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研究生:蔡豐聲
研究生(外文):Feng-Sheng Tsai
論文名稱:定址記憶問題
論文名稱(外文):The Content-Addressable Memory Problem
指導教授:施茂祥
指導教授(外文):Mau-Shiang Shih
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:英文
論文頁數:42
中文關鍵詞:神經網路遞迴神經網路突現集星狀凸集堆球問題Hebb的增強學習規則CAM演算法生成元定址記憶
外文關鍵詞:neural networkrecursive networkemergent seta Hamming star-convexity packingHebb's strengthened learning ruleCAM algorithmgeneratorContent-Addressable
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我們針對神經網路的一個根本問題提出解答 :
"是否存在一個遞迴神經網路模擬人腦記憶儲存功能?"
我們所提出的解答,主要以"突現集","星狀凸集堆球問題",
"Hebb的增強學習規則","CAM演算法"為其中心思想,
並證明了臨界網路的穩定平衡狀態是由01-生成突現集所構成.
據此,我們提出了生成元的概念,
並藉由生成元來建構臨界網路,
導出一組記憶儲存功能的機制.

Abstract. We propose a solution to a fundamental problem in neural nets : " Stored an
arbitrary set of fundamental memories, does there exist a recursive network for which these
fundamental memories are stable equilibrium states of the network ? " The heart of it is
the conception of the emergent set, a Hamming star-convexity packing in the n-cube, the
mathematical framework of Hebb's strengthened learning rule, and the CAM algorithm. We
prove that the set of stable equilibrium states of the threshold network constructed by Hebb's
strengthened learning rule that responds to incoming signals of the states of fundamental
memories is the 01-span of the emergence of fundamental memories. On this basis, we reduce
the question to a problem for constructing a threshold network with sparse connections that
responds to incoming signals of the states of a generator of fundamental memories, and thereby
probing the collective dynamics of the network. One of the great intellectual challenges is to
nd the mechanism for storage of memory. The solution of the Content-Addressable Memory
Problem indicates a mechanism for storage of memory that a network produced in the brains
by sucking the kernel of the received stored memory items as incoming signals can correctly
yield the entire memory items on the basis of sucient partial information by the chaotic
dynamics with a regular strategy-set.

1. Introduction ........................................................................................ 2
2. The emergent set ................................................................................ 3
3. The Hamming star-convexity packing problem ................................. 7
4. The mathematical framework of Hebb's strengthened learning rule .... 12
5. The content-addressable memory algorithm ...................................... 24
6. The threshold X-network as pattern of recognition ........................... 33
7. Comparison between Hopeld network and threshold X-network ...... 37
8. Concluding remarks ............................................................................ 40
References ............................................................................................... 41

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[13] W. S. McCulloch and W. H. Pitts, A logical calculus of the ideas immanent in neural nets, Bulletin of Mathematical Biophysics, 5 (1943), 115-133.
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[15] F. Robert, Les Systemes Dynamiques Discrets, Mathematiques & Applications, Springer-Verlag, Berlin-Heidelberg-New York, 1995.
[16] F. F. Soulie, G. Weisbuch, Random iterations of threshold network and associative memory, SIAM J. Computing, 16 (1987), 203-220.
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[19] C. N. Yang, Introductory note on phase transitions and critical phenomena, In Phase Transitions and Critical Phenomena, Vol I, C. Domb and M. S. Grean, eds. London :
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