Abstract

Despite its successful predictions, the Standard Model (SM) is not a complete theory. There are theoretical issues and experimental observations that it cannot explain. Over the years, experimental measurements of several observables have shown deviations from their SM-predicted values. For instance, the latest measurement of the anomalous magnetic moment of the muon (g − 2)µ by Fermilab shows a deviation of 4.2σ. There is a discrepancy of 7σ between the SM value and the experimentally observed value of the W boson mass as reported by the CDF collaboration. The SM shows lepton-flavour universality (LFU), i.e., the couplings of leptons to the gauge bosons are flavour independent in the SM. However, the measurements of the leptonic decays of B-mesons at BaBar, Belle, and LHCb indicate some LFU violations. These deviations are popularly referred to as B-anomalies—those seen in the RD(∗) and RK(∗) observables are some of the well-known examples. Until recently, the experimental values of RD and RD∗ exceeded their SM predictions by 1.4σ and 2.5σ, respectively. On the other hand, the deviations in the RK and RK∗ measurements were smaller than the theoretical predictions by about 3.1σ. The current measurement of RD still stands 2σ away from the SM, putting the global average of RD(∗) (combined) at 3.2σ. The deviations in the measurement of (g −2)µ, W boson mass anomaly and the B-anomalies led to numerous beyond the Standard Model (BSM) explanations in the literature. Among these, the most popular ones involve a class of hypothetical particles known as the Leptoquarks (LQs). LQs are scalar (sLQ) or vector (vLQ) bosons that are electromagnetically charged. They are colour triplets with nonzero lepton numbers. They can form various weak representations—singlet, doublet or triplet. They appear in theories such as R-parity violating Supersymmetry, SU(5) Grand Unified Theories, Pati-Salam models, Technicolour models, etc. The LHC has an active LQ-search program. Their connections to the lepton and colour sector make them ideal candidates for resolving the above anomalies. In this thesis, we study the phenomenology of TeV-scale LQs, especially of the models proposed to address the anomalies and investigate their current status. We obtain the latest bounds from low-energy observables and the latest LHC data. Many of these LQ models involve sizable cross-generational LQ-lepton-quark couplings, leading to exotic decay modes of LQs. We estimate the discovery/exclusion prospects of all possible LQs in some interesting or new channels at the high-luminosity LHC (HL-LHC)

Abstract

A large number of important mathematical problems do not have perfect solutions which can be computed in a polynomial time. The solution to these problems is often calculated by using polynomial time heuristic algorithms which produce solve the problem with some approximation. If the matrix algorithm can be effectively formulated as a game, reinforcement learning can be used instead of the usual heuristics to improve the quality of the approximation. One such problem is to reduce the fill-in produced during matrix decomposition. A large number of computational and scientific methods commonly require decomposing a sparse matrix into triangular factors as LU decomposition. A common problem that is faced during this decomposition is that even though the given matrix may be very sparse, the decomposition may lead to a denser triangular factors due to fill-in. A significant fill-in may lead to prohibitively larger computational costs and memory requirement during decomposition as well as during the solve phase. To this end, several heuristic sparse matrix reordering methods have been proposed to reduce fill-in before the decomposition. However, finding an optimal reordering algorithm that leads to minimal fill-in during such decomposition is known to be a NP-hard problem. A reinforcement learning based approach is proposed for this problem. The sparse matrix reordering problem is formulated as a single player game. More specifically, Monte-Carlo tree search in combination with a neural network is used as a decision making algorithm to search for the best move in our game. The proposed method, Alpha Elimination was found to produce significantly lesser non-zeros in the LU decomposition as compared to existing state-of-the-art heuristic algorithms with little to no increase in overall running time of the algorithm. In addition to the main problem of the thesis, work was also conducted in the field of extreme classification. In this area, a fast algorithm called LightDXML was developed to solve the problem of extreme classification at scale

