Researchers have studied how minimal representations of controlled stochastic processes, such as transducers, behave under perturbations. They found that for certain types of transducers, there exist interfaces where no approximate homomorphism exists between different implementations. However, they also proved that all minimal linear transducers implementing similar interfaces are connected by an approximate homomorphism with errors proportional to the perturbation size. This work provides theoretical support for the idea that latent representations in AI models exhibit structural convergence. --- Why it matters: This research is relevant to engineers and researchers working on AI because it sheds light on the stability of minimal representations under perturbations, which could have implications for understanding how neural networks represent complex systems. Source: https://arxiv.org/abs/2608.20428