Large language models have emergent capabilities that come unexpectedly at scale, but we need a theoretical framework to explain why and how they emerge. We prove that language models are actually non-ergodic systems while providing a mathematical framework based on Stuart Kauffman's theory of the adjacent possible (TAP) to explain capability emergence. Our resource-constrained TAP equation demonstrates how architectural, training, and contextual constraints interact to shape model capabilities through phase transitions in semantic space. We prove through experiments with three different language models that capacities emerge through discrete transitions guided by constraint interactions and path-dependent exploration. This framework provides a theoretical basis for understanding emergence in language models and guides the development of architectures that can guide capability emergence.

This paper introduces an innovative approach to analyzing and improving multi-hop reasoning in AI systems by drawing inspiration from Hamiltonian mechanics. We propose a novel framework that maps reasoning chains in embedding spaces to Hamiltonian systems, allowing us to leverage powerful analytical tools from classical physics. Our method defines a Hamiltonian function that balances the progression of reasoning (kinetic energy) against the relevance to the question at hand (potential energy). Using this framework, we analyze a large dataset of reasoning chains from a multi-hop question-answering task, revealing intriguing patterns that distinguish valid from invalid reasoning. We show that valid reasoning chains have lower Hamiltonian energy and move in ways that make the best trade-off between getting more information and answering the right question. Furthermore, we demonstrate the application of this framework to steer the creation of more efficient reasoning algorithms within AI systems. Our results not only provide new insights into the nature of valid reasoning but also open up exciting possibilities for physics-inspired approaches to understanding and improving artificial intelligence.

Comprehending how consumers react to advertising inputs is essential for marketers aiming to optimize advertising strategies and improve campaign effectiveness. This study examines the complex nature of consumer behaviour by applying theoretical frameworks derived from physics and social psychology. We present an innovative equation that captures the relation between spending on advertising and consumer response, using concepts such as symmetries, scaling laws, and phase transitions. By validating our equation against well-known models such as the Michaelis-Menten and Hill equations, we prove its effectiveness in accurately representing the complexity of consumer response dynamics. The analysis emphasizes the importance of key model parameters, such as marketing effectiveness, response sensitivity, and behavioural sensitivity, in influencing consumer behaviour. The work explores the practical implications for advertisers and marketers, as well as discussing the limitations and future research directions. In summary, this study provides a thorough framework for comprehending and forecasting consumer reactions to advertising, which has implications for optimizing advertising strategies and allocating resources.

In recent years, significant progress in generative AI has highlighted the important role of physics-inspired models that utilize advanced mathematical concepts based on fundamental physics principles to enhance artificial intelligence capabilities. Among these models, those based on diffusion equations have greatly improved image quality. This study aims to explore the potential uses of Maxwell-Boltzmann equation, which forms the basis of the kinetic theory of gases, and the Michaelis-Menten model in Marketing Mix Modelling (MMM) applications. We propose incorporating these equations into Hierarchical Bayesian models to analyse consumer behaviour in the context of advertising. These equation sets excel in accurately describing the random dynamics in complex systems like social interactions and consumer-advertising interactions.

In this paper, we propose a method for measuring the similarity low sample tabular data with synthetically generated data with a larger number of samples than original. This process is also known as data augmentation. But significance levels obtained from non-parametric tests are suspect when sample size is small. Our method uses a combination of geometry, topology and robust statistics for hypothesis testing in order to compare the "validity" of generated data. We also compare the results with common global metric methods available in the literature for large sample size data.

A person's weight status can have profound implications on their life, ranging from mental health, to longevity, to financial income. At the societal level, "fat shaming'" and other forms of "sizeism'' are a growing concern, while increasing obesity rates are linked to ever raising healthcare costs. For these reasons, researchers from a variety of backgrounds are interested in studying obesity from all angles. To obtain data, traditionally, a person would have to accurately self-report their body-mass index (BMI) or would have to see a doctor to have it measured. In this paper, we show how computer vision can be used to infer a person's BMI from social media images. We hope that our tool, which we release, helps to advance the study of social aspects related to body weight.