Abstract

Recent developments in neural text-to-speech synthesis (NTTS) have been able to produce highquality human-like speech samples. However, these models require large amounts of studio-quality recordings for training. As a result, training NTTS models to serve multiple speakers and styles is resource intensive, both in terms of time and compute costs. In this thesis, we discuss the data-efficiency methods for training an NTTS acoustic model with limited data. We explore several data-efficiency techniques for speaker and style modelling with limited data. We discuss multi-speaker training for NTTS model with limited data for each speaker, and speaker adaptation for fine-tuning a pre-trained multi-speaker NTTS model with few minutes of training data for the target speaker. Controllability is TTS systems refers to the ability of explicitly controlling the prosodic variations of the synthesised speech. We explore controllability in NTTS with latent-variable conditioning with variational autoencoders (VAE). These can be used for one-shot style transfer from a reference speech sample. We further discuss improving the posterior flexibility of latent-variable from VAE using normalising flows. We adapt the multi-speaker training strategy to generate newscaster style speech with limited stylistic training data. We first analyse prosodic variations in the neutral style, newscaster style, and mixed expressive corpora. From this, we conclude that the newscaster style is more dynamic than the neutral style, however with lower dynamic range and prosodic variations than a mixed expressive corpora containing recordings with different emotions. The problem of generating newscaster style of speech with limited training data is posed as that of creating a bi-style model in which a one-hot style ID can be modified to generate either neutral or newscaster style speech. We only use a quarter of the data for newscaster style as opposed to that of neutral style. Combining the two styles gives the model enough volume of training data to learn the textual and acoustic alignments, while only a fractional amount of stylistic data is required to factorise the two styles. To further improve on the naturalness, we condition the NTTS acoustic model with contextualised word embeddings (CWE). This gives the model additional syntactic and semantic context on the input text. The proposed bi-style NTTS model conditioned is shown to improve on naturalness and styleappropriateness for newscaster speech over both neutral NTTS and concatenative systems in MUSHRA evaluations conducted with expert listeners.

Abstract

This thesis presents research on deep learning optimization, emphasizing three separate yet related topics: adaptive learning rates, first-order optimization for generative adversarial networks (GANs), and the effects of label smoothing. Firstly, we propose a novel approach for obtaining adaptive learning rates in gradientbased descent methods for classification tasks. Departing from traditional methods that rely on decayed expectations of gradient-based terms, our approach leverages the angle between the current gradient and a new gradient computed from the orthogonal direction. By incorporating angle history, we determine adaptive learning rates that lead to superior accuracy compared to existing state-of-the-art optimizers. We provide empirical evidence of convergence and evaluate our approach on diverse benchmark datasets, employing prominent image classification architectures. Secondly, we introduce a groundbreaking first-order optimization method tailored specifically for training GANs. Our method builds upon the Gauss-Newton method, approximating the min-max Hessian, and utilizes the Sherman-Morrison inversion formula to calculate the inverse. Operating as a fixed-point method that ensures necessary contraction, our approach produces high-fidelity images with enhanced diversity across multiple datasets. Notably, it outperforms state-of-the-art second-order methods, including achieving the highest inception score for CIFAR10. Additionally, our method demonstrates comparable execution times to first-order min-max methods. Furthermore, we investigate the effects of label smoothing on GAN training, examining various optimizer variants and learning rates. Our research reveals that employing label smoothing with a high learning rate and the CGD optimizer yields results surpassing the quality attained by using ADAM with the same learning rate. Importantly, we establish that label smoothing plays a vital role, as its absence fails to generate comparable results. We also explore the impact of architectural changes on the generator’s conditioning, providing valuable insights into the factors influencing GAN performance Our research advances the deep learning optimization field by delving into these interconnected areas. We present novel methodologies for adaptive learning rates, first-order optimization for GANs, and the importance of label smoothing. These advancements offer improved accuracy in classification tasks, enhanced image generation quality, and a deeper understanding of the nuances of GAN training.

Abstract

Scientific applications like aircraft-design and machine-learning algorithms involve solving a system of linear equations. LU decomposition is helpful if the system needs to be solved repeatedly for the same Coefficient matrix but for different Constants of a Linear Equation. It also aids in other matrix operations, such as computing the determinant and inverse of a matrix. This thesis proposes an architecture of hardware accelerator for computing the LU decomposition of an input matrix. Our accelerator consists of two simple linear arrays of Processing Engines (PEs), one on each of the two SLR regions of the FPGA. All the computations arising from the block LU decomposition are simplified and scheduled on these two PE arrays. On an Alveo U50 FPGA, our design achieves a peak floating-point performance of 128 GLOPS/s and an average performance of 95 GFLOPS/s. We achieve ≈ 15× speedup on latency compared to an Intel MKL implementation on a 4-core Intel Xeon CPU.

