Sudoku 聯想記憶

Abstract

本文探討利用二態神經元設計嵌入檢查規則的資料模式編碼，建構一個具有資訊回復、容錯編碼和聯想式記憶特性的類神經系統。 首先引用兩個微分方程式描述二態神經元的內場與活化，且利用模擬正規化的連結方式，將傳統多個二態神經元間獨立的活化狀態改造為可用來表示多態的artificial Potts neuron。利用提出的inhibitory connection方式，可將多個artificial Potts neuron組織出cell、connected cell以及connected cubical cell，實現二元Latin square編碼、K字元Latin square編碼以及Sudoku編碼。嵌入檢查規則的Sudoku編碼具有自動偵測錯誤與修復錯誤的能力。網路的收斂則使用Kullback-Leibler divergence的最小化機制，有助於找到系統組態的最佳解，也是對應到提供部分提示的Sudoku解答。 藉由應用Hebb’s rule，使提出的類神經系統具備聯想式記憶的功能。記憶多組完整Sudoku之後，將原本提供的32％內容提示降至13％，仍可找出記憶中的Sudoku解答。透過Sudoku在空間上特殊的結構性質，可將多個Sudoku以重疊相同內容的組織方法，建構出可以編寫更複雜資訊的compound pattern。實驗結果驗證compound pattern的設計與再生的可行性，以及可應用在模擬基因與人腦的關聯記憶。

This work explores bipolar neural circuits for constructing a neural system with check-rule embedded pattern restoration, fault-tolerant information encoding and associative memory. A bipolar neural unit is extended with an internal field and an activation, respectively characterized by exponential growth and logistic differential equations, in response to an external field that summarizes inhibitory and excitatory stimuli. On the basis, multiple bipoar neural units are coupled to organize an artificial multi-state Potts neuron, and multiple artificial Potts neurons are interconnected for binary Latin square encoding, K-alphabet Latin square encoding and Sudoku encoding. Check-rule embedded Sudoku patterns are self-correctable for automatic information restoration subject to partial clues. Interactive dynamics of organized bipolar neural units operate in consistent with annealed Kullback-Leibler (KL) divergence minimization, which pursues network relaxation to ground states. By Hebb's rule, the neural system acquires capability of memorizing Sudoku patterns and it has shown great performance in restoring memorized Sudoku puzzles of any level and reducing partial clues from 32% to 13% of the content. Compound Sudoku patterns which encode complex information in the spatial composition are constructed by overlaying common subgrids of multiple Sudoku patterns. Design and regeneration of compound Sudoku patterns in different forms have been experimented and further applied for simulating functionalities of gene and associative memory in human brain.