Related papers: Neural Network Gauge Field Transformation for 4D S…
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs), which can be applied to generic machine learning problems in lattice gauge theory while exactly preserving gauge…
Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states,…
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
We present a progress report on the use of normalizing flows for generating gauge field configurations in pure SU(N) gauge theories. We discuss how the singular value decomposition can be used to construct gauge-invariant quantities, which…
We perform a precision computation of hybrid static potentials with quantum numbers $\Lambda_\eta^\epsilon = \Sigma_g^-,\Sigma_u^+,\Sigma_u^-,\Pi_g,\Pi_u,\Delta_g,\Delta_u$ using SU(3) lattice gauge theory. The resulting potentials are used…
The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge…
Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be…
We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group $\mathrm{SU}(3)$. The new mapping is used to construct splitting methods for separable Hamiltonian systems whose…
The 4-d SU(2) lattice gauge theory is simulated in the minimal Coulomb gauge which aims to maximize the traces of all links in three directions. Fourth-direction links are interpreted as spins in a Heisenberg-like model with varying…
Neural network representations are often analyzed as vectors in a fixed Euclidean space. However, their coordinates are not uniquely defined. If a hidden representation is transformed by an invertible linear map, the network function can be…
Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…
An SO(4) gauge invariant model with extended field transformations is examined in four dimensional Euclidean space. The gauge field is $(A^\mu)^{\alpha\beta} = 1/2 t^{\mu\nu\lambda} (M^{\nu\lambda})^{\alpha\beta}$ where $M^{\nu\lambda}$ are…
Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body…
Gauge link smearing is widely used in lattice QCD computations. The idea is to remove the local (UV) fluctuations of the gauge field configurations while keeping the longer-range (IR) properties intact. Important applications are in the…
Four-dimensional gauge theories based on symplectic Lie groups provide elegant realisations of the microscopic origin of several new physics models. Numerical studies pursued on the lattice provide quantitative information necessary for…
Fixed-point (FP) lattice actions are classically perfect, i.e., they have continuum classical properties unaffected by discretization effects and are expected to have suppressed lattice artifacts at weak coupling. Therefore they provide a…
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…
We propose a Transformer neural network architecture specifically designed for lattice QCD, focusing on preserving the fundamental symmetries required in lattice gauge theory. The proposed architecture is gauge covariant/equivariant,…
Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of…