Update README

README.md

@@ -1,11 +1,10 @@
 # Learning Quantum States with Neural Networks
 
-![Correlations_A](data/correlations_A.png)
-Figure 1: Map of statistical spin configurations of an Ising chain of $n=1000$ spins relative to the middle spin at site $n/2+1=501$ over the course of learning for the antiferromagnetic Ising model $J<0$. The spin configuration approaches the ground state configuration as the energy approaches the ground state energy.
-
 ![Energies_A](data/energies_A.png)
-Figure 2: Statistical expectation of the energy with standard error of the mean over the course of learning for the antiferromagnetic Ising model with $J=-0.5$ and $B=0.1$ for $n=1000$ spins.
+Figure 1: Statistical expectation of the energy and standard error of the mean over the course of learning for the antiferromagnetic Ising model with $J = -0.5$ and $B = 0.1$ for $n = 1000$ spins.
 
+![Correlations_A](data/correlations_A.png)
+Figure 2: Antiferromagnetic Ising model correlations over the course of learning for $n = 1000$ spins with $J = -0.5$ and $B = 0.1$.
 ## Contents
 
 1. [Introduction](#introduction)
@@ -147,22 +146,20 @@ We implement the stochastic optimization algorithm as a type-bound procedure of
 ```fortran
 type RestrictedBoltzmannMachine
  private
- character(len=1) :: alignment = 'N' !! For tracking spin alignment
- integer :: v_units = 0, h_units = 0 !! Number of visble and hidden units
- real(rk), allocatable, dimension(:) :: a !! Visible layer biases
- complex(rk), allocatable, dimension(:) :: b !! Hidden layer biases
- complex(rk), allocatable, dimension(:,:) :: w !! Weights
- real(rk), allocatable, dimension(:) :: p_a, r_a !! ADAM arrays for a
- complex(rk), allocatable, dimension(:) :: p_b, r_b !! ADAM arrays for b
- complex(rk), allocatable, dimension(:,:) :: p_w, r_w !! ADAM arrays for w
+ integer :: v_units = 0 !! Number of visible units
+ integer :: h_units = 0 !! Number of hidden units
+ real(kind=rk), allocatable, dimension(:) :: a, p_a, r_a !! Visible biases & ADAM arrays
+ complex(kind=rk), allocatable, dimension(:) :: b, p_b, r_b !! Hidden biases & ADAM arrays
+ complex(kind=rk), allocatable, dimension(:,:) :: w, p_w, r_w !! Weights & ADAM arrays
+ character(len=1) :: alignment = 'N' !! For tracking spin alignment
  contains
  private
- procedure, pass(self), public :: stochastic_optimization !! Public training routine
- procedure, pass(self) :: init !! Initialization routine
- procedure, pass(self) :: sample_distribution !! MCMC routine for sampling |𝜓|^2
- procedure, pass(self) :: prob_ratio !! Probability ratio |𝜓(s_2)/𝜓(s_1)|^2
- procedure, pass(self) :: ising_energy !! Ising local energy
- procedure, pass(self) :: propagate !! Routine for updating weights and biases
+ procedure, pass(self), public :: stochastic_optimization  !! Public training routine
+ procedure, pass(self) :: init  !! Initialization routine
+ procedure, pass(self) :: sample_distribution  !! MCMC routine for sampling p(s)
+ procedure, pass(self) :: prob_ratio  !! Probability ratio p(s_2)/p(s_1)
+ procedure, pass(self) :: ising_energy  !! Ising local energy
+ procedure, pass(self) :: propagate  !! Routine for updating weights and biases
 end type RestrictedBoltzmannMachine
 ```