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e5c00488-4bd9-499e-8ebf-8900a65a9dce | We train DETReg on the above two tasks without using any manually annotated bounding boxes or categories. A key advantage of this approach is that it trains all DETR model parameters, and thus learns to produce meaningful detections even with no supervision — see Figure REF . We conduct an extensive evaluation of DETReg on standard benchmarks: MS COCO [1]} and PASCAL VOC [2]} under various settings, including “low-data” training regimes. We find that DETReg improves on challenging baselines across the board, and especially when small amounts of annotated data are available. For example, DETReg improves over the supervised pretrained Deformable DETR by 4 points in AP on PASCAL VOC and by 1.6 points on MS COCO. When using only 1% of the data, it improves over the supervised counterpart by over 11 points in AP. Additionally, it improves on the Deformable DETR initialized with SwAV by 2.5 points in AP on PASCAL VOC, and by 0.3 on MS COCO. We also find it improves by 5.7 and 5.8 points on AP when using only 1% and 2% of annotated data on MS COCO. Taken together, these results suggest that DETReg is a highly effective approach to pretraining object detector models.
<FIGURE> | i |
4396408b-e56f-4f35-8337-a6b8ef2655ca | Self-supervised pretraining. Recent work [1]}, [2]}, [3]}, [4]}, [5]} has shown that self-supervised pretraining can generate powerful representations for transfer learning, even outperforming its supervised counterparts on challenging vision benchmarks [6]}, [1]}. Self-supervised learning often involves various image restoration (e.g., inpainting [8]}, colorization [9]}, denoising [10]}) and higher level prediction tasks like image orientation [11]}, context [12]}, temporal ordering [13]}, and cluster assignments [14]}.
The learned representations transfer well to image classification but the improvement is less significant for instance-level tasks, such as object detection and instance segmentation [3]}, [16]}.
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88063201-89d3-42a2-8443-4c46531295df | More recently, a few works [1]}, [2]}, [3]}, [4]} studied instance-level self-supervised representation learning. Roh [1]} et al. propose a
spatially consistent representation learning (SCRL) algorithm to produce coherent spatial representations of a randomly cropped local region according to geometric translations and
zooming operations. Concurrent works, DetCon [2]}, ReSim [3]} and DetCo [4]} adopt contrastive learning on image patches for region similarity learning.
DetCon uses mask priors to align patches from different views while ReSim applies two different transformations (e.g., random cropping) to the image and constructs the positive alignments from the overlapping regions. Our work is in line with these
works on learning useful representations for object detection. In contrast to DetCon, which requires object mask priors, our approach seeks to use the region proposals from the off-the-shelf tools and use them as weak supervision, rather than implicitly embedding them in the contrastive learning
formulation for constructing positive/negative pairs.
Our intuition is that contrastive learning on image patches does not necessarily empower the model to learn what and where an object is, and adding the weak supervision signals from the region priors could be beneficial.
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8d7a8977-0c16-4b14-87bc-0866d7d65ac2 | End-to-end object detection. Detection with transformers (DETR) [1]} builds
the first fully end-to-end object detector and eliminates the need for components such as anchor generation and
non-maximum suppression (NMS) post-processing.
This model has quickly gained traction in the machine vision community.
However, the original DETR suffers from slow
convergence and limited sample efficiency. Deformable DETR [2]} introduces a deformable attention module to attend to a sparsely sampled small set of prominent key elements, and achieves better performance compared to DETR with reduced training epochs. We use Deformable DETR as our base detection architecture given its improved training efficiency. Both DETR and Deformable DETR adopt
the supervised pretrained backbone (i.e., ResNet [3]}) on ImageNet. UP-DETR [4]} pretrains DETR in a self-supervised way by detecting and reconstructing the random patches from the input image. Our work shares the goal of UP-DETR of unsupervised pretraining for object detection, but our approach is very different. In contrast to UP-DETR, we adopt region priors from off-the-shelf unsupervised region proposal algorithms to provide weak supervision for pretraining, which has an explicit notion of object compared to random image patches which do not.
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5e895e47-6a09-4ec4-813e-4fba31e761b3 | Region proposals. A rich study
of region proposals methods [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} exists in the object detection literature.
Grouping based method, Selective Search [2]}, and window scoring based approach, Objectness [1]} are two early and well known proposal methods, which has been widely adopted and supported in the major libraries (e.g., OpenCV [11]}).
Selective search greedily merges superpixels to generate proposals. Objectness relies on visual cues such as multi-scale saliency, color contrast, edge density and superpixel straddling to identify likely regions. While the field has largely drifted to learning based approaches, one benefit of these classic region proposal approaches is that they do not have learned parameters, and thus can be a good source of “free” supervision. Hosang et al. [12]}, [13]} provide a comprehensive analysis over the various region proposals methods and Selective Search is the among the top performing approaches with a high recall rate. In this work, we seek weak supervision from the region proposals generated by Selective Search, which has been widely adopted and proven successful in the well-known detectors such as R-CNN [14]} and Fast R-CNN [15]}. Note however that our proposed approach is not limited to the Selective Search region priors, and can employ other region proposal methods.
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b439e56a-b61d-4aa8-a9c7-376a438ce654 | In this section, we present extensive evaluation of DETReg on standard benchmarks, MS COCO [1]} and PASCAL VOC [2]}, under both full and low data settings in Section REF . We visualize and analyze DETReg in Section REF to better illustrate the “objectness” encoded in the learned representations.
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a4efd279-34b8-4445-a499-d1ca2c4865b1 | Datasets. We conduct the pretraining stage on ImageNet100 (IN100) [1]} following prior work [2]}, [3]}, [4]}, and evaluate the learned representation by fine-tuning the model on MS COCO 2017 [5]}, or PASCAL VOC [6]} with full data or small subsets of the data (1%, 2%, 5% and 10%) that were randomly chosen and remained consistent for all models. IN100 is a subset of the the ImageNet (IN-1K) ILSRVC 2012 challenge data that contains around 125K images (\(\sim \) 10% of the full ImageNet data) from 100 different classes. When using IN100, We only make use of the images and do not use class information. We follow the standard protocols as earlier works [2]}, [8]}, [8]} and train on the train2017 partition and evaluate on the val2017 partition. Similarly, for PASCAL VOC, we utilize the trainval07+12 partitions for fine tuning and the test07 for evaluation.
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3c3a1740-ac0a-4b35-a5b7-fd9f8e2caa43 | Baselines. We adopt the recent Deformable DETR [1]} model with a ResNet-50 [2]} backbone as our base object detector architecture. We compare DETReg against architectures which utilize supervised and unsupervised ImageNet pretrained backbones. For example, the standard Deformable DETR uses a supervised backbone and “Deformable DETR w/ SwAV” uses a SwAV [3]} backbone. DETReg is pretrained on IN100 in an unsupervised way and uses a SwAV backbone that was trained on IN-1K. We also compare to various past works that reported results on MS COCO and PASCAL VOC [3]}, [5]}, [6]} after pretraining on the full IN-1K.
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46a34ba4-d37d-40fe-b73a-c52be68f4461 | In this work, we presented DETReg, an unsupervised pretraining approach for object DEtection with TRansformers using Region priors. Our model and proposed pretext tasks are based on the observation that in order to learn meaningful representations in the unsupervised pretraining stage, the detector model not only has to learn to localize, but also to obtain good embeddings of the detected objects. Our results demonstrate that this approach is beneficial across the board on MS COCO and PASCAL VOC, and especially on low-data regime settings, compared to challenging supervised and unsupervised baselines. In general, unsupervised approaches can allow models to pretrain on large amounts of unlabeled data, which is very advantageous in domains like medical imaging where obtaining human-annotated data is expensive.
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568b387d-93f5-4851-a76a-835b38cdf374 | How can we compute the similarity of one image to another? This is a question that has been asked for hundreds of years, and it is probably the most fundamental question in image processing. Several customer-facing applications leverage images to search and find products and they usually complement that of a text-based search in most use cases. In this paper, we will describe an approach to compute image similarity using deep neural networks. Our method is based on a state-of-the-art model known as the BigTransfer Model, which learns to predict the similarity of two images. Fig 1. Shows examples of Image samples from the tf_flower [1]} dataset on which our BigTransfer(BiT) [2]} model is trained.
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12a7f8ff-35d6-4d8e-9012-5d0df7251107 | Our system has the potential to be used with business-critical applications. With the visual exploration trend rising in the retail sector and the availability of quintillion Gigabytes of data at our disposal our image similarity model is bound to become more and more accurate. We optimized our model for two specific objectives: search accuracy and query duration. We achieved high accuracy by examining a few other candidates. We achieved a query time of under a second. Our system is highly accurate and fast. Our system is fast because we used a few other models such as hand-crafted features, autoencoders [1]}, CNN's [2]} and we only used the most recent pre-trained model.
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4a022790-5a99-45ed-a0ae-a648ab4fafe3 | This approach is highly robust and we believe it could be adopted by the industry. We chose a specific type of deep learning model because of the best performance we have observed and because of the clarity of the approach. The state-of-the-art model we chose, based on the results, can leverage unsupervised learning. With that type of model, it is easier to train data in massive quantities and to have a much better generalization. BigTransfer(BiT) [1]} model uses a feed-forward layer over an unsupervised autoencoder [2]} along with an attention model [3]}. Our paper reports the first use of an attention model [3]} for model-based image retrieval. Model-based image retrieval has been used for a long time in text-based searches for making more accurate queries. But image-based search and image retrieval are very different scenarios. Visual perception works differently than text-based search. So is image-based search and image retrieval. Many other applications besides those highlighted in this paper can be benefitted from this work. Our system is robust, highly accurate, and it can leverage unsupervised learning to produce large amounts of high-quality training data. This has enormous potential in several domains.
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caa5721a-e7de-44d8-91d7-d618a85289a8 | While image search engines like Google or Bing can find similar images with a text search, they are not very effective for a variety of reasons. The most obvious reason is that textual descriptions are limited to 20,000 characters and cannot express detailed semantics or the history of an object. Secondly, people who don’t speak English cannot query image search engines via language translation. This brings about the second problem of a large and growing number of users from emerging markets who may not have access to Google and Bing. More importantly, they do not have a search query language of their own, yet still, they express their need to find images of stars and moons using such complex terms that require a series of complex symbols or gestures to communicate. Indeed, the search relevance of image search engines is heavily dependent on the existence of similar images available on the Internet. This is an issue for all images that are not publically accessible for use, images captured at different times, or cameras with varying parameters. This is a very important point that we take into consideration when working on this project. On one side we have images that are not publicly accessible. The quality of the images will be varied and they will require careful content selection in the selection and processing of training and test data. On the other side, there is a lot of commercial information that "needs to be made publicly available for commercial use but is not yet. It can be difficult for a company to get permission to use their data, and another difficult process to get the images in the public domain. We also expect to expand and improve our existing models to make the selected publicly available images accessible for future work. However, in this project, we are primarily focusing on developing our data collection pipeline to collect images that are currently out of the public domain and publish them on our existing system. The project's goal is to assist small and medium enterprises to more easily produce a high-quality dataset in the image and document domains. The paper has used all possible efforts to make our project as replicable and reproducible as possible.
