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We construct a bipartite generalization of Alon and Szegedy's nearly orthogonal vectors, thereby obtaining strong bounds for several extremal problems involving the Lov\'asz theta function, vector chromatic number, minimum semidefinite rank, nonnegative rank, and extension complexity of polytopes. In particular, we derive a couple of general lower bounds for the vector chromatic number which may be of independent interest.

We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. Though the described Bayesian computational framework is general, we look at a specific application to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the three compartments, and two parameters which control the coupling among the states. The deterministic SIR model with time-invariant parameters has shown to be overly simplistic for modelling the complex long-term dynamics of diseases transmission. Recognizing that certain model parameters will naturally vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects, the estimation procedure must systematically permit these time-varying effects to be captured, without unduly introducing artificial dynamics into the system. To this end, we leverage the robustness of the Markov Chain Monte Carlo (MCMC) algorithm for the estimation of time-invariant parameters alongside nonlinear filters for the joint estimation of the system state and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario.

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

Augmented Reality (AR) has emerged as a significant advancement in surgical procedures, offering a solution to the challenges posed by traditional neuronavigation methods. These conventional techniques often necessitate surgeons to split their focus between the surgical site and a separate monitor that displays guiding images. Over the years, many systems have been developed to register and track the hologram at the targeted locations, each employed its own evaluation technique. On the other hand, hologram displacement measurement is not a straightforward task because of various factors such as occlusion, Vengence-Accomodation Conflict, and unstable holograms in space. In this study, we explore and classify different techniques for assessing an AR-assisted neurosurgery system and propose a new technique to systematize the assessment procedure. Moreover, we conduct a deeper investigation to assess surgeon error in the pre- and intra-operative phases of the surgery based on the respective feedback given. We found that although the system can undergo registration and tracking errors, physical feedback can significantly reduce the error caused by hologram displacement. However, the lack of visual feedback on the hologram does not have a significant effect on the user 3D perception.

We propose a learning-based compression scheme that envelopes a standard codec between pre and post-processing deep CNNs. Specifically, we demonstrate improvements over prior approaches utilizing a compression-decompression network by introducing: (a) an edge-aware loss function to prevent blurring that is commonly occurred in prior works & (b) a super-resolution convolutional neural network (CNN) for post-processing along with a corresponding pre-processing network for improved rate-distortion performance in the low rate regime. The algorithm is assessed on a variety of datasets varying from low to high resolution namely Set 5, Set 7, Classic 5, Set 14, Live 1, Kodak, General 100, CLIC 2019. When compared to JPEG, JPEG2000, BPG, and recent CNN approach, the proposed algorithm contributes significant improvement in PSNR with an approximate gain of 20.75%, 8.47%, 3.22%, 3.23% and 24.59%, 14.46%, 10.14%, 8.57% at low and high bit-rates respectively. Similarly, this improvement in MS-SSIM is approximately 71.43%, 50%, 36.36%, 23.08%, 64.70% and 64.47%, 61.29%, 47.06%, 51.52%, 16.28% at low and high bit-rates respectively. With CLIC 2019 dataset, PSNR is found to be superior with approximately 16.67%, 10.53%, 6.78%, and 24.62%, 17.39%, 14.08% at low and high bit-rates respectively, over JPEG2000, BPG, and recent CNN approach. Similarly, the MS-SSIM is found to be superior with approximately 72%, 45.45%, 39.13%, 18.52%, and 71.43%, 50%, 41.18%, 17.07% at low and high bit-rates respectively, compared to the same approaches. A similar type of improvement is achieved with other datasets also.

In this work we extend the shifted Laplacian approach to the elastic Helmholtz equation. The shifted Laplacian multigrid method is a common preconditioning approach for the discretized acoustic Helmholtz equation. In some cases, like geophysical seismic imaging, one needs to consider the elastic Helmholtz equation, which is harder to solve: it is three times larger and contains a nullity-rich grad-div term. These properties make the solution of the equation more difficult for multigrid solvers. The key idea in this work is combining the shifted Laplacian with approaches for linear elasticity. We provide local Fourier analysis and numerical evidence that the convergence rate of our method is independent of the Poisson's ratio. Moreover, to better handle the problem size, we complement our multigrid method with the domain decomposition approach, which works in synergy with the local nature of the shifted Laplacian, so we enjoy the advantages of both methods without sacrificing performance. We demonstrate the efficiency of our solver on 2D and 3D problems in heterogeneous media.

Data is a cornerstone for fine-tuning large language models, yet acquiring suitable data remains challenging. Challenges encompassed data scarcity, linguistic diversity, and domain-specific content. This paper presents lessons learned while crawling and refining data tailored for fine-tuning Vietnamese language models. Crafting such a dataset, while accounting for linguistic intricacies and striking a balance between inclusivity and accuracy, demands meticulous planning. Our paper presents a multidimensional strategy including leveraging existing datasets in the English language and developing customized data-crawling scripts with the assistance of generative AI tools. A fine-tuned LLM model for the Vietnamese language, which was produced using resultant datasets, demonstrated good performance while generating Vietnamese news articles from prompts. The study offers practical solutions and guidance for future fine-tuning models in languages like Vietnamese.

Novel categories are commonly defined as those unobserved during training but present during testing. However, partially labelled training datasets can contain unlabelled training samples that belong to novel categories, meaning these can be present in training and testing. This research is the first to generalise between what we call observed-novel and unobserved-novel categories within a new learning policy called open-set learning with augmented category by exploiting unlabelled data or Open-LACU. After surveying existing learning policies, we introduce Open-LACU as a unified policy of positive and unlabelled learning, semi-supervised learning and open-set recognition. Subsequently, we develop the first Open-LACU model using an algorithmic training process of the relevant research fields. The proposed Open-LACU classifier achieves state-of-the-art and first-of-its-kind results.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

In recent years, object detection has experienced impressive progress. Despite these improvements, there is still a significant gap in the performance between the detection of small and large objects. We analyze the current state-of-the-art model, Mask-RCNN, on a challenging dataset, MS COCO. We show that the overlap between small ground-truth objects and the predicted anchors is much lower than the expected IoU threshold. We conjecture this is due to two factors; (1) only a few images are containing small objects, and (2) small objects do not appear enough even within each image containing them. We thus propose to oversample those images with small objects and augment each of those images by copy-pasting small objects many times. It allows us to trade off the quality of the detector on large objects with that on small objects. We evaluate different pasting augmentation strategies, and ultimately, we achieve 9.7\% relative improvement on the instance segmentation and 7.1\% on the object detection of small objects, compared to the current state of the art method on MS COCO.