unh_cmac.ps

一个老外写的CMAC Neural Network源代码和说明

(s)2062 4170 MS
(i)2251 4170 MS
(C)2378 4170 MS
(s)2699 4170 MS
(s)2956 4170 MS
(i)3149 4170 MS
(C)3277 4170 MS
(a)1087 4320 MS
(a)1222 4320 MS
(a)1479 4320 MS
(i)2742 4320 MS
(C)3196 4320 MS ( )3262 4320 MS ( )3288 4320 MS ( )3313 4320 MS ( )3339 4320 MS ( )3364 4320 MS ( )3390 4320 MS ( )3415 4320 MS ( )3441 4320 MS ( )3466 4320 MS
[66.5 0 0 -66.5 0 0]/Helvetica MF
(i)867 4203 MS
(N)2748 4193 MS
(N)3005 4193 MS
(i)1141 4343 MS
(i)1276 4343 MS
(i)1533 4343 MS (N)1547 4343 MS
[91.438 0 0 -91.438 0 0]/Symbol MF
(=)924 4170 MS
(<)1008 4170 MS
(\242)1141 4175 MS
(-)1200 4170 MS
(\242)1381 4175 MS
(-)1440 4170 MS
(\242)1859 4175 MS
(-)1931 4170 MS
(\242)2111 4175 MS
(-)2183 4170 MS
(\242)2749 4175 MS
(-)2825 4170 MS
(\242)3005 4175 MS
(-)3081 4170 MS
(>)3405 4170 MS
(=)927 4320 MS
(<)1010 4320 MS
(>)1630 4320 MS
(=)2791 4320 MS
[66.5 0 0 -66.5 0 0]/Helvetica MF
(1)1140 4193 MS
(1)1380 4193 MS
(2)1863 4193 MS
(2)2115 4193 MS
(1)1153 4343 MS
(2)1292 4343 MS
[91.438 0 0 -91.438 0 0]/Helvetica MF
(1)2868 4320 MS
(2)2953 4320 MS
(\()1268 4170 MS (\()1298 4170 MS
(\))1526 4170 MS (%)1556 4170 MS
(\))1703 4170 MS
(,)1757 4170 MS
(\()1999 4170 MS (\()2028 4170 MS
(\))2270 4170 MS (%)2300 4170 MS
(\))2446 4170 MS
(,)2501 4170 MS
(.)2547 4170 MS
(.)2574 4170 MS
(.)2601 4170 MS
(,)2647 4170 MS
(\()2893 4170 MS (\()2923 4170 MS
(\))3168 4170 MS (%)3198 4170 MS
(\))3344 4170 MS
(,)1189 4320 MS
(,)1336 4320 MS
(.)1364 4320 MS
(.)1391 4320 MS
(.)1418 4320 MS
(,)1446 4320 MS
(,)2901 4320 MS
(,)2998 4320 MS
(.)3044 4320 MS
(.)3071 4320 MS
(.)3098 4320 MS
(,)3144 4320 MS
( )3492 4320 MS ( )3517 4320 MS ( )3543 4320 MS ( )3568 4320 MS ( )3594 4320 MS ( )3619 4320 MS ( )3645 4320 MS ( )3670 4320 MS ( )3696 4320 MS ( )3722 4320 MS
( )3747 4320 MS ( )3773 4320 MS ( )3798 4320 MS ( )3824 4320 MS ( )3849 4320 MS ( )3875 4320 MS ( )3900 4320 MS ( )3926 4320 MS ( )3951 4320 MS ( )3977 4320 MS
( )4002 4320 MS ( )4028 4320 MS (\()4053 4320 MS (3)4083 4320 MS (\))4134 4320 MS
[92 0 0 -92 0 0]/Helvetica MF
(where % represents the modulus operator, and the index )496 4488 MS
(i references the C parallel layers of)2839 4488 MS
(receptive fields. )496 4594 MS
(A)1161 4594 MS
[58 0 0 -58 0 0]/Helvetica MF
(i)1222 4632 MS
[92 0 0 -92 0 0]/Helvetica MF
( is the normalized N-dimensional address of one corner of the )1235 4594 MS
(hypercubic)3774 4594 MS
n
60 6 1161 4604 B
f
(region spanned by the single excited receptive field in layer i. Due to the properties of the)496 4725 MS
