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Diffstat (limited to 'hw9/12-12.jl')
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diff --git a/hw9/12-12.jl b/hw9/12-12.jl new file mode 100644 index 0000000..e08eadc --- /dev/null +++ b/hw9/12-12.jl @@ -0,0 +1,253 @@ +# 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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