具有最大吸引範圍之二階非對稱式雙向聯想記憶設計方法

Abstract

雙向聯想記憶(Bidirectional Associative Memory)，簡稱BAM，是將聯想記憶(Associative Memory)推廣為能夠對於圖樣組執行雙向的回憶。近來雙向聯想記憶已經在聯想記憶研究當中扮演一個很重要的角色。非對稱式雙向聯想記憶(Asymmetric Bidirectional Associative Memory)為雙向聯想記憶放寬鍵結權重必須要對稱的限制之結果，且相較於常見的雙向聯想記憶結構有較好的記憶與回想效能。高階非對稱式雙向聯想記憶(High-Order Asymmetric Bidirectional Associative Memory)的記憶容量比一階的好很多，然而新的高階聯想記憶設計法卻很少被提出來。在本篇論文裡，我們所關心的是設計具有最大吸引範圍的二階非對稱式雙向聯想記憶(Second-Order Asymmetric Bidirectional Associative Memory)。將它延伸到高階非對稱式雙向聯想記憶(High-Order Asymmetric Bidirectional Associative Memory)是有可能而且很簡單的。我們首先推導出對於二階非對稱式聯想記憶的鍵結權重矩陣能夠保證將所有標準圖樣組回憶出來之充分條件。為了要遵守完全回憶定理，接著闡述學習步伐大小也是適應性的局部訓練法則，它將導致一個較快的設計時間。最後我們推導出下列定理：在設計SOABAM時，增大符合完全回憶定理的數值，將會增加一個有雜訊的圖樣能夠正確地收斂到它的聯想圖樣之能力；以這個定理當作基礎，我們的演算法也予以修改，能夠保證每一個訓練圖樣能儲存在具有越大的吸引範圍。針對color graphics adapter (CGA)字型的電腦模擬已經證明出我們所提出的局部訓練法則效果優於其他主要的BAM 的設計。

Bidirectional Associative Memory (BAM) generalizes the Associative Memory (AM) to be capable of performing two-way recalling of pattern pairs. Recently﹐BAM has played the vital role in AM research. Asymmetric Bidirectional Associative Memory (ABAM) is a variant of BAM relaxed with connection weight symmetry restriction and enjoys a much better performance than a conventional BAM structure. Higher-Order Associative Memories (HOAMs) are reputed for their higher memory capacity than the first-order counterpart﹐yet there are few HOAMs design schemes proposed up to date. To this need﹐we are concerned in this paper with designing a second-order asymmetric bidirectional associative memory (SOABAM) with a maximal basin of attraction ﹐whose extension to a HOABAM is possible and straightforward. First﹐a sufficient condition is derived for the connection weight matrix of SOABAM that can guarantee the recall of all prototype pattern pairs. To respect the complete recall theorem﹐a local training rule﹐which is also adaptive in learning step size﹐is formulated﹐and it leads to a faster design time. Then derived is a theorem that states designing a SOABAM further enlarging the quantities required to meet the complete theorem will enhance the capability of evolving a noisy pattern to converge to its association pattern vector without error. Based on this theorem﹐our algorithm is also modified to ensure each training pattern is stored with a basin of attraction as large as possible. Computer simulations over the color graphics adapter (CGA) fonts have demonstrated the superiority of the proposed local training rule over other prevailing BAM schemes.