Materials with field-tunable polarization are of broad interest to condensed matter sciences and solid-state device technologies. Here, using hydrogen (H) donor doping, we modify the room temperature metallic phase of a perovskite nickelate NdNiO3 into an insulating phase with both metastable dipolar polarization and space-charge polarization. We then demonstrate transient negative differential capacitance in thin film capacitors. The space-charge polarization caused by long-range movement and trapping of protons dominates when the electric field exceeds the threshold value. First-principles calculations suggest the polarization originates from the polar structure created by H doping. We find that polarization decays within similar to 1 second which is an interesting temporal regime for neuromorphic computing hardware design, and we implement the transient characteristics in a neural network to demonstrate unsupervised learning. These discoveries open new avenues for designing ferroelectric materials and electrets using light-ion doping.