若是每次測試那七十四行的程式，都得重新訓練神經網絡之
腦
腦是由稱為神經元的神經細胞所組成的神經系統控制中心，是所有脊椎動物和大部分無脊椎動物都具有的一個器官，只有少數的無脊椎動物沒有腦，例如海綿、水母、成年的海鞘與海星，它們以分散或者局部的神經網絡代替。
許多動物的腦位於頭部，通常是靠近主要的感覺器官，例如視覺、聽覺、前庭系統、味覺和嗅覺。腦是脊椎動物身體中最複雜的器官 。在普通人類的大腦皮質（腦中最大的部分）中，包含150-330億個神經元，[1]每一個神經元都通過突觸和其他數千個神經元相連接 。這些神經元之間通過稱作軸突的原生質纖維進行較長距離互相聯結，可以將一種稱作動作電位的衝動信號，在腦的不同區域之間或者向身體的特定接收細胞傳遞。脊椎動物的腦由顱骨保護。腦與脊髓構成中樞神經系統。中樞神經系統的細胞依靠複雜的聯繫來處理傳遞信息。腦是感情、思考、生命得以維持的中樞。它控制和協調行為、身體內穩態（身體功能，例如心跳、血壓、體溫等）以及精神活動（例如認知、情感、記憶和學習）。
從生理上來說，腦的功能就是控制身體的其他器官。腦對其他器官的作用方式，一是調製肌肉的運動模式，二是通過分泌一些稱為荷爾蒙的化學物質。集中的控制方式，可以對環境的變化做出迅速而一致的反應。 一些基本的反應，例如反射，可以通過脊髓或者周邊神經節來控制，然而基於多種感官輸入，有心智、有目的的動作，只有通過腦中樞的整合能力才能控制。
關於單個腦細胞的運作機制，現今已經有了比較詳細的了解；然而數以兆億的神經元如何以集群的方式合作，還是一個未解決的問題 。[2]現代神經科學中，新近的模型將腦看作一種生物計算機，雖然運行的機制和電子計算機很不一樣，但是它們從周圍世界中獲得信息、存儲信息、以多種方式處理信息的功能是類似的，它有點像計算機中的中央處理器（CPU）。
本文會對各種動物的腦進行比較，特別是脊椎動物的腦，而人腦將被作為各種腦的其中一種進行討論。人腦的特別之處會在人腦條目中探討，因為其中很多話題在人腦的前提下討論，內容會豐富得多 。其中最重要的，是腦疾病與腦損傷造成的後果，它會被放在人腦條目中探討，因為人腦的大多數常見疾病並不見於其他物種，即使有，它們的表現形式也可能不同。
人腦立體旋轉剖面圖
───
，顯然有點荒謬！所以此處設想如何『保存大腦』？甚或該怎麼『移植』的呢？？研究一下『network.py』︰
"""
network.py
~~~~~~~~~~
A module to implement the stochastic gradient descent learning
algorithm for a feedforward neural network. Gradients are calculated
using backpropagation. Note that I have focused on making the code
simple, easily readable, and easily modifiable. It is not optimized,
and omits many desirable features.
"""
#### Libraries
# Standard library
import random
# Third-party libraries
import numpy as np
class Network(object):
def __init__(self, sizes):
"""The list ``sizes`` contains the number of neurons in the
respective layers of the network. For example, if the list
was [2, 3, 1] then it would be a three-layer network, with the
first layer containing 2 neurons, the second layer 3 neurons,
and the third layer 1 neuron. The biases and weights for the
network are initialized randomly, using a Gaussian
distribution with mean 0, and variance 1. Note that the first
layer is assumed to be an input layer, and by convention we
won't set any biases for those neurons, since biases are only
ever used in computing the outputs from later layers."""
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
就會發現這個『腦』就是保存在
self.sizes
self.biases
self.weights
裡。如是假使知道『numpy』的 array 檔案存取之法︰
numpy.savez
- numpy.savez(file, *args, **kwds)
- Save several arrays into a single file in uncompressed .npz format.
If arguments are passed in with no keywords, the corresponding variable names, in the .npz file, are ‘arr_0’, ‘arr_1’, etc. If keyword arguments are given, the corresponding variable names, in the .npz file will match the keyword names.
Parameters: file : str or file
Either the file name (string) or an open file (file-like object) where the data will be saved. If file is a string, the .npz extension will be appended to the file name if it is not already there.
args : Arguments, optional
Arrays to save to the file. Since it is not possible for Python to know the names of the arrays outside savez, the arrays will be saved with names “arr_0”, “arr_1”, and so on. These arguments can be any expression.
kwds : Keyword arguments, optional
Arrays to save to the file. Arrays will be saved in the file with the keyword names.
Returns: None
See also
- save
- Save a single array to a binary file in NumPy format.
- savetxt
- Save an array to a file as plain text.
