Brains, Pixels, and Energy: The Physics Behind AI Pattern Recognition: John J. Hopfield Nobel Prize Winner 2024.

18 min readOct 27, 2024

Let’s break it down further and look at some real-life examples to understand the contributions of John J. Hopfield in artificial neural networks (ANNs) and how his work helps in everyday technologies.

What is an Artificial Neural Network (ANN)?

An ANN is a type of computer model inspired by the way our brains work. In our brain, we have billions of neurons (tiny nerve cells) that communicate with each other. Each neuron receives signals, processes them, and passes them on. ANNs mimic this structure using “nodes” (like artificial neurons) that pass information and make decisions together.

Imagine an ANN like a team of people working together to solve a problem. If one person knows something useful, they can share that information, and the others will learn from it. Over time, the team gets better at solving that problem.

John Hopfield’s Contribution: Associative Memory

John Hopfield’s work in the 1980s introduced a special type of ANN known as the Hopfield Network. Its key feature is something called associative memory — the ability to store patterns (like images or sounds) and retrieve them later, even if parts of the information are missing or corrupted.

Real-life Example: Recognizing a Friend’s Face in a Blurry Photo

Let’s say you have a blurry or incomplete picture of your friend. A Hopfield network can help you identify that friend by filling in the missing details.

How it works: Think of the picture as made up of many small pixels (tiny dots of color). The Hopfield network remembers what the complete picture of your friend looks like. When it is given a blurry or damaged picture, it goes step by step, comparing the incomplete one with what it has stored in memory. Eventually, it adjusts and sharpens the picture, making it clear and recognizable again.
Physics connection: Hopfield used ideas from physics about how tiny magnets (atoms) behave. Just as atoms try to align their magnetic fields to reach a low-energy, stable state, the nodes in the Hopfield network adjust their connections to reach the most “stable” and accurate version of the image.

Another Real-life Example: Autocorrect in Phones

When you type a word on your phone and make a mistake, the phone often guesses the correct word. This is because it “remembers” similar words and tries to fill in the gaps when you make an error, much like a Hopfield network can complete an incomplete image. This process of associating incomplete or incorrect data with something it has learned before is an application of associative memory.

In Summary

John Hopfield: Created a system that can remember patterns (like images or text) and retrieve them even when the data is incomplete or noisy. Think of it like recognizing your friend in a blurry photo or how autocorrect suggests the right word when you make a typo

I’m still confused about John Hopfield’s work. Wasn’t the concept of recognizing patterns already in place before his contributions?

I understand why it might be confusing! Let me break it down a little more simply and clarify what John Hopfield’s work really did, and why it’s different from just general pattern recognition.

Before Hopfield: How Did Computers Recognize Patterns?

Before Hopfield’s work, computers could recognize patterns, but they did so in a rigid, rule-based way. If you wanted a computer to recognize a face, you’d have to give it a very specific set of instructions (rules) for what a face looks like: for example, “Look for two eyes, a nose, and a mouth in this arrangement.” If the face was slightly different (e.g., one eye was partially covered by hair), the computer might fail to recognize it.

This is because older systems followed hard-coded rules that didn’t handle imperfections or missing parts well. They couldn’t “fill in the gaps” when the pattern wasn’t perfect.

What Did John Hopfield Do?

John Hopfield’s breakthrough was in associative memory — a concept that allowed computers to store and retrieve patterns even when parts were missing, distorted, or incorrect. His Hopfield network could “fix” incomplete patterns and “fill in the gaps.”

To understand this better, let’s compare normal pattern recognition to Hopfield’s associative memory:

1. Regular Pattern Recognition (Before Hopfield):

Example: Imagine you’re using a facial recognition system. The system has a picture of your face stored. If you present a clear, well-lit picture of yourself, the system will recognize you.
Problem: If you present a blurry or incomplete picture, the system might struggle. If the face is partially blocked or distorted, the system might say, “I don’t know who this is.” It lacks flexibility.

