From HMM to Transformers: Sequence Models

Imagine listening to someone speak without being able to see the words they are thinking.
You only hear a sequence of sounds:
🎵 Sound → Sound → Sound → Sound...
Then you try to figure out what was actually said.
Did they say:
"Ahmed went."
or:
"Ahmed wrote."
The system cannot directly see the meaning behind the sounds. It only sees observations produced by something hidden.

This simple idea leads to one of the most important concepts in the history of sequence modeling:
✨ Hidden Markov Models (HMMs)
And from there, we can follow a fascinating path:
HMM → RNN → LSTM → Attention → Transformer → LLMs
Each step was driven by a different problem with handling sequential information.

---

What Is a Hidden Markov Model?​

A Hidden Markov Model assumes that there is an underlying state that we cannot directly observe.
For example, in speech recognition, the hidden state could represent something related to the linguistic structure behind the audio, while the system observes the actual speech signal.

The basic relationship looks like this:

Hidden State​

⬇️​

Observation​

The important part is that the hidden state is not completely independent from what happened before.
The previous state influences the probability of the next state.
That is where the Markov model idea comes in.
In simple terms:

The current state depends on the previous state, rather than requiring the model to remember the entire history explicitly.

HMMs use probabilities to model this relationship.

Two important concepts are:
🔹 Transition probability: How likely one hidden state is to move to another.
🔹 Emission probability: How likely a particular observation is to be produced by a hidden state.

So the model can ask:
"Which sequence of hidden states is most likely to have produced the observations I am seeing?"

---

Why HMMs Became Important​

HMMs became an important tool for working with sequential data, especially in areas such as:

🎙️ Speech recognition​

🧬 Bioinformatics​

📝 Natural language processing​

📈 Time-series modeling​

Speech recognition is a good example.
A spoken sentence is not just a collection of unrelated sounds. The interpretation of one part can depend on what came before and what comes after it.
HMMs provided a mathematical framework for representing these relationships using hidden states and probabilities.
But there was an important limitation.
HMMs were probabilistic sequence models, not neural networks.
They did not learn representations in the same way modern deep learning systems do.
That created a different path in the evolution of sequence modeling.

---

From HMMs to Recurrent Neural Networks​

As neural networks became more capable, researchers wanted a way to process sequences while allowing information from previous steps to influence later steps.
This led to Recurrent Neural Networks (RNNs).
Instead of treating every input as completely independent, an RNN maintains a hidden state that is updated as new inputs arrive.

A simplified view looks like this:

Input₁​

⬇️​

Hidden State​

⬇️​

Input₂​

⬇️​

Hidden State​

⬇️​

Input₃​

⬇️​

Hidden State​

The hidden state acts like a form of memory.
Information from earlier steps can influence how later inputs are processed.

That made RNNs useful for many sequential tasks, including:
🔹 Language modeling
🔹 Speech processing
🔹 Machine translation
🔹 Time-series prediction
But RNNs had a serious weakness.

---

The Problem With Long-Term Memory​

RNNs work well when useful information is relatively close to the current step.
But what happens when the important information appeared much earlier in a long sequence?
This is where the vanishing gradient problem becomes important.
During training, gradients can become extremely small as they are propagated through many time steps.
When that happens, the network can struggle to learn long-range dependencies.
For example, imagine a sentence where the information needed to understand the final word appeared many words earlier.
The RNN may have difficulty preserving that information through all the intermediate steps.
So researchers needed a better way to control what information should be remembered.

---

LSTM: A Better Way to Handle Memory​

In 1997, Sepp Hochreiter and Jürgen Schmidhuber introduced the Long Short-Term Memory (LSTM) architecture.
LSTM was designed to help recurrent networks handle long-term dependencies more effectively.
The key idea was not simply to make the network "remember everything."
Instead, LSTM introduced mechanisms that control information flow.
In simplified terms, the network can learn:

🧠 What information should be kept?​

🗑️ What information should be forgotten?​

➡️ What information should be passed forward?​

This made LSTMs much better suited to situations where useful information might need to survive across many time steps.
LSTMs became widely used in speech recognition, language modeling, translation, and other sequence-processing tasks.
But there was still a fundamental limitation:
The model was still processing the sequence recurrently.
That meant the structure of the model was closely tied to the order of the sequence.
Then a new idea changed the direction of sequence modeling.

