) ≡ f(rU,P, rU,P) (3) Image with U ablated at pixels P : xa = f(0, rU,P)
  Image with U inserted at pixels P : xi = f(k, rU,P)
  An object is caused by U if the object appears in xi and disappears from xa. Figure 1c demonstrates the ablation of units that remove trees, and Figure 1d demonstrates insertion of units at specific locations to make trees appear. This causality can be quantified by comparing the presence of trees in xi and xa and averaging effects over all locations and images. Following prior work (Holland, 1988; Pearl, 2009), we define the average causal effect (ACE) of units U on the generation of on class c as:
  δU→c ≡ Ez,P[sc(xi)]− Ez,P[sc(xa)], (4) where sc(x) denotes a segmentation indicating the presence of class c in the image x at P. To permit comparisons of δU→c between classes c which are rare, we normalize our segmentation sc by Ez,P[sc(x)]. While these measures can be applied to a single unit, we have found that objects tend to depend on more than one unit. Thus we wish to identify a set of units U that maximize the average causal effect δU→c for an object class c.
  Finding sets of units with high ACE. Given a representation r with d units, exhaustively searching for a fixed-size set U with high δU→c is prohibitive as it has ( d |U| )
  subsets. Instead, we optimize a continuous intervention α ∈ [0, 1]d, where each dimension αu indicates the degree of intervention for a unit u. We maximize the following average causal effect formulation δα→c:
  Image with partial ablation at pixels P : x′a = f((1−α) rU,P, rU,P) (5) Image with partial insertion at pixels P : x′i = f(α k+ (1−α) rU,P, rU,P) Objective : δα→c = Ez,P [sc(x′i)]− Ez,P [sc(x′a)] ,
  where rU,P denotes the all-channel featuremap at locations P, rU,P denotes the all-channel featuremap at other locations P, and applies a per-channel scaling vector α to the featuremap rU,P. We optimize
  α over the following loss with an L2 regularization:
  α∗ = argmin α (−δα→c + λ||α||2), (6)
  where λ controls the relative importance of each term. We add the L2 loss as we seek a minimal set of casual units. We optimize using stochastic gradient descent, sampling over both z and featuremap locations P and clamping the coefficient α within the range [0, 1]d at each step (d is the total number of units). More details of this optimization are discussed in Section S-6.4. Finally, we can rank units by α∗u and achieve a stronger causal effect (i.e., removing trees) when ablating successively larger sets of tree-causing units as shown in Figure 4.
sections.heading: 4 RESULTS
sections.text: We study three variants of Progressive GANs (Karras et al., 2018) trained on LSUN scene datasets (Yu et al., 2015). To segment the generated images, we use a recent model (Xiao et al., 2018) trained on the ADE20K scene dataset (Zhou et al., 2017). The model can segment the input image into 336 object classes, 29 parts of large objects, and 25 materials. To further identify units that specialize in object parts, we expand each object class c into additional object part classes c-t, c-b, c-l, and c-r, which denote the top, bottom, left, or right half of the bounding box of a connected component.
  Below, we use dissection for analyzing and comparing units across datasets, layers, and models (Section 4.1), and locating artifact units (Section 4.2). Then, we start with a set of dominant object classes and use intervention to locate causal units that can remove and insert objects in different images (Section 4.3 and 4.4). In addition, our video demonstrates our interactive tool.
sections.heading: 4.1 COMPARING UNITS ACROSS DATASETS, LAYERS, AND MODELS
sections.text: Emergence of individual unit object detectors We are particularly interested in any units that are correlated with instances of an object class with diverse visual appearances; these would suggest that GANs generate those objects using similar abstractions as humans. Figure 3 illustrates two such units. In the dining room dataset, a unit emerges to match dining table regions. More interestingly, the matched tables have different colors, materials, geometry, viewpoints, and levels of clutter: the only obvious commonality among these regions is the concept of a table. This unit’s featuremap correlates to the fully supervised segmentation model (Xiao et al., 2018) with a high IoU of 0.34.
  Interpretable units for different scene categories The set of all object classes matched by the units of a GAN provides a map of what a GAN has learned about the data. Figure 5 examines units from GANs trained on four LSUN scene categories (Yu et al., 2015). The units that emerge are object classes appropriate to the scene type: for example, when we examine a GAN trained on kitchen scenes, we find units that match stoves, cabinets, and the legs of tall kitchen stools. Another striking phenomenon is that many units represent parts of objects: for example, the conference room GAN contains separate units for the body and head of a person.
