Physics

We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

Synchronization is a fundamental phenomenon in complex systems and nonlinear dynamics, driving coordinated behavior across a wide range of natural and artificial systems. From the synchronized flashing of fireflies to the coordinated oscillations in brain networks, the study of synchronization has revealed profound insights into how order emerges in interacting systems. While often associated with order and coherence, synchronization in complex networks can exhibit surprising behaviors, challenging traditional perspectives and revealing new facets of dynamical organization.In this talk, I will first review key contributions from our group to the understanding of synchronization in systems of mobile oscillators. These systems, characterized by the interplay between dynamical states and the physical motion of the oscillators, provide a rich platform to explore novel forms of synchronization.Furthermore, I will highlight the pivotal role of symmetries in shaping synchronization and its breakdown in brain networks. Our work has uncovered how symmetry-breaking mechanisms drive the emergence of localized activity patterns and how symmetry-based principles can be used to design interventions for desynchronization. 

In this talk, I will explain the concept of fault tolerance, which ensures reliable quantum computation. Building on recent advancements in mixed-state phases of matter, I introduce a new diagnostic called the spacetime Markov length. The divergence of this length scale signals the intrinsic breakdown of fault tolerance.