I have been wondering about something for a while: why do we almost always visualize artificial neural networks as flat diagrams? If you have ever looked at a neural network architecture, you have probably seen a standard two-dimensional grid of interconnected nodes.

There is nothing wrong with this representation. In fact, it is useful, simple, and has become almost universal when explaining neural networks. But the more I work with machine learning, the more I find myself asking whether this two-dimensional representation actually captures the way we should think about complex neural networks. A neural network is not really a flat object. It is a collection of interconnected computational units, with potentially thousands or millions of parameters, operating across multiple layers and dimensions. Once the number of neurons, layers, connections, and features becomes large enough, representing everything on a flat page starts to feel like trying to represent a city using only a single road.

That led me to an interesting question: What would happen if we treated a neural network as a three-dimensional structure?

Not simply creating a 3D animation of an ordinary neural network, but thinking about 3D artificial neural networks as a possible machine learning technology and computational representation.

What Do I Mean by a 3D Neural Network?

When I talk about a 3D artificial neural network, I am not simply referring to a neural network displayed using fancy 3D graphics. There is an important distinction. A normal feed-forward neural network can be represented using layers arranged horizontally or vertically. Each neuron is connected to neurons in the next layer, creating a relatively straightforward structure. In a 3D representation, however, neurons can be positioned within a three-dimensional space, where their relationships can be represented through spatial coordinates, depth, distance, orientation, or other geometric properties.

For example, instead of thinking about a neuron simply as:

we could think about neurons as distinct coordinate points within a bounded space.

The third dimension does not automatically make the model more intelligent. That is important to clarify. Simply adding depth to a visualization does not improve machine learning performance. The interesting question is whether spatial organization itself can become part of the computational model. That is where things become much more interesting.

Why Are Most Neural Networks Represented in Two Dimensions?

There is a practical reason why neural networks are usually shown as flat diagrams. We need a way to explain them.

A two-dimensional diagram is easy to draw, easy to understand, and easy to put into a research paper. We can arrange neurons into layers and show connections between them. Even when the actual network contains millions of parameters, we can simplify it into a diagram that gives us an idea of how information flows.

But there is a problem. As networks become more complicated, these diagrams become increasingly difficult to interpret. Imagine a network containing hundreds of neurons across dozens of layers. Drawing every connection quickly produces something that looks more like a tangled web than an understandable model. At that point, we start hiding information:

• We show only a few neurons.
• We omit some connections.
• We represent entire groups of neurons as blocks.

This is useful for communication, but it also makes me wonder whether there is another way of thinking about neural architectures. Could spatial organization help us understand these systems better? And perhaps more importantly, could spatial organization become part of how the network actually computes?

The Connection Between Geometry and Machine Learning

This is where my interest in 3D neural networks becomes particularly interesting. Machine learning already works with geometric ideas. Consider a dataset containing two features:

We can represent every observation as a point in a two-dimensional space. Add another feature:

and suddenly our data exists in three dimensions. Add hundreds of features, and we are working in a high-dimensional feature space.

Neural networks already operate in these spaces. The mathematical operations inside them transform data from one representation into another. So perhaps the idea of using geometry to understand neural computation is not as strange as it initially sounds. A 3D neural architecture could potentially give us another way of representing relationships between neurons, features, activations, or computational processes.

The Third Dimension Needs a Purpose

This is probably the most important point. If we simply take a normal neural network and rotate it in three dimensions, we have not created a new machine learning technology. We have only changed the visualization. A meaningful 3D neural network needs the additional dimension to represent something useful. For example, spatial coordinates could potentially represent:

"Imagine a network where neurons that frequently interact are positioned closer together, while neurons with weaker relationships are positioned farther apart. Now the geometry itself starts telling us something about the model. The network becomes a computational space."

Imagine a Neural Network as a 3D Brain

One reason this idea feels intuitive is because biological brains are not flat diagrams. Neurons exist within a physical three-dimensional structure. Their locations, connections, and local environments all contribute to how information is processed. Of course, an artificial neural network should not be assumed to work exactly like a biological brain. The comparison has limitations. But the biological example raises an interesting question.

If biological neural systems can organize enormous numbers of neurons within physical space, could spatial organization also be useful when designing artificial computational systems? Instead of arranging neurons only according to abstract layers, we could imagine a network where neurons occupy positions in a 3D environment.

• Information could move through this environment.
• Connections could form between nearby regions.
• Groups of neurons could specialize in particular patterns.

The network could potentially develop structures that are easier to analyze visually and, depending on the architecture, computationally meaningful.

Where Would 3D Neural Networks Make Sense?

This is where the idea becomes particularly practical. There are already many problems where the data itself is inherently three-dimensional.

Consider medical imaging. A CT scan is not simply a flat image. It represents a volume containing information across three spatial dimensions. The same is true for many MRI datasets. Instead of flattening or simplifying the spatial structure, a model can work directly with volumetric information. There are already established approaches such as 3D convolutional neural networks, which process three-dimensional data using convolution operations extended into depth.

This is an important distinction from the broader idea I am discussing. 3D CNNs already demonstrate that neural computation can operate directly on volumetric data. The more speculative question is whether we can take the concept further and explore architectures in which the network's own organization becomes explicitly spatial.