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21777973-7865-43d3-890f-9282e62cd75c | So far we have classified on flower dataset [1]} and we have employed an unsupervised feature extraction technique for image preprocessing. In the future, we will release the new datasets, which can be useful to anyone else for training and deploying their system for image retrieval. Also in the future, we will explore a method to integrate our images of objects into deep search engines to improve the depth of the search results. This will add some search value, which is useful to some specific applications such as content discovery on an exhibition. We expect that this will drive towards some additional use cases in the future. Research and industry have benefited enormously from advances in digital communication technology. This technology has enabled tremendous growth in markets such as mobile commerce, social networking, and large-scale community projects. In this project, we envisage that such image-based platforms, which focus on image-based search [2]}, [3]}, discovery, and mobile e-commerce, will present a massive opportunity for new business models.
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64b41c6f-20aa-4897-9845-71f3015003e7 | In this experiment, we have used the dataset of flowers [1]} provided by tensorflow. It is popularly known as tf_flower [1]}. TensorFlow Flower Dataset [1]} consists of five classes. Five classes are labelled as 'Daisy', 'Dandelion', 'Roses', 'Sunflowers', 'Tulips'. The number of classes for the dataset is imbalanced.
<FIGURE> | m |
8b16391d-715d-4148-aa55-2536c366e1fe | The dataset is being loaded using the tensorflow dataset [1]}. The dataset is then divided into train and validation data. 85% of the data is taken as the training data and the rest of the data is taken as validation data. The number of training and validation samples were 3120 and 550. To make our model more robust I applied data augmentation [2]}, [3]}. Used random flip with horizontal and vertically on the images. Used a random rotation with a factor of 0.2. Applied random zoom at a height and width factor of 0.2. Training images are resized to 160 and images are randomly cropped to 128. Validation images are resized to 160.
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901ac098-1420-43e8-979c-2fd5f7811bea | We loaded the pre-trained BigTransfer(BiT) [1]} model which is trained on ImageNet21k [2]} downloaded from TensorFlow Hub [3]}, [4]}, [5]}. We created a BigTransfer(BiT) [1]} model and normalised the dense representation. Used TripletSemiHardLoss [7]} as a loss function. The loss encourages the positive distances (between a pair of embeddings with the same labels) to be smaller than the minimum negative distance among which are at least greater than the positive distance plus the margin constant (called semi-hard negative) in the mini-batch. If no such negative exists, use the largest negative distance instead.
\(\left\Vert f(x_{i}^{a}) - f(x_{i}^{p}) \right\Vert _{2}^{2}\textrm {} < \left\Vert f(x_{i}^{a}) - f(x_{i}^{n}) \right\Vert _{2}^{2}\textrm {}\)
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24ce051c-aa81-44bf-9b62-d5fdfbe0d6bd | After compiling the model and the callbacks for the models are set up. Used Early Stopping to monitor the validation loss with a patience rate of 5 and standard rate for verbose i.e 2. Used CSV Logger to log all the data during training the model.
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5b4d127e-5b0d-40ae-b38f-f12ee2af21f1 | After setting up the experiment, we trained our BigTransfer(BiT) [1]} model on the flower dataset [2]}. Our training started with a loss of 0.94 and a validation loss of 0.91. The training is being done on Tesla V100-SXM2. The average time for an epoch is 2 seconds. The training time was 78.68 seconds with only 21 epochs. Our loss and validation loss after 21 epochs is 0.23 and 0.30 respectively.
<FIGURE> | r |
156d988a-c103-4a9a-9138-173969f77763 | Saved the BigTransfer(BiT) [1]} model after training the model on flower dataset [2]}. Defining the BigTransfer(BiT) Model to load the model weights we saved as our Keras model. Created a validation pipeline for training the nearest neighbor [3]} model. We are calculating our nearest neighbor [3]} for the features of our query image. The model took 0.00043 seconds for 550 samples.
<FIGURE> | r |
34955a47-6421-4c69-8aaa-8ead754aecda | This project shows how to scale up the pre-trained model by training on a larger dataset to extract key features. The model is based on a Resnet152 [1]} backbone and the classifier is an FCN-8s. The model is based on the code release for BiT-M. BigTransfer(BiT) [2]} does not require any pre-processing to the input images, i.e., we can use vanilla ImageNet models to transfer on any visual tasks. We see this as an important step towards practical implementations. The idea behind our model is to build highly accurate and low latency visual search tools that can fit in with many business facing applications.
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2adaf216-1f7f-4d32-bfbb-4831c2649c76 | This paper contains the results that are part of a more general study [1]}, the purpose of which is to perform a large-scale quantitative analysis of the Ukrainian Economics discipline using the publication data predominantly beyond Web of Science and Scopus databases, where currently more than 150 Ukrainian journals are indexed while the National List of recognized scientific journalshttps://mon.gov.ua/ua/nauka/nauka/atestaciya-kadriv-vishoyi-kvalifikaciyi/naukovi-fahovi-vidannya includes almost 1,500 titles.
Motivated by the fact that Ukrainian research is still understudied because of its poor representation in core databases [2]} (and this is especially true for Social Sciences and Humanities – SSH), we have made an attempt to provide a quantitative portrait of one of Ukrainian SSH disciplines using the Crossref database as an alternative data source.
Our interest in Ukraine is natural, as all three authors are Ukrainians and therefore motivated to contribute to a more transparent and evidence-based management of national research.
Nevertheless, we also believe that this is an interesting case study that contributes to the better understanding of the research process in the developing countries of Eastern Europe, countries with a special historical heritage. Ukraine is characterised by non-English speaking and Cyrillic writing; this is especially true for the analysis of SSH. Economics is chosen as one of the most `visible' SSH disciplines, which is often considered as a transitional between the `hard' and `social' sciences [3]}, [4]}.
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a3cb9294-d00e-44df-a3f5-4138bb52fead | The quantitative analysis at the level of publications based on the Crossref data is rather straightforward. For example, an estimation of the number of authors per paper can be done even without sophisticated data pre-processing. However, the consideration of individual publication histories at the level of authors or gender analysis requires name disambiguation.
Obviously, this task is a big challenge, especially when dealing with non-Western names [1]}, [2]}, [3]}. Since the majority of publications in the Ukrainian Economic discipline are related to local authors [4]}), it is natural to find mainly Ukrainian first and last names in our data set.
Although such peculiarities as the use of middle name or a prespecified order of parts in composite names [1]}, [2]} are not typical for Ukraine, a huge problem of transliteration (e.g., see also [7]}) still exists. But there is another side of the coin: the so-called ethnicity can be used to improve gender disambiguation. Therefore, along with the initial motivation to contribute to the quantitative description of Ukrainian Economics discipline, a special emphasis is made on the methods of processing such specific bibliographic data.
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58c44005-d8fc-43c0-85ee-52e28c64be2c | RQ1:
What peculiarities of Ukrainian authors’ names have to be taken into account during the process of name and gender disambiguation?
RQ2:
What gender proportion is typical for the Ukrainian Economics discipline, and how can it be compared with similar results for other data sets (countries)?
RQ3:
What level of alphabetization characterizes the Ukrainian Economics discipline, and is it possible to identify any gender-related distinctions?
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74e2ba14-4898-4e8b-8927-322220f97550 | Answering the main research questions, this paper serves also as another evidence of the usefulness of Crossref data as a potential source for bibliometric analysis. Economic publications are considered in many other studies, where the data from Web of Science or Scopus databases are exploited, see [1]}, [2]}, [3]}, [4]}, [5]}. And this is reasonable in order to assess top-impact output and reveal the research front in Economics. However, if the rest of the entire picture is needed, the potential of other sources such as Crossref can be efficiently used. In this context, Ukraine has an advantage – a special interface called Open Ukrainian Citation Index (OUCI) was developed a few years ago. It provides a possibility to extract structured Crossref metadata related to all journals published in Ukraine [6]}. Moreover, all these journals are labeled by subject category according to the Ukrainian national classification scheme.
While this data source is not as comprehensive as a national current research information system could be, it provides a unique opportunity to supplement knowledge about research output of Ukraine.
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fbc4bab4-72a3-4d2c-8fda-48e0393eeb98 | The paper is organized as follows: the description of our data set is provided in Section ; the applied name disambiguation procedure is described in Section ; Section describes the peculiarities of gender disambiguation procedure for our data and contains the results of gender analysis.
The author name ordering for the Ukrainian Economics discipline is studied in Section ; the final discussion can be found in the last Section.
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0b8b2ef0-f297-4c4d-9527-dbc1257452f9 | The analysis of Ukrainian journals within the Economics discipline, started in the previous work [1]}, is continued in this study.
Revealing the typical features of this particular segment of scholar literature is important for solving many practical issues related to the development of assessment procedures at the national level.
However, another goal of this work is to reinforce the call for complete and qualitative metadata. Crossref database is used here to describe one of SSH disciplines for poorly studied European countries.
Publication metadata related to Ukrainian Economic journals are collected from the Crossref database.
An attempt was made to conduct an analysis with an emphasis on gender effects at the level of individual authors. However, the procedure for disambiguating authors' names can be done only partially. A number of peculiarities of processing author names related to the usage of Cyrillic and local traditions of parallel usage of different forms of names and even surnames are highlighted. Since the gender of an author is inferred from the full first name, even partial merging of authors' records allows one to increase the statistics of publications with authors labeled by gender.
Moreover, a manually created list of gender-specific endings for Slavic last names was used to enlarge the number of genderized authors. Altogether, 63.7% of 23,094 author records were labeled by gender, and the number of female authors is found to be 1.5 times larger than male authors. This result contradicts with the statements about the masculinum nature of Economics research. Alternatively, female dominance in Ukrainian Economics research may be considered as a hint about its specific thematic spectrum. According to [2]}, keywords related to qualitative and exploratory methods are statistically associated with female scholar authors, while other keywords related to quantitative methods are more related to male authors. In some sense, such sensitivity of gender representation to the topic selection is in line with the conclusion in [3]}: considerable differences in this context were observed for different Economics subfields. This reinforces our previous conclusions about the specific patterns of collaborativeness in Ukrainian Economics research. Still, an important caution exists:
this study is one of the rare examples where data beyond internationally recognized databases is used. Therefore, the guess about different nature of locally-oriented and internationally-oriented topics chosen for Economics research remains relevant.
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26188127-cd29-473f-841d-d1fc42a77b60 | Gender mixing is analysed to find the evidence that gender plays a role when forming collaboration teams. All papers labeled according to five gender-related categories (solo-publications by males; solo-publications by females; solo-gender collaborations of males; solo-gender collaborations of females; and cross-gender collaboration) are considered. While only one thirdOne fourth if authors with single papers are considered as well of individual papers are written without coauthors and there is a tendency towards more collaborative papers [1]}, the share of solo-publications remains high. One third of all papers are found to be solo-publications authored by female authors. The corresponding share for male authors is slightly smaller than expected. Finally, while the share of cross-gender teams is larger than the shares of solo-gender teams (see Fig. REF ), the results compared with randomly reshuffled data indicate that the share of cross-gender teams is considerably higher than it can be expected only for publications in the journal indexed in Scopus and/or WoS, see Table REF .
