Capsule Network is a neural network architecture that uses groups of neurons (capsules) to encode both the presence and pose of features — addressing a fundamental limitation of CNNs that discard spatial relationships between features during pooling.

What Is a Capsule?

• Definition: A vector of neurons whose length encodes feature probability and direction encodes instantiation parameters (pose, position, scale, orientation).
• vs. Neuron: A single neuron outputs a scalar; a capsule outputs a vector.
• Key Property: Capsules preserve spatial hierarchies — where features are relative to each other.

Why Capsule Networks Matter

• Viewpoint Equivariance: Capsules recognize objects regardless of orientation — CNNs require extensive augmentation to achieve this.
• Part-Whole Relationships: A face capsule activates only when eye/nose/mouth capsules agree on consistent pose.
• Fewer Data: Parse spatial structure more explicitly, potentially learning from fewer examples.
• No Pooling Required: Dynamic routing replaces pooling, preserving spatial information.

Dynamic Routing Algorithm

• Lower-level capsules send predictions to higher-level capsules.
• If predictions agree, routing coefficient increases (iterative agreement).
• Runs 3-5 iterations per forward pass.
• Computationally expensive — main practical limitation.

Key Papers and Variants

• CapsNet (Hinton et al., 2017): Original capsule architecture, MNIST 99.75% accuracy.
• EM Routing (2018): Expectation-maximization instead of dynamic routing.
• Efficient-CapsNet: Lightweight variant for embedded deployment.

Limitations

• Slow training due to iterative routing.
• Doesn't scale well to ImageNet-level tasks (yet).
• Harder to implement than standard CNNs.

Capsule Networks are a promising rethinking of how neural networks should represent visual information — though they have not yet displaced CNNs for large-scale practical applications.