Inductive Bias in DNNs

Deep neural networks (DNNs), inspired by the human brain, form the core of modern machine learning. As we explore inductive bias, and the inherent assumptions guiding network connectivity, we understand how it shapes adaptability and efficiency.

Deep neural networks (DNNs): Foundations of learning

Artificial neural networks, the backbone of modern machine learning, replicate the interconnected nodes and layered structures inspired by the human brain. In these networks, fully connected layers facilitate the exploration of intricate relationships within input data, aiming to create universal function approximators. Stacking these layers allows for the extraction of complex patterns and abstract features, but the lack of prior assumptions about input relationships can lead to inefficiencies, given the risk of over-parameterization. To address this, specialized architectures like convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have emerged, tailoring connectivity patterns to specific data types, such as images or text.

Let's start by exploring the concept of inductive bias or modeling assumptions and how it applies to neural networks as graphs.

Inductive bias

As we transition from the foundations of DNNs to the concept of inductive bias, it becomes clear that the architecture's connectivity profoundly influences learning. Inductive bias refers to the inherent assumptions or modeling choices that guide network connectivity. Whether it's the comprehensive links in fully connected layers or the spatial and sequential relationships in CNNs and RNNs, these biases shape how a network generalizes from data. The trade-off between weak and strong inductive biases reflects the tension between adaptability and efficiency. Understanding this spectrum equips us to appreciate the design choices behind neural networks and sets the stage for exploring how inductive bias impacts performance.

The connections between nodes in this graph are represented by learnable weights, which are determined during the learning process using optimization methods like gradient descent. For instance, the weight of a specific link could be:

This weight signifies the calculated importance of the connection between the third neuron in a particular layer (in this instance, the first layer) and the fourth neuron in the subsequent layer (in this case, the second layer). The way these nodes are interconnected forms what we call the inductive bias or modeling assumption. This connectivity pattern is shaped by our understanding of the relationships within the input data.

The simplest modeling assumption is to connect all input nodes to all output nodes, which is known as a fully connected network, feedforward neural network, dense layer, or linear layer, depending on the terminology used by various deep learning frameworks. In any case, this means that every output node is linked to every input node, without any prior assumptions about how input features relate to output features or data.

The weights assigned to these connections define the significance of each input feature for each output, with higher weights indicating greater importance and lower weights indicating lesser importance.

Fully connected layers and universal function approximation

The concept behind fully connected layers is to create a universal function approximator capable of modeling any input data and mapping it to the desired output through supervised learning. By stacking these layers, we aim to extract more refined representations, learn features, and gradually abstract input data until we obtain a high-level representation that encapsulates the relevant information for the task at hand.

As illustrated in the example ...