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# System prepended metadata

title: Classifying DQPTs in the TFIM

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# Classifying DQPTs in the TFIM

## The TFIM
TODO

## DQPTs
Points where the Loschmidt echo is non-analytical. For the TFIM, can be computed exactly because TFIM has exact solution (via Jordan Wigner). Also computable/understandable through Fisher zeroes.

## The Dataset
10000 curves without DQPT, 10000 curves with DQPT
Example:
![](https://i.imgur.com/gwUpUSh.png)
Orange line indicates first DQPT point. The dot indicates the right answer (output = 1 for this example).

## Classification using a SimpleRNN
Small batch sizes, with tanh activation, give very noisy loss curve. 
Large batch size (1024) with sigmoid activation give smooth curve:
![](https://i.imgur.com/i7UYW8d.png)
This plot is for an RNN with 4 state units, and achieves an accuracy of about 85%. 

**Investigate more!**

The 4 state units seem to unfortunately just be a re-scaling of the input curves. Together with the weights of the last Dense layer, we get the black & green curves as outputs. The decision (DQPT or not) is made just by saying "is green above black at the last timestep? -> DQPT". So the RNN did **not** realize that it can stick to output = 1 as soon as it sees the first kink.

![](https://i.imgur.com/dXDOhXf.png)
![](https://i.imgur.com/tCgx34R.png)

