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https://student.csc.liv.ac.uk/internal/exams/papers/Jan2018/COMP305.pdf

PAPER CODE NO.

COMP 305

EXAMINER : Dr Irina V. Biktasheva DEPARTMENT : Computer Science Tel. No. 54267

First Semester Examinations 2017/

Biocomputation

TIME ALLOWED: Two and a Half Hours

INSTRUCTIONS TO CANDIDATES

Answer FOUR questions.

If you attempt to answer more questions than the required number of

questions, the marks awarded for the excess questions answered will be

discarded (starting with the lowest mark).

Each question is worth 25 marks

1 History and Concepts.

1(a) Why are biology inspired Artificial Neural Networks and Genetic Algorithms
now considered part of Computer Science, not Computational Biology?
[2 marks]

1(b) What general problems are solved by Artificial Neural Networks? Give a
couple of examples.
[4 marks]

1? What problems can be solved by Genetic Algorithms? Give a couple of
examples.
[4 marks]

1(d) Large numbers of academic texts are stored and made available in online
repositories. For older texts, it is necessary to convert from a paper document to
an electronic document. An Optical Character Recognition (OCR) system can
be used for that purpose.

i) What kind of problem is solved by the OCR system? [3 marks] ii) What are the inputs and outputs of the OCR system? Illustrate your answer with an example. [5 marks] iii) Why does such a system require supervised learning? [3 marks] iv) What data would be used to train an Artificial Neural Network for this task? [4 marks]

2 The McCulloch-Pitts neuron.

2 (a) Draw a flow chart for the McCulloch-Pitts neuron (MP-neuron) algorithm that
is used to compute an output in response to a particular input.
NB. Assume that all weights of connections and the neuron threshold are set up
in advance.
[8 marks]

2 (b) Draw a diagram and explain the workings of an MP-neuron realisation of an
“OR” logical gate.
[4 marks]

2? Draw a diagram and explain the workings of an MP-neuron realisation of a
“NOT” logical gate.
[5 marks]

2(d) Apply your answers for the parts (a-c) of this question to deduce an output X of

the MP-neuron network below in response to the input a 1 =0, a 2 =1, a 3 =.

[8 marks]

3 Learning rules of the Artificial Neural Networks**. Hebb’s Rule.**

3(a) What is a learning rule of an artificial neural network? [3 marks]

3(b) Give the simplest mathematical formulation of Hebb’s learning rule. Explain
how to compute a correction to the weight of a connection according to the
instant input and output. [4 marks]

3? Why is the Hebb’s rule called “activity product rule”? [1 mark]

3(d) Why does the Hebb’s rule represent unsupervised learning? [2 marks]

3(e) The neural network below uses Hebb’s learning rule.

Let the initial weights of connections at the time step t=1 be w 1 t=1 = 1, w 2 t=1 = 0 , w 3 t=1 = - 1; the learning rate C of the network be 0.25, that is, C = 0.25. Complete the following table Time step a 1 t^ a 2 t^ a 3 t^ w 1 t w 2 t w 3 t Xt ?w 1 t ?w 2 t ?w 3 t w 1 t+1 w 2 t+1 w 3 t+ t=1 1 1 1 1 0 - 1 t=2 1 1 0 t=3 1 0 0 by calculating ? the network output value Xt, ? the changes in each of the three weights of connections ?w 1 t, ?w 2 t, and ?w 3 t , ? the new weights (wnt+1) i) at the time step t=1 [5 marks] ii) at the time step t=2 [5 marks] iii) at the time step t=3 [5 marks]

Supervised learning. Perceptron.

4(a) Describe the two-layer fully interconnected architecture of a Perceptron. What is
a bias input unit?
[3 marks]

4(b) What is the Perceptron training set? How is it used during the error-correction
training of the Perceptron? How is an output unit’s error computed and used to
define corrections to the Perceptron weights of connections (i.e. what is the
Perceptron learning rule)?
[7 marks]

4? A perceptron can compute only linear separable functions, that is, the functions
for which the points of the input space with function value (output) of “0” can
be separated from the points with function value of “1” using a line.

