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# my neural net from 12.11
# first, store the memory of A as a lattice of 1, -1, where 1 is the memory and -1 is the absence of memory
A = [
-1 -1 -1 -1 1 1 -1 -1 -1 -1;
-1 -1 -1 1 1 1 1 -1 -1 -1;
-1 -1 1 1 -1 -1 1 1 -1 -1;
-1 1 1 -1 -1 -1 -1 1 1 -1;
1 1 -1 -1 -1 -1 -1 -1 1 1;
1 1 -1 -1 -1 -1 -1 -1 1 1;
-1 1 1 -1 -1 -1 -1 1 1 -1;
-1 -1 1 1 -1 -1 1 1 -1 -1;
-1 -1 -1 1 1 1 1 -1 -1 -1;
-1 -1 -1 -1 1 1 -1 -1 -1 -1
]
B = [
1 1 1 1 1 -1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 1 1 1 -1 -1 -1 -1 -1;
1 1 1 1 1 -1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 1 1 1 -1 -1 -1 -1 -1
]
C = [
-1 1 1 1 1 1 1 -1 -1 -1;
1 1 1 1 1 1 1 -1 -1 -1;
1 1 1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 1 -1 -1 -1 -1 -1 -1 -1;
1 1 1 1 1 1 1 -1 -1 -1;
-1 1 1 1 1 1 1 -1 -1 -1
]
D = [
1 1 1 1 1 -1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 -1 -1 1 1 -1 -1 -1 -1;
1 1 1 1 1 -1 -1 -1 -1 -1
]
E_letter = [
1 1 1 1 1 1 1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 1 1 1 1 1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 1 1 1 1 1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 1 1 1 1 1 1 1 1
]
F = [
1 1 1 1 1 1 1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 1 1 1 1 1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1
]
G = [
1 1 1 1 1 1 1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 -1 -1 -1;
1 1 -1 -1 -1 -1 -1 1 1 1;
1 1 -1 -1 -1 -1 -1 -1 1 1;
1 1 -1 -1 -1 -1 -1 -1 1 1;
1 1 -1 -1 -1 -1 -1 -1 1 1;
-1 1 1 1 1 1 1 1 1 1;
-1 -1 1 1 1 1 1 1 1 1
]
encodings = [A, B, C, D, E_letter, F, G]
spin_numbers(row, col) = (row - 1) * 10 + col
# create strength of interactions between ith and jth spinds in Ji,j
J = zeros(100, 100)
for m in 1:100 # row
for n in 1:100 # col
i = (m - 1) % 10 + 1
j = (n - 1) % 10 + 1
k = (m - 1) ÷ 10 + 1
l = (n - 1) ÷ 10 + 1
J[m, n] = 0
for encoding in encodings
J[m, n] += encoding[i, k] * encoding[j, l]
end
J[m, n] /= length(encodings)
end
end
# the energy function
function energy(s, J)
E = 0
for i in 1:100
for j in 1:100
E += J[i, j] * s[i] * s[j]
end
end
return -E
end
# the update function (uses monte carlo steps)
function monte_carlo(s, J)
for i in 1:100 # systematically go through each point in the lattice
# calculate the energy of the system
E = energy(s, J)
# randomly flip a spin
s[i] = -s[i]
# calculate the new energy of the system
E_new = energy(s, J)
# calculate the change in energy
dE = E_new - E
# if the change in energy is positive, flip the spin back
if dE > 0
s[i] = -s[i]
end
end
return s
end
# create the main function
function main(s, J, nsteps)
E = energy(s, J)
for i in 1:nsteps
s = monte_carlo(s, J)
E = energy(s, J)
end
return s, E
end
# run the main function
# randomly change some values in A to see if NN works
function produce_test_arr(enc, prob_change = 0.1)
tmp = zeros(10, 10)
for i in 1:10
for j in 1:10
if rand() < prob_change
tmp[i, j] = rand([-1, 1]) # set some random values
else
tmp[i, j] = enc[i, j]
end
end
end
return tmp
end
function check_if_same(s, enc)
for i in 1:10
for j in 1:10
if s[i, j] != enc[i, j]
println("The neural net did not work")
return false
end
end
end
# println("The neural net worked")
return true
end
function apply_damage_to_J(J, prob_damage = 0.8)
println("Applying damage to J with probability ", prob_damage)
ret = copy(J)
for i in 1:100
for j in 1:100
if rand() < prob_damage
ret[i, j] = 0
else
ret[i, j] = J[i, j]
end
end
end
return ret
end
function run_tests(num_times, Js, MC_steps = 2)
num_correct = 0
num_total = 0
for i in 1:num_times
# randomly select a memory
enc = encodings[rand(1:length(encodings))]
# produce a test array
s = produce_test_arr(enc)
# run theNN
s, E = main(s, Js, MC_steps)
# check if the NN worked
if check_if_same(s, enc)
num_correct += 1
end
num_total += 1
end
println("Number of correct tests: ", num_correct)
return num_correct / num_total
end
function run_tests_for_damage_range(damages, num_times, MC_steps = 2, init_J = J)
res = []
for damage in damages
damaged_J = apply_damage_to_J(init_J, damage)
p = run_tests(num_times, damaged_J, MC_steps)
push!(res, p)
end
return res
end
damage_range = collect(0.0:0.1:0.15)
res = run_tests_for_damage_range(damage_range, 10)
#plot the results
using Plots
plot(damage_range, res, xlabel = "Damage", ylabel = "Success rate", title = "NN success rate vs damage probability", marker = :circle, label = "MC steps = 2")
res = run_tests_for_damage_range(damage_range, 10, 10)
plot!(damage_range, res, xlabel = "Damage", ylabel = "Success rate", title = "NN success rate vs damage probability", marker = :circle, label = "MC steps = 10")
res = run_tests_for_damage_range(damage_range, 10, 100)
plot!(damage_range, res, xlabel = "Damage", ylabel = "Success rate", title = "NN success rate vs damage probability", marker = :circle, label = "MC steps = 100")
res = run_tests_for_damage_range(damage_range, 10, 1000)
plot!(damage_range, res, xlabel = "Damage", ylabel = "Success rate", title = "NN success rate vs damage probability", marker = :circle, label = "MC steps = 1000")
savefig("12-12-all.png")
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