Abstract

In this thesis two problems have been considered. The first one is related to the structure of higher order MDS codes which are a generalization of traditional MDS codes and the second one is related to distributed multi-user secret sharing. When data is transmitted over noisy channels, errors can occur, corrupting the received information. Traditional error-correcting codes like Reed-Solomon or Hamming codes are designed to correct a specific number of errors. However, they have a limitation that they can only correct up to a certain number of errors beyond which they fail to recover the original message. In many scenarios, such as wireless communication or storage systems, the number of errors can be quite high, and standard error-correction techniques might not be sufficient. This is where list decoding, proposed independently by Elias and Wozencraft, comes into play. Instead of trying to pinpoint the exact original message, list decoding provides a list of possible messages that could have been transmitted. By doing so, it offers a more flexible and robust approach to error correction, allowing for a higher number of correctable errors. The decoding radius is the maximum number of errors that can be corrected by the code. By increasing the decoding radius and allowing for a list of possible codewords, list decodable codes can handle a higher number of errors and provide a more robust approach to error correction. In a recent work by Shangguan and Tamo, an upper bound on the size of a list deocodable codes, called the Generalized Singleton bound, is derived for a given list size and decoding radius. The codes which meet this bound with equality are optimally list decodable codes. In our first problem, we study a recently introduced class of higher order MDS codes which are closely related to the optimally list decodable codes. For certain parameter regimes, we identify conditions under which performing expurgation and shortening (see Section 2.2) like operations on the higher order MDS codes based on Reed-Solomon codes obtained using Vandermonde matrix results in new higher order MDS codes with a related set of parameters. More specifically, we identify the conditions under which (n1, k1)-MDS(ℓ1) codes can be obtained from (n2, k2)-MDS(ℓ2) codes via various techniques where (n, k)-MDS(ℓ) codes denote higher order MDS codes of length n, dimension k and order ℓ ≥ 1. We also obtain a new field size upper bound for the existence of such codes which arguably improves over the best known existing bound in some parameter regimes. We believe that these results will aid in efficient constructions of higher order MDS codes. In the second problem, we focus on a Distributed Multi-User Secret Sharing (DMUSS) problem. Distributed Multi-User Secret Sharing is motivated by the need for secure and efficient ways to share sensitive information among multiple users in a decentralized manner. The traditional secret sharing scheme involves a single dealer dividing a secret into shares and distributing them among a group of users. However, this centralized approach has limitations, especially when dealing with large-scale systems or scenarios with multiple secrets and a large number of users. In DMUSS, each user can request access to a specific subset of secrets. This access control mechanism ensures that users only gain access to the secrets they are authorized to see. In this thesis we consider a DMUSS setting involving a dealer, n storage nodes and m secrets. Each user requests a subset of t out of the m secrets. Previous work in this setting addressed the case of t = 1 which we extend to handle general values of t. The users download shares from storage nodes based on the access structure and reconstruct their secrets. We establish a necessary condition on the access structure to ensure certain privacy conditions. Additionally, we establish a connection between access structures and disjunct matrices which are majorly used in the Group testing. In the Distributed Secret Sharing Protocol proposed for our setting, we utilize various disjunct matrix constructions and compare their performance in terms of the number of storage nodes and communication complexity. Moreover, we derive bounds on the optimal communication complexity of a distributed secret sharing protocol.

Abstract

Autonomous camera systems are vital in capturing dynamic events and creating engaging videos. However, existing filtering techniques used to stabilize and smoothen camera trajectories often fail to replicate the natural behavior of human camera operators. To address these challenges, our work proposes novel approaches for real-time camera trajectory optimization and gaze-guided video editing. We introduce two online filtering methods: CineConvex and CineCNN. CineConvex utilizes a sliding window-based convex optimization formulation, while CineCNN employs a convolutional neural network as an encoder-decoder model. Both methods are motivated by cinematographic principles, producing smooth and natural camera trajectories. Evaluation of basketball and stage performance datasets demonstrates superior performance over previous methods and baselines, both quantitatively and qualitatively. With a minor latency of half a second, CineConvex operates at approximately 250 frames per second (fps), while CineCNN achieves an impressive speed of 1000 fps, making them highly suitable for real-time applications. In the realm of video editing, we present Real Time GAZED, a real-time adaptation of the GAZED framework. It enables users to create professionally edited videos in real-time. Comparative evaluations against baseline methods, including the non-real-time GAZED, demonstrate that Real Time GAZED achieves similar editing results, ensuring high-quality video output. Furthermore, a user study confirms the aesthetic quality of the video edits produced by Real Time GAZED. With the advancements in real-time camera trajectory optimization and video editing presented, the demand for immediate and dynamic content creation in industries such as live broadcasting, sports coverage, news reporting, and social media content creation can be met more efficiently. The elimination of time-consuming post-production processes and the ability to deliver high-quality videos in today’s fast-paced digital landscape are the key advantages offered by these real-time approaches

