How LSTMs Solve the Vanishing Gradient Problem in Sequential Data?

Long Short-Term Memory (LSTM) is a special type of neural network architecture that is great for handling sequences of data — like time series, text, or speech. Whether you’re working on a machine translation project, building a chatbot, or forecasting stock prices, LSTMs are a powerful tool.

In this blog, we’ll break down LSTMs in a way that is easy to understand. We’ll explain their architecture, the different layers that make them work, and where they are used in real-world applications. Most importantly, we’ll dive into the problem LSTMs were created to solve and how they overcome that challenge.

What Problem Was LSTM Created to Solve?

To understand why LSTM is so useful, we need to first understand the problem it was designed to solve. The problem lies in the limitations of traditional Recurrent Neural Networks (RNNs).

The Issue with Traditional RNNs

Recurrent Neural Networks (RNNs) were the first attempts to handle sequential data. These networks have a memory mechanism that allows them to process sequences of inputs. For example, when predicting the next word in a sentence or forecasting the next value in a time series, RNNs attempt to remember earlier inputs in the sequence. However, vanilla RNNs suffer from a significant problem: vanishing gradients.

The vanishing gradient problem occurs when the model tries to learn long-term dependencies. The idea is that as we backpropagate through time to update the weights, the gradients of the earlier layers get smaller and smaller, making it almost impossible for the model to learn long-term dependencies. This is especially problematic in long sequences where important information is often found far in the past.

In simpler terms, RNNs forget what they have learned over time when dealing with long sequences of data, which makes them ineffective for many real-world applications, where context from earlier in the sequence is critical for making accurate predictions.

Differencer b/w Traditional RNN’s and LSTM’s

Enter LSTM: Solving the Vanishing Gradient Problem

Long Short-Term Memory (LSTM) networks were created to address the vanishing gradient problem and enable neural networks to learn long-term dependencies in sequential data. LSTMs were introduced by Sepp Hochreiter and Jürgen Schmidhuber in 1997 and quickly became the go-to model for sequence-based tasks.

How LSTMs Overcome the Problem

LSTMs tackle the vanishing gradient problem through their unique memory cell, which allows the network to store information over long periods of time. Unlike regular RNNs, which rely on a simple hidden state that gets updated at each time step, LSTMs introduce several components that control the flow of information through the network:

LSTM Architecture

1. Memory Cell (Cell State): The most important feature of LSTM. The memory cell acts as a long-term storage for information and helps retain valuable context over time. This allows LSTMs to remember information for long durations and prevents the model from forgetting important details.
2. Gates: LSTMs use three gates to control the flow of information: the forget gate, input gate, and output gate. These gates decide which information should be remembered, which should be forgotten, and which should be passed to the next time step.

• Forget Gate: Determines what information to discard from the memory cell.
• Input Gate: Decides what new information to add to the memory cell.
• Output Gate: Decides what part of the memory cell should be passed as the output (or hidden state) to the next time step.

Together, these components allow LSTMs to retain and update information without losing important context, which is why they excel at learning long-term dependencies.

Architecture of an LSTM

At its core, an LSTM is made up of several components that work together to store and retrieve information. Let’s go step-by-step through the layers and understand what each one does.

LSTM Architecture with states

1. The Cell State (Memory)

• The most important feature of an LSTM is the cell state. Think of it like a conveyor belt that runs through the entire network. The cell state carries information through the sequence, allowing the LSTM to remember things over time.
• At each time step, the cell state is updated by adding new information (which could be relevant to future predictions) and removing irrelevant information (which is no longer needed).

2. The Forget Gate

• The forget gate is like a filter that decides what information to discard from the cell state. It looks at the current input and the previous hidden state (which contains the memory of the previous time step) and outputs a number between 0 and 1 for each number in the cell state.
• A value of 1 means “keep this information” and a value of 0 means “forget this information.”
• The forget gate prevents the network from being overwhelmed by irrelevant data and ensures that only important information is passed along.

Formula:
ft = σ ( Wf ⋅ [ ht−1 , xt ] + bf )
Where:
ft ​ is the forget gate output
σ is the sigmoid activation function
Wf is the weight matrix for the forget gate
ht−1​ is the previous hidden state
xt is the current input
bf​ is the bias term

3. The Input Gate

• The input gate decides what new information will be stored in the cell state. It consists of two parts:

1. A sigmoid layer (the same as the forget gate) that decides which values to update.
2. A tanh layer that creates new candidate values (potential new information to add to the cell state).

