Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on massive computational and energy resources, neuromorphic systems exploit brain-inspired principles of computation to achieve orders of magnitude greater energy efficiency. By drawing on insights from a wide range of disciplines -- including artificial intelligence, physics, chemistry, biology, neuroscience, cognitive science and materials science -- neuromorphic computing promises to deliver intelligent systems that are sustainable, transparent, and widely accessible. A central challenge, however, is to identify a unifying theoretical framework capable of bridging these diverse disciplines. We argue that dynamical systems theory provides such a foundation. Rooted in differential calculus, it offers a principled language for modeling inference, learning, and control in both natural and artificial substrates. Within this framework, noise can be harnessed as a resource for learning, while differential genetic programming enables the discovery of dynamical systems that implement adaptive behaviors. Embracing this perspective paves the way toward emergent neuromorphic intelligence, where intelligent behavior arises from the dynamics of physical substrates, advancing both the science and sustainability of AI.

Neural networks (NN) can be divided into two broad categories, recurrent and non-recurrent. Both types of neural networks are popular and extensively studied, but they are often treated as distinct families of machine learning algorithms. In this position paper, we argue that there is a closer relationship between these two types of neural networks than is normally appreciated. We show that many common neural network models, such as Recurrent Neural Networks (RNN), Multi-Layer Perceptrons (MLP), and even deep multi-layer transformers, can all be represented as iterative maps. The close relationship between RNNs and other types of NNs should not be surprising. In particular, RNNs are known to be Turing complete, and therefore capable of representing any computable function (such as any other types of NNs), but herein we argue that the relationship runs deeper and is more practical than this. For example, RNNs are often thought to be more difficult to train than other types of NNs, with RNNs being plagued by issues such as vanishing or exploding gradients. However, as we demonstrate in this paper, MLPs, RNNs, and many other NNs lie on a continuum, and this perspective leads to several insights that illuminate both theoretical and practical aspects of NNs.

This paper discusses how a robot can learn goal-directed naviga(cid:173) tion tasks using local sensory inputs. The emphasis is that such learning tasks could be formulated as an embedding problem of dynamical systems: desired trajectories in a task space should be embedded into an adequate sensory-based internal state space so that an unique mapping from the internal state space to the motor command could be established. The paper shows that a recurrent neural network suffices in self-organizing such an adequate internal state space from the temporal sensory input. It was also shown that such coherence becomes structurally sta(cid:173) ble as the global attractor is self-organized in the coupling of the internal and the environmental dynamics.

This paper discusses how a robot can learn goal-directed navigation tasksusing local sensory inputs. The emphasis is that such learning tasks could be formulated as an embedding problem of dynamical systems: desired trajectories in a task space should be embedded into an adequate sensory-based internal state space so that an unique mapping from the internal state space to the motor command could be established. The paper shows that a recurrent neural network suffices in self-organizing such an adequate internal state space from the temporal sensory input.

This paper discusses how a robot can learn goal-directed navigation tasks using local sensory inputs. The emphasis is that such learning tasks could be formulated as an embedding problem of dynamical systems: desired trajectories in a task space should be embedded into an adequate sensory-based internal state space so that an unique mapping from the internal state space to the motor command could be established. The paper shows that a recurrent neural network suffices in self-organizing such an adequate internal state space from the temporal sensory input.

This paper discusses how a robot can learn goal-directed navigation tasks using local sensory inputs. The emphasis is that such learning tasks could be formulated as an embedding problem of dynamical systems: desired trajectories in a task space should be embedded into an adequate sensory-based internal state space so that an unique mapping from the internal state space to the motor command could be established. The paper shows that a recurrent neural network suffices in self-organizing such an adequate internal state space from the temporal sensory input.