Time-synthetic optical neural networks with stable programmable gain

Optical neural networks (ONNs) offer ultrafast and energy-efficient artificial intelligence, yet their effective depth remains fundamentally limited because the core linear transformations are overwhelmingly passive, and cumulative loss rapidly degrades the signal-to-noise ratio. Introducing optical gain into spatial photonic meshes could, in principle, counteract this decay, but such amplification is notoriously unstable owing to unavoidable feedback paths and parasitic reflections. Here, we overcome this long-standing limitation by integrating programmable gain into a time-synthetic ONN, where computation unfolds through strictly forward temporal evolution rather than spatial interferometric layers. This causal topology suppresses the backward channels that trigger gain-induced instabilities, enabling stable loss compensation and substantially extending the network's usable depth. Numerical analysis and in-situ experiments demonstrate robust performance on image-classification tasks, establishing gain-assisted time-synthetic ONNs as a stable, scalable, and programmable pathway toward deep photonic intelligence beyond the limitations of predominantly passive architectures.