Dense Connections, or Fully Connected Connections, are a type of layer in a deep neural network that use a linear operation where every input is connected to every output by a weight. This means there are $n_{\text{inputs}}*n_{\text{outputs}}$ parameters, which can lead to a lot of parameters for a sizeable network.
$$h_{l} = g\left(\textbf{W}^{T}h_{l-1}\right)$$
where $g$ is an activation function.
