Softmax-Free Attention in Spiking Transformers as the Zero-Temperature Limit of Two-Level Systems
Roberto C. SoteroPouya TaghipourJose M. Sanchez-Bornot
Oct 2026
Machine Learning
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.
This paper investigates developing real-world perception for active agents, proposes Gibson Environment for this purpose, and showcases a set of perceptual tasks learned therein.
F. Xia, Amir Zamir, Zhi-Yang He et al.· 2018 IEEE/CVF Conference on...· 1,069 citations· ⚡112
The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
The possibility of inferring high-dimensional data inference in a model that consists of a prior and an auxiliary differentiable constraint given some additional information is considered, thereby allowing a range of potential applications in adapting models to new domains and tasks.
Alexandros Graikos, Esmeralda S. Whitammer, N. Jojic et al.· Neural Information Processin...· 316 citations· ⚡15
It is proved that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution, and empirically demonstrate the benefits of the trajectories balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequenc...
Esmeralda S. Whitammer, Moksh Jain, Emmanuel Bengio et al.· Neural Information Processin...· 302 citations· ⚡60
An algorithm is proposed which leverages disentangled semantic factors to generate adversarial perturbation by altering controlled semantic attributes to fool the learner towards various "adversarial" targets.
Haonan Qiu, Chaowei Xiao, Lei Yang et al.· arXiv.org· 208 citations· ⚡17
This work proposes a HALO that directly maximizes the utility of generations instead of maximizing the log-likelihood of preferences, and suggests that the best loss depends on the inductive biases most appropriate for a given setting, an oft-overlooked consideration.
A machine-learning approach called CheMeleon provides a practical way to develop new drugs or other molecules with much less detailed, expensive experimentation.
