使用競爭學習從新格狀細胞模型映射到位置細胞的模擬與分析

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研究生：	蔡睿翔 Tsai, Jui-Shiang
論文名稱：	使用競爭學習從新格狀細胞模型映射到位置細胞的模擬與分析 Simulation and Analysis of Mapping from New Grid Cell Field Model to Place Cell Field by Competitive Learning
指導教授：	呂忠津 Lu, Chung-Chin
口試委員:	林茂昭 Lin, Mao-Chao 蘇育德 Su, Yu-Ted 蘇賜麟 Su, Szu-Lin
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	116
中文關鍵詞：	格狀細胞、競爭學習、計算神經科學、位置細胞
外文關鍵詞：	Grid cell, competitive learning, computational neuroscience, place cell
相關次數：	點閱：3 下載：0
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空間資訊在情節記憶中扮演很重要的角色，首先，在1970年代時，神經科
學家John O’Keefe在海馬迴組織中，發現了位置細胞，當動物在空間中特定的
位置時，位置細胞會發放動作電位，而在2000年左右，神經科學家Moser在解
剖學與測量技術的進步下，成功的在內嗅皮質層發現格狀細胞，格狀細胞在動
物自身位於空間重複排列的網格頂點會引發動作電位，這兩個基本的細胞，使
的動物能使用此資訊記住資訊或者應用在自我導航的功能上。
在此篇論文中，回顧整個空間資訊在海馬迴組織的研究發展與其模擬的結
果，並以其研究成果為基礎，發展出新的格狀細胞模型，使用更為真實的模擬
資料與模擬軟體，重現格狀細胞映射到位置細胞的腦部功能。
本篇論文所使用的映射學習演算法為競爭學習，競爭學習為非監督式學
習，主要用於分群上的演算法。此演算法所使用的資訊主要是區域的資訊，也
就是前級與後級的反應，這樣的原理符合赫布理論，相較於傳統的類神經演算
法，更接近生物可能使用的演算法。

Spatial information plays an important role in episodic memory. In the last decade,
anatomical observations and neurophysiological results give a great detail about grid
cells in the medical entorhinal cortex. In this thesis, we propose a new grid cell model
whose response field is much similar to real grid cell response field. In the simulation
of mapping medical entorhinal cortex grid cells to dentate place cells, we use statistical
properties which are extracted from real observation data. We show that this new grid
cell model with those properties can render almost all DG cells to become one field
place cells and to have a suitable peak field size using competitive learning algorithm.

Introduction 11
Memory 13
1 Basic Idea of Memory . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Hippocampus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Functions and Properties . . . . . . . . . . . . . . . . . . . . 14
3 Hippocampus Simulation . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 Main purpose of simulation . . . . . . . . . . . . . . . . . . 16
3.2 Pair Associate Learning . . . . . . . . . . . . . . . . . . . . 16
4 Network Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Training Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1 Initialize Process . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Run Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 Learning Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.1 Delta Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.2 The Generalized Delta Rule: Backpropagation . . . . . . . . 24
6.3 GeneRec . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.4 Rate-based Hebbian Learning . . . . . . . . . . . . . . . . . 28
6.5 BCM Theory Model . . . . . . . . . . . . . . . . . . . . . . 29
6.6 The eXtended Contrastive Attractor Learning Algorithm . . . 30
6.7 Algorithm Used in Simulation . . . . . . . . . . . . . . . . . 31
7 The Drawbacks of O’Reilly Hippocampus Model . . . . . . . . . . . 32
7.1 Lack of Spatial Information in Input Pattern . . . . . . . . . . 32
7.2 Structure of Connection between Hippocampus and Entorhinal
Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Spatial Information Simulation 34
1 EC Grid Cells Map to DG Place Cells . . . . . . . . . . . . . . . . . 34
1.1 Neural Network Model . . . . . . . . . . . . . . . . . . . . . 34
1.2 Input Layer Pattern Properties . . . . . . . . . . . . . . . . . 34
2 Competitive Learning . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1 Weight Update Algorithm . . . . . . . . . . . . . . . . . . . 36
3 Problems in Rolls Simulation . . . . . . . . . . . . . . . . . . . . . . 39
The Properties of Spatial Information in Hippocampus System 47
1 Grid Cell in the Entorhinal Cortex . . . . . . . . . . . . . . . . . . . 47
1.1 The Grid Cell Properties . . . . . . . . . . . . . . . . . . . . 48
1.2 The Field Size and Spacing . . . . . . . . . . . . . . . . . . . 49
1.3 The Orientation of Grid Cell . . . . . . . . . . . . . . . . . . 51
1.4 The Phase of Grid Cell . . . . . . . . . . . . . . . . . . . . . 51
2 Head Direction Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Simulation Detail and Result 58
1 Neuron model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.1 Neuron Input . . . . . . . . . . . . . . . . . . . . . . . . . . 58
1.2 Neuron Activation Parameter . . . . . . . . . . . . . . . . . . 59
1.3 Neuron Activation Function . . . . . . . . . . . . . . . . . . 60
1.4 Neuron Input Detail . . . . . . . . . . . . . . . . . . . . . . 62
2 Model Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.1 Moser Model Equation . . . . . . . . . . . . . . . . . . . . . 65
2.2 My Model Equation (Product Model) . . . . . . . . . . . . . 66
3 Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1 Analysis Input Pattern by Inner Product . . . . . . . . . . . . 67
3.2 Random Variable of EC Firing Rate . . . . . . . . . . . . . . 70
3.3 Cross Correlation Analysis Method . . . . . . . . . . . . . . 77
4 Simulation Detail and Result . . . . . . . . . . . . . . . . . . . . . . 84
4.1 Moser rat data . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Average number of one peak . . . . . . . . . . . . . . . . . . 95
4.3 Normalize VS no Normalize . . . . . . . . . . . . . . . . . . 100
4.4 Inner product analysis . . . . . . . . . . . . . . . . . . . . . 106
4.5 Connection preference . . . . . . . . . . . . . . . . . . . . . 108
Conclusion 112
Bibliography 113
                                

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