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This technical report introduces Docling, an easy to use, self-contained, MIT-licensed open-source package for PDF document conversion. It is powered by state-of-the-art specialized AI models for layout analysis (DocLayNet) and table structure recognition (TableFormer), and runs efficiently on commodity hardware in a small resource budget. The code interface allows for easy extensibility and addition of new features and models.

Environment, Social, and Governance (ESG) KPIs assess an organization's performance on issues such as climate change, greenhouse gas emissions, water consumption, waste management, human rights, diversity, and policies. ESG reports convey this valuable quantitative information through tables. Unfortunately, extracting this information is difficult due to high variability in the table structure as well as content. We propose Statements, a novel domain agnostic data structure for extracting quantitative facts and related information. We propose translating tables to statements as a new supervised deep-learning universal information extraction task. We introduce SemTabNet - a dataset of over 100K annotated tables. Investigating a family of T5-based Statement Extraction Models, our best model generates statements which are 82% similar to the ground-truth (compared to baseline of 21%). We demonstrate the advantages of statements by applying our model to over 2700 tables from ESG reports. The homogeneous nature of statements permits exploratory data analysis on expansive information found in large collections of ESG reports., Comment: Accepted at the NLP4Climate workshop in the 62nd Annual Meeting of the Association for Computational Linguistics (ACL 2024)

In this paper, we propose Phoneme Discretized Saliency Maps (PDSM), a discretization algorithm for saliency maps that takes advantage of phoneme boundaries for explainable detection of AI-generated voice. We experimentally show with two different Text-to-Speech systems (i.e., Tacotron2 and Fastspeech2) that the proposed algorithm produces saliency maps that result in more faithful explanations compared to standard posthoc explanation methods. Moreover, by associating the saliency maps to the phoneme representations, this methodology generates explanations that tend to be more understandable than standard saliency maps on magnitude spectrograms., Comment: Accepted to Interspeech 2024

With the success of machine learning (ML) applied to climate reaching further every day, emulators have begun to show promise not only for weather but for multi-year time scales in the atmosphere. Similar work for the ocean remains nascent, with state-of-the-art limited to models running for shorter time scales or only for regions of the globe. In this work, we demonstrate high-skill global emulation for surface ocean fields over 5-8 years of model rollout, accurately representing modes of variability for two different ML architectures (ConvNext and Transformers). In addition, we address the outstanding question of generalization, an essential consideration if the end-use of emulation is to model warming scenarios outside of the model training data. We show that 1) generalization is not an intrinsic feature of a data-driven emulator, 2) fine-tuning the emulator on only small amounts of additional data from a distribution similar to the test set can enable the emulator to perform well in a warmed climate, and 3) the forced emulators are robust to noise in the forcing.

In this thesis, we study problems at the interface of analysis and discrete mathematics. We discuss analogues of well known Hardy-type inequalities and Rearrangement inequalities on the lattice graphs $\mathbb{Z}^d$, with a particular focus on behaviour of sharp constants and optimizers.In the first half of the thesis, we analyse Hardy inequalities on $\mathbb{Z}^d$, first for $d=1$ and then for $d \geq 3$. We prove a sharp weighted Hardy inequality on integers with power weights of the form $n^\alpha$. This is done via two different methods, namely super-solution and Fourier method. We also use Fourier method to prove a weighted Hardy type inequality for higher order operators. After discussing the one dimensional case, we study the Hardy inequality in higher dimensions ($d \geq 3$). In particular, we compute the asymptotic behaviour of the sharp constant in the discrete Hardy inequality, as $d \rightarrow \infty$. This is done by converting the inequality into a continuous Hardy-type inequality on a torus for functions having zero average. These continuous inequalities are new and interesting in themselves. In the second half, we focus our attention on analogues of Rearrangement inequalities on lattice graphs. We begin by analysing the situation in dimension one. We define various notions of rearrangements and prove the corresponding Polya-Szeg\H{o} inequality. These inequalities are also applied to prove some weighted Hardy inequalities on integers. Finally, we study Rearrangement inequalities (Polya-Szeg\H{o}) on general graphs, with a particular focus on lattice graphs $\mathbb{Z}^d$, for $d \geq 2$. We develop a framework to study these inequalities, using which we derive concrete results in dimension two. In particular, these results develop connections between Polya-Szeg\H{o} inequality and various isoperimetric inequalities on graphs., Comment: PhD thesis, Imperial College London, 140 pages

Temporal graph neural networks Tgnn have exhibited state-of-art performance in future-link prediction tasks. Training of these TGNNs is enumerated by uniform random sampling based unsupervised loss. During training, in the context of a positive example, the loss is computed over uninformative negatives, which introduces redundancy and sub-optimal performance. In this paper, we propose modified unsupervised learning of Tgnn, by replacing the uniform negative sampling with importance-based negative sampling. We theoretically motivate and define the dynamically computed distribution for a sampling of negative examples. Finally, using empirical evaluations over three real-world datasets, we show that Tgnn trained using loss based on proposed negative sampling provides consistent superior performance., Comment: 10 pages

Pervasive use of social media has become the emerging source for real-time information (like images, text, or both) to identify various events. Despite the rapid growth of image and text-based event classification, the state-of-the-art (SOTA) models find it challenging to bridge the semantic gap between features of image and text modalities due to inconsistent encoding. Also, the black-box nature of models fails to explain the model's outcomes for building trust in high-stakes situations such as disasters, pandemic. Additionally, the word limit imposed on social media posts can potentially introduce bias towards specific events. To address these issues, we proposed CrisisKAN, a novel Knowledge-infused and Explainable Multimodal Attention Network that entails images and texts in conjunction with external knowledge from Wikipedia to classify crisis events. To enrich the context-specific understanding of textual information, we integrated Wikipedia knowledge using proposed wiki extraction algorithm. Along with this, a guided cross-attention module is implemented to fill the semantic gap in integrating visual and textual data. In order to ensure reliability, we employ a model-specific approach called Gradient-weighted Class Activation Mapping (Grad-CAM) that provides a robust explanation of the predictions of the proposed model. The comprehensive experiments conducted on the CrisisMMD dataset yield in-depth analysis across various crisis-specific tasks and settings. As a result, CrisisKAN outperforms existing SOTA methodologies and provides a novel view in the domain of explainable multimodal event classification.

In this paper, we present a comprehensive evaluation to establish a robust and efficient framework for Lagrangian-based particle tracing using deep neural networks (DNNs). Han et al. (2021) first proposed a DNN-based approach to learn Lagrangian representations and demonstrated accurate particle tracing for an analytic 2D flow field. In this paper, we extend and build upon this prior work in significant ways. First, we evaluate the performance of DNN models to accurately trace particles in various settings, including 2D and 3D time-varying flow fields, flow fields from multiple applications, flow fields with varying complexity, as well as structured and unstructured input data. Second, we conduct an empirical study to inform best practices with respect to particle tracing model architectures, activation functions, and training data structures. Third, we conduct a comparative evaluation of prior techniques that employ flow maps as input for exploratory flow visualization. Specifically, we compare our extended model against its predecessor by Han et al. (2021), as well as the conventional approach that uses triangulation and Barycentric coordinate interpolation. Finally, we consider the integration and adaptation of our particle tracing model with different viewers. We provide an interactive web-based visualization interface by leveraging the efficiencies of our framework, and perform high-fidelity interactive visualization by integrating it with an OSPRay-based viewer. Overall, our experiments demonstrate that using a trained DNN model to predict new particle trajectories requires a low memory footprint and results in rapid inference. Following best practices for large 3D datasets, our deep learning approach using GPUs for inference is shown to require approximately 46 times less memory while being more than 400 times faster than the conventional methods., Comment: Accepted by Pacific Vis 2024

Despite the great success of Neural Radiance Fields (NeRF), its data-gathering process remains vague with only a general rule of thumb of sampling as densely as possible. The lack of understanding of what actually constitutes good views for NeRF makes it difficult to actively plan a sequence of views that yield the maximal reconstruction quality. We propose Surrogate Objectives for Active Radiance Fields (SOAR), which is a set of interpretable functions that evaluates the goodness of views using geometric and photometric visual cues - surface coverage, geometric complexity, textural complexity, and ray diversity. Moreover, by learning to infer the SOAR scores from a deep network, SOARNet, we are able to effectively select views in mere seconds instead of hours, without the need for prior visits to all the candidate views or training any radiance field during such planning. Our experiments show SOARNet outperforms the baselines with $\sim$80x speed-up while achieving better or comparable reconstruction qualities. We finally show that SOAR is model-agnostic, thus it generalizes across fully neural-implicit to fully explicit approaches., Comment: 13 pages

Deep graph generative modeling has gained enormous attraction in recent years due to its impressive ability to directly learn the underlying hidden graph distribution. Despite their initial success, these techniques, like much of the existing deep generative methods, require a large number of training samples to learn a good model. Unfortunately, large number of training samples may not always be available in scenarios such as drug discovery for rare diseases. At the same time, recent advances in few-shot learning have opened door to applications where available training data is limited. In this work, we introduce the hitherto unexplored paradigm of few-shot graph generative modeling. Towards this, we develop GSHOT, a meta-learning based framework for few-shot labeled graph generative modeling. GSHOT learns to transfer meta-knowledge from similar auxiliary graph datasets. Utilizing these prior experiences, GSHOT quickly adapts to an unseen graph dataset through self-paced fine-tuning. Through extensive experiments on datasets from diverse domains having limited training samples, we establish that GSHOT generates graphs of superior fidelity compared to existing baselines., Comment: Accepted in Learning on Graph Conference (LOG,2023),https://openreview.net/forum?id=Hy9K2WiVwW

Graph neural networks (GNNs), in general, are built on the assumption of a static set of features characterizing each node in a graph. This assumption is often violated in practice. Existing methods partly address this issue through feature imputation. However, these techniques (i) assume uniformity of feature set across nodes, (ii) are transductive by nature, and (iii) fail to work when features are added or removed over time. In this work, we address these limitations through a novel GNN framework called GRAFENNE. GRAFENNE performs a novel allotropic transformation on the original graph, wherein the nodes and features are decoupled through a bipartite encoding. Through a carefully chosen message passing framework on the allotropic transformation, we make the model parameter size independent of the number of features and thereby inductive to both unseen nodes and features. We prove that GRAFENNE is at least as expressive as any of the existing message-passing GNNs in terms of Weisfeiler-Leman tests, and therefore, the additional inductivity to unseen features does not come at the cost of expressivity. In addition, as demonstrated over four real-world graphs, GRAFENNE empowers the underlying GNN with high empirical efficacy and the ability to learn in continual fashion over streaming feature sets., Comment: 17 pages, 4 figures and 9 tables. Accepted in ICML 2023, DOI will be updated once it is available

We study Hardy inequalities for antisymmetric functions in three different settings: euclidean space, torus and the integer lattice. In particular, we show that under the antisymmetric condition the sharp constant in Hardy inequality increases substantially and grows as d^4 as d \rightarrow \infty in all cases. As a side product, we prove Hardy inequality on a domain whose boundary forms a corner at the point of singularity x=0., Comment: Minor changes