Using a coordinate plane for inputs a 1 and a 2 show that the “IDENTITY” gate (see the table below) is a linear inseparable function.

a 1 a 2 “IDENTITY”

1 1 1

1 0 0

0 1 0

0 0 1

Explain your answer. [4 marks] (to be continued)

4(d) The 3-layer network shown below implements the linear inseparable
“IDENTITY” gate. The network has weights of connections and thresholds of
the processing units as shown below, and it uses the feed forward scheme to
produce an output.

The output unit and both hidden units use the threshold activation step- function

? ?

?? ? ? ? ? ? ? ? l j l j l j l l j j l j S S X f S ? ? 0 , 1 ,

where
l=h for a hidden unit
l=o for the output unit

Following the feedforward scheme of the input processing, Show that this network produces correct IDENTITY output in response for the input a 1 =0, a 2 =1. For that, answer the following questions: i) What is the correct output of IDENTITY gate for the input a 1 =0, a 2 =1? [2 marks] ii) Find the outputs of the hidden units for the input a 1 =0, a 2 =1; [5 marks]

iii) Find the network output for the input a 1 =0, a 2 =1.
[3 marks]
iv) Does the network produce the correct IDENTITY output in
response for the input a 1 =0, a 2 =1?
[1 mark]

Artificial Neural Networks Unsupervised Learning.
Competitive Learning Rule, Kohonen Self-Organised Map.

5(a) Give the simplest mathematical formulation of the Kohonen competitive
learning rule. Explain how to calculate the correction to the weight of a
connection according to the instant input. Why is the rule called “winner-
takes-it-all”? Why does the Kohonen Self-Organised Map represent
unsupervised learning?
[8 marks]

5(b) The neural network below uses the “winner-takes-it-all” learning rule. At

some instant t during the network training, inputs to the network and the

weights of connections are as shown below. (to be continued)

w 11 = 5

θ 1 = 1 θ 2 = 1

w 21 = 1

X 2

w 12 = (^1) X 1

w 22 = 1

w 13 = 5

w 23 = 1

a 1 = 1

a 2 = 2

a 3 = 2

Thus,

the instant input vector is a = {a 1 ; a 2 ; a 3 }={1; 2 ; 2};

the fan-in vector of the weights of connections to the 1st output unit is

w 1 ={w 11 ; w 12 ; w 13 }={5; 1 ; 5};

the fan-in vector of the weights of connections to the 2nd output unit is

w 2 ={w 21 ; w 22 ; w 23 }={1; 1 ; 1};

i) Calculate the state S 1 of the first output unit, and the state S 2 of the second output unit at that instant. [4 marks]

ii) What instant output X = {X 1 , X 2 } will the network produce?

[2 marks] iii) Let the network learning rate C be set to 0.25.

Calculate changes to the weights of connections Δwji at that instant.

[4 marks]

iv) What will be the new updated weights of connections wji at that

instant?
[1 mark]

v) Let the norm of the network weights of connections be defined as

(^) ??
? ?

?

2 1 3 1 2 j i w wji

What will be the new normalised weights of connections wji , j=1,2,

i=1,2,3? [6 marks]

PAPER CODE COMP305 Page 9 of 9 End

Genetic Algorithms.

6(a) Discuss the computational appeal of natural evolution. In particular, consider
parallelism, adaptation to changing environment, and optimisation of possible
“solutions”.
[6 marks]

6(b) Describe the basic structure of a Genetic Algorithm.
[6 marks]

6? What is a Genetic Algorithm chromosome building block, i.e. schema? What
characters are used to describe schemas of a binary chromosome? What is the
order and the defining length of a schema?
[5 marks]

6(d) Fill in the table below with all the schemas of the chromosome “CH” and their
corresponding orders and defining lengths.

Schema Order Defining Length [2 marks]

6(e) Define the fitness f of a bit string x of length l=4 to be the integer represented by
the binary number x. (e.g., f (0011) = 3, f (1111) = 15).

i) What is the average fitness of the schema 10 under f?
[3 marks]

ii) What is the average fitness of the schema 0*1* under f? [3 marks]

PAPER CODE NO.

