Convergence rules for 4 * 4 image weights

In the previous experiment , The weights of the binary neural network converge according to the following rules

Distribute by column ,

Positive and negative symmetry ,

A0 Column or B0 The column height is prominent , And A0 Column or B0 The positive and negative relationships between columns are opposite

coincidence 1 The height of the column is small , And the positive and negative relationship is A0 Column or B0 The column is opposite

coincidence 0 The column does not change

A0 Column ,B0 Column , coincidence 1 Column , coincidence 0 The columns are almost consistent with each other .

This time verify whether this rule applies to larger 4*4 Pictures of the

(A,B)---16*16*2---(1,0)(0,1)

Classify with neural network A and B,A and B There are only 13 individual 1. Such a group of pictures contains all the weights of the binary neural network 4 Components . Yes A0 Column x=0,15;B0 Column x=2,3, coincidence 0 Column x=1; coincidence 1 Column x=4,5,6,7,8,9,10,11,12,13.

According to the rules ,A0 Column sum B0 The positive and negative of the column are opposite , coincidence 1 Column sum A0 Column or B0 The positive and negative of the column are opposite , coincidence 0 No change in column , Reuse rights openscad Draw

It can be clearly observed from the figure x=0,15 The two columns of are consistent with each other ,x=2,3 The two columns of are consistent with each other , And x=0,15 and x=2,3 The two groups of positive and negative are opposite .

convergence w1

-0.329	0.083	0.3359	0.2429	-0.006	0.063	-0.062	0.037	0.004	0.041	0.023	-0.066	-0.05	0.045	0.002	-0.224
1.2635	-0.088	-1.147	-1.238	-0.04	0.0121	-0.046	-0.044	-0.01	-0.082	-0.078	0.0891	0.0771	0.0511	0.0041	1.1565
1.0242	-0.062	-0.968	-1.025	-0.076	-0.046	0.005	0.049	0.019	0.041	0.035	-0.034	-0.066	0.039	0.003	0.9232
-1.357	0.075	1.4721	1.3881	-0.065	-0.006	-0.012	0.0137	-0.018	-0.025	0.0537	-0.085	0.0137	0.0237	0.0637	-1.323
0.6707	-0.016	-0.697	-0.628	-0.099	-0.008	-0.033	-0.012	0.0517	0.0757	0.0397	0.0517	0.0137	0.0017	-0.093	0.5397
-0.121	0.077	0.1824	0.2164	-0.071	-0.033	0.0742	-0.085	0.0582	0.0282	0.0442	0.0862	-0.037	0.0082	0.0102	-0.057
-0.821	0.037	0.868	0.961	-0.072	0.0184	-0.03	0.0974	0.0734	0.1154	-0.012	-0.072	-0.064	0.0064	-0.066	-0.888
1.0992	-0.05	-1.017	-1.057	-0.043	0.0803	-0.007	0.0503	-0.073	-0.075	0.0443	-0.053	-0.049	-0.059	0.0603	1.1132
-1.13	-0.064	1.0965	1.0745	-0.066	0.0056	0.0176	-0.016	-0.064	-0.012	0.1086	0.0866	-0.056	0.0446	0.0056	-1.044
-1.183	-0.026	1.3128	1.1658	######	-0.026	-0.034	0.0509	0.0629	0.0469	-0.046	0.0019	-0.054	0.0429	-0.01	-1.268
0.2227	0.083	-0.182	-0.259	-0.033	0.0896	-0.025	0.0656	-0.055	-0.055	0.0196	-0.043	-0.025	0.0856	0.0356	0.0857
0.6218	-0.008	-0.611	-0.667	-0.05	0.083	0.015	0.025	0.059	0.071	-0.068	-0.11	-0.018	0.019	-0.1	0.6638
1.1543	0.097	-1.257	-1.162	-0.034	-0.104	-0.015	0.0505	0.0305	-0.048	0.0185	-0.096	0.0365	0.0505	0.0565	1.2793
-1.458	0.055	1.4164	1.4184	-0.09	0.0348	0.0548	0.0328	0.0768	-0.015	0.0588	-0.03	-0.013	-0.074	-0.015	-1.327
1.0669	-0.078	-1.172	-1.184	-0.067	0.1082	-0.005	-0.043	0.0522	0.0382	-0.011	0.0222	-0.069	-0.073	0.0182	1.2459
0.1969	0.069	-0.053	-0.214	0.061	0.059	0.011	-0.034	0.015	-0.046	-0.062	-0.042	0.029	0.013	-0.086	0.0939