This research study investigates the efficiency of different information retrieval (IR) systems in accessing relevant information from the scientific literature during the COVID-19 pandemic. The study applies the TREC framework to the COVID-19 Open Research Dataset (CORD-19) and evaluates BM25, Contriever, and Bag of Embeddings IR frameworks. The objective is to build a test collection for search engines that tackle the complex information landscape during a pandemic. The study uses the CORD-19 dataset to train and evaluate the IR models and compares the results to those manually labeled in the TREC-COVID IR Challenge. The results indicate that advanced IR models like BERT and Contriever better retrieve relevant information during a pandemic. However, the study also highlights the challenges in processing large datasets and the need for strategies to focus on abstracts or summaries. Overall, the research highlights the importance of effectively tailored IR systems in dealing with information overload during crises like COVID-19 and can guide future research and development in this field., Comment: 7 pages, 2 figures

Let $d$ be a square-free integer and $\mathbb{Z}[\sqrt{d}]$ a quadratic ring of integers. For a given $n\in\mathbb{Z}[\sqrt{d}]$, a set of $m$ non-zero distinct elements in $\mathbb{Z}[\sqrt{d}]$ is called a Diophantine $D(n)$-$m$-tuple (or simply $D(n)$-$m$-tuple) in $\mathbb{Z}[\sqrt{d}]$ if product of any two of them plus $n$ is a square in $\mathbb{Z}[\sqrt{d}]$. Assume that $d \equiv 2 \pmod 4$ is a positive integer such that $x^2 - dy^2 = -1$ and $x^2 - dy^2 = 6$ are solvable in integers. In this paper, we prove the existence of infinitely many $D(n)$-quadruples in $\mathbb{Z}[\sqrt{d}]$ for $n = 4m + 4k\sqrt{d}$ with $m, k \in \mathbb{Z}$ satisfying $m \not\equiv 5 \pmod{6}$ and $k \not\equiv 3 \pmod{6}$. Moreover, we prove the same for $n = (4m + 2) + 4k\sqrt{d}$ when either $m \not\equiv 9 \pmod{12}$ and $k \not\equiv 3 \pmod{6}$, or $m \not\equiv 0 \pmod{12}$ and $k \not\equiv 0 \pmod{6}$. At the end, some examples supporting the existence of quadruples in $\mathbb{Z}[\sqrt{d}]$ with the property $D(n)$ for the above exceptional $n$'s are provided for $d = 10$., Comment: 18 pages. To appear in `Glasnik matemati\v{c}ki'

Monitoring water is a complex task due to its dynamic nature, added pollutants, and land build-up. The availability of high-resolu-tion data by Sentinel-2 multispectral products makes implementing remote sensing applications feasible. However, overutilizing or underutilizing multispectral bands of the product can lead to inferior performance. In this work, we compare the performances of ten out of the thirteen bands available in a Sentinel-2 product for water segmentation using eight machine learning algorithms. We find that the shortwave infrared bands (B11 and B12) are the most superior for segmenting water bodies. B11 achieves an overall accuracy of $71\%$ while B12 achieves $69\%$ across all algorithms on the test site. We also find that the Support Vector Machine (SVM) algorithm is the most favourable for single-band water segmentation. The SVM achieves an overall accuracy of $69\%$ across the tested bands over the given test site. Finally, to demonstrate the effectiveness of choosing the right amount of data, we use only B11 reflectance data to train an artificial neural network, BandNet. Even with a basic architecture, BandNet is proportionate to known architectures for semantic and water segmentation, achieving a $92.47$ mIOU on the test site. BandNet requires only a fraction of the time and resources to train and run inference, making it suitable to be deployed on web applications to run and monitor water bodies in localized regions. Our codebase is available at https://github.com/IamShubhamGupto/BandNet.

The Polya-Szeg\H{o} inequality in $\mathbb{R}^n$ states that, given a non-negative function $f:\mathbb{R}^{n} \rightarrow \mathbb{R}_{}$, its spherically symmetric decreasing rearrangement $f^*:\mathbb{R}^{n} \rightarrow \mathbb{R}_{}$ is `smoother' in the sense of $\| \nabla f^*\|_{L^p} \leq \| \nabla f\|_{L^p}$ for all $1 \leq p \leq \infty$. We study analogues on the lattice grid graph $\mathbb{Z}^2$. The spiral rearrangement is known to satisfy the Polya-Szeg\H{o} inequality for $p=1$, the Wang-Wang rearrangement satisfies it for $p=\infty$ and no rearrangement can satisfy it for $p=2$. We develop a robust approach to show that both these rearrangements satisfy the Polya-Szeg\H{o} inequality up to a constant for all $1 \leq p \leq \infty$. In particular, the Wang-Wang rearrangement satisfies $\| \nabla f^*\|_{L^p} \leq 2^{1/p} \| \nabla f\|_{L^p}$ for all $1 \leq p \leq \infty$. We also show the existence of (many) rearrangements on $\mathbb{Z}^d$ such that $\| \nabla f^*\|_{L^p} \leq c_d \cdot \| \nabla f\|_{L^p}$ for all $1 \leq p \leq \infty$.

