question:Develop a computational routine that calculates the statistical median value among a trio of numerical entities.

question:You will be shown sections from a scientific research paper, together with a question about the paper. Your task is to answer the question based on the contents of the paper. Your response should be a `json` object with two fields:"answer": An array of strings extracted directly from the paper which, collectively, answer the question."evidence": An array of strings. Each should be an excerpt from the paper, in which one or more of the extracted answers can be found.For instance, for the question "What baselines did the authors compare against?", a sample response might be:{ "answer": ["BERT", "RoBERTa"], "evidence": ["In our experiments, we compare the performance of our model against BERT and RoBERTa."]}Do not include any text in your response other than the json.If the question is unanswerable given the provided excerpts, respond with the single word "null".Paper: Normalized and Geometry-Aware Self-Attention Network for Image CaptioningSelf-attention (SA) network has shown profound value in image captioning. In this paper, we improve SA from two aspects to promote the performance of image captioning. First, we propose Normalized Self-Attention (NSA), a reparameterization of SA that brings the benefits of normalization inside SA. While normalization is previously only applied outside SA, we introduce a novel normalization method and demonstrate that it is both possible and beneficial to perform it on the hidden activations inside SA. Second, to compensate for the major limit of Transformer that it fails to model the geometry structure of the input objects, we propose a class of Geometry-aware Self-Attention (GSA) that extends SA to explicitly and efficiently consider the relative geometry relations between the objects in the image. To construct our image captioning model, we combine the two modules and apply it to the vanilla self-attention network. We extensively evaluate our proposals on MS-COCO image captioning dataset and superior results are achieved when comparing to state-of-the-art approaches. Further experiments on three challenging tasks, i.e. video captioning, machine translation, and visual question answering, show the generality of our methods.IntroductionAutomatically generating captions for images, namely image captioning BIBREF0, BIBREF1, has emerged as a prominent research problem at the intersection of computer vision (CV) and natural language processing (NLP). This task is challenging as it requires to first recognize the objects in the image, the relationships between them, and finally properly organize and describe them in natural language.Inspired by the sequence-to-sequence model for machine translation, most image captioning approaches adopt an encoder-decoder paradigm, which uses a deep convolutional neural network (CNN) to encode the input image as a vectorial representation, and a recurrent neural network (RNN) based caption decoder to generate the output caption. Recently, self-attention (SA) networks, denoted as SANs, have been introduced by BIBREF2, BIBREF3 to replace conventional RNNs in image captioning. Since its first introduction in Transformer BIBREF4, SA and its variants have shown promising empirical results in a wide range of CV BIBREF5, BIBREF6, BIBREF7, BIBREF8, BIBREF9, BIBREF10 and NLP BIBREF11, BIBREF12, BIBREF13 tasks. Although SAN-based framework has achieved state-of-the-art performance in image captioning, it remains two problems to be solved.Firstly, SA is susceptible to the internal covariate shift BIBREF14 problem. Typically, SA is regarded as a mapping of a set of query and key/value pairs. We observe, from another perspective, that computation of the attention weights in SA could be considered as feeding the queries into a fully-connected layer, whose parameters are dynamically computed according to the inputs. Problem could happen when the distribution of the queries shifts due to the change in network parameters during training. That is, the subsequent layers have to continuously adapt to the new input distribution, and consequently, SA may not be learned effectively. This problem is called “Internal Covariate Shift" in BIBREF14 –— the tendency that the distribution of activations drifts during training in a feed-forward network.To eliminate the internal covariate shift problem inside SA, in this paper, we introduce an effective reparameterization of SA, named Normalized Self-Attention (NSA). NSA performs a novel normalization method on the hidden activations of SA to fix their distributions. By doing so, we can effectively decouple the fully-connected layer's parameters from those of other layers, leading to a better-conditioned optimization of SA. While Layer Normalization (LN) BIBREF15 is proven to be very critical for enabling the convergence of Transformer, however, LN is only applied outside SA blocks. To our knowledge, there has not been any deep exploration to find a suitable normalization method inside SA. We demonstrate that our NSA can collaborate with LN to bring improved generalization for SA-based networks.Another