(modulus operator, the receptive field address components in the above equation are only valid)496 4831 MS
(for )496 4937 MS
(s')631 4937 MS
[58 0 0 -58 0 0]/Helvetica MF
(j)695 4950 MS
[92 0 0 -92 0 0]/Helvetica MF
(-i positive. A similar expression can be easily formulated, however, for )708 4937 MS
(s')3575 4937 MS
[58 0 0 -58 0 0]/Helvetica MF
(j)3639 4950 MS
[92 0 0 -92 0 0]/Helvetica MF
(-i negative.)3652 4937 MS
(Since the total number of receptive fields in a space of dimension N can be quite large, the)646 5093 MS
(receptive field addresses )496 5199 MS
(A)1539 5199 MS
[58 0 0 -58 0 0]/Helvetica MF
(i)1600 5237 MS
[92 0 0 -92 0 0]/Helvetica MF
( are typically considered as virtual rather than physical addresses.)1613 5199 MS
n
60 6 1539 5209 B
f
(The next step of the CMAC computation is then to form the scalar physical addresses A')496 5330 MS
[58 0 0 -58 0 0]/Helvetica MF
(i)4081 5368 MS
[92 0 0 -92 0 0]/Helvetica MF
( )4094 5355 MS
(of the)4120 5330 MS
(actual adjustable weights to be used in the output computation:)496 5461 MS
[91.141 0 0 -91.141 0 0]/Symbol MF
(\242)1771 5651 MS
(=)1830 5646 MS
[91.141 0 0 -91.141 0 0]/Helvetica MF
(A)1704 5646 MS
(h)1911 5646 MS
(a)2003 5646 MS
(a)2168 5646 MS
(a)2492 5646 MS
[66.285 0 0 -66.285 0 0]/Helvetica MF
(i)1773 5669 MS
(i)2057 5669 MS
(i)2222 5669 MS
(i)2547 5669 MS (N)2561 5669 MS
[91.141 0 0 -91.141 0 0]/Helvetica MF
(\()1958 5646 MS
(,)2116 5646 MS
(,)2294 5646 MS
(.)2340 5646 MS
(.)2367 5646 MS
(.)2394 5646 MS
(,)2441 5646 MS
(\))2631 5646 MS
[66.285 0 0 -66.285 0 0]/Helvetica MF
(1)2068 5669 MS
(2)2238 5669 MS
[91.141 0 0 -91.141 0 0]/Helvetica MF
( )2664 5646 MS ( )2690 5646 MS ( )2715 5646 MS ( )2741 5646 MS ( )2766 5646 MS ( )2792 5646 MS ( )2817 5646 MS ( )2843 5646 MS ( )2868 5646 MS ( )2894 5646 MS
( )2919 5646 MS ( )2945 5646 MS ( )2971 5646 MS ( )2996 5646 MS ( )3022 5646 MS ( )3047 5646 MS (\()3073 5646 MS (4)3103 5646 MS (\))3154 5646 MS
[92 0 0 -92 0 0]/Helvetica MF
(In this equation, h\(...\) represents any pseudo-random hashing function which operates on the)496 5815 MS
(components )496 5921 MS
(a)1023 5921 MS
[58 0 0 -58 0 0]/Helvetica MF
(ij)1074 5934 MS
[92 0 0 -92 0 0]/Helvetica-Oblique MF
( )1100 5946 MS
[92 0 0 -92 0 0]/Helvetica MF
(of the virtual addresses)1126 5921 MS
[92 0 0 -92 0 0]/Helvetica-Oblique MF
( )2078 5946 MS
%%IncludeFont: Times-Roman
[92 0 0 -92 0 0]/Times-Roman MF
(of  )2104 5921 MS
[92 0 0 -92 0 0]/Helvetica MF
(the receptive fields, producing uniformly distributed)2227 5921 MS
(scalar addresses in the physical weight memory of size M.)496 6029 MS