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54ee6287-1dd0-4c0a-a9d4-dad97e3e6f8e | Interestingly, different results of gender mixing are found for papers published in journals indexed in Scopus or Web of Science, compared to the rest of publications. Remarkably, while the largest share of papers solo-authored by female authors is expected due to the greater general number of female authors, this category of papers indexed in the international databases is the least represented one. Most papers in internationally recognized journals are characterized by cross-gender collaboration. This can be seen as the manifestation of the so-called reactivity of the Ukrainian Economics discipline (see [1]}, [2]}). One can speculate about the adaptive publishing behaviour: a different publishing or even research strategy is chosen depending on the level of recognition and audience of the target journal. The similar conclusion can be drawn for different shares of papers where authors are listed alphabetically. Interestingly, while a high level of alphabetization is found for the Economics discipline in general and even higher for Economic publications in internationally recognized journals, the opposite pattern is observed in Ukrainian Economics research.
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1f981863-879d-418b-a853-c54a8b9a16d6 | To conclude, the results of another case study is presented. Besides the findings specifically related to Ukrainian research, some key aspects related to the processing of non-English metadata are highlighted. It is worth emphasizing once more that many complications become irrelevant if unique digital identifiers are commonly used.
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2212cb7d-f7cb-4d4b-bec2-03f8a1eb2903 | Deep generative models, developed over a decade, are now capable of simulating complex distributions in high dimensional space and synthesizing high quality samples in various domains such as natural images, text and medical data. Many of these models are built with the assumption that data \(x\in \) resides close to a low dimension manifold. In this case, data can be represented using latent variable \(z\) drawn from prior distribution on \(^d\) with density \(p(z)\) and the observation model \(p(x|z) = p(x|f_\theta (z))\) is given by a parametric mapping \(f_\theta :^d\rightarrow \Gamma \) where \(\Gamma \) is the space of parameters of the likelihood \(p(x|z)\) .
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921037af-d402-440e-92e3-fc1a68783655 | For complex \(f_\theta \) mappings, evaluation of log marginal likelihood
p(x) = p(z)p(x|z)dz
is intractable and the posterior density \(p(z|x) \propto p(x|z)p(z)\) is known only up to a constant normalization factorWe use normalization factor and marginal likelihood \(p(x)\) interchangeably in this paper. In this case, latent variable inference, probabilistic model evaluation and model comparison are performed using variational approximation of the posterior [1]}, [2]}, [3]} or via sampling methods like Markov Chain Monte Carlo (MCMC) [4]}, Nested sampling [5]}, [6]}, Sequential Monte Carlo (SMC) [7]} and Annealed Importance Sampling (AIS) [8]}. In Variational Inference (VI) the posterior is approximated with the most similar probability density from the family of distributions \(= \lbrace q_\phi (z|x): \phi \in \mathbb {\phi }\rbrace \) indexed by parameter \(\phi \) . Success of VI depends on sufficient expressivity of members of \(\) and our ability to find the optimal member of this family by, for instance, maximizing the Evidence Lower BOund (ELBO)
() = (p(x,z)q(z|x)) q(z|x)dz p(x)
where the equality happens only when \(q_\phi (z|x) = p(z|x) \in \) .
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81f92d3a-844e-4cf1-ae1a-a9fa5b1d5d7a | In MCMC we use Markov kernels with unique stationary distribution \(p(z|x)\) and sample a Markov chain \(\left(z_k\right)_{k\in [M]}\) by iterative application of this kernel on an initial particle \(z_0\sim q_\phi (z|x)\) . Contrary to parametric VI, under mild assumptions, it is theoretically guaranteed that distribution of \(z_M\) converges to the target distribution \(p(z|x)\) as \(M\) goes to infinity. However, if the posterior has multiple modes or heavy tails, convergence can require large number of iterations and therefore, be computationally prohibitive. Among the sampling methods, SMC and AIS are of particular interest as they produce unbiased estimation of marginal likelihood regardless of the computational budget by assigning importance weights to samples [1]}, [2]}, [3]}. In these algorithms an auxiliary sequence of distributions, \(\left(\pi _k\right)_{k\in [M]}\) , is used to bridge a simple proposal distribution with density \(\pi _0(z) = q_\phi (z|x)\) and the target density \(\pi _M(z) = p(z|x)\) . This sequence is defined via unnormalized densities \(\left(\gamma _k\right)_{k\in [M]}\) where \(\pi _k(z) = \gamma _k(z)/Z_k\) and \(\gamma _0(z) = \pi _0(z)\) and \(\gamma _M(z) = p(x, z)\) . The algorithm produces \(N\) Markov chain samples \(\left(z_k^j\right)_{k\in [M]}\) for \(j\in [N]\) and their corresponding importance weights denoted by \(w^j\) as follows: Initially \(z_0^j\) is sampled from \(\gamma _0\) . Then \(z_k^j\) is approximately sampled from \(\gamma _k\) using a Markov kernel (typically a gaussian distribution around \(z_{k-1}^j\) or a transition with invariant distribution \(\gamma _k\) )SMC has an additional resampling step to draw exact samples from \(\gamma _k\) to reduce the variance of importance weight although it sometimes results in insufficient sample diversity. The marginal likelihood is approximated with Monte Carlo method
p(x) = [w] pN(x) 1Nj[N]wj
where the expectation is taken over joint distribution of the Markov chains. Variance of \(\hat{p}^N(x)\) depends on the selected density sequence and hyperparameters especially when computation resources are scarce. However, little work is available on how to optimize the intermediary distributions. In this paper we focus on optimization of AIS hyperparameters for more accurate estimation of log marginal likelihood with only a few annealing distributions. We optimize the sequence of distributions between proposal and target distributions as well as the hyperparameters of Markov kernels. We have made the following contributions:
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bd0c4bb3-8368-493d-82c0-b1660e8aca8e |
We propose the parameterization of a continuous time density path between the proposal and target distributions which can define general density functions. Contrary to [1]}, [2]} the densities used do not need to be normalized and we don't require their exact samples since we use sampling algorithms to gradually transition between the intermediary distributions.
To optimize the bridging distributions we minimize Jefferys and inverse KL divergences between the distributions of AIS process and its auxiliary reverse process (defined in Section REF ). Inspired from recent developments in Monte Carlo VI (MCVI) methods, we reparameterize particle states with a mixture of Normalizing Flows and derive a low variance consistent estimation of the gradient of our optimization objective.
We show that Jefferys divergence captures both bias and variance of the estimation while optimization of inverse KL divergence reduces the bias of estimation. We further evaluate our method on deep generative models with different training procedures.
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d8b4cf23-a2fe-44fa-942e-7a9c8df419f9 | The combination of both procedures allows reducing the variance of the importance sampling weights providing more accurate estimates with fewer particles and intermediary distributions.
The rest of this paper is organized as follows: Section is dedicated to reviewing vanilla AIS algorithm. In Section we present our parameterization of AIS process which results in flexible bridging distributions and motivate out optimization objective. In Section we illustrate a reparameterization method and derivation of the objective gradient estimates. Finally, we analyze the accuracy of marginal likelihood estimation and its variance on synthetic and image datain Section .
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de2cde91-986d-4f77-8278-1d618c78e6b4 | In this Section we give a brief introduction to AIS algorithm and its popular adaptive versions. For the rest of this section, we assume that the observation \(x\) is fixed and \(\pi (z) = p(z|x)\) is the target density function which we can evaluate up to a normalizing constant \(\tilde{\pi }(z) = p(z, x)\) where \(\pi (z) = \tilde{\pi }(z) / Z\) and \(Z = p(x)\) . We also define a proposal distribution with normalized density \(\gamma _0(z)\) which is easy to sample and evaluate, such as the variational posterior \(\gamma _0(z) = q_\phi (z|x)\) .
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b146c9e2-1a37-4ebc-8e1e-5c6c51409530 | We compare our algorithm to vanilla AIS [1]} with geometric average path and geometric and linear schedule. We use RWMH, HMC and MALA transitions and normal proposal with learnable mean and diagonal covariance matrix. \(M\) between 2-128 bridging distributions and 256 samples are used for training.
\(u_\phi \) is implemented with a DNN with one hidden layer with 4 dimensions and LeakyReLU(0.01) nonlinearty except at the output layer.
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fb79792b-de1f-4bf4-8ab7-b8d3d9280871 | The parametric AIS is trained with Adam optimizer [1]} with learning rate of 0.03 and betas = (0.5, 0.999) for 100 epochs. The RWMH kernels have local normal proposal steps with learnable diagonal covariance matrix and the step size in all transition kernels are trained along with other parameters. We use cross validation to choose the step size in vanilla AIS from \(\lbrace 0.01, 0.05, 0.1, 0.5, 1.\rbrace \) . The normalization constants are estimated using \(N=4096\) samples. To act as the reference normalization constant we use vanilla AIS with \(M=1024\) , 10 MCMC steps per iteration with 3 different step sizes. All the code is written with Pytorch [2]} and experiments are run on a GeForce GTX 1080 Ti. Code is available here: https://github.com/shgoshtasb/op_ais.
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8d265daa-dd82-4921-bfaf-d781345727d4 | In Figure REF we illustrate particles generated from the samplers trained on each distribution with inverse KL divergence (PKL) and Jefferys divergence (PJ) color coded by their weight for \(M=8\) . Warmer colors show particles with higher weights which are main contributors to the partition function estimation, while dark blue particles are less effective in the estimation. We observe that training with KL divergence results in smaller bias, while using Jefferys divergence objective results in more effective particles and lower variance estimation in Target 3-6.
<FIGURE> | m |
13ba633c-12b0-41bc-b2a0-8c2bdf8bb5f6 | Figure REF shows the log partition function estimation and the empirical variance of importance weights for the mentioned samplers. We index the target distributions in the same order they appear in the Figure REF . In most of the experiments, for small number of bridging distributions (\(M\in \lbrace 2, 4, 8\rbrace \) ) our method is able to improve over vanilla AIS algorithm with linear schedule and achieves slightly tighter lower bound in comparison to geometric schedule version. In comparison to training with inverse KL divergence, Jefferys divergence improves the variance of importance weights. we speculate this to be related to higher correlation of Jefferys divergence with weight variances.
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3b1246bc-d2c7-44d5-a043-849eded67e74 | Interestingly, in multimodal and heavy tail distributions, empirical variance for small M remains below the variance of exhaustive AIS (Vl M=1024 in dashed Turquoise) and grows with \(M\) With only one MCMC step used in the experiments, particles ultimately cover a small area and don't reach the high density regions in the target distribution, resulting in low empirical weight variance despite the fact that the actual variance is much larger than our observation. This is specially problematic with the geometric schedule as the few bridging distributions are placed very close to the proposal and the particles are not encouraged to move far. In the low \(M\) setting as it is unlikely to observe high weight particles, it is misleading to use ESS or even empirical \(\chi ^2\) -divergence to tune the hyperparameters, whereas the inverse KL divergence provides better guidance for tuning. Increasing \(M\) results in more dispersed particles and higher variance. For large enough \(M\) as the particles can reach high density regions in the target, we observe that this variance decreases with \(M\) . Variance in parametric samplers is more steady and has a small growth in comparison due to the optimized choice of bridging distributions for each M.
