# netket.nn.DenseEquivariant¶

netket.nn.DenseEquivariant(symmetries, mode='auto', shape=None, point_group=None, **kwargs)[source]

A group convolution operation that is equivariant over a symmetry group.

Acts on a feature map of symmetry poses of shape [num_samples, in_features, num_symm] and returns a feature map of poses of shape [num_samples, out_features, num_symm]

G-convolutions are described in  Cohen et. {it al} <http://proceedings.mlr.press/v48/cohenc16.pdf>_ and applied to quantum many-body problems in  Roth et. {it al} <https://arxiv.org/pdf/2104.05085.pdf>_

The G-convolution generalizes the convolution to non-commuting groups:

$C^i_g = \sum_h {\bf W}_{g^{-1} h} \cdot {\bf f}_h$

Group elements that differ by the same symmetry operation (i.e. $$g = xh$$ and $$g' = xh'$$) are connected by the same filter.

Parameters
• symmetries – A specification of the symmetry group. Can be given by a nk.graph.Graph, an nk.utils.PermuationGroup, a list of irreducible representations or a product table.

• point_group – The point group, from which the space group is built. If symmetries is a graph the default point group is overwritten.

• mode – string “fft, irreps, matrix, auto” specifying whether to use a fast fourier transform over the translation group, a fourier transform using the irreducible representations or by constructing the full kernel matrix.

• shape – A tuple specifying the dimensions of the translation group.

• in_features – The number of symmetry-reduced features. The full input size is n_symm*in_features.

• out_features – The number of symmetry-reduced features. The full output size is n_symm*out_features.

• use_bias – A bool specifying whether to add a bias to the output (default: True).

• mask – An optional array of shape [n_sites] consisting of ones and zeros that can be used to give the kernel a particular shape.

• dtype – The datatype of the weights. Defaults to a 64bit float.

• precision – Optional argument specifying numerical precision of the computation. see jax.lax.Precisionfor details.

• kernel_init – Optional kernel initialization function. Defaults to variance scaling.

• bias_init – Optional bias initialization function. Defaults to zero initialization.