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12.52 782.039 translate 72 600 div dup neg scale
0 0 transform .25 add round .25 sub exch .25 add round .25 sub exch itransform translate
[92 0 0 -92 0 0]/Helvetica MF
(3)2495 6197 MS
(Finally, the CMAC scalar output y\()646 603 MS
(S)2038 603 MS
(\))2099 603 MS
[92 0 0 -92 0 0]/Helvetica-Oblique MF
( )2130 603 MS
[92 0 0 -92 0 0]/Helvetica MF
(is just the average of the addressed weights:)2156 603 MS
n
60 6 2038 613 B
f
1 j
1 setlinecap
16 sl
n
1864 864 M
1915 864 L
CM 0.258 0.258 scale
s
SM
n
2104 816 M
2181 816 L
CM 0.258 0.258 scale
s
SM
[91.559 0 0 -91.559 0 0]/Helvetica MF
(y)1783 848 MS
(S)1861 848 MS
(C)2109 911 MS
(W)2354 848 MS
(A)2475 848 MS
[66.586 0 0 -66.586 0 0]/Helvetica MF
(i)2543 871 MS
(i)2228 944 MS
(C)2244 739 MS
[91.559 0 0 -91.559 0 0]/Helvetica MF
(\()1828 848 MS
(\))1920 848 MS
([)2445 848 MS
(])2571 848 MS
[91.559 0 0 -91.559 0 0]/Symbol MF
(=)1999 848 MS
(\242)2542 853 MS
[66.586 0 0 -66.586 0 0]/Symbol MF
(=)2243 944 MS
[149.82 0 0 -149.82 0 0]/Symbol MF
(\345)2218 858 MS
[91.559 0 0 -91.559 0 0]/Helvetica MF
(1)2121 781 MS
[66.586 0 0 -66.586 0 0]/Helvetica MF
(1)2278 944 MS
[91.559 0 0 -91.559 0 0]/Helvetica MF
( )2591 848 MS ( )2616 848 MS ( )2642 848 MS ( )2667 848 MS ( )2693 848 MS ( )2718 848 MS ( )2744 848 MS ( )2770 848 MS ( )2795 848 MS ( )2821 848 MS
( )2846 848 MS ( )2872 848 MS ( )2897 848 MS ( )2923 848 MS ( )2948 848 MS ( )2974 848 MS (\()2999 848 MS (5)3029 848 MS (\))3081 848 MS
[92 0 0 -92 0 0]/Helvetica MF
(A vector CMAC output is produced by simply considering the weight memory locations to)496 1092 MS
(contain vector rather than scalar values, and by performing a vector rather than scalar average)496 1198 MS
(in the above equation. The weight memory W can contain integer or real values, depending on)496 1304 MS
(the desired implementation.)496 1410 MS
(Network training is typically based on observed training data pairs )646 1566 MS
(S)3344 1566 MS
[58 0 0 -58 0 0]/Helvetica MF
( )3405 1604 MS
[92 0 0 -92 0 0]/Helvetica MF
(and y)3421 1566 MS
[58 0 0 -58 0 0]/Helvetica MF
(d)3645 1579 MS
[92 0 0 -92 0 0]/Helvetica MF
(\()3677 1566 MS
(S)3708 1566 MS
n
60 6 3344 1576 B
f
(\), where y)3769 1566 MS
[58 0 0 -58 0 0]/Helvetica MF
(d)4172 1579 MS
[92 0 0 -92 0 0]/Helvetica MF
(\()4204 1566 MS
(S)4235 1566 MS
n
60 6 3708 1576 B
f
(\))4296 1566 MS
n
60 6 4235 1576 B
f
(is the desired network output in response to the vector input )496 1672 MS
(S)2958 1672 MS
(. The memory training adjustment)3019 1672 MS
