Wilderness search --- search iterations

According to the assumption of the inverse relationship between the number of iterations and entropy

(A,B)---m*n*k---(1,0)(0,1)

It can be reasonably speculated that the entropy between two classification objects depends on the value and distribution of points , This time, we will verify the relationship between the number of iterations and entropy from the perspective of numerical value .

(0,3)---m*n*k---(1,0)(0,1)

Classify with neural network mnist Of 0 and 3, Reduce the picture to 9*9, Give Way 0 Is the original data set 0.mnist 3 Random reservation 70% The point of , And add a coefficient in the normalization operation d. Give Way d Respectively equal to 1,0.9,0.8,…,0.1. For example if d=0.1 That means 3 The maximum value of all points in is 0.1, Equivalent to return 0.1 turn . and 0 Normalized in the normal way . So the distribution of points is exactly the same , The difference in the number of iterations depends only on the value .

Consider two particles n and m,n The range of motion is 0-1, Another particle m The range of motion is 0-0.1, because n The motion range of particles includes m The motion range of particles , therefore m The number of possible states of particles should be less than n The number of possible motion states of particles . therefore n The entropy of particles should be greater than m Entropy of particles . So the coefficient d The larger the entropy is .

Now no matter the form 0 and 3 How do they interact , hold 0 and 3 Consider forming a composite whole , This whole is in the case of no change in the positional relationship of points , The value of the point changes . coefficient d It's worth it 0 and 3 The influence of the complex should be the same as that of n and m The impact is consistent .

Therefore, it is reasonable to assume that with the coefficient d Reduction of 0 and 3 The entropy of the complex decreases , More iterations .

Let the convergence error be 1e-4 To 1e-5, Each convergence error statistic 199 Time , Average. . Get the form

	*d：1	0.9	0.8	0.7	0.6	0.5	0.4	0.3	0.2	0.1
δ	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n	The number of iterations n
1.00E-04	2376.150754	2800.271357	2626.100503	3907.909548	3742	5205.105528	6087.638191	10873.94975	20774.23116	29083.03015
9.00E-05	2524.733668	2889.929648	2886.552764	4186.140704	3742	5209.59799	6454.221106	11297.8995	22375.69849	32312.17588
8.00E-05	2667.58794	2903.487437	2983.366834	4295.537688	3842.110553	5210	7736.271357	12169.38693	23928.75377	36107.54271
7.00E-05	2739.507538	2920.79397	3003.557789	4363.648241	4779.698492	5306.78392	8575.718593	14153.8593	24540.13065	41005.40201
6.00E-05	2953.798995	2961.738693	3026.753769	4597.005025	5197.949749	5557.688442	8658.653266	14807.96985	27646.0804	47307.65327
5.00E-05	3101.477387	2985.085427	3089.326633	4791.095477	5375.537688	5684.693467	8678	15468.83417	31340.38191	57505.47236
4.00E-05	3389.98995	3038.01005	3735.59799	4934.643216	5957.306533	7151.969849	8743.668342	16236.35176	34356.0402	69970.20603
3.00E-05	3531.025126	3569.427136	4368.201005	5044	6266	7600.562814	10017.12563	18448.62312	42366.81407	93417.52764
2.00E-05	3848.40201	4187.688442	4744	5140.020101	6266	9674.452261	12889.20603	23425.88945	52728.90452	134846.8593
1.00E-05	4212.81407	4744	5361.778894	5970	7748.281407	10620	14199.10553	27930.41206	74308.67337	234247.6332

  such as 2739.507538, This value indicates that in d=1, The convergence error is 7e-5 Convergence in the case of 199 The average value of times is 2739.507538. Select convergence error equal to 3e-5,2e-5,1e-5 Several groups of pictures of

You can see that with d The number of iterations increases , So this experimental phenomenon is in good agreement with the hypothesis .

This experiment verifies the assumption that the number of iterations is inversely proportional to entropy , To some extent, it also shows that the completion of convergence 0 and 3 The possibility of looking at it as a complex , It shows that the entropy of two two-dimensional forms can reflect a non progressive two-dimensional form representation , At the same time, there is also a one-dimensional continuous linear progressive representation .

Or the position relationship of points determines a two-dimensional non progressive representation of morphological complex , The value determines the one-dimensional continuous representation of the morphological complex .