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Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the…
Chain-of-Thought (CoT) reasoning enhances the problem-solving ability of large language models (LLMs) but leads to substantial inference overhead, limiting deployment in resource-constrained settings. This paper investigates efficient CoT…
Grokking -- the sudden generalisation that appears long after a model has perfectly memorised its training data -- has been widely observed but lacks a quantitative theory explaining the length of the delay. We show that grokking is a…
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
Generating Chain-of-Thought (CoT) before deriving the answer can effectively improve the reasoning capabilities of large language models (LLMs) and significantly improve the accuracy of the generated answer. However, in most cases, the…
Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counterpart: the possibility of state transitions is not determined by free energy alone, but by an infinite family of free-energy-like…
We compare predictions from two familiar models of the metastable supercooled liquid respectively constructed with thermodynamic and dynamic approach. In the so called density functional theory (DFT) the free energy $F[\rho]$ of the liquid…
The Conti-Boston factorization theorem (CBFT) for linear tail-biting trellis realizations is extended to group realizations with a new and simpler proof, based on a controller granule decomposition of the behavior and known controllability…
We study the generalization of Correlation Clustering which incorporates fairness constraints via the notion of fairlets. The corresponding Fair Correlation Clustering problem has been studied from several perspectives to date, but has so…
Chain-of-Thought (CoT) empowers Large Language Models (LLMs) to tackle complex problems, but remains constrained by the computational cost and reasoning path collapse when grounded in discrete token spaces. Recent latent reasoning…
We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
The studies of collective oscillations induced by higher-order interactions point out the necessity of group effect in coupling modelization. As yet the related advances are mainly concentrated on nonlinear coupling patterns and cannot be…
Chain-of-Thought (CoT) has unlocked advanced reasoning abilities of Large Language Models (LLMs) with intermediate steps, yet incurs prohibitive computational costs due to generation of extra tokens. Recent studies empirically show that…
The production of quantum entanglement between weakly coupled mapping systems, whose classical counterparts are both strongly chaotic, is investigated. In the weak coupling regime, it is shown that time correlation functions of the…
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as…
Chain-of-Thought (CoT) prompting has improved the reasoning performance of large language models (LLMs), but it remains unclear why it works and whether it is the unique mechanism for triggering reasoning in large language models. In this…
We study the properties {of a conformal field theory} (CFT) driven periodically with a continuous protocol characterized by a frequency $\omega_D$. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic…
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and…
We analyze a renormalized perturbation expansion around the mode-coupling theory of the glass transition. We focus on the long-time limit of the irreducible memory function. We discuss a renormalized diagrammatic expansion for this function…