Influence of black and white pixel distribution on iteration times

( A , B)---81*30*2---(1,0)(0,1)

Classify with neural network A and B, Give Way A yes mnist Of 0, Give Way B yes mnist Of 1-9. Reduce it to 9*9. But let B Central African 0 The number of values is equal to 14,14*0.9,14*0.8,…,14*0.2. Compare in Africa 0 When the number of values is the same ,0 And B The number of iterations of classification and non 0 The relationship between the number of values .

	1	2	3	4	5	6	7	8	9
14	8028.492	7170.111	4563.92	6931.015	3712.191	5297.548	7865.568	4449.216	7524.784	1.00E-05
14*0.9	10512.76	7085.307	3957.085	5011.256	4287.045	4568.633	5539.92	3349.618	5888.221	1.00E-05
14*0.8	12175.1	8909.668	5329.327	5052.623	3973.759	3833.618	4698.231	3198.503	4814.271	1.00E-05
14*0.7	14806.39	9178.673	3901.99	4177.176	3760.663	3874.573	5672.623	3730	5220.161	1.00E-05
14*0.6	18403.16	12387.02	4450.814	4873.387	3520	4857.91	4257.085	4653.035	4988.834	1.00E-05
14*0.5	18569.19	16936.02	5504	4610	7360.563	5293.357	5994.452	5058.241	7303.035	1.00E-05
14*0.4	32946.66	21557.49	8226.271	6770	8412	6036	8845.538	6021.759	7886.734	1.00E-05
14*0.3	77674.51	32116.68	10478.2	8889.276	10278.59	9077.477	15703.26	9730.201	10279.68	1.00E-05
14*0.2	104475.7	59634.69	15644.66	15570.22	18435.36	16665.61	28967.59	15053.71	17749.77	1.00E-05

such as 14*0.5 That's ok , Show in B Random reservation in 7 About a non 0 value , The convergence error is 1e-5, convergence 199 Time Statistical average . So every line B The number of white dots in is the same . The difference in the number of iterations depends only on the distribution of white dots .

Statistics can find some obvious rules ,

When B by 3,4,5,6,8,9 when , The shape of the iteration number curve looks very consistent .

7 The value of is only slightly larger than the above situation .

But when B=1,2 The number of iterations is much larger ,

So the shape of the iteration number curve is in the case of equal value , Approximately divided into 3 Kind of ：1,2 and 3-9.

0	1	2	3	4	5	6	7	8	9
44.4698	27.7134	41.7294	17.9278	15.9034	16.9892	17.8176	14.0056	19.4652	15.9438

This phenomenon and 1-9 Central African 0 The proportion of values is highly correlated ,3-9 Non - 0 The number of values is about 16.8 individual , This value is less than 1 Of 27.7 Less than 2 Of 41.7 individual .

3<1<2.

But this order is related to the number of iterations

3<2<1

Not the same. .

because

 C(16,2)<C(27,2)<C(41.2)

If the number of iterations is inversely proportional to entropy , I think it's in 0 In the external environment, from the distribution form, such as 2 Of 41 Click here 3 The number of points may be smaller than that from the distribution form, such as 1 Of 27 Choose... From the points 3 The possibility of a point . Or equivalently think of form 0 hold 2 Medium 41 There are fewer points , But the 1 Of 27 There are more points .

C(16,2) <C(41-m .2) <C(27+n ,2)

Or equivalent understanding form 0 hold 2 Shrunk , But the 1 Magnified . Therefore, the difference between forms may be expressed equivalently by the cardinality in the permutation .