  Interpretable units for different network layers. In classifier networks, the type of information explicitly represented changes from layer to layer (Zeiler & Fergus, 2014). We find a similar phenomenon in a GAN. Figure 6 compares early, middle, and late layers of a progressive GAN with 14 internal convolutional layers. The output of the first convolutional layer, one step away from the input z, remains entangled: individual units do not correlate well with any object classes except for two units that are biased towards the ceiling of the room. Mid-level layers 4 to 7 have many units that match semantic objects and object parts. Units in layers 10 and beyond match local pixel patterns such as materials, edges and colors. All layers are shown in Section S-6.7.
  Interpretable units for different GAN models. Interpretable units can provide insights about how GAN architecture choices affect the structures learned inside a GAN. Figure 7 compares three models from Karras et al. (2018): a baseline Progressive GANs, a modification that introduces minibatch stddev statistics, and a further modification that adds pixelwise normalization. By examining unit semantics, we confirm that providing minibatch stddev statistics to the discriminator increases not only the realism of results, but also the diversity of concepts represented by units: the number of types of objects, parts, and materials matching units increases by more than 40%. The pixelwise normalization increases the number of units that match semantic classes by 19%.
sections.heading: 4.2 DIAGNOSING AND IMPROVING GANS
sections.text: While our framework can reveal how GANs succeed in producing realistic images, it can also analyze the causes of failures in their results. Figure 8a shows several annotated units that are responsible for typical artifacts consistently appearing across different images. We can identify these units efficiently by human annotation: out of a sample of 1000 images, we visualize the top ten highest activating images for each unit, and we manually identify units with noticeable artifacts in this set. It typically takes 10 minutes to locate 20 artifact-causing units out of 512 units in layer4.
  More importantly, we can fix these errors by ablating the above 20 artifact-causing units. Figure 8b shows that artifacts are successfully removed, and the artifact-free pixels stay the same, improving the generated results. In Table 1 we report two standard metrics, comparing our improved images to both the original artifact images and a simple baseline that ablates 20 randomly chosen units. First, we compute the widely used Fréchet Inception Distance (Heusel et al., 2017) between the generated images and real images. We use 50, 000 real images and generate 10, 000 images with high
  activations on these units. Second, we score 1, 000 images per method on Amazon MTurk, collecting 20, 000 human annotations regarding whether the modified image looks more realistic compared to the original. Both metrics show significant improvements. Strikingly, this simple manual change to a network beats state-of-the-art GANs models. The manual identification of “artifact” units can be approximated by an automatic scoring of the realism of each unit, as detailed in Section S-6.1.
sections.heading: 4.3 LOCATING CAUSAL UNITS WITH ABLATION
sections.text: Errors are not the only type of output that can be affected by directly intervening in a GAN. A variety of specific object types can also be removed from GAN output by ablating a set of units in a GAN. In Figure 9 we apply the method in Section 3.2 to identify sets of 20 units that have causal effects on common object classes in conference rooms scenes. We find that, by turning off these small sets of units, most of the output of people, curtains, and windows can be removed from the generated scenes. However, not every object can be erased: tables and chairs cannot be removed. Ablating those units will reduce the size and density of these objects, but will rarely eliminate them.
  The ease of object removal depends on the scene type. Figure 10 shows that, while windows can be removed well from conference rooms, they are more difficult to remove from other scenes. In particular, windows are just as difficult to remove from a bedroom as tables and chairs from a conference room. We hypothesize that the difficulty of removal reflects the level of choice that a GAN has learned for a concept: a conference room is defined by the presence of chairs, so they cannot be altered. And modern building codes mandate that all bedrooms must have windows; the GAN seems to have caught on to that pattern.
  Table 1: We compare generated images before and after ablating 20 “artifacts” units. We also report a simple baseline that ablates 20 randomly chosen units.
  Fréchet Inception Distance (FID)
  original images 43.16 “artifacts” units ablated (ours) 27.14
  random units ablated 43.17
  Human preference score original images
  “artifacts” units ablated (ours) 72.4% random units ablated 49.9%
  ablate person units ablate curtain units
  ablate table unitsablate window units ablate chair units
