Related papers: Demystifying the characterization of SDP matrices …
This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive…
We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…
We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to…
While teaching introductory programming courses for over a decade in reputed institutions we have experienced that several factors play significant role in developing problem solving skills and program development skills in students. There…
Sentence embeddings are central to modern NLP and AI systems, yet little is known about their internal structure. While we can compare these embeddings using measures such as cosine similarity, the contributing features are not…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet…
Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
We investigate a geometric computational framework, called the "scaling-rotation framework", on ${\rm Sym}^+(p)$, the set of $p \times p$ symmetric positive-definite (SPD) matrices. The purpose of our study is to lay geometric foundations…
Statistical shape modeling (SSM) characterizes anatomical variations in a population of shapes generated from medical images. SSM requires consistent shape representation across samples in shape cohort. Establishing this representation…
Word-embeddings are vital components of Natural Language Processing (NLP) models and have been extensively explored. However, they consume a lot of memory which poses a challenge for edge deployment. Embedding matrices, typically, contain…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…
This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of…
Intrinsic image decomposition is an important and long-standing computer vision problem. Given an input image, recovering the physical scene properties is ill-posed. Several physically motivated priors have been used to restrict the…
We propose a method for learning disentangled representations of texts that code for distinct and complementary aspects, with the aim of affording efficient model transfer and interpretability. To induce disentangled embeddings, we propose…
Common programming tools, like compilers, debuggers, and IDEs, crucially rely on the ability to analyse program code to reason about its behaviour and properties. There has been a great deal of work on verifying compilers and static…