  Machine learning photo-z methods, trained directly on spectroscopic
redshifts, provide a viable alternative to traditional template fitting methods
but may not generalise well on new data that deviates from that in the training
set. In this work, we present a Hybrid Algorithm for WI(Y)de-range photo-z
estimation with Artificial neural networks and TEmplate fitting (HAYATE), a
novel photo-z method that combines template fitting and data-driven approaches
and whose training loss is optimised in terms of both redshift point estimates
and probability distributions. We produce artificial training data from
low-redshift galaxy SEDs at z<1.3, artificially redshifted up to z=5. We test
the model on data from the ZFOURGE surveys, demonstrating that HAYATE can
function as a reliable emulator of EAZY for the broad redshift range beyond the
region of sufficient spectroscopic completeness. The network achieves precise
photo-z estimations with smaller errors ($\sigma_{NMAD}$) than EAZY in the
initial low-z region (z<1.3), while being comparable even in the high-z
extrapolated regime (1.3<z<5). Meanwhile, it provides more robust photo-z
estimations than EAZY with the lower outlier rate ($\eta_{0.2}\lesssim 1\%$)
but runs $\sim100$ times faster than the original template fitting method. We
also demonstrate HAYATE offers more reliable redshift PDFs, showing a flatter
distribution of Probability Integral Transform scores than EAZY. The
performance is further improved using transfer learning with spec-z samples. We
expect that future large surveys will benefit from our novel methodology
applicable to observations over a wide redshift range.
