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learn-multiplication.F90
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learn-multiplication.F90
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! Copyright (c), The Regents of the University of California
! Terms of use are as specified in LICENSE.txt
module multiply_inputs
!! Define a function that produces the desired network output for a given network input
use fiats_m, only : tensor_t
use assert_m, only : assert
implicit none
contains
elemental function y(x_tensor) result(a_tensor)
type(tensor_t), intent(in) :: x_tensor
type(tensor_t) a_tensor
associate(x => x_tensor%values())
call assert(ubound(x,1)>=7 .and. lbound(x,1)<=2,"y(x) :: sufficient input")
a_tensor = tensor_t([x(1)*x(2), x(2)*x(3), x(3)*x(4), x(4)*x(5), x(5)*x(6), x(6)*x(8)])
end associate
end function
end module
program learn_multiplication
!! This trains a neural network to learn the following six polynomial functions of its eight inputs.
use fiats_m, only : neural_network_t, trainable_network_t, mini_batch_t, tensor_t, input_output_pair_t, shuffle
use julienne_m, only : string_t, file_t, command_line_t, bin_t
use assert_m, only : assert, intrinsic_array_t
use multiply_inputs, only : y
implicit none
type(string_t) final_network_file
type(command_line_t) command_line
final_network_file = string_t(command_line%flag_value("--output-file"))
if (len(final_network_file%string())==0) then
error stop new_line('a') // new_line('a') // &
'Usage: fpm run --example learn-multiplication --profile release --flag "-fopenmp" -- --output-file "<file-name>"'
end if
block
integer, parameter :: num_pairs = 10, num_epochs = 200000, num_mini_batches= 2 ! num_pairs = # input/output pairs in training data
type(mini_batch_t), allocatable :: mini_batches(:)
type(input_output_pair_t), allocatable :: input_output_pairs(:)
type(tensor_t), allocatable :: inputs(:), desired_outputs(:)
type(trainable_network_t) trainable_network
type(bin_t), allocatable :: bins(:)
real, allocatable :: cost(:), random_numbers(:)
call random_init(image_distinct=.true., repeatable=.true.)
trainable_network = perturbed_identity_network(perturbation_magnitude=0.05)
call output(trainable_network, string_t("initial-network.json"))
associate(num_inputs => trainable_network%num_inputs(), num_outputs => trainable_network%num_outputs())
block
integer i, j
integer, allocatable :: output_sizes(:)
inputs = [(tensor_t(real([(j*i, j = 1,num_inputs)])/(num_inputs*num_pairs)), i = 1, num_pairs)]
desired_outputs = y(inputs)
output_sizes = [(size(desired_outputs(i)%values()),i=1,size(desired_outputs))]
call assert(all([num_outputs==output_sizes]), "fit-polynomials: # outputs", intrinsic_array_t([num_outputs,output_sizes]))
end block
input_output_pairs = input_output_pair_t(inputs, desired_outputs)
block
integer b
bins = [(bin_t(num_items=num_pairs, num_bins=num_mini_batches, bin_number=b), b = 1, num_mini_batches)]
end block
allocate(random_numbers(2:size(input_output_pairs)))
print *,"Cost"
block
integer e, b
do e = 1,num_epochs
call random_number(random_numbers)
call shuffle(input_output_pairs)
mini_batches = [(mini_batch_t(input_output_pairs(bins(b)%first():bins(b)%last())), b = 1, size(bins))]
call trainable_network%train(mini_batches, cost, adam=.true., learning_rate=1.5)
print *,sum(cost)/size(cost)
end do
end block
block
integer p
#if defined _CRAYFTN || __GFORTRAN__
type(tensor_t), allocatable :: network_outputs(:)
network_outputs = trainable_network%infer(inputs)
#else
associate(network_outputs => trainable_network%infer(inputs))
#endif
print "(a,69x,a)"," Outputs", "| Desired outputs"
do p = 1, num_pairs
print "(6G13.5, a1, 6G13.5)",network_outputs(p)%values(), "|", desired_outputs(p)%values()
end do
#if defined _CRAYFTN || __GFORTRAN__
#else
end associate
#endif
end block
end associate
call output(trainable_network, final_network_file)
end block
contains
subroutine output(neural_network, file_name)
class(neural_network_t), intent(in) :: neural_network
type(string_t), intent(in) :: file_name
type(file_t) json_file
json_file = neural_network%to_json()
call json_file%write_lines(file_name)
end subroutine
pure function e(j,n) result(unit_vector)
integer, intent(in) :: j, n
integer k
real, allocatable :: unit_vector(:)
unit_vector = real([(merge(1,0,j==k),k=1,n)])
end function
function perturbed_identity_network(perturbation_magnitude) result(trainable_network)
type(trainable_network_t) trainable_network
real, intent(in) :: perturbation_magnitude
integer, parameter :: n(*) = [8, 64, 64, 64, 6]
integer, parameter :: n_max = maxval(n), layers = size(n)
integer k, l
real, allocatable :: identity(:,:,:), w_harvest(:,:,:), b_harvest(:,:)
identity = reshape( [( [(e(k,n_max), k=1,n_max)], l = 1, layers-1 )], [n_max, n_max, layers-1])
allocate(w_harvest, mold = identity)
allocate(b_harvest(size(identity,1), size(identity,3)))
call random_number(w_harvest)
call random_number(b_harvest)
associate(w => identity + perturbation_magnitude*(w_harvest-0.5)/0.5, b => perturbation_magnitude*(b_harvest-0.5)/0.5)
trainable_network = trainable_network_t( neural_network_t( &
nodes = n, weights = w, biases = b, metadata = &
[string_t("Perturbed Identity"), string_t("Damian Rouson"), string_t("2023-09-23"), string_t("relu"), string_t("false")] &
))
end associate
end function
end program