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0b2b224a-42f4-4308-b8bb-ad4a430236cc | AIS yields an unbiased estimation for any annealing path, schedule and transition operator. However, the variance of the Monte Carlo estimator changes considerably with different choices. We propose an optimization procedure to find the best set of intermediary distributions that matches the distribution of the AIS particle trajectory to joint distribution of backward process with target distribution as its marginal. We formulate AIS algorithm with MH-corrections as a mixture of NFs and minimize the the divergence between the two distributions.
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805abc92-fbcd-49e0-a55c-6d4c2028ab6c | It is important to mention that log-likelihood has to be used with caution for model comparison, since a model with very good or bad generative sample quality or memorization may have high log likelihood [1]}. It is recommended to use other sample quality measures (e.g. [2]}, [3]}) and model comparison methods (e.g. [4]}, [5]}) along with AIS.
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578c5766-d7fe-4a80-8eea-af9e0d8e9dc0 | Social media and online communities allow individuals to freely express opinions, engage in interpersonal communication, and learn about new trends and new stories.
However, these platforms also create spaces for uncivil behavior and misinformation.
Uncivil behavior is defined as explicit language, derogatory, or disrespectful content, which has become native on online platforms [1]}, [2]}, [3]}.
Misinformation is defined as false or inaccurate information [4]}, which has become rampant on the social media platforms.
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68a188ea-59d8-43ce-b16f-e589d2ce9995 | Uncivil behaviors like online harassment have a severe impact on users, as social media provides anonymity, which can lead to disinhibition, deindividuation, and a lack of accountability [1]}, [2]}, [3]}. Users may experience significant emotional problems including anxiety, and depression, in extreme situations, and may even commit suicide [4]}.
Misinformation significantly impacts users with undesirable consequences and wreaks havoc instantly.
The proliferation of misinformation dissemination can have devastating consequences for our wealth, democracy, health, and national security [5]}.
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deda365d-254f-43d4-9544-75d2d223f1fd | During COVID-19, for example, misinformation, conspiracies, and coordinated misinformation campaigns were prevalent throughout the pandemic [1]}, [2]}. Such low-quality posts can also drown out useful content and exhaust the limited attention of users [3]}.
Therefore, platforms need to enact content moderation efficiently.
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e01a2d8f-d1b2-4fe7-937c-94bb679947ac | Since the early incubation of online communities, scholars and community managers alike reminisce over how to best manage online content and how to enable constructive, civil conversations among the users [1]}, [2]}.
However, there is no unified method for content moderation among different social media platforms.
Some employ more restrictive rules, while others emerge to simply promise no or minimal moderation.
For example, fringe social media platforms, such as Parler and Gab, have very minimal restrictions and they rarely ban users, which in turn have seen a huge uptick in new users joining them [3]}, [4]}.
Content moderation consists of several levels, including providing community guidelines, employing simple or sophisticated techniques to detect violations, and then enforcing the moderation.
On each platform, content moderation is not constant but evolves as new challenges emerge, or it becomes clear that the in-use methods are not sufficient to protect information integrity.
For example, Twitter starts using warning labels on posts to counter the misinformation about the 2020 Presidential elections and COVID-19 [5]}, [6]}.
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73a152e1-edd5-4749-aad1-da29bac3f998 | In this paper, we study and categorize the topics covered in content moderation research and investigate the current state of content moderation on several social media platforms, focusing on the enforcement of moderation policies and also the community guidelines and how platforms define and moderate different types of content.
Work in the detection of these contents, however, is currently out of the scope of this paper.
With this analysis, we aim to obtain a comprehensive vision of content moderation from the point of view of both the research community and real-world practices.
In particular, we try to answer the following research questions:
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eac5420a-9718-441e-ab8e-dd29a0a16b7f | RQ2: How does content moderation work in practice?
What content do different social media platforms try to moderate, and how the content moderation policies are defined, implemented, and enforced?
What are the practical and research gaps that need to be filled?
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125e626a-9715-4654-a871-e425b85dddca | To answer these research questions, we not only collate more than one hundred plus research papers and news articles describing the ever-growing changes to the content moderation practices of social media platforms and their impact on the end-user, but also investigate fourteen social media platforms in the US jurisdiction to understand the current state of content moderation practices.
With these analyses, we create three granular taxonomies, which explain and categorize the moderation policies (e.g., soft moderation, hard moderation, etc.), the types of content that are moderated (e.g., defamation, child sexual exploitation, misinformation, etc.), and the comprehensiveness of the provided community guidelines (e.g., their granularity, the use of examples, etc.).
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47d220b6-28ab-4871-9db8-1184bc59dc33 | Note that our work focuses on the end-user who uses social media platforms; hence, social media as a business (i.e., platforms as exploitative data-gathering/surveillance systems for advertising) is currently out of scope.
| i |
e5d5ed9d-ddac-4d93-8b03-b8c8a62c07d1 | Findings from our taxonomies indicate that mainstream social media platforms like TikTok, Reddit, YouTube, Facebook, Instagram, and Twitter employ all of the studied moderation strategies and also moderate content, i.e., do not allow content based on the studied categories.
We also find these platforms' community guidelines are comprehensible as they provide examples and are granular.
However, they lack the ability to provide videos and images in their community guidelines.
Only YouTube provides them, but only for ten out of fifteen categories.
While these platforms are making sure that their platforms remain free of any type of indecent content, misinformation, hate speech, etc., some fraction of users hail these social media platforms as a threat to free speech [1]}.
We find that fringe platforms like Parler, Gab, MeWe, 4chan, & Rumble which are hailed as champions in preserving free speech as all of them do not perform factchecking, have no soft moderation practices, and they keep hard moderation to a minimum.
Interestingly, we also find that misinformation and election integrity, and hate speech are allowed on these platforms, as they suggest that they are protected speech under the First Amendment. Interestingly, our analysis shows that, while certain categories are banned across all the platforms, there is however no consensus among platforms on what content to moderate and what not to.
Hence, moderation happens arbitrarily. Even platforms that are similar in nature (i.e., attract similar-minded people), such as Parler and MeWe, do not always prohibit hate speech content.
Based on our findings, we discuss four main implications for how the community as a whole has to re-imagine practices of content moderation to not only ensure that everyone's voice is heard, but also that they do not step out of bounds.
Our discussion explores ways based on the technical aspects like transparency and opacity that is needed in content moderation and also that a one-size-fits-all model does not fit the ever-changing demographics of social media.
We also touch base with the legal aspect concerning challenges to Section 230 and also the debate on the First Amendment.
Finally, we highlight the importance of human mediation and the need for an impartial jury system to make the final decisions based on all the facts and also have the person affected by the case heard.
We hope that our findings will bring attention to not only the computer research community but also, social media companies to create a more inclusive and transparent moderation process.
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758344e9-d274-4c99-80e5-1826038075c5 | In this work, we have presented three taxonomies based on an extensive review of the social media community guidelines and previous works. Using the taxonomies we answer the two research questions. We concluded that the most popular and mainstream social media platforms moderate for all categories studied as well as using both hard moderation and soft moderation categories.
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83132d24-3d2d-4d0a-af9f-a41f7252cb7e | Out of these six platforms, only YouTube provides image or video examples. On the other hand, fringe platforms do not moderate for all the studied categories.
According to our findings, these platforms also preferred minimal intervention.
Due to these claims, we also look into the legal aspects of moderation i.e., the First Amendment and Section 230 of the Communications Decency Act.
We then discuss the need for transparency and opacity in content moderation, why platforms should shift from a one-size-fits-all model to a more inclusive and broader model, and lastly, we highlight why there is a need for a collaborative human-AI system and also why the need for a jury system is important.
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8b42f86b-2382-401a-890b-68c0d7dc3728 | After receiving paper reviews, authors may optionally submit a rebuttal to address the reviewers' comments, which will be limited to a one page PDF file.
Please follow the steps and style guidelines outlined below for submitting your author response.
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b9558b81-03a9-43a3-a2b0-d3b17b30c77f | The author rebuttal is optional and, following similar guidelines to previous CVPR conferences, is meant to provide you with an opportunity to rebut factual errors or to supply additional information requested by the reviewers.
It is NOT intended to add new contributions (theorems, algorithms, experiments) that were absent in the original submission and NOT specifically requested by the reviewers.
You may optionally add a figure, graph, or proof to your rebuttal to better illustrate your answer to the reviewers' comments.
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44225a12-4311-4c7b-b668-42b2224694d9 | Per a passed 2018 PAMI-TC motion, reviewers should refrain from requesting significant additional experiments for the rebuttal or penalize for lack of additional experiments.
Authors should refrain from including new experimental results in the rebuttal, especially when not specifically requested to do so by the reviewers.
Authors may include figures with illustrations or comparison tables of results reported in the submission/supplemental material or in other papers.
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3d360a29-b88a-40b3-9970-42b18fdcd658 | Just like the original submission, the rebuttal must maintain anonymity and cannot include external links that reveal the author identity or circumvent the length restriction.
The rebuttal must comply with this template (the use of sections is not required, though it is recommended to structure the rebuttal for ease of reading).
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9d54ba86-0f25-4f0f-b871-daa2ea978860 | Detecting OOD [1]}, [2]}, [3]} samples is vital for developing reliable machine learning systems for various industry-scale applications of natural language understanding (NLP) [4]}, [5]} including intent understanding in conversational dialogues [6]}, [7]}, language translation [8]}, [9]}, and text classification [10]}, [11]}. For instance, a language understanding model deployed to support a chat system for medical inquiries should reliably detect if the symptoms reported in a conversation constitute an OOD query so that the model may abstain from making incorrect diagnosis [12]}.
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8b2ec128-4d94-44cc-8c28-45522f0dc6cb | Although OOD detection has attracted a great deal of interest from the research community [1]}, [2]}, [3]}, these approaches are not specifically designed to leverage the structure of textual inputs. Consequently, commonly used OOD approaches often have limited success in real-world NLP applications. Most prior OOD methods for NLP systems [4]}, [5]}, [6]} typically assume additional OOD data for outlier exposure [7]}. However, such methods risk overfitting to the chosen OOD set, while making the assumption that a relevant OOD set is available during the training stage. Other methods [8]}, [9]}, [6]} assume training a calibration model, in addition to the classifier, for detecting OOD inputs. These methods are computationally expensive as they often require re-training the model on the downstream task.
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e711b61f-17e7-40c1-b748-b63229ea75db | Motivated by the above limitations, we propose a framework called POORE that generates pseudo-OOD data using the trained classifier and the IND samples. As opposed to methods that use outlier exposure, our framework doesn't rely on any external OOD set. Moreover, POORE can be easily applied to already deployed large-scale models trained on a classification task, without requiring to re-train the classifier from scratch. In summary, we make the following contributions:
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5cb1080d-e0c0-47f5-83a6-744d1ded1e87 |
We propose a Mahalanobis-based context masking scheme for generating pseudo-OOD samples that can be used during the fine-tuning.
We introduce a new POR loss that maximizes the distance between IND and generated pseudo-OOD samples to improve the OOD detection.
Though extensive experiments on the three benchmarks, we show that our approach performs significantly better than existing baselines.