• These two parts work together: the sigmoid layer decides what part of the cell state should be updated, and the tanh layer generates new values that can be added to the cell state.

Formula:
it = σ ( Wi ⋅ [ ht−1 , xt ] + bi )
Ct = tanh ⁡( WC ⋅ [ ht−1 , xt ] + bC )
Where:
it is the input gate output
Ct​ is the candidate cell state
Wi ​, WC​ are weight matrices for input and cell state
bi ​, bC​ are bias terms

4. Updating the Cell State

• Once the forget gate decides what to forget and the input gate decides what new information to add, the cell state is updated by combining these two pieces of information.
• The cell state is updated by forgetting the old information (using the forget gate) and adding new information (using the input gate).

Formula:
Ct = ft ⋅ Ct−1 + it ⋅ Ct
Where:
Ct is the updated cell state
Ct−1​ is the previous cell state

5. The Output Gate

• The output gate decides what the next hidden state should be, which is used for the next time step or as the final output.
• It looks at the current cell state and decides what part of the cell state should be outputted.
• A tanh function is applied to the cell state to scale the values, and the sigmoid gate determines which of these values will be passed on as the hidden state.

Formula:
ot = σ ( Wo ⋅ [ ht−1 , xt ] + bo )
ht = ot ⋅ tanh⁡(Ct)
Where:
ot is the output gate output
ht​ is the hidden state (output)
Wo​ is the weight matrix for the output gate
bo​ is the bias term

Putting It All Together

Now that we’ve discussed each layer in isolation, let’s look at how everything works together. At each time step, an LSTM network:

1. Decides what to forget from the previous memory (using the forget gate).
2. Updates its memory with new information (using the input gate).
3. Outputs a value for the next time step (using the output gate).

This entire process allows LSTMs to handle long-range dependencies effectively, which is something traditional RNNs struggle with.

Applications of LSTMs

Now that we know how LSTMs work and the problem they solve, let’s look at some of the key areas where LSTMs are applied.

1. Time Series Forecasting: LSTMs are excellent for predicting future values based on past data. For example, they are used in forecasting stock prices, weather conditions, and sales figures. Their ability to learn long-term dependencies makes them perfect for time-based predictions.
2. Natural Language Processing (NLP): LSTMs have been widely used in NLP tasks such as machine translation (translating text from one language to another), text summarization, sentiment analysis, and speech recognition. The ability to remember context from earlier in a sentence allows LSTMs to generate more accurate predictions for language tasks.
3. Speech Recognition: In speech-to-text applications, LSTMs are used to convert spoken language into written text. The network needs to remember earlier sounds to correctly transcribe words, which is where LSTMs excel.
4. Anomaly Detection: LSTMs can detect unusual patterns in sequential data. This is useful in areas like fraud detection, where detecting anomalies in transactions can help identify fraudulent activities.
5. Video Analysis: LSTMs are used in video analysis for tasks like action recognition, where the model needs to understand the sequence of frames to identify the action being performed.

Why LSTMs Are Powerful

LSTMs are powerful because they can learn both short-term and long-term dependencies in sequential data. The memory cell, which is updated with each step, helps the model to remember important information for a longer duration, unlike traditional RNNs that tend to forget as time progresses. This makes LSTMs ideal for tasks where past information is crucial for making predictions.

Conclusion

In this blog, we’ve covered the fundamentals of Long Short-Term Memory (LSTM) networks, breaking down each layer and explaining its function in a simple way. We also explored the problem LSTMs were created to solve — the vanishing gradient problem — and how LSTMs overcome this challenge with their memory cells and gating mechanisms. Finally, we highlighted some of the key applications of LSTMs, from time series forecasting to natural language processing.

LSTMs are an essential tool for anyone working with sequential data, and understanding their architecture and behavior is key to building effective models for tasks that require memory of previous steps.

Now that you have a solid understanding of LSTMs, feel free to dive deeper into their implementation and explore how you can use them in your own projects!

Check out my GitHub for more projects. Let me know your thoughts and feel free to connect with me on LinkedIn for more updates on my projects in Data Science, Analytics, Machine Learning, Deep Learning, Gen AI and Agentic AI.