If you are not familiar with optimizers, here is a brief overview of what an optimizer is and its role in machine learning, particularly in neural networks.

An optimizer is an algorithmic entity designed to minimize a specific function called the loss function. The loss function quantitatively expresses the difference between the predicted output of the neural network and the actual target values. Simply put, an optimizer's role is to change the attributes of the neural network, such as weights and learning rate, to reduce this loss., thereby enhancing the network's accuracy.

Optimizers work through an iterative process. They start by calculating the gradient, which is a partial derivative of the loss function. This gradient indicates how much the weights need to be adjusted to minimize the loss. The optimizer then updates the weights in the opposite direction of the gradient. This process is repeated over multiple iterations or epochs until the loss is minimized, and the model's predictions become as accurate as possible.

Each optimizer has its unique way of navigating the path to minimize loss. Here are a few:

• Adam: Known for its adaptability, it's especially good for large datasets. It is used by default in Edge Impulse.

• VeLO: VeLO represents a novel approach where the optimizer is itself a neural network that is trained on prior training jobs. See Learned Optimizer (VeLO) dedicated page.

• Gradient Descent: Works by iteratively adjusting the values of parameters in the function until the minimum value is reached. In other words, it involves moving downhill along the steepest slope of the function towards its lowest point, hence its name "descent."

• Stochastic Gradient Descent (SGD): A more dynamic cousin of Gradient Descent, updating weights more frequently for quicker learning.

• RMSprop and Adagrad: These optimizers bring their own tweaks to the learning rate, making the journey smoother in specific scenarios.

Changing the Optimizer in Expert Mode

When using the Expert Mode in Edge Impulse, you can access the full Keras API:

1. Import the necessary libraries:

First, make sure to import the necessary modules from Keras. You'll need the model you're working with (like Sequential) and the optimizer you want to use.

import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.optimizers import Adam, SGD, RMSprop  # Import optimizers

1. Define your neural network architecture:

Define your model architecture as you normally would. For example, using Sequential:

model = Sequential()
# Add model layers like Dense, Conv2D, etc.

1. Select an optimizer

Choose the optimizer you wish to use. You can use one of the built-in optimizers in Keras, and even customize its parameters. For example, to use the Adam optimizer with a custom learning rate:

optimizer = Adam(learning_rate=0.001)

Alternatively, you can use other optimizers like SGD or RMSprop in a similar way:

optimizer = SGD(learning_rate=0.01, momentum=0.9)
optimizer = RMSprop(learning_rate=0.001, rho=0.9)

1. Compile and train your model with your optimizer

model.compile(optimizer=optimizer, loss='categorical_crossentropy', metrics=['accuracy'])
model.fit(x_train, y_train, batch_size=32, epochs=10)

A loss function, also known as a cost function, is a method to measure the performance of a machine learning model. Essentially, it calculates the difference between the model's predictions and the actual target values. The goal of training a neural network is to minimize this difference, thereby improving the model's accuracy.

The loss function quantifies how well the model is performing. A higher loss indicates greater deviation from the actual values, while a lower loss signifies that the model's predictions are closer to the target values.

Types of Loss Functions

Each type of neural network task generally has a different loss function that is most suitable for it. Here are some of the common loss functions used:

• Mean Squared Error (MSE): Used primarily for regression problems. It calculates the square of the difference between the predicted values and the actual values. It can be used for both single-step prediction tasks and time series forecasting problems. The goal is to minimize this average error, resulting in more accurate predictions. It is used by default in Edge Impulse regression learning blocks.

• Mean Absolute Error (MAE): The MAE is another regression loss function that measures the average absolute difference between the predicted and actual target values. Unlike MSE, which considers squared errors, MAE uses the direct absolute value of the error, making it more sensitive to outliers but less affected by them. This makes it a good choice for problems with skewed or imbalanced data.

• Binary Cross-Entropy Loss: Ideal for binary classification problems. It measures the difference between the predicted probabilities and the actual labels by minimizing the sum of the losses for each sample. Note that this loss function is commonly used in conjunction with the sigmoid activation function.

• Categorical Cross-Entropy: Similar to the Binary Cross-Entropy, the Categorical Cross-Entropy is mostly used for multi-class classification. It measures the difference between the predicted probabilities and the actual labels for each class in a sample. The sum of these losses across all samples is then minimized. It is used by default in Edge Impulse classification learning blocks. Note that this loss function is commonly used in conjunction with the softmax activation function (also used by default in Edge Impulse for classification problems).

• Huber Loss: A combination of MSE and MAE (Mean Absolute Error). It is less sensitive to outliers than MSE. It starts as the square of the difference between the predicted and actual values for small errors, similar to MSE. However, once the error exceeds a certain threshold, it switches to a linear relationship like MAE. This makes Huber loss more robust against outliers compared to MSE, while still maintaining its smoothness.

• Log Loss: Similar to cross-entropy loss, it measures the performance of a classification model where the output is a probability value between 0 and 1.

Customizing Loss Function in Expert Mode

In Edge Impulse, the Expert Mode allows for advanced customization, including the use of custom loss functions. Here is how you can do it:

1. Import the necessary libraries

import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.losses import MeanSquaredError, BinaryCrossentropy  # Import loss functions

1. Define your neural network architecture

model = Sequential()
# Add model layers

1. Select a loss function

Choose the loss function that suits your problem.

For instance, for a regression problem, you might choose Mean Squared Error:

loss_function = MeanSquaredError()

For a binary classification problem, Binary Cross-Entropy might be more appropriate:

loss_function = BinaryCrossentropy()

1. Compile and train your model with your chosen loss function

model.compile(optimizer='adam', loss=loss_function, metrics=['accuracy'])
model.fit(x_train, y_train, batch_size=32, epochs=10)

An activation function is a mathematical equation that determines the output of a neural network node, or "neuron." It adds non-linearity to the network, allowing it to learn complex patterns in the data. Without activation functions, a neural network would simply be a linear regression model, incapable of handling complex tasks like image recognition or language processing.

Types of Activation Functions in Neural Networks

Several activation functions are used in neural networks, each with its characteristics and typical use cases. Some of the most common include:

• ReLU (Rectified Linear Unit): It allows only positive values to pass through, introducing non-linearity. ReLU is efficient and widely used in deep learning. It is used by default in Edge Impulse for hidden layers.

• Sigmoid: This function maps values into a range between 0 and 1, making it ideal for binary classification problems.

• Tanh (Hyperbolic Tangent): Similar to the sigmoid but maps values between -1 and 1. It is useful in hidden layers of a neural network.

• Softmax: Often used in the output layer of a neural network for multi-class classification; it turns logits into probabilities that sum to one.

• Leaky ReLU: A variation of ReLU, it allows a small, non-zero gradient when the unit is not active.

Implementing Activation Functions in Expert Mode

In Edge Impulse, the Expert Mode allows for advanced customization, including the use of custom activation functions. Here is how you can do it:

1. Import the necessary libraries

import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Activation  # Import activation functions

1. Define your neural network architecture

When adding layers to your model, specify the activation function you want to use:

model = Sequential()
model.add(Dense(units=64, activation='relu'))  # Using ReLU activation
model.add(Dense(units=10, activation='softmax'))  # Using Softmax for output layer

1. Compile and train your model:

model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])
model.fit(x_train, y_train, batch_size=32, epochs=10)

Machine learning model development involves several critical choices, such as the type of problem (classification or regression), the model architecture (e.g., dense layers, convolutions), and the available data. However, one often overlooked choice is the optimizer. This component is essential in the training loop, which typically involves:

• Starting with a model with randomly initialized weights.

• Passing labeled data through the model and comparing the output with the correct output using a "loss function".

• Using an optimizer to make adjustments to the model weights based on the loss function results.

• Repeating the process until the model's performance ceases to improve.

While there are various optimizers available, Adam [1] has become a default choice for many projects due to its general effectiveness. Unlike these traditional optimizers which are described by human-designed function, VeLO represents a novel approach where the optimizer is itself a neural network that is trained on prior training jobs.

VeLO: A Learned Optimizer

VeLO (Versatile Learned Optimizers) is an innovative concept where the optimizer is trained using a large number of training jobs, as detailed in the paper "VeLO: Training Versatile Learned Optimizers by Scaling Up" [2]. This approach contrasts with traditional optimizers, like Adam, which are handcrafted functions.

Studio Integration

The Learned Optimizer can be enabled in Edge Impulse as an option on the training page.

Using VeLO in Expert Mode

The simplest way to use VeLO in expert mode is to enable the flag for a project and then switch to expert mode. This will pre-fill the needed lines of code in the expert mode.

To use VeLO in expert mode for an existing project:

• Remove any existing optimizer creation, model.compile, or model.fit calls.

• Replace with the train_keras_model_with_velo method.

from ei_tensorflow.velo import train_keras_model_with_velo
history = train_keras_model_with_velo(
 keras_model=model,
 training_data=train_dataset,
 validation_data=validation_dataset,
 loss_fn=tf.keras.metrics.categorical_crossentropy, # depending on your model
 num_epochs=num_epochs,
 callbacks=callbacks
)
print("history", history)

How does VeLO compare to Adam?

Consider the following graph which shows several runs of Adam vs VeLO:

The most influential hyperparameter of Adam is the learning rate.

If the learning rate is too low ( e.g. the red graph "adam_0.0001" ) then the model takes too long to make progress. If the learning rate is too high (e.g. the blue graph "adam_0.05") then the optimization becomes unstable.

One of the benefits of VeLO is that it doesn't require a learning rate to do well. In this example we see VeLO (purple graph "velo") doing as well as the best Adam learning rate variant.

As a side note, VeLO was designed for training large models. In this example to get the best result, the batch size was equal to the dataset size.

Examples

The following projects contain both a learning block with and without the learned optimizer so you can easily see the differences:

• Image classification using transfer learning: Microscope - VeLO

• Vibration analysis: Coffee Machine Stages - Multi-label data - VeLO

Resources

• [1] “Adam: A Method for Stochastic Optimization”

• [2] “VeLO: Training Versatile Learned Optimizers by Scaling Up”

Neural network architectures can be composed of multiple layers, each with specific roles and functions. These layers act as the building blocks of the network. The configuration and interaction of these layers define the capabilities of different neural network architectures, allowing them to learn from data and perform a wide array of tasks. From the initial data reception in the input layer through various transformation stages in hidden layers, and finally to the output layer where results are produced, each layer contributes to the network's overall intelligence and performance.

With this page, we want to provide an overview of various neural network layers commonly used in edge machine learning.

Input Layer

The Input Layer serves as the initial phase of the neural network. It is responsible for receiving all the input data for the model. This layer does not perform any computation or transformation. It simply passes the features to the subsequent layers. The dimensionality of the Input Layer must match the shape of the data you're working with. For instance, in image processing tasks, the input layer's shape would correspond to the dimensions of the image, including the width, height, and color channels.

Dense Layer (or Fully Connected Layer)

A Dense layer, often referred to as a fully connected layer, is the most basic form of a layer in neural networks. Each neuron in a dense layer receives input from all the neurons of the previous layer, hence the term "fully connected". It's a common layer that can be used to process data that has been flattened or transformed from a higher to a lower dimension.

Reshape Layer

The Reshape layer is used to change the shape of the input data without altering its contents. It's particularly useful when you need to prepare the dataset for certain types of layers that require the input data to be in a particular shape.

Flatten Layer

Flatten layers are used to convert multi-dimensional data into a one-dimensional array. This is typically done before feeding the data into a Dense layer.

Dropout Layer

The Dropout layer is a regularization technique that reduces the risk of overfitting in neural networks. It does so by randomly setting a fraction of the input units to zero during each update of the training phase, which helps to make the network more robust and less sensitive to the specific weights of neurons.

1D Convolution Layer

The 1D Convolution layer is specifically designed for analyzing sequential data, such as audio signals or time-series data. This type of layer applies a series of filters to the input data to extract features. These filters slide over the data to produce a feature map, capturing patterns like trends or cycles that span over a sequence of data points.

1D Pooling Layer

Complementing the 1D Convolution layer, the 1D Pooling layer aims to reduce the spatial size of the feature maps, thus reducing the number of parameters and computation in the network. It works by aggregating the information within a certain window, usually by taking the maximum (Max Pooling) or the average (Average Pooling) of the values. This operation also helps to make the detection of features more invariant to scale and orientation changes in the input data.

2D Convolution Layer

The 2D Convolution layer is used primarily for image data and other two-dimensional input (like spectrograms). This layer operates with filters that move across the input image's height and width to detect patterns like edges, corners, or textures. Each filter produces a 2D activation map that represents the locations and strength of detected features in the input.

2D Pooling Layer

The 2D Pooling layer serves a similar purpose as its 1D counterpart but in two dimensions. After the convolution layer has extracted features from the input, the pooling layer reduces the spatial dimensions of these feature maps. It summarizes the presence of features in patches of the feature map and reduces sensitivity to the exact location of features. Max Pooling and Average Pooling are common types of pooling operations used in 2D Pooling layers.

Output layer

The Output Layer is the final layer in a neural network architecture, responsible for producing the results based on the learned features and representations from the previous layers. Its design is closely aligned with the specific objective of the neural network, such as classification, regression, or even more complex tasks like image segmentation or language translation.

Building a Model with Multiple Layers in Expert Mode

1. Import the necessary libraries

import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Conv2D, MaxPooling2D, Dropout, Flatten

1. Define your neural network architecture

model = Sequential()
model.add(Conv2D(32, (3, 3), activation='relu', input_shape=(28, 28, 1)))
model.add(MaxPooling2D((2, 2)))
model.add(Flatten())
model.add(Dense(64, activation='relu'))
model.add(Dense(10, activation='softmax'))

1. Compile and train your model

model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])
model.fit(x_train, y_train, batch_size=32, epochs=10)

Neural networks are a set of algorithms, modeled loosely after the human brain, designed to recognize patterns. They interpret sensory data through a kind of machine perception, labeling, or clustering of raw input. The patterns they recognize are numerical, contained in vectors, into which all real-world data, be it images, sound, text, or time series, must be translated.

How do they work?

Neural networks consist of layers of interconnected nodes, also known as neurons.

Neurons (or nodes)

Each node receives input from its predecessors, processes it, and passes its output to succeeding nodes. The processing involves weighted inputs, a bias (threshold), and an activation function that determines whether and to what extent the signal should progress further through the network.

Layers

Neurons are organized into layers: input, hidden, and output layers. The complexity of the network depends on the number and size of these layers.

• Input Layer: Receives raw input data.

• Hidden Layers: Perform computations using weighted inputs.

• Output Layer: Produces the final output.

Neural Network Architectures

Neural networks can vary widely in architecture, adapting to different types of problems and data.

Learning process

The power of neural networks lies in their ability to learn. Learning occurs through a process called training, where the network adjusts its weights based on the difference between its output and the desired output. This process is facilitated by an optimizer, which guides the network in adjusting its weights to minimize error (the loss).

• Training: Neural networks learn by adjusting weights based on the error in predictions. This process is repeated over many training cycles, or epochs, using training data.

• Backpropagation: A key mechanism where the network adjusts its weights starting from the output layer and moving backward through the hidden layers, minimizing error with each pass.

Neural Networks in Edge AI

In Edge AI, neural networks operate under constraints of lower computational power and energy efficiency. They need to be optimized for speed and size without compromising too much on accuracy. This often involves techniques like feature extraction, neural network architectures, transfer learning, quantization, and model pruning.

• Feature Extraction: Extracting meaningful features from the raw data that can be effectively processed by the neural network on resource-constrained devices.

• Neural Networks Architectures: Selecting a model architecture that is designed to run efficiently on the type of processor you are targeting, and fit within memory constraints.

• Transfer Learning: Using a pre-trained model and retraining it with a specific smaller dataset relevant to the edge application.

• Quantization: Reducing the precision of the numbers used in the model to decrease the computational and storage burden.

• Model Pruning: Reducing the size of the model by eliminating unnecessary nodes and layers.

Neural networks, in the context of Edge AI, must be designed and optimized to function efficiently in resource-constrained environments, balancing the trade-off between accuracy and performance.

To learn more about Neural Networks, see the “Introduction to Neural Networks” video in our “Introduction to Embedded Machine Learning” course:

An epoch (also known as training cycle) in machine learning is a term used to describe one complete pass through the entire training dataset by the learning algorithm. During an epoch, the machine learning model is exposed to every example in the dataset once, allowing it to learn from the data and adjust its parameters (weights) accordingly. The number of epochs is a hyperparameter that determines the number of times the learning algorithm will work through the entire training dataset.

Importance of epochs

The number of epochs is an important hyperparameter for the training process of a machine learning model. Too few epochs can result in an underfitted model, where the model has not learned enough from the training data to make accurate predictions. On the other hand, too many epochs can lead to overfitting, where the model has learned too well from the training data, including the noise, making it perform poorly on new, unseen data.

How epochs work

During each epoch, the dataset is typically divided into smaller batches. This approach, known as batch training, allows for more efficient and faster processing, especially with large datasets. The learning algorithm iterates through these batches, making predictions, calculating errors, and updating model parameters using an optimizer. An epoch consists of the following steps:

1. Initialization: Before training begins, the model's internal parameters (weights) are typically initialized randomly or according to a specific strategy.

2. Forward pass: For each example in the training dataset, the model makes a prediction (forward pass). This involves calculating the output of the model given its current weights and the input data.

3. Loss calculation: After making a prediction, the model calculates the loss (or error) by comparing its prediction to the actual target value using a loss function. The loss function quantifies how far the model's prediction is from the target.

4. Backward pass (backpropagation): The model updates its weights to reduce the loss. This is done through a process called backpropagation, where the gradient of the loss function of each weight is computed. The gradients indicate how the weights should be adjusted to minimize the loss.

5. Weight update: Using an optimization algorithm (such as Gradient Descent, Adam, etc.), the model adjusts its weights based on the gradients calculated during backpropagation. The goal is to reduce the loss by making the model's predictions more accurate.

6. Iteration over batches: An epoch consists of iterating over all batches in the dataset, performing the forward pass, loss calculation, backpropagation, and weight update for each batch.

7. Completion of an epoch: Once the model has processed all batches in the dataset, one epoch is complete. The model has now seen each example in the dataset exactly once.

Change the number of epochs in Edge Impulse

In Edge Impulse, you can specify the number of training cycles in the training settings for your neural network-based models. Adjusting this parameter allows you to fine-tune the training process, aiming for the best possible model performance on your specific dataset. It's important to monitor both training and validation loss to determine the optimal number of epochs for your model.

Changing the epochs in Expert Mode

When using the Expert Mode in Edge Impulse, you can access the full Keras API:

You can modify the following line in the expert mode to change the number of training cycles:

EPOCHS = args.epochs or 100

When compiling and training your model, specify the number of epochs in the model.fit() function as follows:

model.fit(train_dataset, epochs=EPOCHS, validation_data=validation_dataset, verbose=2, callbacks=callbacks)

Apply Early Stopping in Expert Mode

The following approach allows your model to stop training as soon as it starts overfitting, or if further training doesn't lead to better performance, making your training process more efficient and potentially leading to better model performance.

Import EarlyStopping from tensorflow.keras.callbacks.

from tensorflow.keras.callbacks import EarlyStopping

Instantiate an EarlyStopping callback, specifying the metric to monitor (e.g., val_loss or val_accuracy), the minimum change (min_delta) that qualifies as an improvement, the number of epochs with no improvement after which training will be stopped (patience), and whether training should stop immediately after improvement (restore_best_weights).

# apply early stopping
callbacks.append(EarlyStopping(
    monitor='val_accuracy',    # Monitor validation accuracy
    min_delta=0.005,           # Minimum change to qualify as an improvement
    patience=15,               # Stop after 15 epochs without improvement
    verbose=1,                 # Print messages
    restore_best_weights=True  # Restore model weights from the epoch with the best value of the monitored quantity.
))

Find the full early stopping documentation on Keras documentation or have a look at this Edge Impulse public project as an example.