  Machine learning, deep learning, has been accelerating computational physics,
which has been used to simulate systems on a lattice. Equivariance is essential
to simulate a physical system because it imposes a strong induction bias for
the probability distribution described by a machine learning model. This
reduces the risk of erroneous extrapolation that deviates from data symmetries
and physical laws. However, imposing symmetry on the model sometimes occur a
poor acceptance rate in self-learning Monte-Carlo (SLMC). On the other hand,
Attention used in Transformers like GPT realizes a large model capacity. We
introduce symmetry equivariant attention to SLMC. To evaluate our architecture,
we apply it to our proposed new architecture on a spin-fermion model on a
two-dimensional lattice. We find that it overcomes poor acceptance rates for
linear models and observe the scaling law of the acceptance rate as in the
large language models with Transformers.
