我正在使用用C ++编写的神经网络库（称为FANN）来尝试学习和预测数学序列。它使用Node.js使用库的包装器实现。在这个特定的例子中，我试图通过将位置作为输入并将数值作为输出来使神经网络学习斐波那契序列。我的网络代码如下：
// This neural network calculates the fibonacci sequence
var net = new fanntom.standard(1,3,1);
var data = [
[[0], [0]],
[[1], [1]],
[[2], [1]],
[[3], [2]],
[[4], [3]],
[[5], [5]],
[[6], [8]],
[[7], [13]],
[[8], [21]],
[[9], [34]]
]
net.activation_function_hidden('FANN_LINEAR');
net.activation_function_output('FANN_LINEAR');
net.train(data, { error: 0.00001 })
;[0,1,2,3,4,5,6,7,8,9].forEach(function(a) {
var c = net.run([a]);
console.log("fibonacci sequence position " + a + " -> " + c)
})
以下是我收到的输出示例：
Max epochs 100000. Desired error: 0.0000100000.
Epochs 1. Current error: 187.3569030762. Bit fail 9.
Epochs 1000. Current error: 34.0731391907. Bit fail 8.
Epochs 2000. Current error: 34.0791511536. Bit fail 8.
Epochs 3000. Current error: 34.0858230591. Bit fail 8.
Epochs 4000. Current error: 34.0767517090. Bit fail 8.
Epochs 5000. Current error: 34.0764961243. Bit fail 8.
Epochs 6000. Current error: 34.0817642212. Bit fail 8.
Epochs 7000. Current error: 34.0817031860. Bit fail 8.
Epochs 8000. Current error: 34.0721969604. Bit fail 8.
Epochs 9000. Current error: 34.0795860291. Bit fail 8.
Epochs 10000. Current error: 34.0741653442. Bit fail 8.
Epochs 11000. Current error: 34.0833320618. Bit fail 8.
Epochs 12000. Current error: 34.0826034546. Bit fail 8.
Epochs 13000. Current error: 34.0909080505. Bit fail 8.
Epochs 14000. Current error: 34.0811843872. Bit fail 8.
Epochs 15000. Current error: 34.0729255676. Bit fail 8.
Epochs 16000. Current error: 34.0812034607. Bit fail 8.
Epochs 17000. Current error: 34.0855636597. Bit fail 8.
Epochs 18000. Current error: 34.0725784302. Bit fail 8.
Epochs 19000. Current error: 34.0898971558. Bit fail 8.
Epochs 20000. Current error: 34.0742073059. Bit fail 8.
Epochs 21000. Current error: 34.0820236206. Bit fail 8.
Epochs 22000. Current error: 34.0867233276. Bit fail 8.
Epochs 23000. Current error: 34.0676040649. Bit fail 8.
Epochs 24000. Current error: 34.0834121704. Bit fail 8.
Epochs 25000. Current error: 34.0862617493. Bit fail 8.
Epochs 26000. Current error: 34.0691108704. Bit fail 8.
Epochs 27000. Current error: 34.0897636414. Bit fail 8.
Epochs 28000. Current error: 34.0828247070. Bit fail 8.
Epochs 29000. Current error: 34.0744514465. Bit fail 8.
Epochs 30000. Current error: 34.0876007080. Bit fail 8.
Epochs 31000. Current error: 34.0852851868. Bit fail 8.
Epochs 32000. Current error: 34.0892257690. Bit fail 8.
Epochs 33000. Current error: 34.0835494995. Bit fail 8.
Epochs 34000. Current error: 34.0838394165. Bit fail 8.
Epochs 35000. Current error: 34.0851097107. Bit fail 8.
Epochs 36000. Current error: 34.0754585266. Bit fail 8.
Epochs 37000. Current error: 34.0893363953. Bit fail 8.
Epochs 38000. Current error: 34.0729141235. Bit fail 8.
Epochs 39000. Current error: 34.0780258179. Bit fail 8.
Epochs 40000. Current error: 34.0776443481. Bit fail 8.
Epochs 41000. Current error: 34.0812759399. Bit fail 8.
Epochs 42000. Current error: 34.0707893372. Bit fail 8.
Epochs 43000. Current error: 34.0810317993. Bit fail 8.
Epochs 44000. Current error: 34.0846099854. Bit fail 8.
Epochs 45000. Current error: 34.0794601440. Bit fail 8.
Epochs 46000. Current error: 34.0818710327. Bit fail 8.
Epochs 47000. Current error: 34.0692596436. Bit fail 8.
Epochs 48000. Current error: 34.0687141418. Bit fail 8.
Epochs 49000. Current error: 34.0702171326. Bit fail 8.
Epochs 50000. Current error: 34.0730400085. Bit fail 8.