2. Hopfield’s Associative Memory (After Hopfield):

Example: Now imagine you’re using a system built with a Hopfield network. This system has a stored memory of your face. If you show it a blurry or incomplete picture, it doesn’t get confused. Instead, the network works to “complete” the image based on its memory. It will try to reconstruct what’s missing or fix the blurry parts to figure out who it is.
How it works: The Hopfield network has a bunch of interconnected nodes (like neurons in the brain). When you feed it an incomplete or messy pattern, it updates its nodes step by step to “reduce energy” (a fancy way of saying it tries to stabilize the image). This is based on a principle from physics: systems in nature try to move toward low-energy, stable states. The network uses this idea to gradually adjust its connections until the stored pattern is recovered.

Real-world Example to Clarify Hopfield’s Contribution:

Imagine you have a photo of your friend’s face in perfect condition. You give this photo to the Hopfield network, and it “remembers” it. Later, you give the network a different photo of the same friend, but it’s blurry or partially hidden.

A regular system might struggle and say, “I don’t know who this is.”
The Hopfield network, on the other hand, uses the blurry photo as a starting point and compares it to the stored memory. It tries to “fix” the image and make it look more like the stored version. The network goes step by step, adjusting the pixels or features until it can confidently say, “Ah, this is your friend!”

How is This Different from Regular Pattern Recognition?

The key difference is that Hopfield’s network can handle incomplete or distorted data. It doesn’t need a perfect input to work. It’s like having the ability to complete a puzzle even if some pieces are missing. This was not possible with earlier pattern recognition systems, which relied on strict, rule-based algorithms.

Why Is This a Big Deal?

Flexibility: Hopfield’s network is flexible. It doesn’t just recognize a perfect version of something; it can figure out what it’s looking at even when the input isn’t ideal.
Inspiration from Physics: The way Hopfield’s network works is inspired by how materials behave at the atomic level in physics. Just like how atoms arrange themselves to reach a stable, low-energy state, the network adjusts its nodes to reach the correct, “remembered” pattern.

Modern Impact

Hopfield’s work laid the foundation for many modern AI systems. For example:

Image reconstruction: If a surveillance camera captures a blurry image of a suspect, AI systems based on Hopfield’s ideas can help “clear up” the image by comparing it to stored data.
Autocorrect: When you type something wrong, autocorrect doesn’t just look at your exact input — it compares it to words it “remembers” and suggests the most likely correct word, even if you made multiple mistakes.
Memory in AI: Today’s AI systems, like those that auto-tag people in photos on social media, owe part of their ability to Hopfield’s associative memory concepts.

In Conclusion:

Hopfield’s key contribution was creating a network that can remember and restore patterns, even if parts of the data are missing or distorted. This associative memory is different from basic pattern recognition because it doesn’t just follow rigid rules — it can adapt and fill in gaps, making it much more powerful and flexible.

Could you explain in simple way. “Memories are stored in a landscape”

Let me break down the idea behind John Hopfield’s theory using some real-life examples and simple terms.

Memories are stored in a landscape

Hopfield used the concept of a landscape to explain how memories (or patterns) are stored and retrieved in his network. To understand this, let’s first look at what a landscape means in this context.

Imagine a bumpy landscape with valleys and hills:

Valleys represent stored memories (or patterns). When the network stores a memory, it creates a valley in the landscape.
Hills represent other areas where the network hasn’t stored memories.

So, you can think of each memory as being located in a low point (valley) on this landscape. The deeper the valley, the stronger the memory.

How memories are stored:

When the network is trained with different patterns (like images, words, or sounds), each pattern creates a valley in this landscape. Think of each memory as shaping the landscape — the more memories the network stores, the more valleys there are.

For example, let’s say you store the image of a dog. The network creates a valley for that image.
Then, you store an image of a cat. Now there’s another valley for the cat.

Each valley is like a “home” for that memory.

What happens when the input is incomplete or distorted?

Now, imagine you show the network an incomplete or blurry picture of a dog. The network starts at some point on the landscape (maybe not directly in the dog’s valley) and works its way towards the nearest valley (the dog’s valley). It does this step by step, adjusting its “position” until it finds the deepest point — which represents the complete, correct memory of the dog.

Why does this happen? The idea is that the network wants to reach the lowest-energy state, just like how water always flows downhill to the bottom of a valley.

