This is not an answer to your question, but an extended comment on the issue that has been raised here in comments by different people, namely: are machine learning "tensors" the same thing as tensors in mathematics?
Now, according to the Cichoki 2014, Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions, and Cichoki et al. 2014, Tensor Decompositions for Signal Processing Applications,
A higher-order tensor can be interpreted as a multiway array, [...]
A tensor can be thought of as a multi-index numerical array, [...]
Tensors (i.e., multi-way arrays) [...]
So in machine learning / data processing a tensor appears to be simply defined as a multidimensional numerical array. An example of such a 3D tensor would be $1000$ video frames of $640\times 480$ size. A usual $n\times p$ data matrix is an example of a 2D tensor according to this definition.
This is not how tensors are defined in mathematics and physics!
A tensor can be defined as a multidimensional array obeying certain transformation laws under the change of coordinates (see Wikipedia or the first sentence in MathWorld article). A better but equivalent definition (see Wikipedia) says that a tensor on vector space $V$ is an element of $V\otimes\ldots\otimes V^*$. Note that this means that, when represented as multidimensional arrays, tensors are of size $p\times p$ or $p\times p\times p$ etc., where $p$ is the dimensionality of $V$.
All tensors well-known in physics are like that: inertia tensor in mechanics is $3\times 3$, electromagnetic tensor in special relativity is $4\times 4$, Riemann curvature tensor in general relativity is $4\times 4\times 4\times 4$. Curvature and electromagnetic tensors are actually tensor fields, which are sections of tensor bundles (see e.g. here but it gets technical), but all of that is defined over a vector space $V$.
Of course one can consider a tensor product $V\otimes W$ of an $p$-dimensional $V$ and $q$-dimensional $W$ and choose to call its elements "tensors", but I am not aware of any useful such "tensor" and Wikipedia says that
In principle, one could define a "tensor" simply to be an element of any tensor product. However, the mathematics literature usually reserves the term tensor for an element of a tensor product of a single vector space $V$ and its dual, as above.
One example of a real tensor in statistics would be a covariance matrix. It is $p\times p$ and transforms in a particular way when the coordinate system in the $p$-dimensional feature space $V$ is changed. It is a tensor. But a $n\times p$ data matrix $X$ is not.
But can we at least think of $X$ as a "generalized" tensor in the sense of an element of tensor product $W\otimes V$, where $W$ is $n$-dimensional and $V$ is $p$-dimensional? For concreteness, let rows in $X$ correspond to people (subjects) and columns to some measurements (features). Linear transformations in $V$ correspond to linear transformation of features, and this is done in statistics all the time (think of PCA). But linear transformations in $W$ do not seem to correspond to anything meaningful: what would be a linear combination of people mean? So it does not seem that there is anything gained by considering $X$ as an element of $W\otimes V$.
My conclusion is: machine learning "tensors" are not actually tensors in any meaningful or useful way.
Instead, they are multidimensional generalizations of matrices. Unfortunately, there is no established mathematical term for that.