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Master equations are of fundamental importance in modeling stochastic dynamical systems.However, solving master equations is challenging due to the exponential increase in the number of possible states or trajectories with the dimension of…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

We present a method for approximating context-free languages with one-counter automata. This approximation allows the reconstruction of parse trees of the original grammar. We identify a decidable superset of regular languages whose…

Large language models have been shown to suffer from reasoning inconsistency issues. That is, they fail more in situations unfamiliar to the training data, even though exact or very similar reasoning paths exist in more common cases that…

The identification and classification of transitions in topological and microstructural regimes in pattern-forming processes are critical for understanding and fabricating microstructurally precise novel materials in many application…

Although supervised deep learning has revolutionized speech and audio processing, it has necessitated the building of specialist models for individual tasks and application scenarios. It is likewise difficult to apply this to dialects and…

Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…

The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in…

The utilization of speech Self-Supervised Learning (SSL) models achieves impressive performance on Automatic Speech Recognition (ASR). However, in low-resource language ASR, they encounter the domain mismatch problem between pre-trained and…

Human conversations can evolve in many different ways, creating challenges for automatic understanding and summarization. Goal-oriented conversations often have meaningful sub-dialogue structure, but it can be highly domain-dependent. This…

Advances in natural language processing tasks have gained momentum in recent years due to the increasingly popular neural network methods. In this paper, we explore deep learning techniques for answering multi-step reasoning questions that…

Phonotactic constraints can be employed to distinguish languages by representing a speech utterance as a multinomial distribution or phone events. In the present study, we propose a new learning mechanism based on subspace-based…

The advent of deep learning has led to a significant gain in machine translation. However, most of the studies required a large parallel dataset which is scarce and expensive to construct and even unavailable for some languages. This paper…

There have been multiple recent proposals on using deep neural networks for code search using natural language. Common across these proposals is the idea of $\mathit{embedding}$ code and natural language queries, into real vectors and then…

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…

Natural language processing (NLP) can be done using either top-down (theory driven) and bottom-up (data driven) approaches, which we call mechanistic and phenomenological respectively. The approaches are frequently considered to stand in…

When a system sends messages through a lossy channel, then the language encoding all sequences of messages can be abstracted by its downward closure, i.e. the set of all (not necessarily contiguous) subwords. This is useful because even if…

This report is a survey of the relationships between various state-of-the-art neural network architectures and formal languages as, for example, structured by the Chomsky Language Hierarchy. Of particular interest are the abilities of a…

We present a language independent, unsupervised method for building word embeddings using morphological expansion of text. Our model handles the problem of data sparsity and yields improved word embeddings by relying on training word…

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…