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1c30b6d8-e3bc-4b01-9847-e1f279ffaacd | OOD Detection. It is a binary classification problem that seeks to identify unfamiliar inputs during inference from in-distribution (IND) data observed during training. Standard OOD methods can be divided into two categories. The first category [1]}, [2]}, [3]}, [4]} corresponds to approximating a density \(p_{IND}(x)\) , where density is used as a confidence estimate for binary classification. The second category of approaches [5]}, [6]}, [7]}, [8]} use the predictive probability to estimate the confidence scores. In our experiments, we compare against approaches from both the categories.
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d4427d91-691c-43c5-bc2f-ad65427f7473 | OOD Detection in NLP. There have been several methods developed for OOD detection in NLP. [1]} proposed using \(k\) sub models, where each model is trained with different masked inputs. [2]} uses an external OOD set to train an additional calibration model for OOD detection. Most related to our proposed framework is MASKER [3]} that leverages IND data to generate pseudo-OOD samples, and uses self-supervision loss inspired from [4]} and predictive entropy regularization for pseudo-OOD inputs. We also use BERT self-supervision inspired keyword masking, however, we propose a novel keyword selection criterion. Moreover, we also introduce a novel model regularization loss that directly increases the distance of IND and pseudo-OOD samples.
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ecc12033-e8a1-4c24-8a1d-772a69287f13 | Our approach is demonstrated on the BERT pre-trained model [1]} with around 110M parameters trained on a single Titan-X GPU. We optimize \(\lambda _{POR}\) for each task through grid search from \(1e-5\) to \(1e2\) by a factor of 10, and use \({1, 1e-2, 1e-5}\) for STAR, FLOW, and ROSTD respectively.
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6be26d88-86ca-427b-a9f6-361227e121c0 | This paper compares our approach (POORE) with existing baseline OOD detection methods including Maxprob, Entropy, Mahalanobis, BERT Embed, Gradient Embed, and Dropout. We also consider MASKER [1]} as a baseline. A detailed analysis of the differences in performance between all the inference methods and our approach appears in Section REF . The baseline methods are trained for 25 epochs using the AdamW optimizer with a learning rate of 1e-5, 3e-5, 1e-5 for STAR, FLOW, and ROSTD respectively. We use minimal post hoc fine-tuning of only 1 additional epoch for MASKER and POORE. We use AUROC and FPR@90 to evaluate OOD detection performance. For more details on these metrics, refer to Appendix .
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9280ed41-a18d-4795-8774-8d27a93ae314 | Table REF shows the performance gains from our approach relative to all the baseline methods on three target tasks namely STAR, FLOW, and ROSTD. POORE outperforms existing evaluation baselines by significant margins. Specifically on the STAR dataset, relative to Bert Embed and Mahalanobis baselines, we observe 9% and 4% respective absolute improvement in AUROC, while observing 26% and 17% respective absolute reduction in FPR@90. Similarly on FLOW, the AUROC gains were 13%, and 1% relative to BERT Embed and Mahalanobis, while doing worse only on the FPR@90 metric compared to the Mahalanobis baseline. We noted similar consistent gains on the ROSTD.
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4bbce388-4bc0-4a51-ac9a-1c20bbe706a7 | We also evaluate our framework POORE by pairing it with other confidence estimators like Maxprob, ODIN [1]}, Entropy, and BERT Embed. Figure REF compares a model trained using POORE with a standard model, while using various confidence estimators during inference. As shown in figure REF , we observe significant gains with our framework over the baseline model for all the confidence estimators. Specifically, the AUROC on FLOW using Bert Embed with POORE achieved an improvement of 9%. We also pair the above estimators with the MASKER baseline and evaluate these combinations in the ablation shown in Appendix . In Appendix , we show an ablation comparing our novel keyword selection criterion with the keyword selection criterion used in the MASKER baseline.
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4b888657-57d8-4eab-990c-0959e49b967f | In this paper, we propose a novel framework, which we call POORE, for improving the robustness of model towards OOD data. Using a combination of Mahalanobis distance and POR regularization that maximizes the distance between IND and OOD representations, we demonstrated significant performance gains in a number of target benchmark tasks. Further work could tap into the potential of using external OOD data to achieve even more gains over other baselines that use outlier exposure.
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d6f66179-8b83-4389-8155-826277142777 | Socially Assistive Robotics (SAR) is a sub-field in robotics that aims to develop intelligent robots that can provide aid and support to users [1]}. For instance, older adults living in senior care facilities often feel lonely and isolated. Social interaction and mental stimulation are critical for improving their well-being [2]}, [3]}. SAR has shown to alleviate this problem by providing companionship to assist older adults through conversation and social interaction [4]}, [5]}.
Furthermore, the global outbreak of COVID-19 and the effects of social distancing and stay-at-home orders drew more attention to the isolation of older adults living in senior care facilities. The COVID-19 pandemic has highlighted the healthcare worker shortage that currently plagues the healthcare system [6]}, and SAR has recently been used to address this problem by researchers [7]}, [8]}, [9]}.
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dd606307-27ba-4bc9-830e-eb2352ce989d | To more naturally and effectively interact with humans, we can endow robots with social capabilities.
A social robot must be equipped [1]} with human-oriented interaction that exhibits context and user-appropriate social behavior and focuses attention and communication on the user. Studies suggest that adding emotional information to SAR enhances user satisfaction [2]} and results in a more positive interaction between robot and human. Empathy is a critical skill in health and elder care; users perceive robots that express empathic behavior as more friendly, understanding, and caring [3]}.
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89ffafa0-1f4a-4a78-8cf1-a168b91b10b2 | A social robot with Artificial Emotional Intelligence (AEI) can recognize, process, simulate, and react to human affects/emotions [1]}. The development of affective and empathic robots that have the capability to recognize users' emotions and interact with them naturally and effectively is in its infancy and more research needs to be carried out in this field [2]}.
<FIGURE> | i |
e64e439d-9b92-46bd-a975-76fc5a62a760 | To demonstrate the use of SAR and the tools necessary to create one, consider the following scenario. Imagine that Katie is an older adult living alone in a nursing home. A nurse checks on her every day for only a few minutes as the nurse has to take care of dozens of residents. Fortunately, Katie has an emotionally intelligent companion robot in her room. She calls the robot Liz. The following is a conversation between Katie and Liz.
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523e1409-b2f7-46f9-88ae-f99d0b0c8c0c | This dialogue example illustrates the different components that can serve to develop a friendly robot.
Liz pro actively asks Katie how she is doing. When a human-oriented robot proactively starts a conversation with a user living in a senior care facility, it is helpful for the robot to detect the duration for which the user has been in the room. For instance, if the robot detects that the user has been in their room for a long period of time, then the user has probably not had a lot of social interaction during that time, and it is probable that the user has been alone.
The robot should also have the ability to engage in a spoken dialogue with the user[1]}.
In the example above, the robot uses Sentiment Analysis (SA) and Facial Expression Recognition (FER) and detects a discrepancy between Katie's response and her facial expression.
Emotional intelligence requires a multimodal emotion perception system [2]}.
To improve Katie's mood, the robot decides to tell a joke and smile.
This means that the robot needs multiple channels to express emotional information.
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97a7d371-8dc5-40e9-80b9-ac3487bf0760 | This paper presents the results of our recent progress in developing an emotionally intelligent and autonomous conversational robot named Ryan. Ryan is designed to assist older adults suffering from mild dementia. Impaired thinking and cognitive decline, apathy, loss of interest in activities and hobbies, social withdrawal, isolation, and trouble concentrating are common symptoms of both dementia and depression [1]}. Figure REF depicts a general diagram of our human-robot-interaction (HRI) system. We utilized state-of-the-art deep learning technology for multimodal emotion recognition (i.e. affective computing), the output of which is integrated into Ryan's dialogue management system. We developed Ryan's dialogue management system by writing scripted conversations on 12 different topics, including science, history, nature, music, movies, and literature. Based on the detection of users' facial expressions and language sentiment analysis, Ryan appears to empathize with users through emotive conversation and mirroring users' positive facial expressions (for example, Ryan smiles when the user smiles). We conducted an HRI study to measure the effectiveness of our emotionally intelligent robot in communicating and empathizing with older adults by creating two versions of the robot, one equipped with emotional intelligence (empathic Ryan) and one unequipped for emotional intelligence (non-empathic Ryan).
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1b96d3b5-3417-483f-be25-fa14e45b2bab | In 2016, we studied the feasibility of using a prototype version of Ryan with a broad range of features (dialogue, calendar reminders, photo album slide shows, music and video play, and facial expression recognition) to interact with older adults with mild depression and cognitive impairments [1]}. The results of our previous study show that elderly individuals were interested in having a robot as a social companion and their interest did not wane over time. The subjects reported to enjoy interacting with Ryan and accepted the robot as a social companion, although they did not believe that Ryan can replace human companionship[1]}. Because Ryan was equipped with several features, we could not thoroughly study the effect of emotional intelligence on measuring users' engagement with respect to conversational interaction. Therefore, in this study, we specifically focused on how emotional intelligence can improve and impact the quality of interaction and engagement with Ryan.
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b294ee98-5fc3-4251-b4c9-0ff878625c1a | The main contributions of this paper are: 1) creating a multimodal emotion sensory and facial expressive system, 2) integrating the developed sensory and expressive system into a physical robot (i.e., creating empathic Ryan), 3) studying the effectiveness of the empathic Ryan with a cohort of older adults living in a senior care facility. Our hypothesis is that an emotionally intelligent robot is perceived as more friendly by users and positively affects their mental well-being (measured by changes in depression score and emotional state) in comparison to a robot without empathic capabilities.
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73a6ac85-367d-45ef-b30e-7158f3875a83 | The remainder of this paper is organized as follows. Section defines the term Emotional Intelligence and details the makeup of an emotionally intelligent robot. Section introduces a social robot named Ryan and explains the robot's hardware and software, concentrating on the components that correspond with the definition of emotional intelligence. Section lays out the design of the study. The results are presented in Section . Finally, Section concludes the paper and outlines future work.
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83128cc1-a432-4aed-b328-90de678ac59d | Participants interacted and conversed with Ryan twice a week over a period of three weeks (October 2018 to November 2018) for six sessions total. Figure REF illustrates the experimental setup and an example of the user's interaction with Ryan during a session. Each session consisted of about 15 minutes of the prepared dialogues.
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7f949680-adf7-45e8-bb6f-5cf408207c32 | In order to assess the impact of Ryan's use of empathy on the user's engagement and emotional state, we randomly assigned participants to two groups (G1 and G2). The first group interacted with a non-empathic version of Ryan that did not show any facial expressions or empathize with the users (Emotion-OFF), while the second group interacted with the fully empathic version of Ryan that mirrored the user's facial expressions and empathized with them throughout the conversation (Emotion-ON). The users were not aware of the different versions of Ryan. After three sessions, we switched the groups to interact with the other version of Ryan. This cross-over study design (illustrated in Table REF ) makes analyzing the results meaningful, as all the subjects were exposed to both versions of Ryan and hence the only independent variable is Emotion (ON/OFF).
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c0619bda-9ea1-4317-82d0-7b3193038804 | The growth of the elderly population and the widespread understaffing across nursing homes can exacerbate feelings of loneliness in the residents and overburden their nurses. During the COVID-19 pandemic, this issue became more evident [1]}. The development of AI technologies drew attention to service robots and SAR as potential solutions to these problems. Robots may effectively relieve the burden on healthcare workers and improve the well-being of elderly individuals. Such robots need to be socio-emotionally intelligent in order to effectively engage the aging population.
