###Batch TensorNetwork

We consider the scenarios that

• There is a core tensor network as model's weight $W$
• There are hundreds of tensor network $B_i$ as input data

Our goal is to calculate the hundreds of inner product $\lang W|B_i\rang$ as fast as possible.

There are three way to make it:

• a naïve for loop and try to call parallel processing to speed up
• use a batch version of the TensorNetwork.
• use einsum to achieve efficient coding.

---

For the batch version of TensorNetwork, please see our paper(coming soon). The conclusion is very simple, the batch is another blockdiag TensorNetwork with larger bond dimension.

The einsum can hold batch contraction like Babcd,Babcd->B which is not a tensor contraction (so it cannot be replicated by tensordot). It is same as treat the batch TensorNetwork as sparse matrix and contracting via sparse way.

---

We now consider a small example, that with MPS Machine Learning. The virtual bond is set 3 and length is set 20.


Notice:

• usually the einsum is provided for modern mathematic package.
• the contraction engine for loop, batch contraction is tn.contractor.auto which will calculate a 'optimized' path first (for uniform matrix chain, the path is just from left to right or verses). The efficient coding use assigned path: right to left path. The way_vectorized_map is parallel version for loop.
• Replicated the result by python speed_benchmark.py