Deep learning is a subset of machine learning that seeks to emulate the way the human brain processes information. The human brain, shaped by millions of years of biological evolution, is a highly efficient data processing machine. It uses networks of neurons to transmit and process information. Inspired by this natural system, deep learning employs artificial neural networks to simulate these biological processes, enabling machines to learn from data in a somewhat analogous manner.
One of the core components of these artificial networks is the concept of nodes, which are analogous to neurons in the biological brain. In a typical neural network architecture, nodes are organized into layers. The initial layer consists of input nodes (denoted as \(( X_1, X_2, \dots, X_m )\)), which receive various forms of data. These input nodes pass data through the network via connections that mimic synaptic interactions in the brain.
Each connection between nodes has an associated weight, which is adjusted during the training process to minimize prediction errors, similar to how synaptic strengths are adjusted in the brain to improve performance based on feedback. Mathematically, the output of a node ( j ) in the next layer might be calculated as:
\(y_j = f\left(\sum_{i=1}^m w_{ij} \cdot x_i + b_j\right)
\)
Here, \(( x_i )\) represents the inputs from the previous layer, \(( w_{ij} )\) are the weights, \(( b_j )\) is a bias term, and \(( f )\) is an activation function that introduces non-linearity into the process, allowing the network to learn complex patterns.
Despite the impressive capabilities of deep learning models, they are not without challenges. Bias in model predictions, for example, can arise from imbalances in the training data or the way the model processes information. Over the course of this series, we will explore these and other difficulties, seeking ways to mitigate them and enhance the robustness and fairness of deep learning applications.
Data enters the deep learning model through input nodes, which can range in number from 1 to \(m\) (or specifically 1 to 3 if there are only three nodes). Each node is responsible for receiving data and processing it through its “activation function.” This function’s role is to determine how to process the data so that the node can decide the best subsequent node to pass the data onto. This mechanism is somewhat analogous to how neurons in the human brain use axons and dendrites to transmit signals.
In this network, each node is connected to others via paths that are each assigned a specific weight (denoted as \(W_1\) to \(W_m\), or \(W_1\) to \(W_3\) in the case of three paths). The data is transferred to the next node based on these weights, effectively guiding the flow of information through the network.
This procedure is replicated across numerous nodes within the network, whether few or many, until the processed data reaches the final layer of the network— the output nodes. At this stage, the ultimate results of the computations are produced, culminating the network’s task.
In deep learning, each node within a neural network operates in a two-step process, crucial for the transformation and transmission of data:
- Summation of Weights and Inputs: Each node first calculates the weighted sum of its inputs. This sum is computed by multiplying each input by its corresponding weight (determined during the training phase) and then adding all these weighted inputs together. The formula for this is represented as \(\sum_{i=1}^m w_{i}x_{i}\), where \(w_{i}\) and \(x_{i}\) are the weights and input values, respectively.
- Application of the Activation Function: After the summation, the result is passed through an activation function. This function is designed to introduce non-linearity into the output of each node, enabling the network to handle complex patterns and data types. Common activation functions include the sigmoid, tanh, and ReLU (Rectified Linear Unit) functions.
To optimize these processes and improve learning accuracy, several advanced techniques and concepts are employed:
- Gradient Descent: This is a method used to minimize the loss function in training neural networks by updating the weights incrementally, based on the derivative of the loss function.
- Stochastic Gradient Descent (SGD): A variation of gradient descent, this method updates the weights using only a single sample, or a subset of the training data, at each iteration. This can lead to faster convergence, especially with large datasets.
- Backpropagation: This is a fundamental method in training artificial neural networks, where the error is propagated backwards through the network to update the weights. It effectively allows the network to learn from mistakes, adjusting weights to minimize the loss.
- Standardization/Normalization of Data: These are preprocessing steps to ensure that input data features have a similar scale. This uniformity helps prevent biases in the weight updates due to the scale of inputs, promoting faster and more stable convergence during training.
- Linear Regression: This is a statistical method that models the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. In machine learning, it’s often used as a baseline prediction model.
For those looking to delve deeper into the mechanisms and optimizations of neural networks, especially backpropagation, a seminal read is “Efficient Backprop” by Yann Lecun. This paper discusses techniques for improving the speed and accuracy of backpropagation, making it an essential resource for understanding advanced neural network training.
