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Transition state theory (TST) is generalized for the nonequilibrium system with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by the…

In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…

An accurate and up-to-date topology is critical for situational awareness of a power grid; however, wrong switch statuses due to physical damage, communication error, or cyber-attack, can often result in topology errors. To maintain…

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…

We present a compact dynamical mean-field theory (DMFT) for large networks of coupled phase oscillators whose phases live on the circle $S^1$ and interact with both coherent mean-field coupling and quenched randomness. Starting from wrapped…

Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…

In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based on a dimensionality reduction technique for Markov State Models, known as local-equilibrium (LE). We show that for a…

Accurate short-term mobile traffic prediction is important for proactive resource allocation and low-latency network management in fifth generation (5G) and sixth generation (6G). While large language models (LLMs) can perform in-context…

While Long Chain-of-Thought (CoT) reasoning significantly improves Large Language Models (LLMs) performance on complex reasoning tasks, the substantial computational and memory costs of generating long CoT sequences limit their efficiency…

This paper introduces a class of generalised linear models (GLMs) driven by latent processes for modelling count, real-valued, binary, and positive continuous time series. Extending earlier latent-process regression frameworks based on…

This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…

Generalization to novel compound tasks under distribution shift is important for deploying transformer-based language models (LMs). This work investigates Chain-of-Thought (CoT) reasoning as a means to enhance OOD generalization. Through…

Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics). Recently, extensions of these methods, such as the…

Large language models (LLMs) have unveiled remarkable reasoning capabilities by exploiting chain-of-thought (CoT) prompting, which generates intermediate reasoning chains to serve as the rationale for deriving the answer. However, current…

Squeeze-and-Excitation (SE) block presents a channel attention mechanism for modeling global context via explicitly capturing dependencies across channels. However, we are still far from understanding how the SE block works. In this work,…

We develop a geometric account of sequence modelling that links patterns in the data to measurable properties of the loss landscape in transformer networks. First, we cast conditional sequence distributions into a Hilbert-space framework…

Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…

Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…

With an increasing influx of classical signal processing methodologies into the field of graph signal processing, approaches grounded in discrete linear canonical transform have found application in graph signals. In this paper, we…