Simulation Visualizations

GIF

Loss vs log_2(n)

Loss vs log(n) EMPIRICAL_TRAIN

Image 1

Loss vs log(n) THEORETICAL

Image 2

Loss vs log(n) EMPIRICAL_TEST

Image 3

Loss vs log(n) 1 features

Image 4

Loss vs log(n) 2 features

Image 5

Loss vs log(n) 3 features

Image 6

Time consumption(n)

Image 1
Image 2
Image 3

Iterations vs log_2(n)

Iterations vs log(n) EMPIRICAL_TRAIN

Image 1

Iterations vs log(n) THEORETICAL

Image 2

Iterations vs log(n) EMPIRICAL_TEST

Image 3

Iterations vs log(n) 1 features

Image 4

Iterations vs log(n) 2 features

Image 5

Iterations vs log(n) 3 features

Image 6

N* Relationship Matrixes

N* theoretical

dim 1 feature(s) 2 feature(s) 3 feature(s)
1 feature(s) NaN NaN 2.5484
2 feature(s) NaN NaN 3.7951
3 feature(s) 2.5484 3.7951 NaN

N* empirical test

dim 1 feature(s) 2 feature(s) 3 feature(s)
1 feature(s) NaN NaN 2.4748
2 feature(s) NaN NaN 3.9097
3 feature(s) 2.4748 3.9097 NaN

Loss Tables

Table EMPIRICAL_TRAIN

n 1 feature(s) 2 feature(s) 3 feature(s)
2 0.000000 0.000000 0.0
4 0.120375 0.030203 0.0
8 0.141217 0.047065 0.0
16 0.150008 0.059789 0.0
32 0.154046 0.066462 0.0
64 0.156090 0.072199 0.0
128 0.157377 0.075296 0.0
256 0.158309 0.076822 0.0
512 0.158491 0.077785 0.0
1024 0.158451 0.078148 0.0

Table THEORETICAL

n 1 feature(s) 2 feature(s) 3 feature(s)
2 0.188263 0.150368 2.159073e-01
4 0.185113 0.139065 1.336852e-01
8 0.178046 0.120117 4.488830e-02
16 0.169725 0.102247 5.040113e-03
32 0.164411 0.091981 2.218743e-04
64 0.161667 0.085602 2.794638e-06
128 0.160187 0.082326 3.099264e-07
256 0.159400 0.080430 1.230080e-08
512 0.158997 0.079580 2.186880e-09
1024 0.158820 0.079111 7.110094e-10

Table EMPIRICAL_TEST

n 1 feature(s) 2 feature(s) 3 feature(s)
2 0.250977 0.171888 2.795665e-01
4 0.207368 0.146602 1.429324e-01
8 0.181411 0.120820 4.512535e-02
16 0.169628 0.102102 5.098302e-03
32 0.164377 0.091475 2.111318e-04
64 0.161512 0.085415 3.625851e-06
128 0.160014 0.082037 3.453191e-07
256 0.159185 0.080138 0.000000e+00
512 0.158985 0.079248 0.000000e+00
1024 0.158759 0.078725 0.000000e+00

Time Consumption Tables

Table EMPIRICAL_TRAIN

loss type time (min)
EMPIRICAL_TRAIN 0.101006
THEORETICAL 0.071191
EMPIRICAL_TEST 0.137958

Table THEORETICAL

# features time (min)
1 0.064439
2 0.056167
3 0.039272

Table EMPIRICAL_TEST

n time (min)
0 0.044595
1 0.034953
2 0.023375
3 0.016233
4 0.012534
5 0.008981
6 0.007689
7 0.008115
8 0.013030
9 0.028018

Iterations Tables

Table EMPIRICAL_TRAIN

n 1 feature(s) 2 feature(s) 3 feature(s)
2 11413 11413 11413
4 16000 16000 8080
8 11200 11200 5656
16 8000 8000 4040
32 5600 5600 2828
64 4000 4000 2020
128 2800 2800 1414
256 2000 2000 1010
512 1400 1400 707
1024 1000 1000 505

Table THEORETICAL

n 1 feature(s) 2 feature(s) 3 feature(s)
2 19323 20792 21018
4 9200 8080 11120
8 6776 5880 11200
16 5800 4720 4760
32 3472 2912 2828
64 2160 2060 2020
128 1456 1414 1414
256 1050 1080 1010
512 714 728 707
1024 505 510 505

Table EMPIRICAL_TEST

n 1 feature(s) 2 feature(s) 3 feature(s)
2 17402 17628 17515
4 8880 15440 16000
8 5936 8064 8176
16 4720 5080 4840
32 4900 4508 3136
64 2700 2040 2020
128 1778 1652 1414
256 1010 1010 1010
512 770 1218 707
1024 815 810 505