So, when the network receives distorted or incomplete input, it “travels” across the landscape, making small adjustments to the image it “sees” until it finds the closest valley, or the closest correct memory. The more distorted the image is, the longer the journey might be, but it still tries to get to the right memory.

In Simple Terms:

The landscape: Imagine the network as a hilly field with lots of dips (valleys). Each valley is a memory (like a photo or piece of information) that the network has stored.
How memories are stored: When you feed the network a new piece of information, it creates a new valley for that memory. The shape of the landscape changes to store that memory.
Finding the correct memory: If you give the network a messed-up or incomplete version of the memory (like a blurry picture), it starts somewhere on the landscape and “rolls” down into the nearest valley — where the correct memory is stored. This process is like the network “fixing” the input until it matches the correct memory.

Real-Life Example:

Let’s say you’re trying to remember the face of a person you met a long time ago, but your memory of them is a bit fuzzy.

The valleys in your brain: The faces you’ve seen before are stored as valleys in your brain. Each face has its own valley.
What happens when you’re unsure: When you see an incomplete or unclear image of that person, your brain starts searching through its “landscape” of faces. It will gradually adjust the unclear face in your mind, comparing it to the closest stored memory, until you say, “Ah, that’s John!” The fuzzy image gets “completed” as your brain finds the closest matching face.

Hopfield’s network works in a similar way — when it sees an incomplete or noisy image, it uses the information it has stored to “fill in the gaps” and get to the right answer.

Summary:

Valleys in a landscape: Memories or patterns are stored as valleys in a landscape.
Low energy = correct memory: The network seeks out valleys (low energy spots) because that’s where the correct memories are stored.
Distorted input: When given incomplete or messy data, the network adjusts itself step by step, like rolling downhill, to find the valley (the correct memory).

Hopfield’s key idea was using this energy landscape analogy to describe how the network can store and retrieve information, even when the input is imperfect!

There’s a game where a distorted image is shown, and you have to figure out what the actual image is. I believe the brain works in a similar way to identify the correct image.

You’re absolutely right! That game where you have to guess the image from a distorted or blurry version is a great example to explain how John Hopfield’s work and the brain operate similarly. Let me explain in a way that connects both ideas.

The Game Example:

In the game, you might see a blurry image of something — maybe an animal, an object, or a person. At first, it’s hard to tell exactly what it is. But, as you look closer, your brain starts to guess: “Maybe this is a dog?” or “Could it be a cat?” Eventually, your brain “figures out” what the blurry image is, and you say, “Yes, this is definitely a dog!”

How the Brain Works (Like Hopfield’s Network):

When you look at the distorted image, your brain doesn’t give up right away. Instead, it tries to match the blurry image with memories you’ve already stored. It compares the unclear image to clearer versions of images in your memory. Little by little, it refines its guess and finds the closest match, until you identify the image correctly.

How Does This Relate to John Hopfield’s Work?

John Hopfield’s work on associative memory is based on this exact idea: when you give the network a distorted or incomplete image, it doesn’t just give up. Instead, it uses the information it has already stored to work through the distortion and figure out the most likely original image.

In both the game and Hopfield’s network:

You start with a distorted or incomplete image. In the game, it’s the blurry picture. In Hopfield’s network, it’s the distorted image that’s fed into the network.
Your brain (or the network) tries to find the closest match. In the game, your brain starts comparing the blurry image to the clear images stored in your memory, like faces, animals, or objects. In Hopfield’s network, the system adjusts its “guesses” by updating the nodes, looking for the best match in its memory (a valley in the landscape).
You identify the correct image! Once your brain recognizes the image as a dog, cat, or whatever it might be, it knows what you’re looking at. Similarly, Hopfield’s network finds the correct, stored memory by lowering its energy until it reaches the right pattern.

Real-life Connection:

Imagine this: if you’ve seen your friend’s face many times before, your brain has stored a clear memory of what they look like. Now, if someone shows you a blurry picture of your friend, your brain doesn’t get confused for long. It says, “Hey, I’ve seen this face before, even if it’s blurry!” and quickly matches the blurry image with the clear memory stored in your brain. That’s exactly how Hopfield’s network works when it tries to recognize a distorted pattern!

