Algebraic Expressions for Complex Deep Learning Systems Modeling and Analysis

Many modern Deep Learning (DL) systems have achieved impressive state-of-the-art results by combining individual sub-systems, including foundation models, to form increasingly more complex DL systems. However, this growing complexity also introduces new challenges in effectively modeling and analyzing these systems. In this paper, we introduce a novel approach to represent complex DL systems using algebraic expressions, by decomposing them into sets of sub-systems arranged in parallel and series configurations, allowing for abstract and efficient representations. We further show how these algebraic expressions can be readily used to compute specific performance metrics of DL systems by formulating specific operations on our algebraic expressions. Specifically, we present the operations for computing system inference time and accuracy. Finally, we present two practical real case studies addressing multi-class visual classification of retail products, demonstrating the effectiveness and advantages of using our methodology in modeling and analyzing these systems.