Related papers: Mechanisms for spontaneous symmetry breaking in de…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
Lifelong learning and adaptability are two defining aspects of biological agents. Modern reinforcement learning (RL) approaches have shown significant progress in solving complex tasks, however once training is concluded, the found…
Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…
When our eyes are presented with the same image, the brain processes it to view it as a single coherent one. The lateral shift in the position of our eyes, causes the two images to possess certain differences, which our brain exploits for…
Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in…
We introduce a system composed of two (2+1)-dimensional baby-skyrmion models (BSMs) set on parallel planes and linearly coupled by tunneling of fields. This system can be realized in a dual-layer ferromagnetic medium. Unlike dual-core…
The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent…
Understanding the mechanisms behind neural network optimization is crucial for improving network design and performance. While various optimization techniques have been developed, a comprehensive understanding of the underlying principles…
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…
We investigate the spontaneous breaking of subsystem symmetries directly in the context of continuum field theories by calculating the correlation function of charged operators. Our methods confirm the lack of spontaneous symmetry breaking…
Depending on the coupling to the environment, symmetries of open quantum systems manifest in two distinct forms, the strong and the weak. We study the spontaneous symmetry breaking among phases with strong symmetry, weak symmetry, and no…
Spontaneous symmetry breaking is a phenomenon of an alteration of a state symmetry without a change in the system symmetry. A transition from a state with unbroken symmetry to a state with broken symmetry leads to a qualitative change in…
Biological neural networks self-organize according to local synaptic modifications to produce stable computations. How modifications at the synaptic level give rise to such computations at the network level remains an open question.…
Spontaneous symmetry breaking in systems with symmetry is a cornerstone phenomenon accompanying second-order phase transitions. Here, we predict the opposite phenomenon, namely, spontaneous symmetry emergence in a system that lacks…
We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulted from the mechanism in two simple supersymmetric Z_2…
Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet, derivations of single-layer networks with such local learning rules from principled…
We investigate two concrete cases of phase transitions breaking a subsystem symmetry. The models are two classical compass models featuring line-flip and plane-flip symmetries and correspond to special limits of a Heisenberg-Kitaev…
The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through…
We show that the spontaneous symmetry breaking can be defined also for finite systems based on the properly defined jump probability between the ground states in the 2d and 3d Ising models on a square and a cubic lattice respectively. Our…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…