A latent linear model for nonlinear coupled oscillators on graphs

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear behavior has been a key challenge in predicting whether all oscillators in such a system will eventually synchronize. In this paper, we demonstrate that, surprisingly, such nonlinear behavior of coupled oscillators can be effectively linearized in certain latent dynamic spaces. The key insight is that there is a small number of `latent dynamics filters', each with a specific association with synchronizing and non-synchronizing dynamics on subgraphs so that any observed dynamics on subgraphs can be approximated by a suitable linear combination of such elementary dynamic patterns. Taking an ensemble of subgraph-level predictions provides an interpretable predictor for whether the system on the whole graph reaches global synchronization. We propose algorithms based on supervised matrix factorization to learn such latent dynamics filters. We demonstrate that our method performs competitively in synchronization prediction tasks against baselines and black-box classification algorithms, despite its simple and interpretable architecture.

Evaluating LLM Agent Group Dynamics against Human Group Dynamics: A Case Study on Wisdom of Partisan Crowds

This study investigates the potential of Large Language Models (LLMs) to simulate human group dynamics, particularly within politically charged contexts. We replicate the Wisdom of Partisan Crowds phenomenon using LLMs to role-play as Democrat and Republican personas, engaging in a structured interaction akin to human group study. Our approach evaluates how agents' responses evolve through social influence. Our key findings indicate that LLM agents role-playing detailed personas and without Chain-of-Thought (CoT) reasoning closely align with human behaviors, while having CoT reasoning hurts the alignment. However, incorporating explicit biases into agent prompts does not necessarily enhance the wisdom of partisan crowds. Moreover, fine-tuning LLMs with human data shows promise in achieving human-like behavior but poses a risk of overfitting certain behaviors. These findings show the potential and limitations of using LLM agents in modeling human group phenomena.

Simulating Opinion Dynamics with Networks of LLM-based Agents

Accurately simulating human opinion dynamics is crucial for understanding a variety of societal phenomena, including polarization and the spread of misinformation. However, the agent-based models (ABMs) commonly used for such simulations lack fidelity to human behavior. We propose a new approach to simulating opinion dynamics based on populations of Large Language Models (LLMs). Our findings reveal a strong inherent bias in LLM agents towards accurate information, leading to consensus in line with scientific reality. However, this bias limits the simulation of individuals with resistant views on issues like climate change. After inducing confirmation bias through prompt engineering, we observed opinion fragmentation in line with existing agent-based research. These insights highlight the promise and limitations of LLM agents in this domain and suggest a path forward: refining LLMs with real-world discourse to better simulate the evolution of human beliefs.

Reprogramming under constraints: Revisiting efficient and reliable transferability of lottery tickets

In the era of foundation models with huge pre-training budgets, the downstream tasks have been shifted to the narrative of efficient and fast adaptation. For classification-based tasks in the domain of computer vision, the two most efficient approaches have been linear probing (LP) and visual prompting/reprogramming (VP); the former aims to learn a classifier in the form of a linear head on the features extracted by the pre-trained model, while the latter maps the input data to the domain of the source data on which the model was originally pre-trained on. Although extensive studies have demonstrated the differences between LP and VP in terms of downstream performance, we explore the capabilities of the two aforementioned methods via the sparsity axis: (a) Data sparsity: the impact of few-shot adaptation and (b) Model sparsity: the impact of lottery tickets (LT). We demonstrate that LT are not universal reprogrammers, i.e., for certain target datasets, reprogramming an LT yields significantly lower performance than the reprogrammed dense model although their corresponding upstream performance is similar. Further, we demonstrate that the calibration of dense models is always superior to that of their lottery ticket counterparts under both LP and VP regimes. Our empirical study opens a new avenue of research into VP for sparse models and encourages further understanding of the performance beyond the accuracy achieved by VP under constraints of sparsity. Code and logs can be accessed at \url{https://github.com/landskape-ai/Reprogram_LT}.