  Figure 9: Measuring the effect of ablating units in a GAN trained on conference room images. Five different sets of units have been ablated related to a specific object class. In each case, 20 (out of 512) units are ablated from the same GAN model. The 20 units are specific to the object class and independent of the image. The average causal effect is reported as the portion of pixels that are removed in 1 000 randomly generated images. We observe that some object classes are easier to remove cleanly than others: a small ablation can erase most pixels for people, curtains, and windows, whereas a similar ablation for tables and chairs only reduces object sizes without deleting them.
sections.heading: 4.4 CHARACTERIZING CONTEXTUAL RELATIONSHIPS VIA INSERTION
sections.text: We can also learn about the operation of a GAN by forcing units on and inserting these features into specific locations in scenes. Figure 11 shows the effect of inserting 20 layer4 causal door units in church scenes. In this experiment, we insert these units by setting their activation to the fixed mean value for doors (further details in Section S-6.4). Although this intervention is the same in each case, the effects vary widely depending on the objects’ surrounding context. For example, the doors added to the five buildings in Figure 11 appear with a diversity of visual attributes, each with an orientation, size, material, and style that matches the building.
  We also observe that doors cannot be added in most locations. The locations where a door can be added are highlighted by a yellow box. The bar chart in Figure 11 shows average causal effects of insertions of door units, conditioned on the background object class at the location of the intervention. We find that the GAN allows doors to be added in buildings, particularly in plausible locations such as where a window is present, or where bricks are present. Conversely, it is not possible to trigger a door in the sky or on trees. Interventions provide insight on how a GAN enforces relationships between objects. Even if we try to add a door in layer4, that choice can be vetoed later if the object is not appropriate for the context. These downstream effects are further explored in Section S-6.5.
sections.heading: 5 DISCUSSION
sections.text: By carefully examining representation units, we have found that many parts of GAN representations can be interpreted, not only as signals that correlate with object concepts but as variables that have a causal effect on the synthesis of objects in the output. These interpretable effects can be used to compare, debug, modify, and reason about a GAN model. Our method can be potentially applied to other generative models such as VAEs (Kingma & Welling, 2014) and RealNVP (Dinh et al., 2017).
  We have focused on the generator rather than the discriminator (as did in Radford et al. (2016)) because the generator must represent all the information necessary to approximate the target distribution, while the discriminator only learns to capture the difference between real and fake images. Alternatively, we
  can train an encoder to invert the generator (Donahue et al., 2017; Dumoulin et al., 2017). However, this incurs additional complexity and errors. Many GANs also do not have an encoder.
  Our method is not designed to compare the quality of GANs to one another, and it is not intended as a replacement for well-studied GAN metrics such as FID, which estimate realism by measuring the distance between the generated distribution of images and the true distribution (Borji (2018) surveys these methods). Instead, our goal has been to identify the interpretable structure and provide a window into the internal mechanisms of a GAN.
  Prior visualization methods (Zeiler & Fergus, 2014; Bau et al., 2017; Karpathy et al., 2016) have brought new insights into CNN and RNN research. Motivated by that, in this work we have taken a small step towards understanding the internal representations of a GAN, and we have uncovered many questions that we cannot yet answer with the current method. For example: why can a door not be inserted in the sky? How does the GAN suppress the signal in the later layers? Further work will be needed to understand the relationships between layers of a GAN. Nevertheless, we hope that our work can help researchers and practitioners better analyze and develop their own GANs.
sections.heading: S-6 SUPPLEMENTARY MATERIAL
sections.heading: S-6.1 AUTOMATIC IDENTIFICATION OF ARTIFACT UNITS
sections.text: In Section 4.2, we have improved GANs by manually identifying and ablating artifact-causing units. Now we describe an automatic procedure to identify artifact units using unit-specific FID scores.
  To compute the FID score (Heusel et al., 2017) for a unit u, we generate 200, 000 images and select the 10, 000 images that maximize the activation of unit u, and this subset of 10, 000 images is compared to the true distribution (50, 000 real images) using FID. Although every such unit-maximizing subset of images represents a skewed distribution, we find that the per-unit FID scores fall in a wide range, with most units scoring well in FID while a few units stand out with bad FID scores: many of them were also manually flagged by humans, as they tend to activate on images with clear visible artifacts.