Epochs 51000. Current error: 34.0896568298. Bit fail 8.
Epochs 52000. Current error: 34.0715599060. Bit fail 8.
Epochs 53000. Current error: 34.0734481812. Bit fail 8.
Epochs 54000. Current error: 34.0772285461. Bit fail 8.
Epochs 55000. Current error: 34.0646171570. Bit fail 8.
Epochs 56000. Current error: 34.0669212341. Bit fail 8.
Epochs 57000. Current error: 34.0733718872. Bit fail 8.
Epochs 58000. Current error: 34.0881729126. Bit fail 8.
Epochs 59000. Current error: 34.0861282349. Bit fail 8.
Epochs 60000. Current error: 34.0846023560. Bit fail 8.
Epochs 61000. Current error: 34.0738449097. Bit fail 8.
Epochs 62000. Current error: 34.0877456665. Bit fail 8.
Epochs 63000. Current error: 34.0803222656. Bit fail 8.
Epochs 64000. Current error: 34.0794219971. Bit fail 8.
Epochs 65000. Current error: 34.0926132202. Bit fail 8.
Epochs 66000. Current error: 34.0831146240. Bit fail 8.
Epochs 67000. Current error: 34.0780830383. Bit fail 8.
Epochs 68000. Current error: 34.0757255554. Bit fail 8.
Epochs 69000. Current error: 34.0820083618. Bit fail 8.
Epochs 70000. Current error: 34.0746269226. Bit fail 8.
Epochs 71000. Current error: 34.0959663391. Bit fail 8.
Epochs 72000. Current error: 34.0699691772. Bit fail 8.
Epochs 73000. Current error: 34.0816230774. Bit fail 8.
Epochs 74000. Current error: 34.0853195190. Bit fail 8.
Epochs 75000. Current error: 34.0910835266. Bit fail 8.
Epochs 76000. Current error: 34.0766525269. Bit fail 8.
Epochs 77000. Current error: 34.0885848999. Bit fail 8.
Epochs 78000. Current error: 34.0684432983. Bit fail 8.
Epochs 79000. Current error: 34.0836944580. Bit fail 8.
Epochs 80000. Current error: 34.0931396484. Bit fail 8.
Epochs 81000. Current error: 34.0903816223. Bit fail 8.
Epochs 82000. Current error: 34.0796318054. Bit fail 8.
Epochs 83000. Current error: 34.0709342957. Bit fail 8.
Epochs 84000. Current error: 34.0812988281. Bit fail 8.
Epochs 85000. Current error: 34.0859451294. Bit fail 8.
Epochs 86000. Current error: 34.0641326904. Bit fail 8.
Epochs 87000. Current error: 34.0925521851. Bit fail 8.
Epochs 88000. Current error: 34.0828132629. Bit fail 8.
Epochs 89000. Current error: 34.0705337524. Bit fail 8.
Epochs 90000. Current error: 34.0698318481. Bit fail 8.
Epochs 91000. Current error: 34.0850410461. Bit fail 8.
Epochs 92000. Current error: 34.0921783447. Bit fail 8.
Epochs 93000. Current error: 34.0679855347. Bit fail 8.
Epochs 94000. Current error: 34.0932426453. Bit fail 8.
Epochs 95000. Current error: 34.0735969543. Bit fail 8.
Epochs 96000. Current error: 34.0687332153. Bit fail 8.
Epochs 97000. Current error: 34.0628662109. Bit fail 8.
Epochs 98000. Current error: 34.0813598633. Bit fail 8.
Epochs 99000. Current error: 34.0901985168. Bit fail 8.
Epochs 100000. Current error: 34.0652198792. Bit fail 8.
fibonacci sequence position 0 -> -3.7995970795170027
fibonacci sequence position 1 -> -1.3996559488192886
fibonacci sequence position 2 -> 1.0002851818784273
fibonacci sequence position 3 -> 3.4002263125761414
fibonacci sequence position 4 -> 5.800167443273858
fibonacci sequence position 5 -> 8.200108573971574
fibonacci sequence position 6 -> 10.60004970466929
fibonacci sequence position 7 -> 12.999990835367003
fibonacci sequence position 8 -> 15.39993196606472
fibonacci sequence position 9 -> 17.799873096762436
我的问题是，如果所有输入都是正数，神经网络如何产生负输出？另外，为什么误差如此之大，特别是对于第一个时期？
答案 0 :(得分：2)
The output can be negative because it's a combination of inputs, weights, and transfer functions. Weights are randomly initialized with average 0, so about half of them are negative. And since they're randomly initialized, you expect a huge error before the first training. It's literally a guess.
BTW, your error stabilizes after 1000 iterations. Considering the size of the problem domain, it probably stabilized after 50 iterations. You probably spent 2000x more time than necessary.