We focus on the task of far-field 3D detection (Far3Det) of objects beyond a certain distance from an observer, e.g., $>$50m. Far3Det is particularly important for autonomous vehicles (AVs) operating at highway speeds, which require detections of far-field obstacles to ensure sufficient braking distances. However, contemporary AV benchmarks such as nuScenes underemphasize this problem because they evaluate performance only up to a certain distance (50m). One reason is that obtaining far-field 3D annotations is difficult, particularly for lidar sensors that produce very few point returns for far-away objects. Indeed, we find that almost 50% of far-field objects (beyond 50m) contain zero lidar points. Secondly, current metrics for 3D detection employ a "one-size-fits-all" philosophy, using the same tolerance thresholds for near and far objects, inconsistent with tolerances for both human vision and stereo disparities. Both factors lead to an incomplete analysis of the Far3Det task. For example, while conventional wisdom tells us that high-resolution RGB sensors should be vital for 3D detection of far-away objects, lidar-based methods still rank higher compared to RGB counterparts on the current benchmark leaderboards. As a first step towards a Far3Det benchmark, we develop a method to find well-annotated scenes from the nuScenes dataset and derive a well-annotated far-field validation set. We also propose a Far3Det evaluation protocol and explore various 3D detection methods for Far3Det. Our result convincingly justifies the long-held conventional wisdom that high-resolution RGB improves 3D detection in the far-field. We further propose a simple yet effective method that fuses detections from RGB and lidar detectors based on non-maximum suppression, which remarkably outperforms state-of-the-art 3D detectors in the far-field., Comment: WACV 2023 12 Pages, 8 Figures, 10 Tables

Image inpainting is the process of regenerating lost parts of the image. Supervised algorithm-based methods have shown excellent results but have two significant drawbacks. They do not perform well when tested with unseen data. They fail to capture the global context of the image, resulting in a visually unappealing result. We propose a novel self-supervised learning framework for image-inpainting: Weighted Self-Supervised Learning (WSSL) to tackle these problems. We designed WSSL to learn features from multiple weighted pretext tasks. These features are then utilized for the downstream task, image-inpainting. To improve the performance of our framework and produce more visually appealing images, we also present a novel loss function for image inpainting. The loss function takes advantage of both reconstruction loss and perceptual loss functions to regenerate the image. Our experimentation shows WSSL outperforms previous methods, and our loss function helps produce better results., Comment: 9 Pages, document submitted for publication at CGVCVIP 2022 - ISBN 978-989-8704-42-9

Let $d\equiv 2\pmod 4$ be a square-free integer such that $x^2 - dy^2 =- 1$ and $x^2 - dy^2 = 6$ are solvable in integers. We prove the existence of infinitely many quadruples in $\mathbb{Z}[\sqrt{d}]$ with the property $D(n)$ when $n \in \{(4m + 1) + 4k\sqrt{d}, (4m + 1) + (4k + 2)\sqrt{d}, (4m + 3) + 4k\sqrt{d}, (4m + 3) + (4k + 2)\sqrt{d}, (4m + 2) + (4k + 2)\sqrt{d}\}$ for $m, k \in \mathbb{Z}$. As a consequence, we provide few counter examples to a conjecture of Franu\v si\'c and Jadrijevi\' c (see Conjecture 1.1)., Comment: 14 Pages. To appear in 'Results in Mathematics'

ConnectX is a two-player game that generalizes the popular game Connect 4. The objective is to get X coins across a row, column, or diagonal of an M x N board. The first player to do so wins the game. The parameters (M, N, X) are allowed to change in each game, making ConnectX a novel and challenging problem. In this paper, we present our work on the implementation and modification of various reinforcement learning algorithms to play ConnectX.

Temporal graphs represent the dynamic relationships among entities and occur in many real life application like social networks, e commerce, communication, road networks, biological systems, and many more. They necessitate research beyond the work related to static graphs in terms of their generative modeling and representation learning. In this survey, we comprehensively review the neural time dependent graph representation learning and generative modeling approaches proposed in recent times for handling temporal graphs. Finally, we identify the weaknesses of existing approaches and discuss the research proposal of our recently published paper TIGGER[24]., Comment: 27 pages, 2 figures

Scanning acoustic microscopy (SAM) has been employed since microscopic images are widely used for biomedical or materials research. Acoustic imaging is an important and well-established method used in nondestructive testing (NDT), bio-medical imaging, and structural health monitoring.The imaging is frequently carried out with signals of low amplitude, which might result in leading that are noisy and lacking in details of image information. In this work, we attempted to analyze SAM images acquired from low amplitude signals and employed a block matching filter over time domain signals to obtain a denoised image. We have compared the images with conventional filters applied over time domain signals, such as the gaussian filter, median filter, wiener filter, and total variation filter. The noted outcomes are shown in this article., Comment: 3 figures

In this paper, we study the asymptotic behaviour of the sharp constant in discrete Hardy and Rellich inequality on the lattice $\mathbb{Z}^d$ as $d \rightarrow \infty$. In the process, we proved some Hardy-type inequalities for the operators $\Delta^m$ and $\nabla(\Delta^m)$ for non-negative integers $m$ on a $d$ dimensional torus. It turns out that the sharp constant in discrete Hardy and Rellich inequality grows as $d$ and $d^2$ respectively as $ d \rightarrow \infty$., Comment: minor changes: some references and remarks added

We prove that for every integer $n$, there exist infinitely many $D(n)$-triples which are also $D(t)$-triples for $t\in\mathbb{Z}$ with $n\ne t$. We also prove that there are infinitely many triples with the property $D(-1)$ in $\mathbb{Z}[i]$ which are also $D(n)$-triple in $\mathbb{Z}[i]$ for two distinct $n$'s other than $n = -1$ and these triples are not equivalent to any triple with the property $D(1)$., Comment: Comments are welcome

In this paper, we develop a theory of symmetrization on the one dimensional integer lattice. More precisely, we associate a radially decreasing function $u^*$ with a function $u$ defined on the integers and prove the corresponding Polya-Szeg\"{o} inequality. Along the way we also prove the weighted Polya-Szeg\"{o} inequality for the decreasing rearrangement on the half-line, i.e., non-negative integers. As a consequence, we prove the discrete weighted Hardy's inequality with the weight $n^\alpha$ for $1 < \alpha \leq 2$.