  Figure 12 shows the performance of FID scores as a predictor of manually flagged artifact units. The per-unit FID scores can achieve 50% precision and 50% recall. That is, of the 20 worst-FID units, 10 are also among the 20 units manually judged to have the most noticeable artifacts. Furthermore, repairing the model by ablating the highest-FID units works: qualitative results are shown in Figure 13 and quantitative results are shown in Table 2.
sections.heading: S-6.2 HUMAN EVALUATION OF DISSECTION
sections.text: As a sanity check, we evaluate the gap between human labeling of object concepts correlated with units and our automatic segmentation-based labeling, for one model, as follows.
  For each of 512 units of layer4 of a “living room” Progressive GAN, 5 to 9 human annotations were collected (3728 labels in total). In each case, an AMT worker is asked to provide one or two words describing the highlighted patches in a set of top-activating images for a unit. Of the 512 units, 201 units were described by the same consistent word (such as ”sofa”, ”fireplace” or ”wicker”) in 50% or more of the human labels. These units are interpretable to humans.
  Applying our segmentation-based dissection method, 154/201 of these units are also labeled with a confident label with IoU > 0.05 by dissection. In 104/154 cases, the segmentation-based model gave the same label word as the human annotators, and most others are slight shifts in specificity. For example, the segmentation labels “ottoman” or “curtain” or “painting” when a person labels “sofa” or “window” or “picture,” respectively. A second AMT evaluation was done to rate the accuracy of both segmentation-derived and human-derived labels. Human-derived labels scored 100% (of the 201 human-labeled units, all of the labels were rated as consistent by most raters). Of the 154 segmentation-generated labels, 149 (96%) were rated by most AMT raters as accurate as well.
  The five failure cases (where the segmentation is confident but rated as inaccurate by humans) arise from situations in which human evaluators saw one concept after observing only 20 top-activating images, while the algorithm, in evaluating 1000 images, counted a different concept as dominant. Figure 14a shows one example: in the top images, mostly sofas are highlighted and few ceilings, whereas in the larger sample, mostly ceilings are triggered.
  There are also 47/201 cases where the segmenter is not confident while humans have consensus. Some of these are due to missing concepts in the segmenter. Figure 14b shows a typical example, where a unit is devoted to letterboxing (white stripes at the top and bottom of images), but the segmentation has no confident label to assign to these. We expect that as future semantic segmentation models are developed to be able to identify more concepts such as abstract shapes, more of these units can be automatically identified.
sections.heading: S-6.3 PROTECTING SEGMENTATION MODEL AGAINST UNREALISTIC IMAGES
sections.text: Our method relies on having a segmentation function sc(x) that identifies pixels of class c in the output x. However, the segmentation model sc can perform poorly in the cases where x does not resemble the original training set of sc. This phenomenon is visible when analyzing earlier GAN models. For example, Figure 15 visualizes two units from a WGAN-GP model (Gulrajani et al., 2017) for LSUN bedrooms (this model was trained by Karras et al. (2018) as a baseline in the original paper). For these two units, the segmentation network seems to be confused by the distorted images.
  To protect against such spurious segmentation labels, we can use a technique similar to that described in Section S-6.1: automatically identify units that produce unrealistic images, and omit those “unrealistic” units from semantic segmentation. An appropriate threshold to apply will depend on the distribution being modeled: in Figure 16, we show how applying a filter, ignoring segmentation on units with FID 55 or higher, affects the analysis of this base WGAN model. In general, fewer irrelevant labels are associated with units.
sections.heading: S-6.4 COMPUTING CAUSAL UNITS
sections.text: In this section we provide more details about the ACE optimization described in Section 3.2.
  Specifying the per-class positive intervention constant k. In Eqn. 3, the negative intervention is defined as zeroing the intervened units, and a positive intervention is defined as setting the intervened units to some big class-specific constant k. For interventions for class c, we set k to be mean featuremap activation conditioned on the presence of class c at that location in the output, with each pixel weighted by the portion of the featuremap locations that are covered by the class c. Setting all units at a pixel to k will tend to strongly cause the target class. The goal of the optimization is to find the subset of units that is causal for c.
  Sampling c-relevant locations P. When optimizing the causal objective (Eqn. 5), the intervention locations P are sampled from individual featuremap locations. When the class c is rare, most featuremap locations are uninformative: for example, when class c is a door in church scenes, most regions of the sky, grass, and trees are locations where doors will not appear. Therefore, we focus the optimization as follows: during training, minibatches are formed by sampling locations P that are