COMP 305

考官：Irina V. Biktasheva博士 Irina V. Biktasheva博士 系別：計算機科學系 電話：54267 電話：54267

2017年第一學期考試/

生物計算

允許的時間： 兩個半小時

##對候選人的說明。

□回答四個問題。

如果你試圖回答的問題超過了規定的數目

＃＃題，多答題的分數為

棄權（從最低分開始）。

每題25分

1歷史和概念。

1(a)為什么生物學啟發的是人工神經網絡和遺傳算法？
現在被認為是計算機科學的一部分，而不是計算生物學的一部分？
[2分]

1(b)人工神經網絡能解決哪些一般問題？給出一個
幾個例子。
[4分]

1（三）遺傳算法可以解決哪些問題？請舉出幾個
舉例說明。
[4分]

1(d)大量的學術文本在網上儲存和提供。
儲存庫。對于較舊的文本，有必要將紙質文件轉換為紙質文件。
電子文件。光學字符識別(OCR)系統可以實現以下功能
用于這一目的。

一）OCR系統解決了什么樣的問題？ [3分] 二）OCR系統的輸入和輸出是什么？說明你的答案 并舉例說明。 [5分] 三）為什么這樣的系統需要監督學習？ [3分] 四）對于這個任務，將使用什么數據來訓練人工神經網絡？ [4分]

2 McCulloch-Pitts神經元。

2 (a)畫出McCulloch-Pitts神經元(MP-neuron)算法的流程圖，該算法為
用于計算對特定輸入的輸出。
NB. 假設所有連接的權重和神經元閾值都被設置為
預先。
[8分]

2 (b) 畫出一個MP-神經元實現的示意圖，并解釋其工作原理。
"OR "邏輯門。
[4分]

2?畫出一個MP-神經元實現的示意圖并解釋其工作原理。
"NOT "邏輯門。
[5分]

2(d)運用本題(a-c)部分的答案，推導出輸出X為

##下面的MP-神經元網絡對輸入a 1 =0，a 2 =1，a 3 =。

[8分]

人工神經網絡的3個學習規則**。Hebb規則.**

3（a）什么是人工神經網絡的學習規則？[3分]

3(b)給出希伯學習法則的最簡單數學公式。解釋
如何根據連接的權重計算修正。
即時輸入和輸出。[4分]

3?為什么希伯規則被稱為 “活動積規則”？[1分]

3(d)為什么Hebb規則能代表無監督學習？[2分]

3(e)下面的神經網絡使用Hebb的學習規則。

讓時間步t=1時連接的初始權重為 w 1 t=1 = 1，w 2 t=1 = 0 ，w 3 t=1 = - 1。 網絡的學習率C為0.25，即C=0.25。 填寫下表 時間 步驟 a 1 t^ a 2 t^ a 3 t^ w 1 t w 2 t w 3 t Xt ?w 1 t ?w 2 t ?w 3 t w 1 t+1 w 2 t+1 w 3 t+。 t=1 1 1 1 1 0 - 1 t=2 1 1 0 t=3 1 0 0 通過計算 網絡輸出值Xt。 ?w 1 t、?w 2 t 和 ?w 3 t 三個連接的權重變化。 新權重(wnt+1) 一）在時間步長t=1時[5分]。 二）在時間步長t=2時[5分]。 三）在時間步驟t=3時[5分]。

監督學習。Perceptron。

4（a）描述Perceptron的兩層全互連結構。什么是
一個偏置輸入單元？
[3分]

4（b）什么是Perceptron訓練集？它在糾錯過程中是如何使用的？
Perceptron的訓練？如何計算輸出單元的誤差并將其用于
定義對連接的Perceptron權重的修正（即什么是
Perceptron學習規則）？)
[7分]

4?感知器只能計算線性可分離函數，即函數
其中輸入空間中函數值(輸出)為 "0 "的點可以是
與函數值為 "1 "的點用一條線分開。

利用坐標平面對輸入a 1和a 2進行顯示，"IDENTITY "門 (見下表)是一個線性不可分割的函數。

A 1 A 2 “IDENTITY”

