Visual Question Answering(VQA) is a highly complex problem set, relying on many sub-problems to produce reasonable answers. In this paper, we present the hypothesis that Visual Question Answering should be viewed as a multi-task problem, and provide evidence to support this hypothesis. We demonstrate this by reformatting two commonly used Visual Question Answering datasets, COCO-QA and DAQUAR, into a multi-task format and train these reformatted datasets on two baseline networks, with one designed specifically to eliminate other possible causes for performance changes as a result of the reformatting. Though the networks demonstrated in this paper do not achieve strongly competitive results, we find that the multi-task approach to Visual Question Answering results in increases in performance of 5-9% against the single-task formatting, and that the networks reach convergence much faster than in the single-task case. Finally we discuss possible reasons for the observed difference in performance, and perform additional experiments which rule out causes not associated with the learning of the dataset as a multi-task problem.
Video Question Answering is a challenging problem in visual information retrieval, which provides the answer to the referenced video content according to the question. However, the existing visual question answering approaches mainly tackle the problem of static image question, which may be ineffectively for video question answering due to the insufficiency of modeling the temporal dynamics of video contents. In this paper, we study the problem of video question answering by modeling its temporal dynamics with frame-level attention mechanism. We propose the attribute-augmented attention networ…
UC Berkeley EECS（加州大学伯克利分校电子工程与计算机科学系）；Sony Corp.（索尼公司）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）
Modeling textual or visual information with vector representations trained from large language or visual datasets has been successfully explored in recent years. However, tasks such as visual question answering require combining these vector representations with each other. Approaches to multimodal pooling include element-wise product or sum, as well as concatenation of the visual and textual representations. We hypothesize that these methods are not as expressive as an outer product of the visual and textual vectors. As the outer product is typically infeasible due to its high dimensionality,…
The task of Outside Knowledge Visual Question Answering (OKVQA) requires an automatic system to answer natural language questions about pictures and images using external knowledge. We observe that many visual questions, which contain deictic referential phrases referring to entities in the image, can be rewritten as "non-grounded" questions and can be answered by existing text-based question answering systems. This allows for the reuse of existing text-based Open Domain Question Answering (QA) Systems for visual question answering. In this work, we propose a potentially data-efficient approac…
Understanding visual question answering is going to be crucial for numerous human activities. However, it presents major challenges at the heart of the artificial intelligence endeavor. This paper presents an update on the rapid advancements in visual question answering using images that have occurred in the last couple of years. Tremendous growth in research on improving visual question answering system architecture has been published recently, showing the importance of multimodal architectures. Several points on the benefits of visual question answering are mentioned in the review paper by M…
Visual Question Answering (VQA) is an increasingly popular topic in deep learning research, requiring coordination of natural language processing and computer vision modules into a single architecture. We build upon the model which placed first in the VQA Challenge by developing thirteen new attention mechanisms and introducing a simplified classifier. We performed 300 GPU hours of extensive hyperparameter and architecture searches and were able to achieve an evaluation score of 64.78%, outperforming the existing state-of-the-art single model's validation score of 63.15%.
Imperial College London（帝国理工学院）；University of Sheffield（谢菲尔德大学）；Department of Computing, Imperial College London（帝国理工学院计算机系）；Department of Computer Science, University of Sheffield（谢菲尔德大学计算机科学系）
Current work on Visual Question Answering (VQA) explore deterministic approaches conditioned on various types of image and question features. We posit that, in addition to image and question pairs, other modalities are useful for teaching machine to carry out question answering. Hence in this paper, we propose latent variable models for VQA where extra information (e.g. captions and answer categories) are incorporated as latent variables, which are observed during training but in turn benefit question-answering performance at test time. Experiments on the VQA v2.0 benchmarking dataset demonstr…
University of Rochester（罗切斯特大学）；Adobe Research（Adobe研究院）
Answering open-ended questions is an essential capability for any intelligent agent. One of the most interesting recent open-ended question answering challenges is Visual Question Answering (VQA) which attempts to evaluate a system's visual understanding through its answers to natural language questions about images. There exist many approaches to VQA, the majority of which do not exhibit deeper semantic understanding of the candidate answers they produce. We study the importance of generating plausible answers to a given question by introducing the novel task of `Answer Proposal': for a given…
In this paper, we study the problem of geometric reasoning in the context of question-answering. We introduce Dynamic Spatial Memory Network (DSMN), a new deep network architecture designed for answering questions that admit latent visual representations. DSMN learns to generate and reason over such representations. Further, we propose two synthetic benchmarks, FloorPlanQA and ShapeIntersection, to evaluate the geometric reasoning capability of QA systems. Experimental results validate the effectiveness of our proposed DSMN for visual thinking tasks.