There has been a recent surge in learning generative models for graphs. While impressive progress has been made on static graphs, work on generative modeling of temporal graphs is at a nascent stage with significant scope for improvement. First, existing generative models do not scale with either the time horizon or the number of nodes. Second, existing techniques are transductive in nature and thus do not facilitate knowledge transfer. Finally, due to relying on one-to-one node mapping from source to the generated graph, existing models leak node identity information and do not allow up-scaling/down-scaling the source graph size. In this paper, we bridge these gaps with a novel generative model called TIGGER. TIGGER derives its power through a combination of temporal point processes with auto-regressive modeling enabling both transductive and inductive variants. Through extensive experiments on real datasets, we establish TIGGER generates graphs of superior fidelity, while also being up to 3 orders of magnitude faster than the state-of-the-art., Comment: To be published in AAAI-2022, additionally contains technical appendices/supplementary material

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under population-level constraints. These constraints are specified by additional information available in the form of auxiliary categorical node attributes. In this paper, we consider a scenario where these attributes may not be observable, but manifest as latent features of an auxiliary graph. Motivated by this, we study constrained spectral clustering with the aim of finding balanced clusters in a given \textit{similarity graph} $\mathcal{G}$, such that each individual is adequately represented with respect to an auxiliary graph $\mathcal{R}$ (we refer to this as representation graph). We propose an individual-level balancing constraint that formalizes this idea. Our work leads to an interesting stochastic block model that not only plants the given partitions in $\mathcal{G}$ but also plants the auxiliary information encoded in the representation graph $\mathcal{R}$. We develop unnormalized and normalized variants of spectral clustering in this setting. These algorithms use $\mathcal{R}$ to find clusters in $\mathcal{G}$ that approximately satisfy the proposed constraint. We also establish the first statistical consistency result for constrained spectral clustering under individual-level constraints for graphs sampled from the above-mentioned variant of the stochastic block model. Our experimental results corroborate our theoretical findings., Comment: arXiv admin note: text overlap with arXiv:2105.03714

Rule-based decision models are attractive due to their interpretability. However, existing rule induction methods often result in long and consequently less interpretable rule models. This problem can often be attributed to the lack of appropriately expressive vocabulary, i.e., relevant predicates used as literals in the decision model. Most existing rule induction algorithms presume pre-defined literals, naturally decoupling the definition of the literals from the rule learning phase. In contrast, we propose the Relational Rule Network (R2N), a neural architecture that learns literals that represent a linear relationship among numerical input features along with the rules that use them. This approach opens the door to increasing the expressiveness of induced decision models by coupling literal learning directly with rule learning in an end-to-end differentiable fashion. On benchmark tasks, we show that these learned literals are simple enough to retain interpretability, yet improve prediction accuracy and provide sets of rules that are more concise compared to state-of-the-art rule induction algorithms.

In this paper, we consider a weighted version of one-dimensional discrete Hardy inequalities with power weights of the form $n^\alpha$. We prove the inequality when $\alpha$ is an even natural number with the sharp constant and remainder terms. We also find explicit constants in standard and weighted Rellich inequalities and its higher order versions. As a by-product of this work we derive a combinatorial identity using purely analytic methods. This suggests a correlation between combinatorial identities and functional identities., Comment: Constant in the Lemma 3.5 corrected. This changed the constants in some of the main theorems; in particular the constant in Corollary 2.4 is 5/16 instead of previous incorrect value of 8/16. Few additional details added and some minor layout changes. This version appears in Journal of Fourier Analysis and Applications

We study the problem of \emph{dynamic regret minimization} in $K$-armed Dueling Bandits under non-stationary or time varying preferences. This is an online learning setup where the agent chooses a pair of items at each round and observes only a relative binary `win-loss' feedback for this pair, sampled from an underlying preference matrix at that round. We first study the problem of static-regret minimization for adversarial preference sequences and design an efficient algorithm with $O(\sqrt{KT})$ high probability regret. We next use similar algorithmic ideas to propose an efficient and provably optimal algorithm for dynamic-regret minimization under two notions of non-stationarities. In particular, we establish $\tO(\sqrt{SKT})$ and $\tO({V_T^{1/3}K^{1/3}T^{2/3}})$ dynamic-regret guarantees, $S$ being the total number of `effective-switches' in the underlying preference relations and $V_T$ being a measure of `continuous-variation' non-stationarity. The complexity of these problems have not been studied prior to this work despite the practicability of non-stationary environments in real world systems. We justify the optimality of our algorithms by proving matching lower bound guarantees under both the above-mentioned notions of non-stationarities. Finally, we corroborate our results with extensive simulations and compare the efficacy of our algorithms over state-of-the-art baselines., Comment: Accepted to International Conference on Machine Learning (ICML), 2022 [both authors contributed equally]

This paper is a contribution to the Hate Speech and Offensive Content Identification in Indo-European Languages (HASOC) 2021 shared task. Social media today is a hotbed of toxic and hateful conversations, in various languages. Recent news reports have shown that current models struggle to automatically identify hate posted in minority languages. Therefore, efficiently curbing hate speech is a critical challenge and problem of interest. We present a multilingual architecture using state-of-the-art transformer language models to jointly learn hate and offensive speech detection across three languages namely, English, Hindi, and Marathi. On the provided testing corpora, we achieve Macro F1 scores of 0.7996, 0.7748, 0.8651 for sub-task 1A and 0.6268, 0.5603 during the fine-grained classification of sub-task 1B. These results show the efficacy of exploiting a multilingual training scheme., Comment: submitted to FIRE 2021 in the HASOC-FIRE shared task on hate speech and offensive language detection

In this work, we develop a neural network based model which leverages dependency parsing to capture cross-positional dependencies and grammatical structures. With the help of linguistic signals, sentence-level relations can be correctly captured, thus improving news documents summarization performance. Empirical studies demonstrate that this simple but effective method outperforms existing works on the benchmark dataset. Extensive analyses examine different settings and configurations of the proposed model which provide a good reference to the community.