Abstract

This thesis delves into the critical field of Domain Generalization (DG) in machine learning, where models are trained on multiple source distributions with the objective of generalizing to unseen tar- get distributions. We begin by dissecting various facets of DG, including distribution shifts, shortcut learning, representation learning, and data imbalances. This foundational investigation sets the stage for understanding the challenges associated with DG and the complexities that arise. A comprehensive literature review is conducted, highlighting existing challenges and contextualizing our contributions to the field. The review encompasses learning invariant features, parameter sharing techniques, meta-learning techniques, and data augmentation approaches. One of the key contributions of this thesis is the examination of the role low-dimensional representa- tions play in enhancing DG performance. We introduce a method to compute the implicit dimensionality of latent representations, exploring its correlation with performance in a domain generalization context. This essential finding motivated us to further investigate the effects of low-dimensional representations. Building on these insights, we present Cross-Domain Class-Contrastive Learning (CDCC), a tech- nique that learns sparse representations in the latent space, resulting in lower-dimensional represen- tations and improved domain generalization performance. CDCC establishes competitive results on various DG benchmarks, comparing favorably with numerous existing approaches in DomainBed. Venturing beyond traditional DG, we discuss a series of experiments conducted for domain general- ization in long-tailed settings, which are common in real-world applications. Additionally, we present supplementary experiments yielding intriguing findings. Our analysis reveals that the CDCC approach exhibits greater robustness in long-tailed distributions and that the order of performances across test do- mains remains unaffected by the order of training domains in the long-tailed setting. This section aims to inspire researchers to further probe the outcomes of these experiments and advance the understanding of domain generalization. In conclusion, this thesis offers a well-rounded exploration of DG by combining a comprehensive literature review, the discovery of the importance of low-dimensional representations in DG, the devel- opment of the CDCC method, and the meticulous analysis of long-tailed settings and other experimental findings.

Abstract

We address the problem of achieving fair and efficient allocation of resources in the era of rapid technological advancements, including Artificial Intelligence (AI) and the Internet of Things (IoT). The allocation of resources among autonomous agents is a crucial problem, and achieving fairness while ensuring efficiency is challenging. The objective is to determine the best way to divide resources among interested agents so that everyone is happy with their allocation, while ensuring fairness. We explore various fairness notions and relaxations that could apply to the problem of resource allocation. One of the main issues addressed in the thesis is the challenge of achieving fairness in the allocation of indivisible resources. We address several critical questions related to fair division, such as how to ensure fairness, how to generalize the notion of fairness, and what criteria to choose for different contexts. On top of it, fair division for goods and chores requires different approaches. We examine this issue in more detail and survey the existing approaches and provide solutions to overcome the challenges. We provide a detail survey on fairness notion and their approximate relaxations and evaluates their effectiveness in achieving fair and efficient allocations. In recent literature, researchers have delved into data-driven approaches in game theory and mechanism design to tackle the challenges of traditional approaches. Given the success of neural networks (NNs) in learning algorithms, and mechanisms, and solving mixedinteger programs, they offer a promising tool for achieving fair and efficient allocations of resources. Thus, we aim to use NNs to find an approximate fair allocation that maximizes social welfare in our pursuit of equitable and efficient resource distribution. Another criticaL issue addressed in the thesis is the presence of externalities, where the utility of an agent depends not only on their allocated resources but also on the resources allocated to other agents. Such scenarios are prevalent, especially in allocating critical resources such as hospital beds, ventilators, and vaccines during the COVID-19 pandemic. We evaluate the challenges of achieving fair and efficient allocations in the presence of externalities and propose potential solutions. Overall, in this thesis, we provide a comprehensive analysis of the challenges of achieving fair and efficient allocation of resources in the era of rapid technological advancements. The research proposes efficient algorithms and solutions to overcome the challenges and achieve approximately fair allocation in different contexts. Achieving fair and efficient resource allocation is crucial for various domains, including economics, politics, and social welfare, and the results of this could have significant implications in these domains.

Abstract

Global access to electricity has increased from 78.2% to 2000 to 90.5% in 2020, resulting in an increased electricity demand worldwide. Residential energy feedback is about providing personalized information on household energy use to consumers to encourage energy saving. Unlike commercial electricity consumption, which is managed by professionals, residential consumption is managed by the householders, who often lack insight into their energy usage. Quality feedback, including detailed energy consumption and tips, can lead to substantial household savings. There are several mediums for providing energy feedback, such as Short Message Service (SMS), postal letter, email, mobile app, and In-Home Display (IHD). Studies suggest that feedback through electronic media, like IHD, can save up to 20% of energy consumption. In this work, we aim to design mobile application interfaces that can maximize energy savings through effective feedback. The level of savings realized is dependent on the user’s preferences and understanding of the information presented. User preferences are subjective of their profile (e.g., age, occupation, income) and the cultural context (e.g., country). It is assumed that the possibility of energy reduction is high when the provided information matches the user’s display preferences. Despite the growing demand for quality energy feedback in India, we lack research that examines the Indian population perspective on energy feedback display user interface (UI) design. We conducted two questionnaire-based surveys, one to understand users’ preferences for feedback information and another to validate the designed mobile application interface screens. The surveys were conducted on two age groups, young and middle-aged adults. A Chi-Square Test of Independence was performed to assess the relationship between the user’s preference for feedback information and their age group. Participants identified total energy consumption, appliance level disaggregated information, energy-saving tips, goals, and historical consumption comparisons as the top five information types. In contrast, the normative comparison was the least preferred information. The follow-up design validations suggest that the interface should be customizable to accommodate the varying preferences of users. The current findings will help customize the energy feedback display UI design as per the Indian population.