With the rapid development of knowledge base,question answering based on knowledge base has been a hot research issue. In this paper, we focus on answering singlerelation factoid questions based on knowledge base. We build a question answering system and study the effect of context information on fact selection, such as entity's notable type,outdegree. Experimental results show that context information can improve the result of simple question answering.
This paper presents a new video question answering task on screencast tutorials. We introduce a dataset including question, answer and context triples from the tutorial videos for a software. Unlike other video question answering works, all the answers in our dataset are grounded to the domain knowledge base. An one-shot recognition algorithm is designed to extract the visual cues, which helps enhance the performance of video question answering. We also propose several baseline neural network architectures based on various aspects of video contexts from the dataset. The experimental results de…
The correct interpretation of quantifier statements in the context of a visual scene requires non-trivial inference mechanisms. For the example of "most", we discuss two strategies which rely on fundamentally different cognitive concepts. Our aim is to identify what strategy deep learning models for visual question answering learn when trained on such questions. To this end, we carefully design data to replicate experiments from psycholinguistics where the same question was investigated for humans. Focusing on the FiLM visual question answering model, our experiments indicate that a form of ap…
This paper introduces speech-based visual question answering (VQA), the task of generating an answer given an image and a spoken question. Two methods are studied: an end-to-end, deep neural network that directly uses audio waveforms as input versus a pipelined approach that performs ASR (Automatic Speech Recognition) on the question, followed by text-based visual question answering. Furthermore, we investigate the robustness of both methods by injecting various levels of noise into the spoken question and find both methods to be tolerate noise at similar levels.
In this paper, we propose a novel deep multi-level attention model to address inverse visual question answering. The proposed model generates regional visual and semantic features at the object level and then enhances them with the answer cue by using attention mechanisms. Two levels of multiple attentions are employed in the model, including the dual attention at the partial question encoding step and the dynamic attention at the next question word generation step. We evaluate the proposed model on the VQA V1 dataset. It demonstrates state-of-the-art performance in terms of multiple commonly …
Video question answering has recently received a lot of attention from multimodal video researchers. Most video question answering datasets are usually in the form of multiple-choice. But, the model for the multiple-choice task does not infer the answer. Rather it compares the answer candidates for picking the correct answer. Furthermore, it makes it difficult to extend to other tasks. In this paper, we challenge the existing multiple-choice video question answering by changing it to open-ended video question answering. To tackle open-ended question answering, we use the pretrained GPT2 model.…
Vision And Text Transformer For Predicting Answerability On Visual Question Answering
Japan Advanced Institute of Science and Technology（日本先端科学技术大学院大学）；University of Science, Ho Chi Minh City（胡志明市理科大学）；Vietnam National University, Ho Chi Minh City（越南国家大学胡志明市分校）；Zalo Research Center（Zalo研究中心）
We describe a method for visual question answering which is capable of reasoning about contents of an image on the basis of information extracted from a large-scale knowledge base. The method not only answers natural language questions using concepts not contained in the image, but can provide an explanation of the reasoning by which it developed its answer. The method is capable of answering far more complex questions than the predominant long short-term memory-based approach, and outperforms it significantly in the testing. We also provide a dataset and a protocol by which to evaluate such m…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Science and Technology of China（中国科学技术大学）；Bytedance Inc（字节跳动公司）
