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Fuzzy graph-based structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models, fuzzy social networks and fuzzy interpretations in fuzzy description logics are useful in various applications. Given two states,…

We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…

The Expectation--Maximization Maximum Likelihood (EMML) algorithm belongs to the Expectation--Maximization family and is widely used for image reconstruction problems under Poisson noise.In this paper, we reinterpret EMML as a mirror…

There remains an open question about the usefulness and the interpretation of Machine learning (MLE) approaches for discrimination of spatial patterns of brain images between samples or activation states. In the last few decades, these…

This paper deals with a parametrized family of partially observed bivariate Markov chains. We establish that, under very mild assumptions, the limit of the normalized log-likelihood function is maximized when the parameters belong to the…

Many important functional and security properties--including non-interference, determinism, and generalized non-interference (GNI)--are hyperproperties, i.e., properties relating multiple executions of a program. Existing separation logics…

High-level synthesis (HLS) refers to the automatic translation of a software program written in a high-level language into a hardware design. Modern HLS tools have moved away from the traditional approach of static (compile time) scheduling…

In this paper, we introduce harmonic loss as an alternative supervisory signal for training neural networks and large language models (LLMs). Harmonic loss differs from standard cross-entropy loss by (a) replacing the usual SoftMax…

The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…

Large language models (LLMs) now achieve near-human performance on standard math word problem benchmarks (e.g., GSM8K), yet their true reasoning ability remains disputed. A key concern is that models often produce confident, yet unfounded,…

Hallucinations in large language models (LLMs) produce fluent continuations that are not supported by the prompt, especially under minimal contextual cues and ambiguity. We introduce Distributional Semantics Tracing (DST), a model-native…

Modern statistical machine translation (SMT) systems usually use a linear combination of features to model the quality of each translation hypothesis. The linear combination assumes that all the features are in a linear relationship and…

Structure-inducing Language Models (SiLM) are trained on a self-supervised language modeling task, and induce a hierarchical sentence representation as a byproduct when processing an input. SiLMs couple strong syntactic generalization…

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and…

High-level synthesis (HLS) is a widely used tool in designing Field Programmable Gate Array (FPGA). HLS enables FPGA design with software programming languages by compiling the source code into an FPGA circuit. The source code includes a…

Large Language Models (LLMs) struggle with complex Text-to-SQL queries that demand both sophisticated mathematical reasoning and intricate schema navigation. Existing methods often tackle these challenges in isolation, creating a fractured…

Semi-supervised learning (SSL) is a machine learning methodology that leverages unlabeled data in conjunction with a limited amount of labeled data. Although SSL has been applied in various applications and its effectiveness has been…

Generalized linear mixed models (GLMMs) are often used for analyzing correlated non-Gaussian data. The likelihood function in a GLMM is available only as a high dimensional integral, and thus closed-form inference and prediction are not…

Fine-grained classification of whole slide images (WSIs) is essential in precision oncology, enabling precise cancer diagnosis and personalized treatment strategies. The core of this task involves distinguishing subtle morphological…

We investigate a natural generalization to trees of Hennie machines, a known automaton model for regular string functions. Tree-to-tree Hennie machines are tree-walking tree transducers with the ability to rewrite the node labels of their…