- Hidden Layers Effect 連續幾篇的Neural Network的介紹與最佳化,我們已經可以透過Trainer有效的讓神經網路學習玩Tic-Tac-Toe遊戲,從上一篇[ANN] Self-Adaptation Gaussian Mutation的結果我們可以看到網路學習能力因為使用自適應參數而下降。這裡我們依然延續著[ANN] Spatial Layer Effect這一篇的架構移除Self-Adaptation Gaussian Mutation去探討多一層隱藏層的影響。
- Neural Network Architecture
- Simulation Parameters
- Results
- Discussion
- Randomizing Trainer
- Spatial Layer
- Self-Adaptation Parameters
- Activation Function Coefficient
- Population
- Mutation Rate Coefficient
- Hidden Layers
- Selection Mechanism
- Win/Lose Value Assignment
- 參考
- D.B. Fogel "Using evolutionary programing to create neural networks that are capable of playing tic-tac-toe," Neural Networks, 1993., IEEE International Conference on Volume , Issue , Page(s):875 - 880 vol.2
- D.B. Fogel "Blondie24: Playing at the Edge of AI, San Francisco, CA: Morgan Kaufmann, 2002.
- "Training an artificial neural network to play tic-tac-toe," Sebastian Siegel, ECE 539 Term Project, 2001.
- Lucas, S. M. "Learning to Play Othello with N-Tuple Systems, Australian Journal of Intelligent Information Processing Systems," Special Issue on Game Technology, Vol 9, No. 4 pp 01--20, 2007.
- Hornik, K., Stinchcombe, M. and White, H. "Multilayer feedforward networks are universal approximators," Neural Networks, 1989., 2, 359-366.
- Chester, D.L. "Why Two Hidden Layers are Better than One," IJCNN-90-WASH-DC, Lawrence Erlbaum, 1990., volume 1, 265-268.
- Weigend, A. "On overfitting and the effective number of hidden units," Proceedings of the 1993 Connectionist Models Summer School, 335-342, 1994.
- Geman, S., Bienenstock, E. and Doursat, R. "Neural Networks and the Bias/Variance Dilemma", Neural Computation, 4, 1-58, 1992.
- AI FAQ, http://www.faqs.org/faqs/ai-faq/
跟之前的架構相比只是多了一層隱藏層,且節點數為9個,總共的weights和biases值為166,比原先的76大了一倍多。Total weights & biases計算方式如下:
Spatial Layer : (5+1)+(7+1)+(5+1)+(5+1)+(9+1)+(5+1)+(7+1)+(5+1)+(7+1) = 66
Hidden Layer: (9+1) * 9 = 90
Output Layer: (9+1) * 1 = 10
Total: 66+ 90 +10 = 166
Population: 100
Generation: 1000
Win/Lose Score: Winner: +1, Loser: -1 , Draw: 0
Number of Games: 10
Selection : Tournament Selection
Trainer: AI_Level III with random moves
除此之外為了因應多一層隱藏層的效應,我將activation function的參數調大了一點。
在這個例子裡多了一層隱藏層之後,整體網路的學習能力並沒有什麼提升,但不能就這樣否決掉多一層隱藏層的所帶來的優點。我在其他模擬實例中,多一層隱藏層確實有效的幫助提昇網路的網定性。連續幾篇的介紹,我們分別討論Spatial Layer, Self-Adaptation Gaussian Mutation 和 Hidden Layer對網路學習能力的影響,在數據的比較分析中我們一直執意在有多少個網路能更贏過我預先設計好的專家程式,但是事實上我們並不能一味的追求整體的學習能力,因為在這個模擬案例裡我並不是使用嚴謹的Supervised Learing,所以學習後的網路整體的能力我們是無法在在上面的數據可以得知的。但是在更深層的數據分析之下,我發現多一層隱藏層的Spatial Layer的Neural Network在多次模擬下僅能產生出Average Strong的fitness function。但是在沒有多一層隱藏層的spatial layer的神經網路卻能產生出extraordinary strong的fitness function。
總結一下這一系列的主題研究我調整了什麼
紅色的部份代表極具影響力的因子,綠色的部份代表著必須小心的細節設定,而藍色的部份則是為可選擇性調整的部份,重要性依顏色深淺而定。雖然藍色部份我列為可選擇性調整替代,但不代表他不影響著結果,除了像本主題Hidden Layers改變會有劇烈的結果變動之外,另外像是Selection的使用也是有不少人在研究的議題,不同的選擇方式會有不同的選擇壓力,影響也是不小的,有機會的話再針對這部份做說明。
總結一下這一系列使用的文章:
[ANN] FeedForward MultiLayer Perceptron
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