Crear una Red Hopfield

TODO: collapasable, copyable, download, etc

What are Hopfield networks? Can we implement a toy one to recognize handwritten letters?Hopfield networks are a type of recurrent artificial neural network that serve as a form of associative memory. They were invented by John Hopfield in 1982. Here are some key characteristics:

1. Structure: A Hopfield network consists of a set of interconnected neurons, each connecting to all others except itself. The connections have weights that determine the influence of one neuron on another.

2. Binary Neurons: Each neuron in a Hopfield network can be in one of two states, often represented as -1 (off) or +1 (on).

3. Energy Function: The network is defined by an energy function, and its dynamics aim to minimize this energy. As the network evolves, it will eventually settle into a stable state, which is a local minimum of the energy function.

4. Memory Storage and Recall: Hopfield networks can store a number of patterns or memories. When a pattern similar to a stored memory is presented to the network, it will converge to the closest memory, thus demonstrating associative recall.

5. Learning Rule: The most common learning rule for setting the weights in a Hopfield network is Hebbian learning, which reinforces connections between simultaneously active neurons.

As for implementing a Hopfield network to recognize handwritten letters, it is theoretically possible but with limitations. Hopfield networks are not typically used for complex pattern recognition tasks like handwriting recognition because they are prone to errors and have limited capacity. More advanced neural network architectures, like convolutional neural networks, are more suitable for such tasks.

However, as a toy example or educational exercise, it is possible to implement a simple Hopfield network to recognize a very limited set of small, binary (black and white) handwritten letters. The network would be trained on a set of predefined patterns representing these letters, and after training, it could recognize noisy or incomplete versions of these patterns. Keep in mind that the performance would be quite limited, especially compared to modern neural network approaches.

Would you like to proceed with a simple implementation of such a Hopfield network?Yesimport numpy as np

class HopfieldNetwork: def init(self, size): self.size = size self.weights = np.zeros((size, size))

def train(self, data):
    for pattern in data:
        self.weights += np.outer(pattern, pattern)
    np.fill_diagonal(self.weights, 0)
    self.weights /= len(data)

def predict(self, pattern):
    result = pattern.copy()
    for _ in range(100):  # iteration limit to prevent infinite loops
        new_result = np.sign(self.weights @ result)
        if np.array_equal(new_result, result):
            break
        result = new_result
    return result

def to_pattern(self, letter):
    return np.array([1 if char == 'X' else -1 for char in letter])

def from_pattern(self, pattern):
    return ''.join(['X' if val == 1 else '.' for val in pattern])

Define the letters as patterns

letters = { 'A': "X..X..XXXX..XX..X..X", 'B': "XXXX..XX..XXXX..XX..XXXX", 'C': ".XXXXX..X....X.....XXXX." }

Initialize and train the Hopfield Network

network = HopfieldNetwork(size=25) training_data = [network.to_pattern(letters[letter]) for letter in letters] network.train(training_data)

Create a noisy version of 'A' to test

noisy_A = network.to_pattern("X..X..X.XX..XX..X..X")

Predict and print the result

predicted = network.predict(noisy_A) predicted_letter = network.from_pattern(predicted)

predicted_letter

ValueError Traceback (most recent call last) Cell In[1], line 39 37 network = HopfieldNetwork(size=25) 38 training_data = [network.to_pattern(letters[letter]) for letter in letters] ---> 39 network.train(training_data) 41 # Create a noisy version of 'A' to test 42 noisy_A = network.to_pattern("X..X..X.XX..XX..X..X")

Cell In[1], line 10, in HopfieldNetwork.train(self, data) 8 def train(self, data): 9 for pattern in data: ---> 10 self.weights += np.outer(pattern, pattern) 11 np.fill_diagonal(self.weights, 0) 12 self.weights /= len(data)

ValueError: operands could not be broadcast together with shapes (25,25) (20,20) (25,25) It looks like there was a mismatch in the dimensions of the patterns and the network size. The letters 'A', 'B', and 'C' are represented as patterns of length 20, but the network was initialized with a size of 25. To fix this, I'll adjust the network size to match the pattern size. Let's correct this and try again.# Correcting the network size to match the pattern size network = HopfieldNetwork(size=20) training_data = [network.to_pattern(letters[letter]) for letter in letters] network.train(training_data)

Create a noisy version of 'A' to test

noisy_A = network.to_pattern("X..X..X.XX..XX..X..X")

Predict and print the result

predicted = network.predict(noisy_A) predicted_letter = network.from_pattern(predicted)

predicted_letter

ValueError Traceback (most recent call last) Cell In[2], line 4 2 network = HopfieldNetwork(size=20) 3 training_data = [network.to_pattern(letters[letter]) for letter in letters] ----> 4 network.train(training_data) 6 # Create a noisy version of 'A' to test 7 noisy_A = network.to_pattern("X..X..X.XX..XX..X..X")

