CurriculumSeq2Seq: Curriculum Learning in LSTM-Based Sequence-to-Sequence Models

Table of Contents

• Introduction
• Model Architecture
  • Encoder
  • Decoder
• Curriculum Learning Strategy
  • Motivation
  • Implementation
• Mathematical Formulation
• Advantages of Curriculum Learning
• Integration with LSTM Models
• Experimental Results
  • Baseline Model
  • Curriculum Learning Model
  • Analysis
• Conclusion
• References

Introduction

Curriculum Learning (CL) is a training strategy inspired by the educational process, where models are first exposed to simpler examples and gradually introduced to more complex ones. This approach can lead to improved convergence rates and enhanced performance, particularly in tasks involving complex data distributions.

In the context of sequence-to-sequence (Seq2Seq) models, such as those used for text generation or sentiment analysis, curriculum learning can be leveraged to systematically introduce the model to varying levels of input complexity. This strategy ensures that the model builds a robust understanding of simpler patterns before tackling more intricate structures.

Model Architecture

The proposed architecture, CurriculumSeq2Seq, consists of an LSTM-based encoder-decoder framework enhanced with an attention mechanism. The architecture is defined as follows:

Encoder

The encoder processes the input sequence and captures its contextual information. Key components include:

• Embedding Layer: Transforms input tokens into dense vector representations.
• LSTM Layers: Captures temporal dependencies within the input sequence. The encoder is bidirectional, allowing it to process the sequence both forwards and backwards, thereby enriching the context.
• Attention Projection: If bidirectional, the hidden states from both directions are projected back to the original hidden size to maintain consistency.
• Classifier: A linear layer that predicts the type of the input sequence, aiding in conditional generation.

Decoder

The decoder generates the output sequence based on the encoder's representations and the attention context. Key components include:

• Embedding Layer: Transforms target tokens into dense vectors.
• Attention Mechanism: Computes a context vector by attending to relevant parts of the encoder's outputs, facilitating focused generation.
• Type Embedding: Incorporates the predicted type information into the generation process, allowing for type-conditioned responses.
• LSTM Layers: Generates the output sequence step-by-step, utilizing the concatenated embeddings, context vectors, and type embeddings.
• Output Layer: Maps the LSTM outputs to the vocabulary space, producing probability distributions over possible next tokens.

Curriculum Learning Strategy

Motivation

Training deep neural networks on complex data distributions from the outset can lead to suboptimal convergence and generalization. By adopting curriculum learning, models can develop a foundational understanding through simpler examples before addressing complexity, thereby enhancing overall performance.

Implementation

In the CurriculumSeq2Seq model, curriculum learning is implemented based on the length of input-output pairs (i.e., the number of words in questions and answers). The primary steps are as follows:

1. Sorting by Difficulty: The training dataset is sorted in ascending order based on the combined length of input and output sequences. Shorter sequences are deemed simpler and are presented to the model first.
2. Defining Curriculum Stages: The sorted dataset is divided into multiple stages. Each stage incrementally includes more data, progressively introducing longer and more complex sequences.
3. Incremental Training: The model is trained iteratively over these stages. At each stage, the model is exposed to a larger subset of the data, allowing it to build upon the knowledge acquired in previous stages.
4. Evaluation: After training across all curriculum stages, the model's performance is evaluated to assess the impact of curriculum learning.

Mathematical Formulation

Let the training dataset be defined as:

$$ \mathcal{D} = {(x_i, y_i)}_{i=1}^N $$

where $$( x_i )$$ and $$( y_i )$$ represent the input and output sequences, respectively. The difficulty measure $$( d_i )$$ for each data point is given by the sum of the lengths of the input and output sequences:

$$ d_i = |x_i| + |y_i| $$

Here, $$( |x_i| )$$ and $$( |y_i| )$$ denote the lengths of the sequences $$( x_i )$$ and $$( y_i )$$.

The dataset is sorted in ascending order based on the difficulty measure:

$$ d_1 \leq d_2 \leq \dots \leq d_N $$

Next, the sorted dataset is divided into $$( K )$$ curriculum stages. Each stage $$( \mathcal{D}_k )$$ consists of a subset of the dataset, defined as:

$$ \mathcal{D}_k = {(x_i, y_i) \mid i = 1, 2, \dots, k \cdot \frac{N}{K}} $$

where $$( k = 1, 2, \dots, K )$$.

The model $$( \theta )$$ is trained iteratively, starting with simpler examples in early stages, and progressively including more complex examples. The training process for each stage is expressed as:

$$ \theta^{(k)} = \text{Train}(\theta^{(k-1)}, \mathcal{D}_k) $$

where $$\textit{Train}$$ represents the training procedure, such as gradient descent, on the $$( k )th$$ curriculum stage.

Advantages of Curriculum Learning

• Improved Convergence: By starting with simpler examples, the model can achieve better convergence properties, avoiding poor local minima that might arise from complex initial gradients.
• Enhanced Generalization: Curriculum learning encourages the model to first grasp fundamental patterns before generalizing to more intricate ones, potentially leading to better performance on unseen data.
• Stabilized Training: Gradually increasing the difficulty of training samples can lead to more stable training dynamics, reducing the likelihood of vanishing or exploding gradients.

Integration with LSTM Models

Long Short-Term Memory (LSTM) networks are well-suited for sequence modeling tasks due to their ability to capture long-range dependencies. Integrating curriculum learning with LSTM-based Seq2Seq models leverages the strengths of both methodologies:

• LSTM's Sequential Processing: LSTMs process sequences step-by-step, maintaining a hidden state that captures contextual information.
• Curriculum Learning's Progressive Exposure: By controlling the complexity of input sequences presented during training, curriculum learning facilitates the LSTM's gradual adaptation to varying sequence lengths and structures.

Experimental Results

Baseline Model

A baseline LSTM model was trained without curriculum learning, achieving the following performance metrics on the IMDB test set:

Curriculum Learning Model

The CurriculumSeq2Seq model, trained using the proposed curriculum learning strategy, achieved:

Analysis

The curriculum-trained model demonstrated improved test accuracy compared to the baseline, indicating that curriculum learning effectively enhanced the model's ability to generalize from the training data.

Conclusion

The integration of curriculum learning with LSTM-based sequence-to-sequence models offers a promising avenue for enhancing model performance in complex tasks such as sentiment analysis. By systematically introducing training samples based on difficulty, models can achieve better convergence, stability, and generalization.

References

1. Bengio, Y., Louradour, J., Collobert, R., & Weston, J. (2009). Curriculum Learning. Proceedings of the 26th Annual International Conference on Machine Learning, 28, 41-48.
2. Graves, A. (2013). Speech Recognition with Deep Recurrent Neural Networks. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 6645-6649.
3. Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y. (2014). Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation. arXiv preprint arXiv:1406.1078.