Answering complex questions involving multiple entities and relations is a challenging task. Logically, the answer to a complex question should be derived by decomposing the complex question into multiple simple sub-questions and then answering those sub-questions. Existing work has followed this strategy but has not attempted to optimize the order of how those sub-questions are answered. As a result, the sub-questions are answered in an arbitrary order, leading to larger search space and a higher risk of missing an answer. In this paper, we propose a novel reinforcement learning(RL) approach …
In this paper, we present a novel approach for the task of eXplainable Question Answering (XQA), i.e., generating natural language (NL) explanations for the Visual Question Answering (VQA) problem. We generate NL explanations comprising of the evidence to support the answer to a question asked to an image using two sources of information: (a) annotations of entities in an image (e.g., object labels, region descriptions, relation phrases) generated from the scene graph of the image, and (b) the attention map generated by a VQA model when answering the question. We show how combining the visual …
Problems at the intersection of language and vision, like visual question answering, have recently been gaining a lot of attention in the field of multi-modal machine learning as computer vision research moves beyond traditional recognition tasks. There has been recent success in visual question answering using deep neural network models which use the linguistic structure of the questions to dynamically instantiate network layouts. In the process of converting the question to a network layout, the question is simplified, which results in loss of information in the model. In this paper, we enri…
University of Electronic Science and Technology of China（电子科技大学）
Visual question answering (VQA) is a challenging task, which has attracted more and more attention in the field of computer vision and natural language processing. However, the current visual question answering has the problem of language bias, which reduces the robustness of the model and has an adverse impact on the practical application of visual question answering. In this paper, we conduct a comprehensive review and analysis of this field for the first time, and classify the existing methods according to three categories, including enhancing visual information, weakening language priors, …
Question answering systems may find the answers to users' questions from either unstructured texts or structured data such as knowledge graphs. Answering questions using supervised learning approaches including deep learning models need large training datasets. In recent years, some datasets have been presented for the task of Question answering over knowledge graphs, which is the focus of this paper. Although many datasets in English were proposed, there have been a few question-answering datasets in Persian. This paper introduces \textit{PeCoQ}, a dataset for Persian question answering. This…
POSTECH（浦项科技大学）；OpenAI；Seoul National University（首尔国立大学）
We study how to leverage off-the-shelf visual and linguistic data to cope with out-of-vocabulary answers in visual question answering task. Existing large-scale visual datasets with annotations such as image class labels, bounding boxes and region descriptions are good sources for learning rich and diverse visual concepts. However, it is not straightforward how the visual concepts can be captured and transferred to visual question answering models due to missing link between question dependent answering models and visual data without question. We tackle this problem in two steps: 1) learning a…
Universitat de Barcelona（巴塞罗那大学）；Computer Vision Center（计算机视觉中心）；PRHLT Research Center（PRHLT研究中心）；Universitat Politècnica de València（瓦伦西亚理工大学）
In this paper, we address the problem of visual question answering by proposing a novel model, called VIBIKNet. Our model is based on integrating Kernelized Convolutional Neural Networks and Long-Short Term Memory units to generate an answer given a question about an image. We prove that VIBIKNet is an optimal trade-off between accuracy and computational load, in terms of memory and time consumption. We validate our method on the VQA challenge dataset and compare it to the top performing methods in order to illustrate its performance and speed.
Universität Koblenz-Landau（科布伦茨-兰道大学）；Harz University of Applied Sciences（哈尔茨应用科学大学）
This paper briefly characterizes the field of cognitive computing. As an exemplification, the field of natural language question answering is introduced together with its specific challenges. A possibility to master these challenges is illustrated by a detailed presentation of the LogAnswer system, which is a successful representative of the field of natural language question answering.
