Matthew Murphy

David Pearl, Matthew Murphy, James Intriligator

The Polymorphic Combinatorial Framework (PCF) leverages Large Language Models (LLMs) and mathematical frameworks to guide the meta-prompt enabled design of solution spaces and adaptive AI agents for complex, dynamic environments. Unlike static agent architectures, PCF enables real-time parameter reconfiguration through mathematically-grounded combinatorial spaces, allowing agents to adapt their core behavioral traits dynamically. Grounded in combinatorial logic, topos theory, and rough fuzzy set theory, PCF defines a multidimensional SPARK parameter space (Skills, Personalities, Approaches, Resources, Knowledge) to capture agent behaviors. This paper demonstrates how LLMs can parameterize complex spaces and estimate likely parameter values/variabilities. Using PCF, we parameterized mock café domains (five levels of complexity), estimated variables/variabilities, and conducted over 1.25 million Monte Carlo simulations. The results revealed trends in agent adaptability and performance across the five complexity tiers, with diminishing returns at higher complexity levels highlighting thresholds for scalable designs. PCF enables the generation of optimized agent configurations for specific scenarios while maintaining logical consistency. This framework supports scalable, dynamic, explainable, and ethical AI applications in domains like customer service, healthcare, robotics, and collaborative systems, paving the way for adaptable and cooperative next-generation polymorphic agents.

Bilge Acun, Matthew Murphy, Xiaodong Wang et al.

The use of GPUs has proliferated for machine learning workflows and is now considered mainstream for many deep learning models. Meanwhile, when training state-of-the-art personal recommendation models, which consume the highest number of compute cycles at our large-scale datacenters, the use of GPUs came with various challenges due to having both compute-intensive and memory-intensive components. GPU performance and efficiency of these recommendation models are largely affected by model architecture configurations such as dense and sparse features, MLP dimensions. Furthermore, these models often contain large embedding tables that do not fit into limited GPU memory. The goal of this paper is to explain the intricacies of using GPUs for training recommendation models, factors affecting hardware efficiency at scale, and learnings from a new scale-up GPU server design, Zion.