---

Attention Changes the Question​

Instead of asking:
"What information can I carry forward from previous steps?"
researchers began asking:
"What parts of the sequence should I focus on right now?"
This is the basic intuition behind Attention.
Rather than relying only on a single recurrent hidden state to carry information through the sequence, attention allows a model to assign different levels of importance to different parts of the available context.
For example, when processing a word in a sentence, the model may need to pay more attention to another word that is directly relevant to its meaning.

The important idea is:
🎯 Not every part of the context is equally important.
Attention gives the model a mechanism for deciding what information deserves more focus.

---

The Transformer Arrives​

In 2017, researchers at Google published the influential paper "Attention Is All You Need".
It introduced the Transformer architecture.
The Transformer made attention the central mechanism for processing relationships between elements in a sequence, rather than building the model around recurrence.
This was a major shift.
Instead of processing information strictly step by step like a traditional RNN, Transformer architectures can process relationships between many tokens using attention mechanisms.
That made them much more suitable for large-scale training and parallel computation.
And this scalability became extremely important.
🚀 Transformers could be trained at a scale that was difficult to achieve with traditional recurrent architectures.

---

The Evolution in One Picture​

The progression becomes easier to understand when we look at the main question each approach was trying to answer:

HMM​

❓ What hidden state most likely explains these observations?​

⬇️​

RNN​

❓ How can information from previous steps influence the current step?​

⬇️​

LSTM​

❓ How can important information be preserved for much longer?​

⬇️​

Attention​

❓ Which parts of the context are most relevant right now?​

⬇️​

Transformer​

❓ What if attention becomes the main mechanism for modeling relationships across the sequence?​

⬇️​

Large Language Models​

❓ What happens when Transformer-based architectures are trained on enormous amounts of data and compute?​

---

These Were Not Separate Stories​

The interesting part is that these technologies are not isolated inventions.
They represent a broader evolution in how researchers approached sequential information.
🔹 HMMs provided a probabilistic way to reason about hidden states and observations.
🔹 RNNs introduced recurrent neural memory for sequence processing.
🔹 LSTMs improved the ability of recurrent networks to preserve useful information over longer periods.
🔹 Attention introduced a more direct way to focus on relevant parts of a sequence.
🔹 Transformers made attention the foundation of a highly scalable architecture.
🔹 Modern LLMs use Transformer-based architectures at enormous scale to learn complex patterns from large datasets.
Each step addressed important limitations or opened new possibilities.

---

Why This History Matters for Modern AI​

When you use ChatGPT today and type a complete sentence, you are seeing the result of decades of research into questions such as:

🧠 How should information be represented?​

🧠 How should a model handle sequential information?​

🧠 How can useful context be preserved?​

🧠 Which parts of the context matter most?​

🧠 How can these ideas scale to much larger models and datasets?​

The technology behind modern language models did not appear overnight.
It emerged from a long progression of ideas about states, memory, probabilities, context, and attention.
And that makes the next question especially interesting:
❓ If HMMs introduced the idea of hidden states, RNNs gave neural networks a form of sequential memory, and LSTMs improved long-term memory...
How does Attention actually allow a Transformer to connect different parts of the context?
🔥 That is where the story of Attention really begins.

---

Frequently Asked Questions​

-----------------

What is a Hidden Markov Model?​

A Hidden Markov Model is a probabilistic model for sequential data in which the underlying states are hidden, while the system observes outputs generated by those states.

What is the main difference between HMM and RNN?​

An HMM is a probabilistic sequence model based on hidden states and transition and emission probabilities. An RNN is a neural network that maintains a learned hidden state while processing a sequence.

Why was LSTM introduced?​

LSTM was introduced to help recurrent neural networks handle long-term dependencies and reduce problems associated with learning across long sequences, including vanishing gradients.

What problem does Attention solve?​

Attention allows a model to assign different importance to different parts of its context instead of relying only on information carried through recurrent hidden states.

Why are Transformers important?​

Transformers made attention the central mechanism of the architecture and enabled highly parallel processing and large-scale training, which helped make modern large language models possible.

Are HMMs still used today?​

Yes. Although deep learning has replaced HMMs in many applications, HMMs remain useful for probabilistic sequence modeling, teaching, research, and specialized applications.