Sluice resolution is a problem where a system needs to output the corresponding antecedents of wh-ellipses. The antecedents are elided contents behind the wh-words but are implicitly referred to using contexts. Previous work frames sluice resolution as question answering where this setting outperforms all its preceding works by large margins. Ellipsis and questions are referentially dependent expressions (anaphoras) and retrieving the corresponding antecedents are like answering questions to output pieces of clarifying information. However, the task is not fully solved. Therefore, we want to f…
Human conversation is a complex mechanism with subtle nuances. It is hence an ambitious goal to develop artificial intelligence agents that can participate fluently in a conversation. While we are still far from achieving this goal, recent progress in visual question answering, image captioning, and visual question generation shows that dialog systems may be realizable in the not too distant future. To this end, a novel dataset was introduced recently and encouraging results were demonstrated, particularly for question answering. In this paper, we demonstrate a simple symmetric discriminative …
Answering questions related to art pieces (paintings) is a difficult task, as it implies the understanding of not only the visual information that is shown in the picture, but also the contextual knowledge that is acquired through the study of the history of art. In this work, we introduce our first attempt towards building a new dataset, coined AQUA (Art QUestion Answering). The question-answer (QA) pairs are automatically generated using state-of-the-art question generation methods based on paintings and comments provided in an existing art understanding dataset. The QA pairs are cleansed by…
Visual question answering (VQA) has witnessed great progress since May, 2015 as a classic problem unifying visual and textual data into a system. Many enlightening VQA works explore deep into the image and question encodings and fusing methods, of which attention is the most effective and infusive mechanism. Current attention based methods focus on adequate fusion of visual and textual features, but lack the attention to where people focus to ask questions about the image. Traditional attention based methods attach a single value to the feature at each spatial location, which losses many usefu…
Sri Lanka Institute of Information Technology（斯里兰卡信息技术学院）；College of Science, Health, Engineering and Education（科学、健康、工程与教育学院）
Question Answering has recently received high attention from artificial intelligence communities due to the advancements in learning technologies. Early question answering models used rule-based approaches and moved to the statistical approach to address the vastly available information. However, statistical approaches are shown to underperform in handling the dynamic nature and the variation of language. Therefore, learning models have shown the capability of handling the dynamic nature and variations in language. Many deep learning methods have been introduced to question answering. Most of …
Deep neural networks have shown striking progress and obtained state-of-the-art results in many AI research fields in the recent years. However, it is often unsatisfying to not know why they predict what they do. In this paper, we address the problem of interpreting Visual Question Answering (VQA) models. Specifically, we are interested in finding what part of the input (pixels in images or words in questions) the VQA model focuses on while answering the question. To tackle this problem, we use two visualization techniques -- guided backpropagation and occlusion -- to find important words in t…
University of California Santa Barbara（加州大学圣巴巴拉分校）
As an important part of Artificial Intelligence (AI), Question Answering (QA) aims at generating answers to questions phrased in natural language. While there has been substantial progress in open-domain question answering, QA systems are still struggling to answer questions which involve geographic entities or concepts and that require spatial operations. In this paper, we discuss the problem of geographic question answering (GeoQA). We first investigate the reasons why geographic questions are difficult to answer by analyzing challenges of geographic questions. We discuss the uniqueness of g…
University of Cambridge（剑桥大学）；University of Washington（华盛顿大学）
The widely used Fact-based Visual Question Answering (FVQA) dataset contains visually-grounded questions that require information retrieval using common sense knowledge graphs to answer. It has been observed that the original dataset is highly imbalanced and concentrated on a small portion of its associated knowledge graph. We introduce FVQA 2.0 which contains adversarial variants of test questions to address this imbalance. We show that systems trained with the original FVQA train sets can be vulnerable to adversarial samples and we demonstrate an augmentation scheme to reduce this vulnerabil…
Humans apprehend the world through various sensory modalities, yet language is their predominant communication channel. Machine learning systems need to draw on the same multimodal richness to have informed discourses with humans in natural language; this is particularly true for systems specialized in visually-dense information, such as dialogue, recommendation, and search engines for clothing. To this end, we train a visual question answering (VQA) system to answer complex natural language questions about apparel in fashion photoshoot images. The key to the successful training of our VQA mod…
The design or simulation analysis of special equipment products must follow the national standards, and hence it may be necessary to repeatedly consult the contents of the standards in the design process. However, it is difficult for the traditional question answering system based on keyword retrieval to give accurate answers to technical questions. Therefore, we use natural language processing techniques to design a question answering system for the decision-making process in pressure vessel design. To solve the problem of insufficient training data for the technology question answering syste…