initial w1

-0.084	0.083	0.079	-0.014	-0.018	0.051	-0.074	0.025	-0.008	0.029	0.011	-0.078	-0.062	0.033	-0.01	0.021
0.023	-0.088	0.077	-0.014	-0.056	-0.004	-0.062	-0.06	-0.026	-0.098	-0.094	0.073	0.061	0.035	-0.012	-0.084
0.047	-0.062	0.029	-0.028	-0.056	-0.026	0.025	0.069	0.039	0.061	0.055	-0.014	-0.046	0.059	0.023	-0.054
0.041	0.075	0.097	0.013	-0.042	0.017	0.011	0.037	0.005	-0.002	0.077	-0.062	0.037	0.047	0.087	0.075
0.041	-0.016	-0.046	0.023	-0.078	0.013	-0.012	0.009	0.073	0.097	0.061	0.073	0.035	0.023	-0.072	-0.09
0.029	0.077	0.031	0.065	-0.072	-0.034	0.073	-0.086	0.057	0.027	0.043	0.085	-0.038	0.007	0.009	0.093
0.041	0.037	-0.02	0.073	-0.098	-0.008	-0.056	0.071	0.047	0.089	-0.038	-0.098	-0.09	-0.02	-0.092	-0.026
-0.02	-0.05	0.093	0.053	-0.052	0.071	-0.016	0.041	-0.082	-0.084	0.035	-0.062	-0.058	-0.068	0.051	-0.006
-0.088	-0.064	0.035	0.013	-0.086	-0.014	-0.002	-0.036	-0.084	-0.032	0.089	0.067	-0.076	0.025	-0.014	-0.002
0.047	-0.026	0.055	-0.092	-0.028	-0.054	-0.062	0.023	0.035	0.019	-0.074	-0.026	-0.082	0.015	-0.038	-0.038
0.039	0.083	0.009	-0.068	-0.026	0.097	-0.018	0.073	-0.048	-0.048	0.027	-0.036	-0.018	0.093	0.043	-0.098
-0.046	-0.008	0.069	0.013	-0.038	0.095	0.027	0.037	0.071	0.083	-0.056	-0.098	-0.006	0.031	-0.088	-0.004
-0.028	0.097	-0.042	0.053	-0.002	-0.072	0.017	0.083	0.063	-0.016	0.051	-0.064	0.069	0.083	0.089	0.097
-0.054	0.055	0.033	0.035	-0.07	0.055	0.075	0.053	0.097	0.005	0.079	-0.01	0.007	-0.054	0.005	0.077
-0.096	-0.078	-0.026	-0.038	-0.084	0.091	-0.022	-0.06	0.035	0.021	-0.028	0.005	-0.086	-0.09	0.001	0.083
0.085	0.069	0.063	-0.098	0.065	0.063	0.015	-0.03	0.019	-0.042	-0.058	-0.038	0.033	0.017	-0.082	-0.018

convergence w1	initial w1
0.083	0.083
-0.088	-0.088
-0.062	-0.062
0.075	0.075
-0.016	-0.016
0.077	0.077
0.037	0.037
-0.05	-0.05
-0.064	-0.064
-0.026	-0.026
0.083	0.083
-0.008	-0.008
0.097	0.097
0.055	0.055
-0.078	-0.078
0.069	0.069

Compare the second column of the two sets of weights , It's the same , So coincidence 0 Column weights do not change . These two are in line with the rules .

But coincidence 1 The changing relationship of columns becomes complicated . coincidence 1 The columns are not consistent with each other , It is also difficult to find and A0 and B0 And coincidence 1 The positive and negative relationship of columns . Therefore, the distribution of weight can be modified as

Distribute by column , Positive and negative symmetry ,

A0 Column or B0 The column is significant , And A0 Column or B0 The positive and negative relationships between columns are opposite

coincidence 1 The height of the column is small

coincidence 0 The column does not change