  relevant to class c by including locations where the class c is present in the output (and are therefore candidates for removal by ablating a subset of units), and an equal portion of locations where class c is not present at P, but it would be present if all the units are set to the constant k (candidate locations for insertion with a subset of units). During the evaluation, causal effects are evaluated using uniform samples: the region P is set to the entire image when measuring ablations, and to uniformly sampled pixels P when measuring single-pixel insertions.
  Initializing α with IoU. When optimizing causal α for class c, we initialize with
  αu = IoUu,c
  maxv IoUv,c (7)
  That is, we set the initial α so that the largest component corresponds to the unit with the largest IoU for class c, and we normalize the components so that this largest component is 1.
  Applying a learned intervention α When applying the interventions, we clip α by keeping only its top n components and zeroing the remainder. To compare the interventions of different classes an different models on an equal basis, we examine interventions where we set n = 20.
sections.heading: S-6.5 TRACING THE EFFECT OF AN INTERVENTION
sections.text: To investigate the mechanism for suppressing the visible effects of some interventions seen in Section 4.4, in this section we insert 20 door-causal units on a sample of individual featuremap locations at layer4 and measure the changes caused in later layers.
  To quantify effects on downstream features, the change in each feature channel is normalized by that channel’s mean L1 magnitude, and we examine the mean change in these normalized featuremaps at each layer. In Figure 17, these effects that propagate to layer14 are visualized as a heatmap: brighter colors indicate a stronger effect on the final feature layer when the door intervention is in the neighborhood of a building instead of trees or sky. Furthermore, we plot the average effect on every layer at right in Figure 17, separating interventions that have a visible effect from those that do not. A small identical intervention at layer4 is amplified to larger changes up to a peak at layer12.
sections.heading: S-6.6 MONITORING GAN UNITS DURING TRAINING
sections.text: Dissection can also be used to monitor the progress of training by quantifying the emergence, diversity, and quality of interpretable units. For example, in Figure 18 we show dissections of layer4 representations of a Progressive GAN model trained on bedrooms, captured at a sequence of checkpoints during training. As training proceeds, the number of units matching objects increases, as does the number of object classes with matching units, and the quality of object detectors as
  cloud 0.01 buildingb 0.10 glass 0.04 floor 0.11
  wallb 0.13 floort 0.09 glass 0.14 wood 0.14
  ceiling 0.01 bedt 0.10 window 0.18 painting 0.08
  lamp 0.05 bedt 0.17 window 0.25 painting 0.11
  lamp 0.05 bedt 0.20 window 0.30 painting 0.10
  lamp 0.05 bedt 0.19 window 0.32 painting 0.11
  lamp 0.05 bedt 0.23 window 0.30 painting 0.12
  Iteration 4800 27 object units  25 part units  23 material units  IoU avg 0.045
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  Iteration 8000 65 object units  146 part units  10 material units  IoU avg 0.070
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  Iteration 10001 70 object units  166 part units  6 material units  IoU avg 0.077
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  Iteration 15009 79 object units  182 part units  11 material units  IoU avg 0.084
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  Iteration 17413 87 object units  184 part units  12 material units  IoU avg 0.086
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  Iteration 20000 95 object units  164 part units  12 material units  IoU avg 0.085
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  Figure 18: The evolution of layer4 of a Progressive GAN bedroom generator as training proceeds. The number and quality of interpretable units increases during training. Note that in early iterations, Progressive GAN generates images at a low resolution. The top-activating images for the same four selected units is shown for each iteration, along with the IoU and the matched concept for each unit at that checkpoint.
  measured by average IoU over units increases. During this successful training, dissection suggests that the model is gradually learning the structure of a bedroom, as increasingly units converge to meaningful bedroom concepts.
sections.heading: S-6.7 ALL LAYERS OF A GAN
sections.text: In Section 4.1 we show a small selection of layers of a GAN; in Figure 19 we show a complete listing of all the internal convolutional layers of that model (a Progressive GAN trained on LSUN living room images). As can be seen, the diversity of units matching high-level object concepts peaks at layer4-layer6, then declines in later layers, with the later layers dominated by textures, colors, and shapes.
    Units in layer   Unit class distribution layer1  512 units total
  0 object units  2 part units  0 material units 
   