Lockdowns are one of the most effective measures for containing the spread of a pandemic. Unfortunately, they involve a heavy financial and emotional toll on the population that often outlasts the lockdown itself. This article argues in favor of ``local'' lockdowns, which are lockdowns focused on regions currently experiencing an outbreak. We propose a machine learning tool called CoviHawkes based on temporal point processes, called CoviHawkes that predicts the daily case counts for Covid-19 in India at the national, state, and district levels. Our short-term predictions ($<30$ days) may be helpful for policymakers in identifying regions where a local lockdown must be proactively imposed to arrest the spread of the virus. Our long-term predictions (up to a few months) simulate the progression of the pandemic under various lockdown conditions, thereby providing a noisy indicator for a potential third wave of cases in India. Extensive experimental results validate the performance of our tool at all levels.

In this paper we consider a weighted version of one dimensional discrete Hardy's Inequality on half-line with power weights of the form $n^\alpha$. Namely we consider: \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq c(\alpha) \sum_{n=1}^\infty \frac{|u(n)|^2}{n^2}n^\alpha \end{equation} We prove the above inequality when $\alpha \in [0,1) \cup [5,\infty)$ with the sharp constant $c(\alpha)$. Furthermore when $\alpha \in [1/3,1) \cup \{0\}$ we prove an improved version of the above inequality. More precisely we prove \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq c(\alpha) \sum_{n=1}^\infty \frac{|u(n)|^2}{n^2} n^\alpha + \sum_{k=3}^\infty b_k(\alpha) \sum_{n=2}^\infty \frac{|u(n)|^2}{n^k}n^\alpha. \end{equation} for non-negative constants $b_k(\alpha)$., Comment: minor changes in v2: corrected some typos and added some references. The paper has been accepted in the Journal of mathematical analysis and applications

Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be ``balanced'' with respect to a categorical sensitive node attribute (e.g. the race distribution in clusters must match the race distribution in the population). In this paper, we consider a setting where sensitive attributes indirectly manifest in an auxiliary \textit{representation graph} rather than being directly observed. This graph specifies node pairs that can represent each other with respect to sensitive attributes and is observed in addition to the usual \textit{similarity graph}. Our goal is to find clusters in the similarity graph while respecting a new individual-level fairness constraint encoded by the representation graph. We develop variants of unnormalized and normalized spectral clustering for this task and analyze their performance under a \emph{fair} planted partition model induced by the representation graph. This model uses both the cluster membership of the nodes and the structure of the representation graph to generate random similarity graphs. To the best of our knowledge, these are the first consistency results for constrained spectral clustering under an individual-level fairness constraint. Numerical results corroborate our theoretical findings., Comment: Accepted at NeurIPS 2022

In this paper, we address the problem of image captioning specifically for molecular translation where the result would be a predicted chemical notation in InChI format for a given molecular structure. Current approaches mainly follow rule-based or CNN+RNN based methodology. However, they seem to underperform on noisy images and images with small number of distinguishable features. To overcome this, we propose an end-to-end transformer model. When compared to attention-based techniques, our proposed model outperforms on molecular datasets.

The Dual-Frequency synthetic aperture radar (DFSAR) system manifested on the Chandrayaan-2 spacecraft represents a significant step forward in radar exploration of solid solar system objects. It combines SAR at two wavelengths (L- and S-bands) and multiple resolutions with several polarimetric modes in one lightweight ($\sim$ 20 kg) package. The resulting data from DFSAR support calculation of the 2$\times$2 complex scattering matrix for each resolution cell, which enables lunar near surface characterization in terms of radar polarization properties at different wavelengths and incidence angles. In this paper, we report on the calibration and preliminary performance characterization of DFSAR data based on the analysis of a sample set of crater regions on the Moon. Our calibration analysis provided a means to compare on-orbit performance with pre-launch measurements and the results matched with the pre-launch expected values. Our initial results show that craters in both permanently shadowed regions (PSRs) and non-PSRs that are classified as Circular Polarization Ratio (CPR)-anomalous in previous S-band radar analyses appear anomalous at L-band also. We also observe that material evolution and physical properties at their interior and proximal ejecta are decoupled. For Byrgius C crater region, we compare our analysis of dual-frequency radar data with the predicted behaviours of theoretical scattering models. If crater age estimates are available, comparison of their radar polarization properties at multiple wavelengths similar to that of the three unnamed south polar crater regions shown in this study may provide new insights into how the rockiness of craters evolves with time., Comment: 30 pages, 16 figures; accepted by The Planetary Science Journal

We consider the problem of pure exploration with subset-wise preference feedback, which contains $N$ arms with features. The learner is allowed to query subsets of size $K$ and receives feedback in the form of a noisy winner. The goal of the learner is to identify the best arm efficiently using as few queries as possible. This setting is relevant in various online decision-making scenarios involving human feedback such as online retailing, streaming services, news feed, and online advertising; since it is easier and more reliable for people to choose a preferred item from a subset than to assign a likability score to an item in isolation. To the best of our knowledge, this is the first work that considers the subset-wise preference feedback model in a structured setting, which allows for potentially infinite set of arms. We present two algorithms that guarantee the detection of the best-arm in $\tilde{O} (\frac{d^2}{K \Delta^2})$ samples with probability at least $1 - \delta$, where $d$ is the dimension of the arm-features and $\Delta$ is the appropriate notion of utility gap among the arms. We also derive an instance-dependent lower bound of $\Omega(\frac{d}{\Delta^2} \log \frac{1}{\delta})$ which matches our upper bound on a worst-case instance. Finally, we run extensive experiments to corroborate our theoretical findings, and observe that our adaptive algorithm stops and requires up to 12x fewer samples than a non-adaptive algorithm.

