Smarty is a fully-reconfigurable on-chip feed-forward artificial neural network (ANN) with ten integrated time-to-digital converters (TDCs) designed in a 16 nm FinFET CMOS technology node. The integration of TDCs together with an ANN aims to reduce system complexity and minimize data throughput requirements in positron emission tomography (PET) applications. The TDCs have an average LSB of 53.5 ps. The ANN is fully reconfigurable, the user being able to change its topology as desired within a set of constraints. The chip can execute 363 MOPS with a maximum power consumption of 1.9 mW, for an efficiency of 190 GOPS/W. The system performance was tested in a coincidence measurement setup interfacing Smarty with two groups of five 4 mm x 4 mm analog silicon photomultipliers (A-SiPMs) used as inputs for the TDCs. The ANN successfully distinguished between six different positions of a radioactive source placed between the two photodetector arrays by solely using the TDC timestamps.