- savez_compressed
- Save several arrays into a compressed .npz archive
───
以及
numpy.load
- numpy.load(file, mmap_mode=None, allow_pickle=True, fix_imports=True, encoding=’ASCII’)
- Load arrays or pickled objects from .npy, .npz or pickled files.
Parameters: file : file-like object or string
The file to read. File-like objects must support the seek() and read() methods. Pickled files require that the file-like object support the readline() method as well.
mmap_mode : {None, ‘r+’, ‘r’, ‘w+’, ‘c’}, optional
If not None, then memory-map the file, using the given mode (see numpy.memmap for a detailed description of the modes). A memory-mapped array is kept on disk. However, it can be accessed and sliced like any ndarray. Memory mapping is especially useful for accessing small fragments of large files without reading the entire file into memory.
allow_pickle : bool, optional
Allow loading pickled object arrays stored in npy files. Reasons for disallowing pickles include security, as loading pickled data can execute arbitrary code. If pickles are disallowed, loading object arrays will fail. Default: True
fix_imports : bool, optional
Only useful when loading Python 2 generated pickled files on Python 3, which includes npy/npz files containing object arrays. If fix_imports is True, pickle will try to map the old Python 2 names to the new names used in Python 3.
encoding : str, optional
What encoding to use when reading Python 2 strings. Only useful when loading Python 2 generated pickled files on Python 3, which includes npy/npz files containing object arrays. Values other than ‘latin1’, ‘ASCII’, and ‘bytes’ are not allowed, as they can corrupt numerical data. Default: ‘ASCII’
Returns: result : array, tuple, dict, etc.
Data stored in the file. For .npz files, the returned instance of NpzFile class must be closed to avoid leaking file descriptors.
Raises: IOError
If the input file does not exist or cannot be read.
ValueError
The file contains an object array, but allow_pickle=False given.
See also
save, savez, savez_compressed, loadtxt
- memmap
- Create a memory-map to an array stored in a file on disk.
───
再輔之以 list → array 轉換之法︰
Array creation
See also
Introduction
There are 5 general mechanisms for creating arrays:
- Conversion from other Python structures (e.g., lists, tuples)
- Intrinsic numpy array array creation objects (e.g., arange, ones, zeros, etc.)
- Reading arrays from disk, either from standard or custom formats
- Creating arrays from raw bytes through the use of strings or buffers
- Use of special library functions (e.g., random)
This section will not cover means of replicating, joining, or otherwise expanding or mutating existing arrays. Nor will it cover creating object arrays or structured arrays. Both of those are covered in their own sections.
Converting Python array_like Objects to Numpy Arrays
In general, numerical data arranged in an array-like structure in Python can be converted to arrays through the use of the array() function. The most obvious examples are lists and tuples. See the documentation for array() for details for its use. Some objects may support the array-protocol and allow conversion to arrays this way. A simple way to find out if the object can be converted to a numpy array using array() is simply to try it interactively and see if it works! (The Python Way).
Examples:
>>> x = np.array([2,3,1,0])
>>> x = np.array([2, 3, 1, 0])
>>> x = np.array([[1,2.0],[0,0],(1+1j,3.)]) # note mix of tuple and lists,
