Related papers: Mechanisms for spontaneous symmetry breaking in de…
We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen as to produce frustration. At zero temperature, this system…
The dynamics of learning in modern large AI systems is hierarchical, often characterized by abrupt, qualitative shifts akin to phase transitions observed in physical systems. While these phenomena hold promise for uncovering the mechanisms…
The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local and gauge dependent. For that reason they are also ambiguous as a guide to phase structure. We point out that a global…
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…
A one-dimensional driven two-species model with parallel sublattice update and open boundaries is considered. Although the microscopic many-body dynamics is symmetric with respect to the two species and interactions are short-ranged, there…
Symmetry is an important inductive bias that can improve model robustness and generalization across many deep learning domains. In multi-agent settings, a priori known symmetries have been shown to address a fundamental coordination failure…
Equivariant neural networks (ENNs) have been shown to be extremely effective in applications involving underlying symmetries. By construction ENNs cannot produce lower symmetry outputs given a higher symmetry input. However, symmetry…
The fundamental `plasticity' of the nervous system (i.e high adaptability at different structural levels) is primarily based on Hebbian learning mechanisms that modify the synaptic connections. The modifications rely on neural activity and…
The scalar field is quantized in the discretized light-front framework following the {\em standard} Dirac procedure and its infinite volume limit taken. The background field and the nonzero mode variables do not commute for finite volume;…
Learning and the ability to learn are important factors in development and evolutionary processes [1]. Depending on the level, the complexity of learning can strongly vary. While associative learning can explain simple learning behaviour…
Symmetry in biological and physical systems is a product of self organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry based feature extrac-tion or representation by neural networks may unravel the…
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which…
Continuous symmetries and their breaking play a prominent role in contemporary physics. Effective low-energy field theories around symmetry breaking states explain diverse phenomena such as superconductivity, magnetism, and the mass of…
An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological…
What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…
Kinematical and dynamical mechanisms leading to the spontaneous breaking of space-time symmetries are described. The symmetries affected are space and time translations, space rotations, scale and conformal transformations. Applications are…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…
Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…
Deep artificial neural networks have surpassed human-level performance across a diverse array of complex learning tasks, establishing themselves as indispensable tools in both social applications and scientific research. Despite these…
The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfy constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining…