Predictive contract mechanisms such as dead reckoning are widely employed to support scalable remote entity modeling in distributed interactive applications (DIAs). By employing a form of controlled inconsistency, a reduction in network traffic is achieved. However, by relying on the distribution of instantaneous derivative information, dead reckoning trades remote extrapolation accuracy for low computational complexity and ease-of-implementation. In this article, we present a novel extension of dead reckoning, termed neuro-reckoning, that seeks to replace the use of instantaneous velocity information with predictive velocity information in order to improve the accuracy of entity position extrapolation at remote hosts. Under our proposed neuro-reckoning approach, each controlling host employs a bank of neural network predictors trained to estimate future changes in entity velocity up to and including some maximum prediction horizon. The effect of each estimated change in velocity on the current entity position is simulated to produce an estimate for the likely position of the entity over some short time-span. Upon detecting an error threshold violation, the controlling host transmits a predictive velocity vector that extrapolates through the estimated position, as opposed to transmitting the instantaneous velocity vector. Such an approach succeeds in reducing the spatial error associated with remote extrapolation of entity state. Consequently, a further reduction in network traffic can be achieved. Simulation results conducted using several human users in a highly interactive DIA indicate significant potential for improved scalability when compared to the use of IEEE DIS standard dead reckoning. Our proposed neuro-reckoning framework exhibits low computational resource overhead for real-time use and can be seamlessly integrated into many existing dead reckoning mechanisms.