Causal Convolution
Causal Convolution
**Causal convolutions** are a type of [convolution](https://paperswithcode.com/method/convolution) used for temporal data which ensures the model cannot violate the ordering in which we model the data: the prediction $p(x_{t+1} | x_{1}, \ldots, x_{t})$ emitted by the model at timestep $t$ cannot depend on any of the future timesteps $x_{t+1}, x_{t+2}, \ldots, x_{T}$. For images, the equivalent of a causal convolution is a [masked convolution](https://paperswithcode.com/method/masked-convolution) which can be implemented by constructing a mask tensor and doing an element-wise multiplication of this mask with the convolution kernel before applying it. For 1-D data such as audio one can more easily implement this by shifting the output of a normal convolution by a few timesteps.
WaveNet: A Generative Model for Raw Audio
https://paperswithcode.com/paper/wavenet-a-generative-model-for-raw-audio
WaveNet: A Generative Model for Raw Audio