How to Construct Deep Recurrent Neural Networks AUTHORS: R. - - PowerPoint PPT Presentation
How to Construct Deep Recurrent Neural Networks AUTHORS: R. PASCANU, C. GULCEHRE, K. CHO, Y. BENGIO PRESENTATION: HAROUN HABEEB PAPER: HTTPS://ARXIV.ORG/ABS/1312.6026 This presentation Motivation Formal RNN paradigm Deep RNN designs
AUTHORS: R. PASCANU, C. GULCEHRE, K. CHO, Y. BENGIO PRESENTATION: HAROUN HABEEB PAPER: HTTPS://ARXIV.ORG/ABS/1312.6026
Motivation Formal RNN paradigm Deep RNN designs Experiments Note on training Takeaways
Depth makes feedforward neural networks more expressive What about RNNS? How do you make them deep? Does depth help?
Conventional RNNs
▪How general is this? ▪How easy is it to represent an LSTM/GRU in this form? ▪What about bias terms? ▪How would you make an LSTM deep? 𝒊𝑢 = 𝑔
ℎ(𝒚𝑢, 𝒊𝑢−1)
𝒛𝑢 = 𝑔
𝑝 𝒊𝑢
Specifically: 𝑔
ℎ 𝒚𝑢, 𝒊𝑢−1; 𝑿, 𝑽 = 𝜚ℎ 𝑿𝑈𝒊𝑢−1 + 𝑽𝑼𝒚𝑢
𝑔
𝑝 𝒊𝑢; 𝑾 = 𝜚𝑝(𝑾𝑈𝒊𝑢)
THE DEEPENING
DT(S)-RNN
𝒛𝑢 = 𝑔
𝑝 𝒊𝑢
𝒊𝑢 = 𝑔
ℎ( 𝒚𝑢, 𝒊𝑢−1 , 𝒚𝑢, 𝒊𝑢−1)
Specifically: 𝑧𝑢 = 𝜔(𝑋ℎ𝑢) ℎ𝑢 = 𝜚𝑀( 𝑊
𝑀 𝑈𝜚𝑀−1 … 𝑊 2 𝑈𝜚1 𝑊 1 𝑈ℎ𝑢−1 + 𝑉𝑦𝑢
+ ഥ 𝑋𝑈ℎ𝑢−1 +ഥ 𝑉𝑈𝑦𝑢)
DOT(S)-RNN
𝒛𝑢 = 𝑔
𝑝 𝒊𝑢
𝒊𝑢 = 𝑔
ℎ( 𝒚𝑢, 𝒊𝑢−1 , 𝒚𝑢, 𝒊𝑢−1)
Specifically: 𝑧𝑢 = 𝜔0(𝑋
𝑀 𝑈𝜔𝑀(… 𝑋 1 𝑈𝜔1 𝑋𝑈ℎ𝑢 )
ℎ𝑢 = 𝜚𝑀( 𝑊
𝑀 𝑈𝜚𝑀−1 … 𝑊 2 𝑈𝜚1 𝑊 1 𝑈ℎ𝑢−1 + 𝑉𝑦𝑢
+ ഥ 𝑋𝑈ℎ𝑢−1 +ഥ 𝑉𝑈𝑦𝑢)
sRNN
𝒊𝑢
0 = 𝒈ℎ 0(𝒚𝑢, 𝒊𝑢−1
) ∀𝑚 ∶ 𝒊𝑢
(𝑚) = 𝑔 ℎ (𝑚)(𝒊𝑢 𝑚−1, 𝒊𝑢−1 𝑚
) 𝒛𝑢 = 𝑔
𝑝 𝒊𝑢 (𝑀)
Specifically: 𝒛𝑢 = 𝜔 𝑋𝑈𝒊𝑢
(𝑀)
ℎ𝑢
(0) = 𝜚 0
𝑉0
𝑈𝒚𝑢 + 𝑋 𝑈𝒊𝑢−1 (0)
∀𝑚: 𝒊𝑢
𝑚 = 𝜚 𝑚
𝑉𝑚
𝑈𝒊𝑢 𝑚−1 + 𝑋 𝑚 𝑈𝒊𝑢−1 (𝑚)
Food for thought: Not clear which
number of parameters – sRNN
Task:
Sequence of musical notes
Next note(s)
Food for thought: Sure, depth helps, but * helps a lot more in this case. What about RNN* and other models with *?
Task (LM on PTB) Sequence of characters/words Next character/word
:
Food for thought: Deepening LSTMs? Stack them or DOT(S) them?
Training RNNs can be hard because of vanishing/exploding ▪ gradients. Authors did a bunch of things: ▪
Clipped gradients, threshold = ▪ 1 Sparse ▪ weight matrices ( 𝑋
0 = 20)
Normalized weight matrices ▪ ⇒ max
𝑗,𝑘 𝑋 𝑗,𝑘 = 1
Add gaussian noise to ▪ gradients Used ▪ dropout, maxout, 𝑀𝑞 units
▪Plain, shallow RNNs are not great. ▪DOT-RNNs do well. Following should be deep networks
▪𝑧 = 𝑔(ℎ, 𝑦) ▪ℎ𝑢 = 𝑔 𝑦𝑢, ℎ𝑢−1 , 𝑦𝑢, ℎ𝑢−1 - both 𝑔 and
▪Training can be really hard. ▪Thresholding gradients, Dropout, maxout units are helpful/needed ▪LSTMs are good
Questions?