While deep learning is a powerful tool for natural language processing (NLP) problems, successful solutions to these problems rely heavily on large amounts of annotated samples. However, manually annotating data is expensive and time-consuming. Active Learning (AL) strategies reduce the need for huge volumes of labeled data by iteratively selecting a small number of examples for manual annotation based on their estimated utility in training the given model. In this paper, we argue that since AL strategies choose examples independently, they may potentially select similar examples, all of which may not contribute significantly to the learning process. Our proposed approach, Active$\mathbf{^2}$ Learning (A$\mathbf{^2}$L), actively adapts to the deep learning model being trained to eliminate further such redundant examples chosen by an AL strategy. We show that A$\mathbf{^2}$L is widely applicable by using it in conjunction with several different AL strategies and NLP tasks. We empirically demonstrate that the proposed approach is further able to reduce the data requirements of state-of-the-art AL strategies by an absolute percentage reduction of $\approx\mathbf{3-25\%}$ on multiple NLP tasks while achieving the same performance with no additional computation overhead., Comment: Two of the authors had published similar manuscripts on arXiv. So withdrawing this one. All further updations will be reflected at arXiv:1911.00234

E-commerce platforms consistently aim to provide personalized recommendations to drive user engagement, enhance overall user experience, and improve business metrics. Most e-commerce platforms contain multiple carousels on their homepage, each attempting to capture different facets of the shopping experience. Given varied user preferences, optimizing the placement of these carousels is critical for improved user satisfaction. Furthermore, items within a carousel may change dynamically based on sequential user actions, thus necessitating online ranking of carousels. In this work, we present a scalable end-to-end production system to optimally rank item-carousels in real-time on the Walmart online grocery homepage. The proposed system utilizes a novel model that captures the user's affinity for different carousels and their likelihood to interact with previously unseen items. Our system is flexible in design and is easily extendable to settings where page components need to be ranked. We provide the system architecture consisting of a model development phase and an online inference framework. To ensure low-latency, various optimizations across these stages are implemented. We conducted extensive online evaluations to benchmark against the prior experience. In production, our system resulted in an improvement in item discovery, an increase in online engagement, and a significant lift on add-to-carts (ATCs) per visitor on the homepage.

Crowdsourcing is a process wherein an individual or an organisation utilizes the talent pool present over the Internet to accomplish their task. The existing crowdsourcing platforms and their reputation computation are centralised and hence prone to various attacks or malicious manipulation of the data by the central entity. A few distributed crowdsourcing platforms have been proposed but they lack a robust reputation mechanism. So we propose a decentralised crowdsourcing platform having an immutable reputation mechanism to tackle these problems. It is built on top of Ethereum network and does not require the user to trust a third party for a non malicious experience. It also utilizes IOTAs consensus mechanism which reduces the cost for task evaluation significantly.

Multi-Agent Reinforcement Learning (MARL) methods find optimal policies for agents that operate in the presence of other learning agents. Central to achieving this is how the agents coordinate. One way to coordinate is by learning to communicate with each other. Can the agents develop a language while learning to perform a common task? In this paper, we formulate and study a MARL problem where cooperative agents are connected to each other via a fixed underlying network. These agents can communicate along the edges of this network by exchanging discrete symbols. However, the semantics of these symbols are not predefined and, during training, the agents are required to develop a language that helps them in accomplishing their goals. We propose a method for training these agents using emergent communication. We demonstrate the applicability of the proposed framework by applying it to the problem of managing traffic controllers, where we achieve state-of-the-art performance as compared to a number of strong baselines. More importantly, we perform a detailed analysis of the emergent communication to show, for instance, that the developed language is grounded and demonstrate its relationship with the underlying network topology. To the best of our knowledge, this is the only work that performs an in depth analysis of emergent communication in a networked MARL setting while being applicable to a broad class of problems., Comment: An abridged version of this paper has been accepted as a short paper at AAMAS 2020

Let $K$ be an imaginary quadratic field and $ \mathcal{O}_K$ be its ring of integers. A set $\{a_1, a_2, \cdots,a_m\} \subset \mathcal{O}_K\setminus\{0\}$ is called a Diophantine $m$-tuple in $\mathcal{O}_K$ with $D(-1)$ if $a_ia_j -1 = x_{ij}^2$, where $x_{ij} \in \mathcal{O}_K$ for all $i,j$ such that $1 \leq i < j \leq m$. Here we prove the non-existence of Diophantine $m$-tuples in $\mathcal{O}_K$ with $D(-1)$ for $m > 36$., Comment: 14 pages,comments are welcome

Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its effects on the dynamics of social networks. In this paper, we propose a statistical model for dynamically evolving networks, together with a variational inference approach. Our model, Neural Latent Space Model with Variational Inference, encodes edge dependencies across different time snapshots. It represents nodes via latent vectors and uses interaction matrices to model the presence of edges. These matrices can be used to incorporate multiple relations in heterogeneous networks by having a separate matrix for each of the relations. To capture the temporal dynamics, both node vectors and interaction matrices are allowed to evolve with time. Existing network analysis methods use representation learning techniques for modelling networks. These techniques are different for homogeneous and heterogeneous networks because heterogeneous networks can have multiple types of edges and nodes as opposed to a homogeneous network. Unlike these, we propose a unified model for homogeneous and heterogeneous networks in a variational inference framework. Moreover, the learned node latent vectors and interaction matrices may be interpretable and therefore provide insights on the mechanisms behind network evolution. We experimented with a single step and multi-step link forecasting on real-world networks of homogeneous, bipartite, and heterogeneous nature, and demonstrated that our model significantly outperforms existing models., Comment: Accepted at AAAI-21