The University of Sydney（悉尼大学）；The University of Western Australia（西澳大学）；FortifyEdge
We propose a PiggyBack, a Visual Question Answering platform that allows users to apply the state-of-the-art visual-language pretrained models easily. The PiggyBack supports the full stack of visual question answering tasks, specifically data processing, model fine-tuning, and result visualisation. We integrate visual-language models, pretrained by HuggingFace, an open-source API platform of deep learning technologies; however, it cannot be runnable without programming skills or deep learning understanding. Hence, our PiggyBack supports an easy-to-use browser-based user interface with several …
Visual question answering (VQA) and image captioning require a shared body of general knowledge connecting language and vision. We present a novel approach to improve VQA performance that exploits this connection by jointly generating captions that are targeted to help answer a specific visual question. The model is trained using an existing caption dataset by automatically determining question-relevant captions using an online gradient-based method. Experimental results on the VQA v2 challenge demonstrates that our approach obtains state-of-the-art VQA performance (e.g. 68.4% on the Test-stan…
AI systems' ability to explain their reasoning is critical to their utility and trustworthiness. Deep neural networks have enabled significant progress on many challenging problems such as visual question answering (VQA). However, most of them are opaque black boxes with limited explanatory capability. This paper presents a novel approach to developing a high-performing VQA system that can elucidate its answers with integrated textual and visual explanations that faithfully reflect important aspects of its underlying reasoning while capturing the style of comprehensible human explanations. Ext…
Free-form and open-ended Visual Question Answering systems solve the problem of providing an accurate natural language answer to a question pertaining to an image. Current VQA systems do not evaluate if the posed question is relevant to the input image and hence provide nonsensical answers when posed with irrelevant questions to an image. In this paper, we solve the problem of identifying the relevance of the posed question to an image. We address the problem as two sub-problems. We first identify if the question is visual or not. If the question is visual, we then determine if it's relevant t…
Visual Question Answering (VQA) task has showcased a new stage of interaction between language and vision, two of the most pivotal components of artificial intelligence. However, it has mostly focused on generating short and repetitive answers, mostly single words, which fall short of rich linguistic capabilities of humans. We introduce Full-Sentence Visual Question Answering (FSVQA) dataset, consisting of nearly 1 million pairs of questions and full-sentence answers for images, built by applying a number of rule-based natural language processing techniques to original VQA dataset and captions…
Research on open-domain question answering (QA) has a long tradition. A challenge in this domain is answering complex questions (CQA) that require complex inference methods and large amounts of knowledge. In low resource languages, such as Persian, there are not many datasets for open-domain complex questions and also the language processing toolkits are not very accurate. In this paper, we propose a knowledge-based approach for answering Persian complex questions using Farsbase; the Persian knowledge graph, exploiting PeCoQ; the newly created complex Persian question dataset. In this work, we…
Massachusetts Institute of Technology（麻省理工学院）；Facebook AI Research（脸书人工智能研究院）
We describe a very simple bag-of-words baseline for visual question answering. This baseline concatenates the word features from the question and CNN features from the image to predict the answer. When evaluated on the challenging VQA dataset [2], it shows comparable performance to many recent approaches using recurrent neural networks. To explore the strength and weakness of the trained model, we also provide an interactive web demo and open-source code. .
Neural network architectures with memory and attention mechanisms exhibit certain reasoning capabilities required for question answering. One such architecture, the dynamic memory network (DMN), obtained high accuracy on a variety of language tasks. However, it was not shown whether the architecture achieves strong results for question answering when supporting facts are not marked during training or whether it could be applied to other modalities such as images. Based on an analysis of the DMN, we propose several improvements to its memory and input modules. Together with these changes we int…
Several deep learning models have been proposed for question answering. However, due to their single-pass nature, they have no way to recover from local maxima corresponding to incorrect answers. To address this problem, we introduce the Dynamic Coattention Network (DCN) for question answering. The DCN first fuses co-dependent representations of the question and the document in order to focus on relevant parts of both. Then a dynamic pointing decoder iterates over potential answer spans. This iterative procedure enables the model to recover from initial local maxima corresponding to incorrect …
Visual Question Answering (VQA) deep-learning systems tend to capture superficial statistical correlations in the training data because of strong language priors and fail to generalize to test data with a significantly different question-answer (QA) distribution. To address this issue, we introduce a self-critical training objective that ensures that visual explanations of correct answers match the most influential image regions more than other competitive answer candidates. The influential regions are either determined from human visual/textual explanations or automatically from just signific…
Bar-Ilan University（巴伊兰大学）；Allen Institute for AI（艾伦人工智能研究所）；University of Washington（华盛顿大学）