Why It’s Important:

Hopfield’s network is great because it can recognize things even when they aren’t perfect — like the blurry images in the game.
Your brain does something very similar, using past memories to make sense of new, unclear information.

So, John Hopfield’s invention mimics the way our brain fills in the gaps when we see distorted images, helping computers do the same thing in a smarter, more brain-like way!

How actually our brain neuron work while showing blurry image?

Great question! Let’s explore how neurons in our brain work when you see a blurry image. I’ll explain it in simple terms and connect it to how our brain processes information.

How Neurons Work (in Simple Terms):

Neurons are like tiny messengers in the brain. They are specialized cells that communicate with each other using electrical and chemical signals. Each neuron is connected to many others, forming a network that allows us to think, learn, and remember.
Synapses are the connections between neurons. When a neuron wants to send a message to another neuron, it sends an electrical signal through the synapse. The strength of these connections is what helps our brain make decisions and recognize things.

What Happens When You See a Blurry Image?

Visual input reaches the brain: When you look at a blurry image, light enters your eyes and forms an image on your retina (the back part of your eye). The retina sends this image as an electrical signal to your brain.
Neurons get to work: Your brain’s neurons, especially in the visual cortex (the part of the brain that processes images), start analyzing this blurry input. Even though the image is unclear, neurons in your brain compare it with memories of clear images you’ve seen before. These memories are stored in the form of patterns of connected neurons.
Recognizing patterns (like Hopfield’s network): Even though the image is distorted, your brain recognizes familiar features — maybe the shape, color, or general structure of the object. Your neurons work together, comparing the blurry image with stored memories of similar clear images. They try to match the blurry input with something you already know.
Filling in the gaps: As your brain’s neurons analyze the image, they use past experiences (memories) to fill in the missing details. Even though the image isn’t perfect, your neurons adjust their signals based on what you’ve seen in the past. For example, if you’ve seen many dogs before, your neurons will pick up on certain features — like the ears or tail — and guess that it’s a dog, even though the image isn’t fully clear.
Decision-making: After processing the blurry image and finding the best match, your brain reaches a decision: “This is a dog!” This decision happens because the neurons in your brain strengthen certain connections (synapses) that are linked to dog-like features and weaken others that don’t match the blurry image.

How is This Similar to Hopfield’s Work?

Just like how John Hopfield’s network finds the closest match by adjusting its values step by step, your brain’s neurons do the same:

Neurons adjust their connections (synapses) based on the blurry input.
They compare the distorted image with memories of similar images stored in your brain, much like how Hopfield’s network compares the input to patterns it has saved.
As more neurons fire and send signals, your brain finds the best match — the memory of the clear image that’s closest to the blurry one.

Real-life Example:

Let’s say you’re looking at a blurry picture of a person. Your brain’s neurons start by detecting simple features like the shape of the head or the color of the hair. If you’ve seen this person before, your neurons will start activating patterns (memories) associated with them. The more familiar the person is, the quicker your brain fills in the gaps and recognizes them, even from the blurry picture.

Key Takeaway:

When you see a blurry image, your brain’s neurons work together to:

Analyze the blurry features it receives.
Compare these features with stored memories of clearer images.
Adjust their connections to recognize the image, filling in the gaps and figuring out what it is.

In short, your brain uses its network of neurons to recognize distorted or incomplete images, much like how Hopfield’s artificial network works!

But for still John work, we need to provide images to train so that it could identify?

You’re absolutely right! For John Hopfield’s network (and most AI systems), we need to provide images or data to train the system. Let’s break this down simply and compare it to how our brains work.

Hopfield’s Network:

Training with Images: For Hopfield’s network to work, we need to first give it clear images (or patterns). These images are stored in the network by adjusting the connections (or synapses, similar to the brain) between the nodes. Each image is saved in the network’s “memory” as a kind of pattern of connected nodes. Think of it like the network remembering what each image looks like.
Recognizing Distorted Images: After training, if we show the network a blurry or incomplete version of the image, it can try to recognize it by comparing the blurry input to the stored images in its memory. The network adjusts the connections between the nodes until it finds the stored image that is most similar to the blurry one. This is how it “fills in the gaps” to recognize the image.

