Sparse autoencoders create latent representations where only a few units are active for each input—this is known as sparsity. Sparsity encourages each neuron in the latent layer to detect specific, distinct patterns in the data, so the learned codes are easier for you to interpret.

For any input, most latent units in a sparse autoencoder remain near zero, while only a few show significant activation. In contrast, dense autoencoders have many active units at once, making it harder to relate each unit to a meaningful input feature.

Sparse representations help you see what each latent unit is "looking for" in the input. In image data, one unit might activate for edges in a certain direction, while another responds to a particular texture. This selectivity improves interpretability and shows how the autoencoder organizes information.

You can see this in the following text-based visualization, which connects sparse activations to specific input patterns.

Input patterns

Sparse latent activations

Table for clarity

In this example, each input pattern activates a distinct set of latent units, and most units remain inactive for each sample. This activation pattern can be described mathematically as follows:

Let $x$ be an input vector and $z = f(x)$ the sparse latent representation, where $f$ is the encoder function. For most entries $z_i$ in $z$, $z_i \approx 0$, and only a few $z_j$ have significant values. This sparsity makes it straightforward to associate each nonzero $z_j$ with a specific feature in $x$.

Such a structure enables you to clearly trace which features in the input are captured by each latent unit, enhancing the interpretability of the learned representations.