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9866913e-21e8-475f-80c1-0a9f236da30c | In this paper, we discussed Ryan, a socially assistive robot, and its multimodal emotion recognition and multimodal emotion expression systems. More specifically, we compared two versions of the robot: one that uses a scripted dialogue that does not factor in the users' emotions and is lacking facial expressions (non-empathic version), and one with facial expressions that uses an affective dialogue manager to generate a response and has the capability to recognize users' emotions (empathic version).
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0dd16113-325c-4609-aaec-29b37ca3f0cc | We studied the differences and effects of Ryan's two versions with a cohort of older adults living in a senior care facility. The statistical analysis of the users' face-scale mood measurement (illustrated in Figure REF ) indicates an overall positive effect as a result of the interaction with Ryan, irrespective of the robot being empathic or non-empathic. However, the word count measurement (Table REF ) and the exit survey analyses (Table REF ) suggest that the empathic Ryan is perceived as more engaging and likable. Considering that the only difference between Ryan's two versions is empathic versus non-empathic, the findings suggest that empathy can encourage users to have longer conversations. Nonetheless, more experiments are needed to further study interactions using a more natural dialogue manager (chatbot). The changes in users' depression measurement scores (Table REF ) suggest that Ryan can potentially decrease users' depression, although to verify this finding more subjects and long-term studies are required.
| d |
8c3e9673-c6be-48e8-a5b7-ef5efcdda182 | Throughout this paper all graphs are finite, undirected, and have no
loops or multiple edges. Let \(V(G)\) and \(E(G)\) denote the sets of
vertices and edges of \(G\) , respectively. For \(F\subseteq E(G)\) , the
subgraph obtained by deleting the edges of \(F\) from \(G\) is denoted
by \(G-F\) . The maximum degree of \(G\) is denoted by \(\Delta (G)\) . The
terms and concepts that we do not define can be found in [1]}.
| i |
692be11c-9c2b-41f0-8189-9587247b4732 | An edge-coloring of a graph \(G\) is a mapping \(\alpha :E(G)\rightarrow \mathbb {N}\) . A proper edge-coloring of a graph \(G\) is an
edge-coloring \(\alpha \) of \(G\) such that \(\alpha (e)\ne \alpha (e^{\prime })\) for any pair of adjacent edges \(e,e^{\prime }\in E(G)\) . The edge-chromatic number \(\chi ^{\prime }(G)\) of \(G\) is the
least number of colors needed for a proper edge-coloring of \(G\) .
Clearly, \(\chi ^{\prime }(G)\ge \Delta (G)\) for every graph \(G\) . On
the other hand, the well-known theorem of Vizing [1]} states
that the edge-chromatic number of any graph \(G\) is either
\(\Delta (G)\) or \(\Delta (G)+1\) . One of the most important, interesting
and long-standing problem in this field is the problem of
determining the exact value of the edge-chromatic number of graphs.
There are many results in this direction, in particular, the exact
value of the edge-chromatic number is known for bipartite graphs
[2]}, complete graphs [3]}, [4]}, complete multipartite
graphs [5]}, [6]}, split graphs with odd maximum degree
[7]}, outerplanar graphs [8]}, planar graphs \(G\) with
\(\Delta (G)\ge 7\) [9]}, [10]}.
| i |
9562e60e-68c7-4898-b1fa-11ae2048ee9b | A graph \(G\) is a complete \(k\) -partite (\(k\ge 2\) ) graph if its
vertices can be partitioned into \(k\) independent sets
\(V_{1},\ldots ,V_{k}\) such that each vertex in \(V_{i}\) is adjacent to
all the other vertices in \(V_{j}\) for \(1\le i<j\le k\) . A complete
\(k\) -partite graph \(G\) is a complete balanced \(k\) -partite graph if
\(\vert V_{1}\vert =\vert V_{2}\vert =\cdots =\vert V_{k}\vert \) .
Clearly, if \(G\) is a complete balanced \(k\) -partite graph with \(n\)
vertices in each part, then \(\Delta (G)=(k-1)n\) . Note that the
complete graph \(K_{n}\) and the complete balanced bipartite graph
\(K_{n,n}\) are special cases of the complete balanced \(k\) -partite
graph. In [1]}, Laskar and Hare proved the following:
| i |
f4615cac-c5ff-42d5-8d8d-773596c26614 | A more general result was obtained by Hoffman and Rodger [1]}.
Before we formulate this result we need a definition of the overfull
graph. A graph \(G\) is overfull if \(\vert E(G)\vert >\left\lfloor \frac{\vert V(G)\vert }{2}\right\rfloor \Delta (G)\) . Clearly, if \(G\) is overfull,
then \(\chi ^{\prime }(G)=\Delta (G)+1\) .
| i |
6157316d-3d19-4fc8-9a82-e0b3ceb7289d | An edge-coloring of a graph \(G\) with colors \(1,\ldots ,t\) is an
interval \(t\) -coloring if all colors are used, and the colors of
edges incident to each vertex of \(G\) are distinct and form an
interval of integers. A graph \(G\) is interval colorable if \(G\) has
an interval \(t\) -coloring for some positive integer \(t\) . For an
interval colorable graph \(G\) , the least and the greatest values of
\(t\) for which \(G\) has an interval \(t\) -coloring are denoted by \(w(G)\)
and \(W(G)\) , respectively. The concept of interval edge-coloring was
introduced by Asratian and Kamalian [1]}. In [1]}, [3]}, they
proved the following:
| i |
9088205d-14d8-4426-b025-11a60ed9e28d | (1)
\(w\left(K_{r,s}\right)=r+s-\gcd (r,s)\) ,
(2)
\(W\left(K_{r,s}\right)=r+s-1\) ,
(3)
if \(w\left(K_{r,s}\right)\le t\le W\left(K_{r,s}\right)\) , then \(K_{r,s}\)
has an interval \(t\) -coloring.
| i |
e1a5b0d5-f550-4275-9acb-9f63e96ad549 | Clearly, this bound is sharp for the complete graph \(K_{2}\) , but if
\(G\ne K_{2}\) , then this upper bound can be improved to \(2\left|V(G)\right|-4\) [1]}. For an \(r\) -regular graph \(G\) ,
Kamalian and Petrosyan [2]} showed that if \(G\) with at least
\(2r+2\) vertices admits an interval \(t\) -coloring, then \(t\le 2\left|V(G)\right|-5\) . For a planar graph \(G\) , Axenovich
[3]} showed that if \(G\) has an interval \(t\) -coloring, then
\(t\le \frac{11}{6}\left|V(G)\right|\) . In [4]},
Petrosyan investigated interval colorings of complete graphs and
\(n\) -dimensional cubes. First note that \(K_{2n+1}\) is not interval
colorable, but \(K_{2n}\) is interval colorable and \(w(K_{2n})=2n-1\)
for any \(n\in \mathbb {N}\) . For \(W(K_{2n})\) , Petrosyan [4]}
proved the following:
| i |
6a0e2ac2-16d2-4984-a9aa-3113cbcfb369 | In this paper we investigate interval colorings of complete balanced
\(k\) -partite graphs. In particular, we generalize Theorem
REF for complete balanced \(k\) -partite graphs.
Also, we discuss some other corollaries of our result.
| i |
80fd0800-5b49-407c-b919-fd0c2d299669 | Let \([t]\) denote the set of the first \(t\) natural numbers. Let
\(\left\lfloor a\right\rfloor \) denote the largest integer less than
or equal to \(a\) . For two positive integers \(a\) and \(b\) with \(a\le b\) , the set \(\left\lbrace a,\ldots ,b\right\rbrace \) is denoted by \([a,b]\) and
called an interval. For an interval \([a,b]\) and a nonnegative number
\(p\) , the notation \([a,b]\oplus p\) means: \([a+p,b+p]\) .
| r |
1e9aeaaa-c521-49c2-a7e0-231e8dd70af3 | Lemma 7 If \(K_{n,n}\) is a complete balanced bipartite graph
with a bipartition \((U,V)\) , where \(U=\lbrace u_{1},\ldots ,u_{n}\rbrace \) and
\(V=\lbrace v_{1},\ldots ,v_{n}\rbrace \) , then \(K_{n,n}\) has an interval
\((2n-1)\) -coloring \(\alpha \) such that
\(S(u_{i},\alpha )=S(v_{i},\alpha )=[i,i+n-1]\) for \(1\le i\le n\)
| r |
d103fdfd-cac8-49e0-b842-8ab6e5cb0fb7 | Let \((U,V)\) be a bipartition of \(K_{n,n}\) , where
\(U=\lbrace u_{1},\ldots ,u_{n}\rbrace \) and \(V=\lbrace v_{1},\ldots ,v_{n}\rbrace \) . Define a
coloring \(\alpha \) of the edges of \(K_{n,n}\) as follows: for each
edge \(u_{i}v_{j}\in E(K_{n,n})\) , let \(\alpha (u_{i}v_{j})=i+j-1\) ,
where \(1\le i\le n, 1\le j\le n\) . Clearly \(\alpha \) is an
interval \((2n-1)\) -coloring of \(K_{n,n}\) and
\(S(u_{i},\alpha )=S(v_{i},\alpha )=[i,i+n-1]\) for \(1\le i\le n\) . \(\square \)
Let \(G\) be a complete balanced \(k\) -partite graph with \(n\) vertices
in each part. By Theorems REF and REF , we
have that \(G\) is interval colorable if and only if \(nk\) is even.
Moreover, if \(nk\) is even, then \(w(G)=\Delta (G)=(k-1)n\) . On the
other hand, by Theorem REF , we obtain \(W(G)\le 2nk-3\)
whenever \(nk\) is even. Now we derive a lower bound for \(W(G)\) .
Theorem 8 If \(G\) is a complete balanced \(k\) -partite graph
with \(n\) vertices in each part and \(nk\) is even, then \(W(G)\ge \left(\frac{3}{2}k-1\right)n-1\) .
| r |
7216760e-7a67-4724-b2d1-58c78b260325 | We distinguish our proof into two cases.
Case 1: \(k\) is even.
Let \(V(G)=\left\lbrace v^{(i)}_{j}\colon \,1\le i\le k,1\le j\le n\right\rbrace \) and
\(E(G)=\left\lbrace v^{(i)}_{p}v^{(j)}_{q}\colon \,1\le i<j\le k,1\le p\le n,1\le q\le n\right\rbrace \) .
Define an edge-coloring \(\alpha \) of the graph \(G\) .
