Softmax-Free Attention in Spiking Transformers as the Zero-Temperature Limit of Two-Level Systems

Abstract:Spiking Transformers achieve energy efficiency by discarding softmax normalization in favor of thresholded, binary attention. However, this removal breaks the thermodynamic framework used to analyze attention networks, as the normalized measure and partition function cease to exist. We restore this theoretical foundation by proving that softmax-free spiking attention operates exactly as the zero-temperature limit of a product of independent two-level systems. This correspondence places spiking attention strictly in the frozen ordered phase of the thermodynamic phase diagram for all inputs. Consequently, the entropic cost of organizing attention collapses, replaced by a Landauer-type physical floor governed by action-potential generation. Furthermore, this ordered-phase pinning mathematically explains the optimization difficulty caused by vanishing surrogate gradients. We validate this theory with forward-relaxation experiments, placing both standard and neuromorphic attention mechanisms on a unified thermodynamic axis.

Machine Learning (cs.LG)

arXiv:2610.15968 [cs.LG]

(or arXiv:2610.15968v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.15968 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.