Note 3: GPT

Improving Language Understanding by Generative Pre-Training

Radford et al., (2018)

  1. GPT (Generative Pre-Training) is semi-supervised approach for language understanding tasks using a combination of unsupervised pre-training and supervised fine-tuning.
    • Goal: It can learn a universal representation that transfers with little adaptation to a wide range of tasks.
    • Assumption: We have a large corpus of unlabeled text and several annotated training sets.

2. Two-stage training procedure

  • Unsupervised pre-training : Use a language modeling objective on the unlabeled data to learn the initial parameters of a neural network model (This paper selects the Transformer (Vaswani et al., 2017) as its model architecture).
  • supervised fine-tuning: Adapt these parameters to a target task using the corresponding supervised objective.

3. Unsupervised pre-training

Given an unsupervised corpus of tokens U=\{u_1, \ldots, u_n\}.

  • A multi-layer Transformer applies a multi-headed self-attention operation over the input context tokens followed by position-wise feedforward layers to produce an output distribution over target tokens:
    \begin{aligned} h_0 &= UW_e+W_p\\ h_l &={ transformer\_block(h_{l-1}) \forall{i}\in[1,n]}\\ P(u) &= softmax(h_nW_e^T) \end{aligned}
    where U=(u_{-k},\ldots,u_{-1}) is the context vector of tokens, n is the number of layerts, W_eis the token embedding matrix, and W_p is the position embedding matrix.
  • The objective is to maximize the following likelihood L_1:
    L_1(U)=\sum_{i}{\log{P(u_i|u_{i-k},\ldots,u_{i-1};\Theta)}}
    where k is the size of the context window and \Theta is the model's parameters.

4. Supervised fine-tuning

Given a labeled dataset C where each instance is a sequence of input tokens [x^1, \ldots, x^m] along with a label y.

  • Pass the inputs through the pre-trained model to get the h_l^m and then fed h_l^m into an added linear output layer with parameters W_y to predict y:
    P(p|x^1,\ldots, x^m)=softmax(h_l^m W_y)
  • The objective is to maximize the following likelihood L_3:
    \begin{aligned} L_3(C) &= L_2(C)+\lambda*L_1(C)\\ L_2(C) &= \sum_{(x,y)}{\log{P(y|x^1,\ldots,x^m)}} \end{aligned}
    • Including the language modeling L_1 as auxiliary objective to the fine-tuning can not only improve the generalization of the supervised model, but also accelerate convergence during training.

5. Task-specific input transformations

All following transformations include adding randomly initialized start and end tokens (\langle s \rangle, \langle e \rangle).

Radford et al., (2018)


Reference

Radford, A., Narasimhan, K., Salimans, T., & Sutskever, I. (2018). Improving language understanding by generative pre-training.
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., ... & Polosukhin, I. (2017). Attention is all you need. In Advances in neural information processing systems (pp. 5998-6008).

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