Networks with node covariates offer two advantages to community detection methods, namely, (i) exploit covariates to improve the quality of communities, and more importantly, (ii) explain the discovered communities by identifying the relative importance of different covariates in them. Recent methods have almost exclusively focused on the first point above. However, the quantitative improvements offered by them are often due to complex black-box models like deep neural networks at the expense of explainability. Approaches that focus on the second point are either domain-specific or have poor performance in practice. This paper proposes explainable, domain-independent statistical models for networks with node covariates that additionally offer good quantitative performance. Our models combine the strengths of Stochastic Block Models and Restricted Boltzmann Machines to provide interpretable insights about the communities. They support both pure and mixed community memberships. Besides providing explainability, our approach's main strength is that it does not explicitly assume a causal direction between community memberships and node covariates, making it applicable in diverse domains. We derive efficient inference procedures for our models, which can, in some cases, run in linear time in the number of nodes and edges. Experiments on several synthetic and real-world networks demonstrate that our models achieve close to state-of-the-art performance on community detection and link prediction tasks while also providing explanations for the discovered communities.

While deep learning is a powerful tool for natural language processing (NLP) problems, successful solutions to these problems rely heavily on large amounts of annotated samples. However, manually annotating data is expensive and time-consuming. Active Learning (AL) strategies reduce the need for huge volumes of labeled data by iteratively selecting a small number of examples for manual annotation based on their estimated utility in training the given model. In this paper, we argue that since AL strategies choose examples independently, they may potentially select similar examples, all of which may not contribute significantly to the learning process. Our proposed approach, Active$\mathbf{^2}$ Learning (A$\mathbf{^2}$L), actively adapts to the deep learning model being trained to eliminate such redundant examples chosen by an AL strategy. We show that A$\mathbf{^2}$L is widely applicable by using it in conjunction with several different AL strategies and NLP tasks. We empirically demonstrate that the proposed approach is further able to reduce the data requirements of state-of-the-art AL strategies by $\approx \mathbf{3-25\%}$ on an absolute scale on multiple NLP tasks while achieving the same performance with virtually no additional computation overhead., Comment: Accepted in NAACL-HLT 2021

With growing consumer adoption of online grocery shopping through platforms such as Amazon Fresh, Instacart, and Walmart Grocery, there is a pressing business need to provide relevant recommendations throughout the customer journey. In this paper, we introduce a production within-basket grocery recommendation system, RTT2Vec, which generates real-time personalized product recommendations to supplement the user's current grocery basket. We conduct extensive offline evaluation of our system and demonstrate a 9.4% uplift in prediction metrics over baseline state-of-the-art within-basket recommendation models. We also propose an approximate inference technique 11.6x times faster than exact inference approaches. In production, our system has resulted in an increase in average basket size, improved product discovery, and enabled faster user check-out

Humans use language to collectively execute abstract strategies besides using it as a referential tool for identifying physical entities. Recently, multiple attempts at replicating the process of emergence of language in artificial agents have been made. While existing approaches study emergent languages as referential tools, in this paper, we study their role in discovering and implementing strategies. We formulate the problem using a voting game where two candidate agents contest in an election with the goal of convincing population members (other agents), that are connected to each other via an underlying network, to vote for them. To achieve this goal, agents are only allowed to exchange messages in the form of sequences of discrete symbols to spread their propaganda. We use neural networks with Gumbel-Softmax relaxation for sampling categorical random variables to parameterize the policies followed by all agents. Using our proposed framework, we provide concrete answers to the following questions: (i) Do the agents learn to communicate in a meaningful way and does the emergent communication play a role in deciding the winner? (ii) Does the system evolve as expected under various reward structures? (iii) How is the emergent language affected by the community structure in the network? To the best of our knowledge, we are the first to explore emergence of communication for discovering and implementing strategies in a setting where agents communicate over a network., Comment: A shorter version of this paper has been accepted as an extended abstract at AAMAS 2020

This paper describes Infosys's participation in the "2nd Social Media Mining for Health Applications Shared Task at AMIA, 2017, Task 2". Mining social media messages for health and drug related information has received significant interest in pharmacovigilance research. This task targets at developing automated classification models for identifying tweets containing descriptions of personal intake of medicines. Towards this objective we train a stacked ensemble of shallow convolutional neural network (CNN) models on an annotated dataset provided by the organizers. We use random search for tuning the hyper-parameters of the CNN and submit an ensemble of best models for the prediction task. Our system secured first place among 9 teams, with a micro-averaged F-score of 0.693., Comment: 2nd Workshop on Social Media Mining for Health

Networks observed in real world like social networks, collaboration networks etc., exhibit temporal dynamics, i.e. nodes and edges appear and/or disappear over time. In this paper, we propose a generative, latent space based, statistical model for such networks (called dynamic networks). We consider the case where the number of nodes is fixed, but the presence of edges can vary over time. Our model allows the number of communities in the network to be different at different time steps. We use a neural network based methodology to perform approximate inference in the proposed model and its simplified version. Experiments done on synthetic and real world networks for the task of community detection and link prediction demonstrate the utility and effectiveness of our model as compared to other similar existing approaches., Comment: Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19)