  iou=0.10ceilingt layer1 #457 iou=0.07ceilingt layer1 #194
    layer2  512 units total
  97 object units  63 part units  5 material units 
   
  iou=0.23window layer2 #70 iou=0.25floor layer2 #315
    layer3  512 units total
  86 object units  121 part units  10 material units 
   
  iou=0.27window layer3 #305 iou=0.24sofat layer3 #55
    layer4  512 units total
  86 object units  149 part units  10 material units 
   
  iou=0.28sofa layer4 #37 iou=0.15fireplace layer4 #23
    layer5  512 units total
  75 object units  153 part units  19 material units 
   
  iou=0.29sofat layer5 #190 iou=0.15paintingb layer5 #133
    layer6  512 units total
  72 object units  129 part units  16 material units 
   
  iou=0.31window layer6 #393 iou=0.04bookcase layer6 #308
    layer7  256 units total
  59 object units  48 part units  9 material units 
   
  iou=0.23painting layer7 #15 iou=0.07coffee tablet #247
    layer8  256 units total
  51 object units  52 part units  12 material units 
   
  iou=0.17curtain layer8 #186 iou=0.17foliage layer8 #234
    layer9  128 units total
  26 object units  17 part units  9 material units 
   
  iou=0.16window layer9 #89 iou=0.23wood layer9 #78
    layer10  128 units total
  19 object units  8 part units  11 material units 
   
  iou=0.14carpet layer10 #53 iou=0.21glass layer10 #126
    layer11  64 units total
  9 object units  1 part units  7 material units 
   
  iou=0.06sky layer11 #14 iou=0.11ceiling layer11 #49
    layer12  64 units total
  8 object units  1 part units  4 material units 
   
  iou=0.23wood layer12 #26 iou=0.04sky layer12 #19
    layer13  32 units total
  6 object units  0 part units  3 material units 
   
  iou=0.12carpet layer13 #13 iou=0.17wood layer13 #23
   
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  un its
  cei ling win dowpla nt sky pai ntin g cur tainfloo r win dow -t floo r-b wa ll-b cei ling -t win dow -b wo od gla ss car pet
  7 ob
  jec ts
  5 pa
  rts
  3 m
  at er
  ial s
  1
  3
  5
  un its
  cei ling win dow cur tainpla nt skywa ll-bwo od gla ss
  5 ob
  jec ts
  1 pa
  rt
  2 m
  at er
  ial s
  1
  2
  un its
  cei ling win dow cur tain skypla nt cei ling -t wo od gla ss
  5 ob
  jec ts
  1 pa
  rt
  2 m
  at er
  ial s
  1
  2
  3
  un its
  win dowcei ling cur tainwo od car pet
  3 ob
  jec ts
  2 m
  at er
  ial s
  Figure 19: All layers of a Progressive GAN trained to generate LSUN living room images.