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General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…
Nonnegative Tucker Factorization (NTF) minimizes the euclidean distance or Kullback-Leibler divergence between the original data and its low-rank approximation which often suffers from grossly corruptions or outliers and the neglect of…
As a probabilistic modeling technique, the flow-based model has demonstrated remarkable potential in the field of lossless compression \cite{idf,idf++,lbb,ivpf,iflow},. Compared with other deep generative models (eg. Autoregressive, VAEs)…
How to reduce compute and memory requirements of neural networks (NNs) without sacrificing performance? Many recent works use sparse Mixtures of Experts (MoEs) to build resource-efficient large language models (LMs). Here we introduce…
Obtaining a non-trivial (super-linear) lower bound for computation of the Fourier transform in the linear circuit model has been a long standing open problem for over 40 years. An early result by Morgenstern from 1973, provides an $\Omega(n…
We identify two orthogonal sources of structural entropy in rattler-free granular systems - affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…
The asymptotic behavior for entropy numbers of general Fourier multiplier operators of multiple series with respect to an abstract complete orthonormal system $\{\phi_{\textbf{m}}\}_{\textbf{m}\in \mathbb{N}^d_0}$ on a probability space and…
We address the generic problem of extracting the scaling exponents of a stationary, self-affine process realised by a timeseries of finite length, where information about the process is not known a priori. Estimating the scaling exponents…
Automating the Extract Method refactoring (EMR) remains challenging and largely manual despite its importance in improving code readability and maintainability. Recent advances in open-source, resource-efficient Large Language Models (LLMs)…
A technique of lossless compression via substring enumeration (CSE) attains compression ratios as well as popular lossless compressors for one-dimensional (1D) sources. The CSE utilizes a probabilistic model built from the circular string…
The number of random bits required to approximate a target distribution in terms of un-normalized informational divergence is considered. It is shown that for a variable-to-variable length encoder, this number is lower bounded by the…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
In this paper, new inner and outer bounds on the achievable compression-equivocation rate region for generalized secure data compression with side information are given that do not match in general. In this setup, two senders, Alice and…
Constructing explicit RIP matrices is an open problem in compressed sensing theory. In particular, it is quite challenging to construct explicit RIP matrices that break the square-root bottleneck. On the other hand, providing explicit…
Entropy or randomness represents a foundational security property in security-related operations, such as key generation. Key generation in turn is central to security protocols such as authentication and encryption. Physical unclonable…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
We consider estimation and inference in a linear model with endogenous regressors where the parameters of interest change across two samples. If the first-stage is common, we show how to use this information to obtain more efficient…
A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources.…