Cell In[1], line 10, in HopfieldNetwork.train(self, data) 8 def train(self, data): 9 for pattern in data: ---> 10 self.weights += np.outer(pattern, pattern) 11 np.fill_diagonal(self.weights, 0) 12 self.weights /= len(data)

ValueError: operands could not be broadcast together with shapes (20,20) (24,24) (20,20) The issue persists because the patterns for the letters 'A', 'B', and 'C' are not of the correct length. They should be 20 characters long to match the size of the network. Let's modify the patterns to ensure they are of the correct length and then try the implementation again.# Adjusting the letter patterns to be 20 characters long adjusted_letters = { 'A': "X..X.XXXX.XX.X..X", 'B': "XXXX.XX.XXXX.XX.XXXX", 'C': "XXXXX.X...X....XXXX" }

Re-initialize and re-train the network with the adjusted patterns

network = HopfieldNetwork(size=20) training_data = [network.to_pattern(adjusted_letters[letter]) for letter in adjusted_letters] network.train(training_data)

Create a noisy version of 'A' to test

noisy_A = network.to_pattern("X..X.X.XX.XX.X..X")

Predict and print the result

predicted = network.predict(noisy_A) predicted_letter = network.from_pattern(predicted)

predicted_letter

ValueError Traceback (most recent call last) Cell In[3], line 11 9 network = HopfieldNetwork(size=20) 10 training_data = [network.to_pattern(adjusted_letters[letter]) for letter in adjusted_letters] ---> 11 network.train(training_data) 13 # Create a noisy version of 'A' to test 14 noisy_A = network.to_pattern("X..X.X.XX.XX.X..X")

Cell In[1], line 10, in HopfieldNetwork.train(self, data) 8 def train(self, data): 9 for pattern in data: ---> 10 self.weights += np.outer(pattern, pattern) 11 np.fill_diagonal(self.weights, 0) 12 self.weights /= len(data)

ValueError: operands could not be broadcast together with shapes (20,20) (17,17) (20,20) It appears there was another mismatch in the length of the letter patterns. They need to be exactly 20 characters long to match the network size. Let's adjust the patterns again to ensure they are the correct length and retry the implementation.Yes, in JavaScript Implementing a Hopfield Network in JavaScript for recognizing handwritten letters is a bit complex, especially for a toy example. However, I can guide you through a simplified version.

The key steps are:

1. Create the Hopfield Network class.
2. Define the training and prediction methods.
3. Represent the letters in a binary format suitable for the network.
4. Train the network with these letters.
5. Test the network with a noisy input to see if it can recall the correct letter.

Here's a basic structure of how you might implement this in JavaScript:

class HopfieldNetwork {
    constructor(size) {
        this.size = size;
        this.weights = Array.from({ length: size }, () => new Array(size).fill(0));
    }

    train(patterns) {
        for (let p of patterns) {
            for (let i = 0; i < this.size; i++) {
                for (let j = 0; j < this.size; j++) {
                    if (i !== j) {
                        this.weights[i][j] += p[i] * p[j];
                    }
                }
            }
        }

        for (let i = 0; i < this.size; i++) {
            for (let j = 0; j < this.size; j++) {
                this.weights[i][j] /= patterns.length;
            }
        }
    }

    predict(input) {
        let result = input.slice();
        let stable = false;

        while (!stable) {
            stable = true;
            for (let i = 0; i < this.size; i++) {
                let sum = 0;
                for (let j = 0; j < this.size; j++) {
                    sum += this.weights[i][j] * result[j];
                }
                let updatedValue = sum >= 0 ? 1 : -1;
                if (result[i] !== updatedValue) {
                    stable = false;
                    result[i] = updatedValue;
                }
            }
        }

        return result;
    }
}

To use this class:

1. Create an instance of HopfieldNetwork with the size of your patterns.
2. Define your letter patterns as arrays of 1s and -1s (you'll need to decide how to represent your letters in this binary format).
3. Train the network with these patterns.
4. Test the network with a slightly altered version of one of your patterns.

This is a rudimentary implementation and might not perform well with complex or numerous patterns due to the limitations of Hopfield networks. Also, JavaScript might not be the most efficient language for this kind of computation-heavy task, but it's certainly possible to build a basic example as a learning exercise.

For a real-world application, especially for something as complex as handwriting recognition, more advanced neural network models and a language more suited for numerical computations, like Python, would be recommended.

Crear una Red Hopfield created at Tue Jan 20 1970 16:32:29 GMT+0000 (Coordinated Universal Time)