Vinko Zlatić

Sven Benjamin Kožić, Vinko Zlatić, Fabio Franchini et al.

Neural Quantum States (NQS) use neural networks to represent wavefunctions of quantum many-body systems, but their performance depends on the choice of basis, yet the underlying mechanism remains poorly understood. We use a fully solvable one-dimensional Ising model to show that local basis rotations leave the loss landscape unchanged while relocating the exact wavefunction in parameter space, effectively increasing its geometric distance from typical initializations. By sweeping a rotation angle, we compute quantum Fisher information and Fubini-Study distances to quantify how the rotated wavefunction moves within the loss landscape. Shallow architectures (with focus on Restricted Boltzmann Machines (RBMs)) trained with quantum natural gradient are more likely to fall into saddle-point regions depending on the rotation angle: they achieve low energy error but fail to reproduce correct coefficient distributions. In the ferromagnetic case, near-degenerate eigenstates create high-curvature barriers that trap optimization at intermediate fidelities. We introduce a framework based on an analytically solvable rotated Ising model to investigate how relocating the target wavefunction within a fixed loss landscape exposes information-geometric barriers,such as saddle points and high-curvature regions,that hinder shallow NQS optimization, underscoring the need for landscape-aware model design in variational training.

Sebastian M. Krause, Michael M. Danziger, Vinko Zlatić

Redundancy is commonly used to guarantee continued functionality in networked systems. However, often many nodes are vulnerable to the same failure or adversary. A "backup" path is not sufficient if both paths depend on nodes which share a vulnerability.For example, if two nodes of the Internet cannot be connected without using routers belonging to a given untrusted entity, then all of their communication-regardless of the specific paths utilized-will be intercepted by the controlling entity.In this and many other cases, the vulnerabilities affecting the network are disjoint: each node has exactly one vulnerability but the same vulnerability can affect many nodes. To discover optimal redundancy in this scenario, we describe each vulnerability as a color and develop a "color-avoiding percolation" which uncovers a hidden color-avoiding connectivity. We present algorithms for color-avoiding percolation of general networks and an analytic theory for random graphs with uniformly distributed colors including critical phenomena. We demonstrate our theory by uncovering the hidden color-avoiding connectivity of the Internet. We find that less well-connected countries are more likely able to communicate securely through optimally redundant paths than highly connected countries like the US. Our results reveal a new layer of hidden structure in complex systems and can enhance security and robustness through optimal redundancy in a wide range of systems including biological, economic and communications networks.