Introduction:

In the realm of recurrent neural networks (RNNs), Long Short-Term Memory (LSTM) networks have emerged as a powerful solution to overcome the limitations of traditional RNNs. In this blog, we will delve into the inner workings of LSTMs, exploring their architecture and the key components that make them adept at capturing long-term dependencies in sequential data.

What is LSTM and Its Advancements:

Long Short-Term Memory Networks, or LSTMs, are a type of recurrent neural network designed to address the vanishing and exploding gradient problems encountered by traditional RNNs. LSTMs excel in capturing dependencies in sequential data over extended periods, making them suitable for tasks such as natural language processing, speech recognition, and time series prediction.

Overview of LSTM Architecture:

At its core, the LSTM architecture consists of memory cells, each equipped with three crucial gates: Forget Gate, Input Gate, and Output Gate. These gates regulate the flow of information, enabling the network to decide what to remember, what to forget, and what information to pass to the output.

Understanding LSTM Gates and Their Formulas

a. Forget Gate

The Forget Gate determines which information from the previous state should be discarded. Its mathematical expression involves the sigmoid activation function.

Forget Gate operates in 2 stages

1) In the first stage there are 2 inputs: a) output from the last stage and b) new input word in the form of a word. These 2 inputs are provided to the neural network having sigmoid as an activation function. The output of this stage is given as:

[ \(f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f)\) ]

2) In the second stage output of pointwise multiplication operation between \(f_t\) and \(C_t-1\) is taken.

b. Input Gate

The Input Gate governs the update of the cell state. It decides what new information should be stored in the memory. The computations involve both sigmoid and hyperbolic tangent functions.

Input gate operations can be also summed up in 2 steps:

1) \(x_t\) and \(h_t-1\) are given as inputs to tanh and sigmoid activation functions and output are calculated as follows.​

[ \(i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i) ] [ \tilde{C}t = \tanh(W_C \cdot [h{t-1}, x_t] + b_C) \) ]

2) In this stage the outputs of earlier stage are calculated as pointwise operations.

c. Output Gate

The Output Gate controls what information should be output based on the current cell state. It utilizes both sigmoid and hyperbolic tangent functions.

[ \(o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o) ] [ h_t = o_t \cdot \tanh(C_t)\) ]

4. Conclusion

In conclusion, Long Short-Term Memory networks have revolutionized the field of sequence modeling by effectively addressing the challenges posed by vanishing and exploding gradients. By incorporating Forget, Input, and Output Gates, LSTMs empower neural networks to capture intricate dependencies in sequential data, making them indispensable for a wide array of applications.

Through this blog, we have unraveled the complexity of LSTM architecture and its key components. Armed with a deeper understanding of LSTMs, you are now equipped to leverage their power in tackling real-world problems requiring robust sequential modeling.