This problem covers the following topics related to sequence modeling architectures:

1. Recurrent Neural Networks (RNNs)
   • Main idea behind RNNs and their use in sequence modeling tasks
   • Vanishing gradient problem and its impact on learning long-term dependencies
2. Long Short-Term Memory (LSTM) Networks
   • How LSTMs address the limitations of vanilla RNNs
   • The role of forget gate, input gate, and output gate in an LSTM cell
3. Transformer Architecture
   • Key differences between Transformers and RNN-based models
   • The role of multi-head attention mechanism in Transformers
4. Use Cases and Trade-offs
   • Scenarios for choosing LSTMs over vanilla RNNs
   • When to consider using Transformers instead of LSTMs for sequence modeling tasks

By exploring these topics, you will gain a solid understanding of the fundamental concepts, strengths, and weaknesses of RNNs, LSTMs, and Transformers, as well as their typical use cases in machine learning and deep learning applications.