and types
>>> x = np.array([[ 1.+0.j, 2.+0.j], [ 0.+0.j, 0.+0.j], [ 1.+1.j, 3.+0.j]])
果可保存『大腦』乎？？！！
>>> s = network.np.array(net.sizes)
>>> w1 = net.weights[0]
>>> w2 = net.weights[1]
>>> b1 = net.biases[0]
>>> b2 = net.biases[1]
>>> network.np.savez("swb",s=s,w1=w1,w2=w2,b1=b1,b2=b2)
>>> npzfile = network.np.load("swb.npz")
>>> npzfile.files
['s', 'b2', 'w2', 'w1', 'b1']
>>> list(npzfile["s"])
[784, 30, 10]
>>>
pi@raspberrypi ~ 
cd src
pi@raspberrypi ~/neural-networks-and-deep-learning/src ![python Python 2.7.9 (default, Mar 8 2015, 00:52:26) [GCC 4.9.2] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> import mnist_loader >>> training_data, validation_data, test_data = \ ... mnist_loader.load_data_wrapper() >>> import network >>> net = network.Network([784, 30, 10]) >>> net.SGD(training_data, 30, 10, 3.0, test_data=test_data) Epoch 0: 9013 / 10000 Epoch 1: 9181 / 10000 Epoch 2: 9277 / 10000 Epoch 3: 9333 / 10000 Epoch 4: 9374 / 10000 Epoch 5: 9374 / 10000 Epoch 6: 9375 / 10000 Epoch 7: 9369 / 10000 Epoch 8: 9415 / 10000 Epoch 9: 9435 / 10000 Epoch 10: 9428 / 10000 Epoch 11: 9423 / 10000 Epoch 12: 9452 / 10000 Epoch 13: 9442 / 10000 Epoch 14: 9434 / 10000 Epoch 15: 9453 / 10000 Epoch 16: 9480 / 10000 Epoch 17: 9468 / 10000 Epoch 18: 9461 / 10000 Epoch 19: 9483 / 10000 Epoch 20: 9462 / 10000 Epoch 21: 9477 / 10000 Epoch 22: 9474 / 10000 Epoch 23: 9491 / 10000 Epoch 24: 9474 / 10000 Epoch 25: 9487 / 10000 Epoch 26: 9453 / 10000 Epoch 27: 9462 / 10000 Epoch 28: 9472 / 10000 Epoch 29: 9482 / 10000 >>> </pre> <span style="color: #666699;">大約經過五十分鐘後，在樹莓派 3 上可以訓練完成！或許是作者的運氣不好，最好的成績只有](http://www.freesandal.org/wp-content/ql-cache/quicklatex.com-6adaba18cc234b30b19f584e36f90fac_l3.png "Rendered by QuickLaTeX.com")
9491 / 10000$ 而已？？
是『多項式』 
的『解』，此處係數 
都是『有理數』。如果我們建構一個『對稱函數』
應該就是 
的吧。如果將這些『解』 
，此處是說上一排的『解』的『位置』用下一排的『解』來『置換』，由於 
函數的特殊『形式』，我們會得到 
。事實上對於任意的『置換』，都會有 
。所以函數 
有兩個根 
，
，和
與 
。
是方程式的一個根，假設另一個根是 
，由於
。而且 
。也就是說這兩個根是熟悉的 
與 
。於是一個『對稱函數』 
是 
的形式﹐那麼必然有另一個根 
是 
的形式，這就是由於那個『多項式』的係數是『有理數』的原故，它的『二次方根』的解，總是『成對』出現的啊！於是『二次方根』解的個數也必然是『偶數』的了！！
有三個根 
的情況，此時 
，假使說 
就必然是『有理數』。而 且從 
與 
來看，三次方程式至少有一個實數解。如果我們用 
來消去 
這個『平方項』
![= x^3 - (\lambda_1 + \lambda_2 + \lambda_3) x^2 + \left[\lambda_1 \cdot \lambda_2 + \lambda_3 \cdot (\lambda_1 + \lambda_2) \right] x - \lambda_1 \lambda_2 \lambda_3](http://www.freesandal.org/wp-content/ql-cache/quicklatex.com-88a0e25d80a5ce8700bd12746923c483_l3.png "Rendered by QuickLaTeX.com")
，這建議著 
，也就是說有一個根可以表示成『特殊兩數』之和。假使我們將 
代入方程式，得到
，假使『選擇』 
，又可以得到 
，是這一組 
所滿足的『聯立方程式』，可以將它改寫成
，與
，這卻正是說 
是一個『二次方程式』的根。求解後可以得到
![z=u+v=\sqrt[3]{-{q\over 2}+ \sqrt{{q^{2}\over 4}+{p^{3}\over 27}}} +\sqrt[3]{-{q\over 2}- \sqrt{{q^{2}\over 4}+{p^{3}\over 27}}}](http://www.freesandal.org/wp-content/ql-cache/quicklatex.com-b6ec5b37806db9464e40ea7e4aa87795_l3.png "Rendered by QuickLaTeX.com")
。然而三次方程式不是應該有三個解的嗎？假使 
，那個 『根號』 
是正實數，因此 
是兩個『立方根』 之和，所以也是實數。那麼要如何求得另外兩個解的呢？假使設想 
而 
，然而 
，所以可以解得 
，於是 
的三個解是 ![\sqrt[3]{\alpha}, \sqrt[3]{\alpha} \ \omega, \sqrt[3]{\alpha} \ {\omega}^2](http://www.freesandal.org/wp-content/ql-cache/quicklatex.com-b3364f61c4c014492188e13ce8072b71_l3.png "Rendered by QuickLaTeX.com")
，最終我們可以得到 
、
，以及 
三組答案，現今人們將這個方法叫做『卡爾達諾法』。『吉羅拉莫‧卡爾達諾』 Girolamo Cardano 是意大利文藝復興時期百科全書式的學者，主要成就在數學、物理、醫學方面。在一五四五年出版的《大術》一書中，他首先發表了三次方程式的一般解法。然而就數學史而言，真正發現此三次代數方程式解法的或許是『尼科洛‧塔塔利亞』 Niccolò Tartaglia，兩人也因此而結怨。這本書中還記載了四次代數方程的一般解法，其實是由他的學生『費拉里』所發現的？這簡直是特別為那個『
看成『行向量』的耶？所謂『手寫阿拉伯數字』難道不是『二維圖象』的乎？？