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We provide some constructions using Lagrangian cobordisms which improve known examples for some symplectic squeezing problems. Additionally, we prove a flexibility result that Lagrangian submanifolds which are Lagrangian isotopic are also…

The performance of large language models (LLMs) has recently improved to the point where models can perform well on many language tasks. We show here that--for the first time--the models can also generate valid metalinguistic analyses of…

Large language models (LLMs) can support democratic deliberation at scales previously constrained by turn-taking and facilitation bandwidth. Recent work shows that LLM-generated group statements are often preferred over human-mediated…

Recent years have witnessed remarkable progress made in large language models (LLMs). Such advancements, while garnering significant attention, have concurrently elicited various concerns. The potential of these models is undeniably vast;…

Artificial intelligence (AI) has achieved human-level performance in specialized tasks such as Go, image recognition, and protein folding, raising the prospect of an AI singularity-where machines not only match but surpass human reasoning.…

The planning ability of Large Language Models (LLMs) has garnered increasing attention in recent years due to their remarkable capacity for multi-step reasoning and their ability to generalize across a wide range of domains. While some…

This work presents an analytical framework for the design and analysis of LLM-based algorithms, i.e., algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of…

Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…

Multimodal Large Language Models (MLLMs) combine the natural language understanding and generation capabilities of LLMs with perception skills in modalities such as image and audio, representing a key advancement in contemporary AI. This…

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover.

Developments in the field of Artificial Intelligence (AI), and particularly large language models (LLMs), have created a 'perfect storm' for observing 'sparks' of Artificial General Intelligence (AGI) that are spurious. Like simpler models,…

This paper investigates Large Language Models (LLMs) ability to assess the economic soundness and theoretical consistency of empirical findings in spatial econometrics. We created original and deliberately altered "counterfactual" summaries…

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a…

Theaimofthepresentpaperistosuggestthatstatisticalphysicsprovides the correct language to understand the practical behavior of the LLL algorithm, most of which are left unexplained to this day. To this end, we propose sandpile models that…

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open…

The sequential recommendation problem has attracted considerable research attention in the past few years, leading to the rise of numerous recommendation models. In this work, we explore how Large Language Models (LLMs), which are nowadays…

This paper explores the potential of large language models (LLMs) as reliable analytical tools in linguistic research, focusing on the emergence of affective meanings in temporal expressions involving manner-of-motion verbs. While LLMs like…

Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…

Autoregressive Large Language Models (LLMs) trained for next-word prediction have demonstrated remarkable proficiency at producing coherent text. But are they equally adept at forming coherent probability judgments? We use probabilistic…

Artificial intelligence is making spectacular progress, and one of the best examples is the development of large language models (LLMs) such as OpenAI's GPT series. In these lectures, written for readers with a background in mathematics or…