For each edge \(v^{(i)}_{p}v^{(j)}_{q}\in E(G)\) with \(1\le i<j\le k\) and \(p=1,\ldots ,n\) , \(q=1,\ldots ,n\) , define a
color \(\alpha \left(v^{(i)}_{p}v^{(j)}_{q}\right)\) as follows:
for \(i=1,\ldots ,\left\lfloor \frac{k}{4}\right\rfloor \) , \(j=2,\ldots ,\frac{k}{2}\) , \(i+j\le \frac{k}{2}+1\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-3\right)n+p+q-1\) ;
for \(i=2,\ldots ,\frac{k}{2}-1\) ,
\(j=\left\lfloor \frac{k}{4}\right\rfloor +2,\ldots ,\frac{k}{2}\) ,
\(i+j\ge \frac{k}{2}+2\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j+\frac{k}{2}-4\right)n+p+q-1\) ;
for \(i=3,\ldots ,\frac{k}{2}\) , \(j=\frac{k}{2}+1,\dots ,k-2\) , \(j-i\le \frac{k}{2}-2\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(\frac{k}{2}+j-i-1\right)n+p+q-1\) ;
for \(i=1,\ldots ,\frac{k}{2}\) , \(j=\frac{k}{2}+1,\ldots ,k\) , \(j-i\ge \frac{k}{2}\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(j-i-1\right)n+p+q-1\) ;
for \(i=2,\ldots ,1+\left\lfloor \frac{k-2}{4}\right\rfloor \) ,
\(j=\frac{k}{2}+1,\dots ,\frac{k}{2}+\left\lfloor \frac{k-2}{4}\right\rfloor \) , \(j-i=\frac{k}{2}-1\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(2i-3\right)n+p+q-1\) ;
for \(i=\left\lfloor \frac{k-2}{4}\right\rfloor +2,\ldots ,\frac{k}{2}\) ,
\(j=\frac{k}{2}+1+\left\lfloor \frac{k-2}{4}\right\rfloor ,\ldots ,k-1\) ,
\(j-i=\frac{k}{2}-1\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-3\right)n+p+q-1\) ;
for \(i=\frac{k}{2}+1,\dots ,\frac{k}{2}+\left\lfloor \frac{k}{4}\right\rfloor -1\) , \(j=\frac{k}{2}+2,\ldots ,k-2\) , \(i+j\le \frac{3}{2}k-1\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-k-1\right)n+p+q-1\) ;
for \(i=\frac{k}{2}+1,\ldots ,k-1\) , \(j=\frac{k}{2}+\left\lfloor \frac{k}{4}\right\rfloor +1,\dots ,k\) , \(i+j\ge \frac{3}{2}k\) , let
\(\alpha \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-\frac{k}{2}-2\right)n+p+q-1\) .
Let us prove that \(\alpha \) is an interval
\(\left(\left(\frac{3}{2}k-1\right)n-1\right)\) -coloring of the graph
\(G\) .
First we show that for each \(t\in \left[\left(\frac{3}{2}k-1\right)n-1\right]\) , there is an edge \(e\in E(G)\) with \(\alpha (e)=t\) .
Consider the vertices
\(v_{1}^{(1)},\ldots ,v_{n}^{(1)},v_{1}^{(k)},\ldots ,v_{n}^{(k)}\) .
Now, by Lemma REF and the definition of \(\alpha \) , for
\(1\le j\le n\) ,
\(S\left(v_{j}^{(1)},\alpha \right)=\bigcup _{l=1}^{k-1}\left([j,j+n-1]\oplus (l-1)n\right)\) and
\(S\left(v_{j}^{(k)},\alpha \right)=\bigcup _{l=\frac{k}{2}}^{\frac{3}{2}k-2}\left([j,j+n-1]\oplus (l-1)n\right)\) .
Let \(\overline{C}\) and \(\overline{\overline{C}}\) be the subsets of
colors appear on edges incident to the vertices
\(v_{1}^{(1)},\ldots ,v_{n}^{(1)}\) and
\(v_{1}^{(k)},\ldots ,v_{n}^{(k)}\) in the coloring \(\alpha \) ,
respectively, that is:
\(\overline{C}=\bigcup _{j=1}^{n} S\left(v_{j}^{(1)},\alpha \right)\)
and \(\overline{\overline{C}}=\bigcup _{j=1}^{n}S\left(v_{j}^{(k)},\alpha \right)\) .
It is straightforward to check that \(\overline{C}\cup \overline{\overline{C}}=\left[\left(\frac{3}{2}k-1\right)n-1\right]\) ,
so for each \(t\in \left[\left(\frac{3}{2}k-1\right)n-1\right]\) ,
there is an edge \(e\in E(G)\) with \(\alpha (e)=t\) .
Next we show that the edges incident to any vertex of \(G\) are
colored by \((k-1)n\) consecutive colors.
Let \(v_{j}^{(i)}\in V(G)\) , where \(1\le i\le k\) , \(1\le j\le n\) .
Subcase 1.1. \(1\le i\le 2\) , \(1\le j\le n\) .
By Lemma REF and the definition of \(\alpha \) , we have
\(S\left(v_{j}^{(1)},\alpha \right)=S\left(v_{j}^{(2)},\alpha \right)=\bigcup _{l=1}^{k-1}\left([j,j+n-1]\oplus (l-1)n\right)=\left[j,j+(k-1)n-1\right]\) .
Subcase 1.2. \(3\le i\le \frac{k}{2}\) , \(1\le j\le n\) .
By Lemma REF and the definition of \(\alpha \) , we have
\(S\left(v_{j}^{(i)},\alpha \right)=\bigcup _{l=i-1}^{k-3+i}\left([j,j+n-1]\oplus (l-1)n\right)=\left[j+(i-2)n,j+(k-3+i)n-1\right]\) .
Subcase 1.3. \(\frac{k}{2}+1\le i\le k-2\) , \(1\le j\le n\) .
By Lemma REF and the definition of \(\alpha \) , we have
\(S\left(v_{j}^{(i)},\alpha \right)=\bigcup _{l=i-\frac{k}{2}+1}^{\frac{k}{2}-1+i}\left([j,j+n-1]\oplus (l-1)n\right)=\left[j+\left(i-\frac{k}{2}\right)n,j+\left(\frac{k}{2}-1+i\right)n-1\right]\) .
Subcase 1.4. \(k-1\le i\le k,1\le j\le n\) .
By Lemma REF and the definition of \(\alpha \) , we have
\(S\left(v_{j}^{(k-1)},\alpha \right)=S\left(v_{j}^{(k)},\alpha \right)=\bigcup _{l=\frac{k}{2}}^{\frac{3}{2}k-2}\left([j,j+n-1]\oplus (l-1)n\right)=\left[j+\left(\frac{k}{2}-1\right)n,j+\left(\frac{3k}{2}-2\right)n-1\right]\) .
This shows that \(\alpha \) is an interval
\(\left(\left(\frac{3}{2}k-1\right)n-1\right)\) -coloring of \(G\) ; thus
\(W(G)\ge \left(\frac{3}{2}k-1\right)n-1\) for even \(k\ge 2\) .
Case 2: \(n\) is even.
Let \(n=2m\) , \(m\in \mathbb {N}\) . Let
\(U_{i}=\left\lbrace v_{1}^{(i)},\ldots ,v_{m}^{(i)},v_{1}^{(k+i)},\ldots ,v_{m}^{(k+i)}\right\rbrace \)
(\(1\le i\le k\) ) be the \(k\) independent sets of vertices of \(G\) .
For \(i=1,\ldots ,2k\) , define the set \(V_{i}\) as follows:
\(V_{i}=\left\lbrace v_{1}^{(i)},\ldots ,v_{m}^{(i)}\right\rbrace \) . Clearly,
\(V(G)=\bigcup _{i=1}^{2k}V_{i}\) . For \(1\le i<j\le 2k\) , define
\((V_{i},V_{j})\) as the set of all edges between \(V_{i}\) and \(V_{j}\) .
It is easy to see that for \(1\le i<j\le 2k\) , \(\left|(V_{i},V_{j})\right|=m^{2}\) except for \(\left|(V_{i},V_{k+i})\right|=0\) whenever \(i=1,\ldots ,k\) . If we
consider the sets \(V_{i}\) as the vertices and the sets
\((V_{i},V_{j})\) as the edges, then we obtain that \(G\) is isomorphic
to the graph \(K_{2k}-F\) , where \(F\) is a perfect matching. Now we
define an edge-coloring \(\beta \) of the graph \(G\) .
For each edge \(v^{(i)}_{p}v^{(j)}_{q}\in E(G)\) with \(1\le i<j\le 2k\) and \(p=1,\ldots ,m\) , \(q=1,\ldots ,m\) , define a
color \(\beta \left(v^{(i)}_{p}v^{(j)}_{q}\right)\) as follows:
for \(i=1,\ldots ,\left\lfloor \frac{k}{2}\right\rfloor \) , \(j=2,\ldots ,k\) , \(i+j\le k+1\) , let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-3\right)m+p+q-1\) ;
for \(i=2,\ldots ,k-1\) ,
\(j=\left\lfloor \frac{k}{2}\right\rfloor +2,\ldots ,k\) , \(i+j\ge k+2\) ,
let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j+k-5\right)m+p+q-1\) ;
for \(i=3,\ldots ,k\) , \(j=k+1,\dots ,2k-2\) , \(j-i\le k-2\) , let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(k+j-i-2\right)m+p+q-1\) ;
for \(i=1,\ldots ,k-1\) , \(j=k+2,\ldots ,2k\) , \(j-i\ge k+1\) , let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(j-i-2\right)m+p+q-1\) ;
for \(i=2,\ldots ,1+\left\lfloor \frac{k-1}{2}\right\rfloor \) ,
\(j=k+1,\dots ,k+\left\lfloor \frac{k-1}{2}\right\rfloor \) , \(j-i=k-1\) ,
let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(2i-3\right)m+p+q-1\) ;
for \(i=\left\lfloor \frac{k-1}{2}\right\rfloor +2,\ldots ,k\) ,
\(j=k+1+\left\lfloor \frac{k-1}{2}\right\rfloor ,\ldots ,2k-1\) ,
\(j-i=k-1\) , let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-4\right)m+p+q-1\) ;
for \(i=k+1,\dots ,k+\left\lfloor \frac{k}{2}\right\rfloor -1\) ,
\(j=k+2,\ldots ,2k-2\) , \(i+j\le 3k-1\) , let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-2k-1\right)m+p+q-1\) ;
for \(i=k+1,\ldots ,2k-1\) , \(j=k+\left\lfloor \frac{k}{2}\right\rfloor +1,\dots ,2k\) , \(i+j\ge 3k\) , let
\(\beta \left(v_{p}^{(i)}v_{q}^{(j)}\right)=\left(i+j-k-3\right)m+p+q-1\) .
Let us prove that \(\beta \) is an interval
\(\left(\left(\frac{3}{2}k-1\right)n-1\right)\) -coloring of the graph
\(G\) .
First we show that for each \(t\in \left[\left(\frac{3}{2}k-1\right)n-1\right]\) , there is an edge \(e\in E(G)\) with \(\beta (e)=t\) .
Consider the vertices
\(v_{1}^{(1)},\ldots ,v_{m}^{(1)},v_{1}^{(2k)},\ldots ,v_{m}^{(2k)}\) .
Now, by Lemma REF and the definition of \(\beta \) , for
\(1\le j\le m\) ,
\(S\left(v_{j}^{(1)},\beta \right)=\bigcup _{l=1}^{2k-2}\left([j,j+m-1]\oplus (l-1)m\right)\) and
\(S\left(v_{j}^{(2k)},\beta \right)=\bigcup _{l=k}^{3k-3}\left([j,j+m-1]\oplus (l-1)m\right)\) .
