Affiliation：Department of Physics, Osaka University¹　Cybermedia Center, Osaka University²

Abstract：Spatially heterogenous replica symmetry breaking (RSB) is a phenomenon in complex systems that has only been observed before in multilayer Perceptrons [1, 2]. There is however no reason that it should be unique to Perceptrons. Our aim in this research is to explore and characterize the properties of spatially heterogeneous RSB in simpler, canonical models of complex systems. To this end we study a generalized minimalistic model of quasi-1-dimensional spin glasses (SG) – the layered p-spin model – using replica theory. We focus on the simplest non-trivial case p=4. Our results show that at low temperature, successive layer-by-layer glass transitions cause the phase space of the model to form complex clusters. Just below the first glass transition temperature the first layer enters the full RSB phase, while deeper layers remain in the “liquid” phase. Then as one progressively lowers the temperature one observes that successive layers enter the 1-step RSB phase. Interestingly, the previous layers that were previously in the 1-RSB phase enter the 2-RSB phase, and so on. At very low temperatures the first layer is in a “full RSB + k-RSB” phase, a new hybrid phase that is not well understood and requires further research.

Publication related to your research:
（Journal paper）

• H. Yoshino, From complex to simple: hierarchical free-energy landscape renormalized in deep neural networks, SciPost Phys., Core 5, 002 (2020).
• H. Yoshino, Spatially heterogeneous learning by a deep student machine, arXiv:2302.07419 (2023)