n
60 6 2958 1682 B
f
[92 0 0 -92 0 0]/Symbol MF
(D)496 1785 MS
[92 0 0 -92 0 0]/Helvetica MF
(W is given by:)552 1785 MS
n
2272 1961 M
2323 1961 L
CM 0.258 0.258 scale
s
SM
n
2555 1961 M
2606 1961 L
CM 0.258 0.258 scale
s
SM
[91.141 0 0 -91.141 0 0]/Symbol MF
(D)1683 1945 MS
[91.141 0 0 -91.141 0 0]/Helvetica MF
(W)1739 1945 MS
(y)2137 1945 MS
(S)2269 1945 MS
(y)2474 1945 MS
(S)2552 1945 MS
[66.285 0 0 -66.285 0 0]/Helvetica MF
(d)2191 1968 MS
[91.141 0 0 -91.141 0 0]/Symbol MF
(=)1863 1945 MS
(-)2388 1945 MS
(b)1946 1945 MS
[91.141 0 0 -91.141 0 0]/Helvetica MF
(*)2026 1945 MS
(\()2090 1945 MS
(\()2236 1945 MS
(\))2328 1945 MS
(\()2519 1945 MS
(\))2611 1945 MS
(\))2653 1945 MS
( )2686 1945 MS ( )2711 1945 MS ( )2737 1945 MS ( )2762 1945 MS ( )2788 1945 MS ( )2813 1945 MS ( )2839 1945 MS ( )2864 1945 MS ( )2890 1945 MS ( )2915 1945 MS
( )2941 1945 MS ( )2966 1945 MS ( )2992 1945 MS ( )3017 1945 MS ( )3043 1945 MS ( )3069 1945 MS (\()3094 1945 MS (6)3124 1945 MS (\))3175 1945 MS
[92 0 0 -92 0 0]/Helvetica MF
(where the same value )496 2121 MS
[92 0 0 -92 0 0]/Symbol MF
(D)1420 2121 MS
[92 0 0 -92 0 0]/Helvetica MF
(W is added to each of the C memory locations W[)1476 2121 MS
(A')3507 2121 MS
[58 0 0 -58 0 0]/Helvetica MF
(i)3586 2134 MS
[92 0 0 -92 0 0]/Helvetica MF
(] accessed in the)3599 2121 MS
(computation of y\()496 2234 MS
(S)1203 2234 MS
(\). This is equivalent to the well known LMS adaptation rule for linear adaptive)1264 2234 MS
n
60 6 1203 2244 B
f
(elements. )496 2347 MS
[92 0 0 -92 0 0]/Symbol MF
(b)921 2347 MS
[92 0 0 -92 0 0]/Helvetica MF
( is a constant )972 2347 MS
(training gain)1541 2347 MS
(. If )2043 2347 MS
[92 0 0 -92 0 0]/Symbol MF
(b)2174 2347 MS
[92 0 0 -92 0 0]/Helvetica MF
( is 1.0, the weights are adjusted to force the network)2225 2347 MS
n
501 6 1541 2357 B
f
(output y\()496 2467 MS
(S)854 2467 MS
(\) to be exactly equal to the training target y)915 2467 MS
[58 0 0 -58 0 0]/Helvetica MF
(d)2657 2480 MS
[92 0 0 -92 0 0]/Helvetica MF
(\()2689 2467 MS
(S)2720 2467 MS
n
60 6 854 2477 B
f
(\). If )2781 2467 MS
[92 0 0 -92 0 0]/Symbol MF
(b)2943 2467 MS
[92 0 0 -92 0 0]/Helvetica MF
( is 0.5, the network output is)2994 2467 MS
n
60 6 2720 2477 B
f
(adjusted to fall halfway between the old output value and the training target. If )496 2587 MS
[92 0 0 -92 0 0]/Symbol MF
(b)3682 2587 MS
[92 0 0 -92 0 0]/Helvetica MF
( is 0.0, the)3733 2587 MS
(weights are not changed.)496 2700 MS
[92 0 0 -92 0 0]/Helvetica-Bold MF
(EXTENSIONS TO THE ALBUS CMAC NEURAL NETWORK)496 2959 MS