What are Liquid Neural Networks?

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Neural Networks have modified the way in which we carry out mannequin coaching. Current day, we see many neural community varieties utilized throughout the sector of machine studying: Convolutional Neural Networks, Recurrent Neural Networks, Liquid Neural Networks, and extra. These developments have paved the way in which for the emergence of a subset of machine studying: Deep Studying.

With the rise within the utilization of the pc and machine studying techniques, the provision of knowledge has grow to be simple. Neural networks, generally known as Neural Nets, want giant datasets for environment friendly coaching. This availability of knowledge made it simple to coach and undertake throughout the business.

Despite the fact that they work effectively, they do have some challenges. For instance, if the mannequin we educated encounters one thing exterior the coaching set, it received’t work correctly because it has by no means encountered it. Additionally, with giant quantities of knowledge, the complexity of the mannequin will increase. So, what if we have now a neural community that may adapt itself to new knowledge and has much less complexity?

Liquid Neural Networks clear up the issues posed by conventional networks. On this article, we are going to study extra in regards to the Liquid Neural Networks (LNNs).

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What’s a Liquid Neural Community?

Within the 12 months 2020, researchers at MIT’s Pc Science and Synthetic Intelligence Laboratory (CSAIL), Ramin Hasani, Daniela Rus, and the group launched a sort of neural community often known as Liquid Neural Networks (LNNs). LNNs are a kind of Recurrent Neural Community (RNN) that’s time-continuous.

Their dynamic structure can adapt its construction based mostly on the information. That is one thing just like liquids that may take the form of the container they’re in. Therefore, they’re known as Liquid Neural Networks. They’ll study on the job even after coaching.

These neural networks are impressed by the nervous system of a microscopic worm often known as C. elegans. It has 302 neurons. Nevertheless, regardless of a low variety of neurons, it might exhibit intricate behaviors which is an excessive amount of for the variety of neurons it has. Subsequent, let’s see how these liquid neural networks work.


How do Liquid Neural Networks Work?

Liquid Neural Networks are a category of Recurrent Neural Networks (RNNs) which are time-continuous. LNNs are made up of first-order dynamical techniques managed by non-linear interlinked gates. The tip mannequin is a dynamic system with various time constants in a hidden state. That is an enchancment of Recurrent Neural Networks the place time-dependent unbiased states are launched.

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Numerical differential equation solvers compute the outputs. Every differential equation represents a node of that system. The closed-form answer makes positive that they carry out effectively with a smaller variety of neurons. This provides rise to fewer and richer nodes.

They present steady and bounded habits with improved efficiency on time collection knowledge. The differential equation solver updates the algorithm as per the below-given guidelines.


liquid neural networks
LTC replace by fused ODE Solver – source.


LNN structure has three layers. They’re:

  • Enter layer.
  • Liquid layer (Reservoir).
  • Output layer.

Enter layer: That is the layer that has the inputs to the community. All of the enter knowledge that we need to practice the mannequin on is given to this layer. This layer feeds the enter knowledge to the liquid layer.

Liquid layer: This layer is often known as a reservoir. It comprises a big recurrent community of neurons. They’re initialized with synaptic weights. Enter knowledge is reworked right into a wealthy non-linear house.

Output layer: It consists of output neurons. This receives the knowledge from the liquid layer.

Now, let’s see the right way to implement a easy Liquid Neural Community utilizing TensorFlow.

Implementation of a Liquid Neural Community (LNN)

We’ll use the MNIST dataset out there within the TensorFlow datasets. MNIST dataset comprises handwritten digits and is extensively used for academic and analysis functions. It has 70000 samples, of which 60000 samples are used as a coaching dataset, and the remainder of the samples are used as a take a look at dataset. The dimension of every picture is (28,28,1).

Import Libraries

To implement LNN, we are going to start by importing the mandatory libraries as proven beneath:

import numpy as np
import tensorflow as tf
from tensorflow import keras

Within the code above, we have now imported Numpy, tensorflow, and keras.

