I’m not aware of a double backward for ctc loss being available
By their very nature, finite differences compute approximate directional derivatives (so jacobian-vector products if you want, what you would get with forward mode) rather than gradients (aka vector-jacobian products). As such generally compute-intensive to approximate gradients with finite differences because you would need as many evaluations as you have inputs.
You can use CTC loss with doubles just by passing them, enabling this was one of my goals with having an integrated open source implementation.
Best regards
Thomas