Let \(\tilde{C}\) and \(\tilde{\tilde{C}}\) be the subsets of colors
appear on edges incident to the vertices
\(v_{1}^{(1)},\ldots ,v_{m}^{(1)}\) and
\(v_{1}^{(2k)},\ldots ,v_{m}^{(2k)}\) in the coloring \(\beta \) ,
respectively, that is:
\(\tilde{C}=\bigcup _{j=1}^{m} S\left(v_{j}^{(1)},\beta \right)\) and
\(\tilde{\tilde{C}}=\bigcup _{j=1}^{m}S\left(v_{j}^{(2k)},\beta \right)\) .
It is straightforward to check that \(\tilde{C}\cup \tilde{\tilde{C}}=\left[\left(\frac{3}{2}k-1\right)n-1\right]\) , so
for each \(t\in \left[\left(\frac{3}{2}k-1\right)n-1\right]\) , there
is an edge \(e\in E(G)\) with \(\beta (e)=t\) .
Next we show that the edges incident to any vertex of \(G\) are
colored by \((k-1)n\) consecutive colors.
Let \(v_{j}^{(i)}\in V(G)\) , where \(1\le i\le 2k\) , \(1\le j\le m\) .
Subcase 2.1. \(1\le i\le 2\) , \(1\le j\le m\) .
By Lemma REF and the definition of \(\beta \) , we have
\(S\left(v_{j}^{(1)},\beta \right)=S\left(v_{j}^{(2)},\beta \right)=\bigcup _{l=1}^{2k-2}\left([j,j+m-1]\oplus (l-1)m\right)=\left[j,j+(2k-2)m-1\right]\) .
Subcase 2.2. \(3\le i\le k\) , \(1\le j\le m\) .
By Lemma REF and the definition of \(\beta \) , we have
\(S\left(v_{j}^{(i)},\beta \right)=\bigcup _{l=i-1}^{2k-4+i}\left([j,j+m-1]\oplus (l-1)m\right)=\left[j+(i-2)m,j+(2k-4+i)m-1\right]\) .
Subcase 2.3. \(k+1\le i\le 2k-2\) , \(1\le j\le m\) .
By Lemma REF and the definition of \(\beta \) , we have
\(S\left(v_{j}^{(i)},\beta \right)=\bigcup _{l=i-k+1}^{k-2+i}\left([j,j+m-1]\oplus (l-1)m\right)=\left[j+(i-k)m,j+(k-2+i)m-1\right]\) .
Subcase 2.4. \(2k-1\le i\le 2k,1\le j\le m\) .
By Lemma REF and the definition of \(\beta \) , we have
\(S\left(v_{j}^{(2k-1)},\beta \right)=S\left(v_{j}^{(2k)},\beta \right)=\bigcup _{l=k}^{3k-3}\left([j,j+m-1]\oplus (l-1)m\right)=\left[j+(k-1)m,j+(3k-3)m-1\right]\) .
This shows that \(\beta \) is an interval
\(\left(\left(\frac{3}{2}k-1\right)n-1\right)\) -coloring of \(G\) ; thus
\(W(G)\ge \left(\frac{3}{2}k-1\right)n-1\) for even \(n\ge 2\) .
\(\square \)
From Theorems REF (1) and REF , and taking
into account that a complete balanced \(k\) -partite graph \(G\) with \(n\)
vertices in each part is overfull when \(nk\) is odd, we have:
Corollary 9 If \(G\) is a complete balanced \(k\) -partite graph
with \(n\) vertices in each part, then \(\chi ^{\prime }(G)=(k-1)n\) if
and only if \(nk\) is even.
From Theorems REF (2) and REF , we have:
Corollary 10 Let \(G\) be a complete balanced \(k\) -partite
graph with \(n\) vertices in each part and \(nk\) is even. If
\((k-1)n\le t\le \left(\frac{3}{2}k-1\right)n-1\) , then \(G\) has an
interval \(t\) -coloring.
Also, note that the proof of the case 2 implies that if a graph \(G\)
with \(n\) vertices is \((n-2)\) -regular, then \(\chi ^{\prime }(G)=n-2\) .
The next theorem improves the lower bound in Theorem
REF for complete balanced \(k\) -partite graphs with even
\(k\) .
Theorem 11 Let \(G\) be a complete balanced \(k\) -partite graph
with \(n\) vertices in each part. If \(k=p2^{q}\) , where \(p\) is odd and
\(q\in \mathbb {N}\) , then \(W(G)\ge (2k-p-q)n-1\) .
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866cd13c-656e-4622-9f28-4e6246e33fab | Let \(V(G)=\left\lbrace v^{(i)}_{j}\colon \,1\le i\le k,1\le j\le n\right\rbrace \) and \(V(K_{k})=\lbrace u_{1},\ldots ,u_{k}\rbrace \) . Also, let
\(E(G)=\left\lbrace v^{(i)}_{r}v^{(j)}_{s}\colon \,1\le i<j\le k,1\le r\le n,1\le s\le n\right\rbrace \) and
\(E(K_{k})=\lbrace u_{i}u_{j}\colon \,1\le i<j\le k\rbrace \) .
Since \(k=p2^{q}\) , where \(p\) is odd and \(q\in \mathbb {N}\) , by Theorem
REF , there exists an interval \((2k-1-p-q)\) -coloring
\(\alpha \) of \(K_{k}\) . Now we define an edge-coloring \(\beta \) of the
graph \(G\) .
For each edge \(v^{(i)}_{r}v^{(j)}_{s}\in E(G)\) with \(1\le i<j\le k\) and \(r=1,\ldots ,n\) , \(s=1,\ldots ,n\) , define a color
\(\beta \left(v^{(i)}_{r}v^{(j)}_{s}\right)\) as follows:
\(\beta \left(v^{(i)}_{r}v^{(j)}_{s}\right)=\left(\alpha \left(u_{i}u_{j}\right)-1\right)n+r+s-1\) .
By Lemma REF and the definition of \(\beta \) , and taking
into account that \(\max S\left(u_{i},\alpha \right)-\min S\left(u_{i},\alpha \right)=k-2\) for \(i=1,\ldots ,k\) , we have
\(S\left(v_{j}^{(i)},\beta \right)&=&\bigcup _{l=\min S(u_{i},\alpha )}^{\max S(u_{i},\alpha )}\left([j,j+n-1]\oplus (l-1)n\right)=\\&=&[j+\left(\min S(u_{i},\alpha )-1\right)n,j+\max S(u_{i},\alpha )n-1]\)
for \(i=1,\ldots ,k\) and \(j=1,\ldots ,n\) , and
\(\bigcup _{i=1}^{k}\bigcup _{j=1}^{n}S\left(v_{j}^{(i)},\beta \right)&=&[(2k-p-q)n-1].\)
This shows that \(\beta \) is an interval \(((2k-p-q)n-1)\) -coloring of
the graph \(G\) ; thus \(W(G)\ge (2k-p-q)n-1\) . \(\square \)
From Theorems REF (2) and REF , we have:
Corollary 12 Let \(G\) be a complete balanced \(k\) -partite graph
with \(n\) vertices in each part and \(k=p2^{q}\) , where \(p\) is odd and
\(q\in \mathbb {N}\) . If \((k-1)n\le t\le (2k-p-q)n-1\) , then \(G\) has
an interval \(t\) -coloring.
Problems
In the previous section we obtained some results on interval
colorings of complete balanced multipartite graphs, but very small
is known about interval colorings of complete unbalanced
multipartite graphs. In fact, there are only two results on interval
colorings of complete unbalanced multipartite graphs. Let
\(n_{1}\le \cdots \le n_{k}\) be positive integers. The complete
multipartite graph \(K_{n_{1},\ldots ,n_{k}}\) is a complete
\(k\) -partite graph for which \(\vert V_{i}\vert =n_{i}\) ,
\(i=1,\ldots ,k\) . The first result is Theorem REF which
gives all possible values of the number of colors in interval
colorings of \(K_{n_{1},n_{2}}\) . The second result was obtained by
Feng and Huang [1]}. In [1]}, they proved that the
complete 3-partite graph \(K_{1,1,n}\) is interval colorable if and
only if \(n\) is even. Now we would like to formulate some problems on
interval colorings of complete multipartite graphs:
Problem 1
Characterize all interval colorable complete multipartite graphs.
Problem 2
Find the exact values of \(w(G)\) and \(W(G)\) for interval colorable
complete multipartite graphs G.
Problem 3
Find the exact value of \(W\left(K_{n,\ldots ,n}\right)\) for interval
colorable complete balanced \(k\) -partite graphs \(K_{n,\ldots ,n}\) .
Note that even a special case of Problem REF is open:
the problem of determining the exact value of \(W(K_{2n})\) for
complete graph \(K_{2n}\) .
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26dc2997-9f99-487e-9110-1ae35b4d9040 | Real-time rendering of photorealistic scenes with complex lighting is still an overly demanding problem. However, today, consumer machine learning accelerators are widespread from desktop GPUs to mobile phones and vr headsets, making evaluation of neural networks fast and power-efficient.
Recent advances in implicit neural scene representations , , impressively show that machine learning can be used for compact encoding and high-quality rendering of 3D scenes.
nerf use only 1000000 parameters divided among two mlp networks to encode scene structure alongside lighting effects.
For image generation, nerf uses traditional volume rendering drawing 256 samples for each view ray, where each sample requires a full network evaluation.
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46ec7533-eeb0-4477-8018-2fde4a3431ce | Although nerf-like methods show significant potential for compact high-quality object and scene representations, they are too expensive to evaluate in real-time.
Real-time rendering of such a representation onto a vr headset at \(1440\times 1600\) pixel per eye with 90 would require 37 petaFLOPS (256 network evaluations each with \(256^2\cdot 7\) multiply add operations).
Clearly, this is not possible on current GPU hardware and evaluation cost is a major limiting factor for neural representations to be used for real-time rendering.
Additionally, nerf only works well for small scale content, requiring splitting larger scenes into multiple nerf , , multiplying both the memory and evaluation cost.
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eb68ef2c-98b2-42a7-98b9-58e5f20f9750 | In this work, we make neural representations practical for interactive and real-time rendering, while sticking to a tight memory budget.
Particularly, our goal is to enable large scale synthetic content in movie quality in real-time rendering.
We make the following contributions with donerf:
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69068a73-9ada-48aa-a6cb-e4766f51bf78 |
We propose a compact dual network design to reduce evaluation costs for neural rendering. An oracle network predicts sample locations along view rays and a shading network places a small number of samples guided by the oracle to deliver the final color.
We present a robust depth oracle network design and training scheme to efficiently provide sample locations for the shading network.
The oracle uses filtered, discretized target depth values, which are readily available in synthetic content, and it learns to solve a classification task rather than to directly estimate depth.
We introduce a non-linear transformation to handle large, open scenes and show that sampling of the shading network should happen in a warped space, to better capture different frequencies in the fore- and background, capturing content in a single network beyond the capability of previous work.
Combining our efforts, we demonstrate high-quality real-time neural rendering of large synthetic scenes. At the same tight memory budget used by the original nerf, we show equal quality for small scenes and significant improvements for large scenes, while reducing the computational cost by 2498\(\times \) .
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