1 1 1

1 0 0

0 1 0

0 0 1

解釋一下你的答案。[4分] (待續)

4(d)下圖所示的3層網絡實現了線性不可分離
"IDENTITY "門。網絡中連接的權重和閾值為
處理單元，如下圖所示，它采用前饋方案以
產生產出。

輸出單元和兩個隱藏單元都使用閾值激活步長-。 功能

l j l j l j l l j j l j S S X f S 0 , 1 ,

哪兒
l=h為隱藏單位
輸出單元的l=o

按照輸入處理的前饋方案。 顯示該網絡在以下情況下產生正確的IDENTITY輸出。 輸入a 1=0，a 2=1的響應。 為此，請回答以下問題。 一）輸入的IDENTITY門的正確輸出是什么？ A 1=0，A 2=1？ [2分] 二）求輸入a 1=0，a 2=1的隱藏單元的輸出。 [5分]

三）求輸入a 1=0，a 2=1的網絡輸出。
[3分]
四）網絡是否產生正確的IDENTITY輸出，在
輸入a 1=0，a 2=1的響應？
[1分]

人工神經網絡無監督學習。
競爭性學習規則，Kohonen自組織圖。

5(a)給出Kohonen競爭性學習的最簡單的數學計算公式
學習規則。解釋如何計算對權重的修正。
根據即時輸入的情況進行連接。為什么這個規則被稱為 “贏家”？
占有一切"？為什么科霍寧自組織地圖代表了 “自組織”？
無監督學習？
[8分]

5(b)下面的神經網絡采用 "贏家通吃 "的學習規則。在

##在網絡訓練期間的某個瞬間t，網絡的輸入和。

連接的權重如下所示。 (待續)

w 11 = 5

θ 1 = 1 θ 2 = 1

w 21 = 1

X 2

w 12 = (^1) X 1

w 22 = 1

w 13 = 5

w 23 = 1

a 1 = 1

a 2 = 2

a 3 = 2

因此：

瞬間輸入向量為a = {a 1 ; a 2 ; a 3 }={1; 2 ; 2}。

第1個輸出單元的連接權重的扇形輸入向量是

W 1 ={W 11 ; W 12 ; W 13 }={5; 1 ; 5};

連接到第2個輸出端的權重的扇形輸入向量。 單位是

W 2 ={W 21 ; W 22 ; W 23 }={1; 1 ; 1};

一）計算第一輸出單元的狀態S1，以及第一輸出單元的狀態S2。 在該瞬間，第二個輸出單元。 [4分]

二）網絡將產生什么即時輸出X = {X 1 , X 2 }？

[2分] 三）設網絡學習率C為0.25。

＃＃計算該時刻連接權重Δwji的變化。

[4分]

＃＃四）什么將是新的更新權重的連接wji在該。

瞬?
[1分]

五）讓連接的網絡權重的規范定義為： 1．

(^)

2 1 3 1 2 j i w wji

＃＃什么將是新的規范化權重的連接wji ，j=1，2。

i=1,2,3? [6分]

文件編號 COMP305 第 9 頁，共 9 頁。

遺傳算法。

6(a)討論自然進化的計算魅力。特別是，考慮
并行性，適應不斷變化的環境，并優化可能的環境。
“解決方案”。
[6分]

6（b）描述遺傳算法的基本結構。
[6分]

6?什么是遺傳算法染色體構件，即模式？什么是
字符是用來描述二元染色體的模式？是什么？
順序和模式的定義長度？
[5分]

6(d)在下表中填入 "CH "染色體的所有圖式及其。
相應的順序和定義長度。

模式順序定義長度 [2分]

6(e)定義長度為l=4的比特串x的適格度f為整數，用以下方法表示： 1．
二進制數x.（如：f（0011）=3，f（1111）=15）。

一）在f下，模式10的平均適合度是多少？
〔3分

二）在f下，模式0*1*的平均適合度是多少？ [3分]

總結

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