critical issue in SA is its inability to model the geometric relationships among input elements. The vanilla self-attention treats its inputs as “bag-of-features", simply neglecting their structure and the relationships between them. However, the objects in the image, from which the region-based visual features are extracted for image captioning, inherently have geometric structure — 2D spatial layout and variations in scale/aspect ratio. Such inherent geometric relationships between objects play a very complex yet critical role in understanding the image content. One common solution to inject position information into SA is adding representations of absolute positions to each element of the inputs, as is often used in the case of 1D sentences. Nonetheless, this solution does not work well for image captioning because the 2D geometry relations between objects are harder to infer from their absolute positions.We present a more efficient approach to the above problem: explicitly incorporating relative geometry relationships between objects into SA. The module is named Geometry-aware Self-Attention (GSA). GSA extends the original attention weight into two components: the original content-based weight, and a new geometric bias, which is efficiently calculated by the relative geometry relations and, importantly, the content of the associated elements, i.e. query or key.By combining both NSA and GSA, we obtain an enhanced SA module. We then construct our Normalized and Geometry-aware Self-Attention Network, namely NG-SAN, by replacing the vanilla SA modules in the encoder of the self-attention network with the proposed one. Extensive experiments on MS-COCO validates the effectiveness of our proposals. In particular, our NG-SAN establishes a new state-of-the-art on the MS-COCO evaluation sever, improving the best single-model result in terms of CIDEr from 125.5 to 128.6. To demonstrate the generality of NSA, we further present video captioning, machine translation, and visual question answering experiments on the VATEX, WMT 2014 English-to-German, and VQA-v2 datasets, respectively. On top of the strong Transformer-based baselines, our methods can consistently increase accuracies on all tasks at a negligible extra computational cost.To summarize, the main contributions of this paper are three-fold:We presented Normalized Self-Attention, an effective reparameterization of self-attention, which brings the benefits of normalization technique inside SA.We introduce a class of Geometry-aware Self-Attention that explicitly makes use of the relative geometry relationships and the content of objects to aid image understanding.By combining the two modules and apply it on the self-attention network, we establish a new state-of-the-art on the MS-COCO image captioning benchmark. Further experiments on video captioning, machine translation, and visual question answering tasks demonstrate the generality of our methods.Related Work ::: Position encoding in self-attention networksTo inject sequence ordering into SA module, in Transformer, absolute position encodings based on sinusoids are added to the input elements both in the encoder and decoder. Recently, BIBREF22 modulates SA by incorporating the relative distances between sequence elements. BIBREF6 proposes an SA-like module for object detection, which multiplies a new relation weight on the original self-attention weight, and is used by BIBREF23 in Transformer. Its relation weight is computed solely with the relative coordinates and sizes between bounding boxes. Different from these works, our GSA module explores a broader range of geometric biases that involve not only the geometry information but also the content of the associated objects.Preliminaries ::: Self-attention network for image captioningFigure FIGREF12 shows self-attention network (SAN), which is our baseline architecture for image captioning. Similar to Transformer, the model consists of an image encoder and a caption decoder, both of which are composed of a stack of L layers. Each layer consists of one (for the encoder layer) or two (for the decoder layer) multi-head attention (MHA) sub-layers followed by a feed-forward network (FFN). The MHA sub-layer contains h parallel “heads" with each head corresponding to an independent scaled dot-product attention function. Besides, a residual connection and layer normalization are used between all the sub-layers.The inputs to the encoder are the region-based visual features extracted from Faster-RCNN BIBREF24 object detector. Each input element corresponds to an object in the image. Before feeding the input vectors into the encoder, they are first passed through a dense layer followed by a ReLU layer to adapt their dimension to be consistent with the encoder. The decoder takes the attended visual features and the embeddings of the previous words to predict the next word recursively. Following Transformer, we add sinusoidal “positional encodings" to the inputs at the bottoms of the decoder. Because the regions in the image don't have a natural order like sequences, no position information is added in the encoder side.Experiments on Image Captioning ::: Analysis on the full model (NG-SAN) ::: Complexity.As can be seen in the “#params" column in Table TABREF49, NG-SAN requires very few (about 2k) additional parameters compared with SAN. For NSA, it does not require any parameters, and the computation overhead of the additional normalization process is almost ignorable. While GSA indeed requires some additional parameters, the amount is ignorable. GSA can be efficiently implemented by matrix multiplication and the einstein summation (einsum) operations provided by mainstream deep learning frameworks.Extension: Experiments on Other TasksWe further investigate the effectiveness and generality of our methods on Video Captioning (VC) BIBREF37, Machine Translation (MT) BIBREF38, and Visual Question Answering (VQA) BIBREF39 tasks. Since VC and MT are both sequence-to-sequence problems, we directly use Transformer as the baseline models, and we replace the SA modules in their encoder with the proposed NSA module to construct our methods. As for VQA, we use MCAN BIBREF40 as the baseline model, which uses a SAN-based network to simultaneously encode image and question information. To build our method for VQA, we replace all the SA modules in MCAN with our GSA modules.Extension: Experiments on Other Tasks ::: Machine TranslationWe also evaluate NSA on MT task, for which the Transformer was originally proposed. We trained on the widely-used WMT 2014 English to German (En-–De) dataset, which consists of about 4.56 million sentence pairs. The models were validated on newstest-2013 and tested on newstest-2014 with BLEU. We use the well-known Transformer-Base BIBREF4 variant of Transformer as the baseline model, which has 6 layers in both the encoder and decoder. Specifically, we follow the implementation of the fairseq-py BIBREF43 toolkit.As shown in Table TABREF53, Compared to Transformer-Base model, NSA increases the BLEU score by 0.36 points without adding any parameters.Appendix ::: Visualization of Geometric WeightsTo gain a better insight about the effect of the relative geometry information on attention weights, we visualize the geometric weights in GSA. Specifically, we use the content-dependent version (phi ^1) of GSA, and use a trained one-layer G-SAN model. We visualize how the geometric weight phi ^1_{ij} between object i and j changes as the relative geometry feature mathbf {f}^g_{ij} between them changes.Review that the relative geometry feature mathbf {f}^g_{ij} is a 4-dimensional vector:where (x_i, y_i), w_i, h_i are the center coordinate, width, and height of box i, respectively. We simplify the above equation asWe then keep one of (Delta x, Delta y) and (Delta w, Delta h) fixed, change the other one, and see plot the values of phi ^1_{ij}.Figure FIGREF61 shows the cases when Delta w=Delta h in lbrace 0.5, 1, 2rbrace are fixed, and Delta x and Delta y change in range of [0,3]. We can observer that, basically, the geometric weight gets smaller when the relative distance between the two objects increases. Exceptions are found near (Delta x, Delta y)=(0,0), where the weights are relatively smaller than neighboring point. That is probably because when two boxes i and j have similar sizes, e.g. Delta w=Delta h=1, and their center coordinates almost coincide, then they likely refer to the same object. Therefore, the weight of box j should be reduced to avoid repeating the object.Figure FIGREF62 shows the cases when Delta x=Delta y in lbrace 0.5, 1, 2rbrace are fixed, and Delta w and Delta h change in range of [0,3]. We have the following observations. 1) The geometric weight is small when the size difference between the two boxes is too large, i.e. Delta w or Delta h is close to 0 or too large. 2) The geometric weight tends to be larger when two objects are close to each other, e.g. (Delta x, Delta y) = (0.5, 0.5), than when their distance is large, e.g. (Delta x, Delta y) = (2, 2).Table 1. Comparisons between N-SAN and SAN using different numbers of self-attention layers L.Question: What datasets are used for experiments on three other tasks?

question:Write Java code for finding the maximum value in an array of integers.

question:Design a function to implement a merge sort algorithm for a given array.

question:Visualize Covid-19 World Vaccination Progress dataset from kaggle using a stacked bar chart. Each country is a bar, differentiated by vaccine types used, and combines these bars into a single plot. Additionally, highlight countries using a specific vaccine with a marked difference.

question:Develop a full-stack CRUD application using React for the frontend and Node.js for the backend. The application should be a task management system where users can create, read, update, and delete tasks. Each task should have a title, description, due date, and priority level. The application should also support user authentication, where only authenticated users can perform CRUD operations on their own tasks. In addition, implement a feature that allows users to sort their tasks based on due date or priority level. The application should also have error handling and validation checks for the input fields. Finally, write unit tests for your components and integration tests for your API endpoints.