Outline Weight Initialize, Prepare, and Predict Features

Subsequent, we outline a operate to initialize the weights of the mannequin.

def initialize_weights(input_dim, reservoir_dim, output_dim, spectral_radius):
    # Initialize reservoir weights randomly
    reservoir_weights = np.random.randn(reservoir_dim, reservoir_dim)
    # Scale reservoir weights to attain desired spectral radius
    reservoir_weights *= spectral_radius / np.max(np.abs(np.linalg.eigvals(reservoir_weights)))
    # Initialize input-to-reservoir weights randomly
    input_weights = np.random.randn(reservoir_dim, input_dim)
    # Initialize output weights to zero
    output_weights = np.zeros((reservoir_dim, output_dim))
    return reservoir_weights, input_weights, output_weights

The above operate initializes the burden matrices of the LNN. It begins by randomly initializing the reservoir weights matrix. Then, it scales the reservoir weights to get the suitable spectral radius.

After this, it randomly initializes the input-to-reservoir weights and the output weights as a zero matrix. Lastly, it returns reservoir weights, enter weights, and output weights.

Within the subsequent step, we outline a operate to coach our mannequin as proven beneath:

def train_lnn(input_data, labels, reservoir_weights, input_weights, output_weights, leak_rate, num_epochs):
    num_samples = input_data.form[0]
    reservoir_dim = reservoir_weights.form[0]
    reservoir_states = np.zeros((num_samples, reservoir_dim))
    for epoch in vary(num_epochs):
        for i in vary(num_samples):
            # Replace reservoir state
            if i > 0:
                reservoir_states[i, :] = (1 - leak_rate) * reservoir_states[i - 1, :]
            reservoir_states[i, :] += leak_rate * np.tanh(np.dot(input_weights, input_data[i, :]) +
                                                           np.dot(reservoir_weights, reservoir_states[i, :]))
        # Prepare output weights
        output_weights = np.dot(np.linalg.pinv(reservoir_states), labels)
        # Compute coaching accuracy
        train_predictions = np.dot(reservoir_states, output_weights)
        train_accuracy = np.imply(np.argmax(train_predictions, axis=1) == np.argmax(labels, axis=1))
        print(f"Epoch {epoch + 1}/{num_epochs}, Prepare Accuracy: {train_accuracy:.4f}")
    return output_weights

This operate trains the LNN based mostly on the enter parameters. It initializes the reservoir states as a zero matrix, iterates over the given variety of epochs, and trains the output weights. After this, the coaching accuracy is computed, and the output weights are returned.

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Subsequent, we outline a operate to foretell the values based mostly on the take a look at knowledge.

def predict_lnn(input_data, reservoir_weights, input_weights, output_weights, leak_rate):
    num_samples = input_data.form[0]
    reservoir_dim = reservoir_weights.form[0]
    reservoir_states = np.zeros((num_samples, reservoir_dim))
    for i in vary(num_samples):
        # Replace reservoir state
        if i > 0:
            reservoir_states[i, :] = (1 - leak_rate) * reservoir_states[i - 1, :]
        reservoir_states[i, :] += leak_rate * np.tanh(np.dot(input_weights, input_data[i, :]) +
                                                       np.dot(reservoir_weights, reservoir_states[i, :]))
    # Compute predictions utilizing output weights
    predictions = np.dot(reservoir_states, output_weights)
    return predictions

This operate provides the predictions utilizing the educated LNN. It initializes the reservoir states as a zero matrix and iterates over the variety of samples to replace the reservoir states. After this, it makes predictions utilizing the reservoir states and output weights and returns the predictions.

Knowledge Loading and Pre-processing

Now that we have now all of the capabilities wanted for coaching the mannequin, let’s load and preprocess the information as proven beneath:

# Load and preprocess MNIST dataset
(x_train, y_train), (x_test, y_test) = keras.datasets.mnist.load_data()
y_train = keras.utils.to_categorical(y_train)
y_test = keras.utils.to_categorical(y_test)
x_train = x_train.reshape((60000, 784)) / 255.0 
x_test = x_test.reshape((10000, 784)) / 255.0

We load the coaching and take a look at datasets utilizing the Keras library. Within the subsequent step, we scale the information for environment friendly coaching.

Now we set the hyperparameters for coaching as proven beneath:

# Set LNN hyperparameters
input_dim = 784
reservoir_dim = 1000
output_dim = 10
leak_rate = 0.1
spectral_radius = 0.9
num_epochs = 10
Initializing Weights and Coaching

Within the subsequent step, we initialize the reservoir weights utilizing the above parameters as proven beneath:

# Initialize LNN weights
reservoir_weights, input_weights, output_weights = initialize_weights(input_dim, reservoir_dim, output_dim, spectral_radius)

We practice the LNN to get the output weights in order that we will make predictions utilizing these weights.