How This Differs from the Brain:

While Hopfield’s network needs to be explicitly trained with clear images, your brain works a little differently because:

Your brain learns over time: From a very young age, your brain is constantly learning and storing information from your experiences — like seeing objects, people, or animals. Your brain doesn’t need to be re-trained every time it sees something new. It can generalize and use past experiences to recognize new things.
Neurons adjust on their own: Your neurons can adjust their connections automatically when you experience new things. So, if you’ve never seen a blurry picture of an object before, your brain will try to use past memories (similar objects) to figure out what it is. In contrast, a Hopfield network has to be trained on specific images in advance to recognize a blurry version of them.

Real-Life Example (AI vs Brain):

Hopfield’s Network (AI): Imagine we’re training a Hopfield network to recognize pictures of cats. We feed it many clear images of cats during training, and it stores them in its memory. Later, if we give the network a blurry picture of a cat, it compares it with the stored images and adjusts its nodes (neurons) to match the blurry picture with one of the clear ones it already knows.
Your Brain: Let’s say you’ve seen lots of cats in real life, not just pictures. Now, if someone shows you a blurry picture of a cat, your brain won’t need special training. It will try to recognize the features — like the ears or whiskers — and automatically match the blurry image to what you’ve seen before.

In summary:

Hopfield’s network needs to be trained with specific images (like clear cat pictures) before it can recognize blurry or incomplete versions.
Your brain can learn and adapt from experiences, and doesn’t need as much explicit training. It uses past memories and general knowledge to figure out what it’s seeing, even if it’s blurry.

Both systems work similarly in that they fill in gaps and match distorted input to something they’ve seen before. But while Hopfield’s network is trained on specific data, your brain is a lot more flexible and can handle new, unexpected information better.

Sorry I am still trying to understand what physics is doing here for John.

I see where you’re coming from! It can be a bit tricky to grasp the physics connection in John Hopfield’s work. Let’s break it down simply:

What John Hopfield Did with Physics:

John Hopfield used ideas from physics to create a network that can store and recognize patterns, like how the brain remembers things. The key concept from physics he used is related to energy minimization — how systems naturally settle into states of lower energy. Let’s look at this with an example to understand better.

1. Energy and Systems in Physics (Simple Explanation):

In physics, many systems try to reach a state of low energy. For example:

Imagine a ball rolling down a hill. The ball naturally wants to roll to the bottom because that’s where its energy is the lowest. Once it reaches the bottom (the low-energy state), it stays there.

Now, think of Hopfield’s neural network like a similar system.

2. Hopfield’s Network and Energy:

Hopfield’s network can be thought of as trying to reach a state of low energy. In the network, the energy is like the “difficulty” the network faces in matching an input (like a blurry image) to one of its stored patterns (like a clear image).
Physics helped Hopfield model this process. Just like the ball wants to reach the bottom of the hill, Hopfield’s network tries to find a state where the connections between neurons lead to the lowest possible energy (which means the best match between the blurry input and the clear stored pattern).

3. How This Works with Pattern Recognition:

Let’s connect this to the example of recognizing blurry images.

When you give a blurry image to Hopfield’s network, the network starts in a high-energy state because it doesn’t recognize the image right away.
As the network adjusts the connections between its nodes (neurons), it lowers the energy step by step. This is like the ball rolling down the hill.
When the network finds the correct pattern that matches the blurry image, it reaches a low-energy state. This is the point where it has recognized the image.

4. Physics Analogy to Memory:

Think of the stored images (clear memories) in Hopfield’s network as valleys in a landscape. Each valley represents a memory or a pattern that the network knows well.
When you give the network a blurry image, it’s like dropping the ball on the landscape. The network then tries to find the nearest valley (the correct memory) by lowering its energy, just like the ball rolling to the bottom of a valley.

So, physics helps Hopfield’s network by providing the idea of energy minimization — just like in nature, where systems tend to move toward lower energy states. This allows the network to gradually match distorted inputs (like blurry images) to stored patterns (memories) by adjusting its connections and finding the lowest energy state.