Suppose I have a time series data written in a matrix $\mathbf{X} \in \mathbb{R}^{N \times d}$. The sequence length is $N$ and $d$ is the number of features (I have $d$ series). Say I have a batch of $B$ samples. So I have one batch of data in the form of a tensor $\mathcal{X}$ of size $B \times N \times d$. $\mathcal{X}$ is then passed in a 1D convolution layer, say the number of filter is $d_f$ and assume the padding is same.
In a standard deep learning process, how is $\mathcal{X}$ treated?
Is every sample $\mathbf{X}_i$ $(i = 1, \dots, B)$ convoluted independently and then the result are combined again into a tensor? In this way, $\mathbf{X}_i \in \mathbb{R}^{N \times d}$ is convoluted to $\mathbf{Z}_i \in \mathbb{R}^{N \times d_f}$ then all $\mathbf{Z}_i$ is concatenated again to become a tensor $\mathcal{Z}$ of size $B \times N \times d$. Is it correct?