# Prepare the LNN
output_weights = train_lnn(x_train, y_train, reservoir_weights, input_weights, output_weights, leak_rate, num_epochs)

We will now make the predictions utilizing the educated weights and consider them.

Prediction and Analysis
# Consider the LNN on take a look at set
test_predictions = predict_lnn(x_test, reservoir_weights, input_weights, output_weights, leak_rate)
test_accuracy = np.imply(np.argmax(test_predictions, axis=1) == np.argmax(y_test, axis=1))
print(f"Check Accuracy: {test_accuracy:.4f}")

The above code gave a take a look at accuracy of 0.3584 which is kind of low. We will enhance this through the use of hyperparameter tuning.


Benefits and Disadvantages of Liquid Neural Networks

  • They’re adaptable to the enter knowledge.
  • Appropriate for multi-sensory knowledge.
  • They’ll course of multi-modal data from totally different time scales.
  • These neural nets can course of time-series knowledge very effectively.
  • Mimics the mind extra precisely in comparison with standard neural networks.
  • Liquid neural networks face a vanishing gradient downside.
  • Hyperparameter tuning may be very tough as there’s a excessive variety of parameters contained in the liquid layer because of randomness.
  • That is nonetheless a analysis downside, and therefore a smaller variety of assets can be found to get began with these.
  • They require time-series knowledge and don’t work correctly on common tabular knowledge.
  • They’re very sluggish in real-world situations.
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Variations Between Liquid Networks and Conventional Networks

Liquid Neural Networks Typical Neural Networks
They don’t require a giant coaching dataset. They require a big coaching set as extra knowledge means extra accuracy for them.
Requires much less computational assets. They require extra computational assets.
It produces much less mannequin complexity and, therefore, is extra interpretable. Fashions have excessive complexity because of extra variety of parameters.
Have synaptic weights that alter themselves based mostly on incoming knowledge. They’ve fastened weights and activation capabilities that may’t be modified after coaching.
Requires re-training on new knowledge as they adapt themselves to the incoming knowledge. Requires coaching on new knowledge.
They’re scalable on the enterprise stage with much less labeled knowledge. To scale conventional neural nets, we want extra labeled knowledge.

Purposes of LNNs

Liquid Neural Networks have purposes in a number of domains as they carry out effectively on time-series knowledge. A few of the domains the place they are often extra environment friendly than conventional neural nets are as beneath.

Autonomous Drones: Drones based mostly on LNNs outperformed drones based mostly on conventional AI methods. Particularly, drones carried out effectively on unknown territory because of the adaptability of LNNs. This has lots of potential in army and catastrophe administration the place conditions are unpredictable.


image taken using drones
Drone imagery


Medical Prognosis: Since LNNs have a dynamic structure, they can be utilized in medical prognosis as they will adapt to new conditions with out costly coaching. These healthcare use circumstances can embody medical picture evaluation, well being information evaluation, and biomedical sign processing.


Lung cancer classification model to analyze CT medical imaging
Lung most cancers classification mannequin to research CT medical imaging


Self-Driving Automobiles: The dynamic structure of LNNs has the potential to drastically enhance the efficiency of self-driving vehicles. Generally AI fashions utilized in vehicles encounter knowledge that’s not a part of their coaching knowledge. The mannequin doesn’t know what to do on this state of affairs and this may result in accidents. LNNs may also help keep away from this as they study on the job and adapt their habits.


View from Self-Driving Vehicle Using Computer Vision
Car and object detection from self-driving automobile.


Pure language Processing (NLP): Coaching enormous textual knowledge utilizing Typical Neural Networks (CNNs) for sentiment evaluation, entity recognition, and many others., could be a time-consuming course of requiring enormous computational assets. LNNs clear up this downside as they require much less computational assets and may adapt to the incoming knowledge with out repeated coaching of the mannequin.


Simple Prompt to ChatGPT
Easy Immediate to the Giant Language Mannequin, ChatGPT


What’s Subsequent?

Liquid Neural Networks symbolize a brand new space of analysis that’s nonetheless unexplored and has lots of potential in varied sectors. They provide lots of advantages over conventional neural networks. Nevertheless, in addition they have some drawbacks. Analysis is happening on this course, and hopefully, in the future, they might change the panorama of Synthetic Intelligence.

If you wish to study extra in regards to the various kinds of networks and perceive them, learn the beneath blogs for additional data.

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