Non Associativity

Non-associativity, the violation of the associative property (a + b) + c = a + (b + c), is emerging as a critical issue across diverse computational domains. Current research focuses on understanding and mitigating the effects of non-associativity in floating-point arithmetic within high-performance computing and deep learning, where it impacts reproducibility and accuracy, and in analog computing, where inherent physical limitations introduce order-dependent results. Investigations explore how non-associative operations can encode sequential information, potentially offering advantages in cognitive computing models. Addressing non-associativity is crucial for ensuring reliable results in scientific simulations, improving the robustness of machine learning models, and advancing the development of novel computing paradigms.