Long-context question answering (QA) tasks require reasoning over a long document or multiple documents. Addressing these tasks often benefits from identifying a set of evidence spans (e.g., sentences), which provide supporting evidence for answering the question. In this work, we propose a novel method for equipping long-context QA models with an additional sequence-level objective for better identification of the supporting evidence. We achieve this via an additional contrastive supervision signal in finetuning, where the model is encouraged to explicitly discriminate supporting evidence sen…
Complex knowledge base question answering can be achieved by converting questions into sequences of predefined actions. However, there is a significant semantic and structural gap between natural language and action sequences, which makes this conversion difficult. In this paper, we introduce an alignment-enhanced complex question answering framework, called ALCQA, which mitigates this gap through question-to-action alignment and question-to-question alignment. We train a question rewriting model to align the question and each action, and utilize a pretrained language model to implicitly align…
Indian Institute Of Technology Dharwad（印度理工学院达瓦德分校）
While a lot of work has been done on developing models to tackle the problem of Visual Question Answering, the ability of these models to relate the question to the image features still remain less explored. We present an empirical study of different feature extraction methods with different loss functions. We propose New dataset for the task of Visual Question Answering with multiple image inputs having only one ground truth, and benchmark our results on them. Our final model utilising Resnet + RCNN image features and Bert embeddings, inspired from stacked attention network gives 39% word acc…
University of Maryland（马里兰大学）；Google Research（谷歌研究院）
In addition to the traditional task of getting machines to answer questions, a major research question in question answering is to create interesting, challenging questions that can help systems learn how to answer questions and also reveal which systems are the best at answering questions. We argue that creating a question answering dataset -- and the ubiquitous leaderboard that goes with it -- closely resembles running a trivia tournament: you write questions, have agents (either humans or machines) answer the questions, and declare a winner. However, the research community has ignored the d…
This paper revisits visual representation in knowledge-based visual question answering (VQA) and demonstrates that using regional information in a better way can significantly improve the performance. While visual representation is extensively studied in traditional VQA, it is under-explored in knowledge-based VQA even though these two tasks share the common spirit, i.e., rely on visual input to answer the question. Specifically, we observe that in most state-of-the-art knowledge-based VQA methods: 1) visual features are extracted either from the whole image or in a sliding window manner for r…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；School of Information Sciences（信息科学学院）
Question answering (QA) has demonstrated impressive progress in answering questions from customized domains. Nevertheless, domain adaptation remains one of the most elusive challenges for QA systems, especially when QA systems are trained in a source domain but deployed in a different target domain. In this work, we investigate the potential benefits of question classification for QA domain adaptation. We propose a novel framework: Question Classification for Question Answering (QC4QA). Specifically, a question classifier is adopted to assign question classes to both the source and target data…
Object detection plays an important role in current solutions to vision and language tasks like image captioning and visual question answering. However, popular models like Faster R-CNN rely on a costly process of annotating ground-truths for both the bounding boxes and their corresponding semantic labels, making it less amenable as a primitive task for transfer learning. In this paper, we examine the effect of decoupling box proposal and featurization for down-stream tasks. The key insight is that this allows us to leverage a large amount of labeled annotations that were previously unavailabl…
We analyze the language learned by an agent trained with reinforcement learning as a component of the ActiveQA system [Buck et al., 2017]. In ActiveQA, question answering is framed as a reinforcement learning task in which an agent sits between the user and a black box question-answering system. The agent learns to reformulate the user's questions to elicit the optimal answers. It probes the system with many versions of a question that are generated via a sequence-to-sequence question reformulation model, then aggregates the returned evidence to find the best answer. This process is an instanc…
Multi-hop question answering (QA) requires a model to retrieve and integrate information from different parts of a long text to answer a question. Humans answer this kind of complex questions via a divide-and-conquer approach. In this paper, we investigate whether top-performing models for multi-hop questions understand the underlying sub-questions like humans. We adopt a neural decomposition model to generate sub-questions for a multi-hop complex question, followed by extracting the corresponding sub-answers. We show that multiple state-of-the-art multi-hop QA models fail to correctly answer …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present a method that learns to answer visual questions by selecting image regions relevant to the text-based query. Our method exhibits significant improvements in answering questions such as "what color," where it is necessary to evaluate a specific location, and "what room," where it selectively identifies informative image regions. Our model is tested on the VQA dataset which is the largest human-annotated visual question answering dataset to our knowledge.
