nmODE: neural memory ordinary differential equation

Abstract Brain neural networks are regarded as dynamical systems in science, which memories interpreted attractors of the systems. Mathematically, ordinary differential equations (ODEs) can be utilized to describe Any ODE that is employed dynamics a network called neuralODE. Inspired by rethinking nonlinear representation ability existing artificial together with functions columns neocortex, this paper proposes theory memory-based neuralODE, composed two novel models: nmODE and $$\epsilon$$ ϵ -net, learning algorithms: nmLA -LA. The (neural memory Ordinary Differential Equation) designed special structure separates neurons from neurons, making its clear. Given any external input, possesses global attractor property thus embedded mechanism. establishes mapping input associated does not have problem features homeomorphic data space, occurs frequently most neuralODEs. Learning Algorithm) developed proposing an interesting three-dimensional inverse (invODE) has advantages parameter efficiency. proposed -net discrete version nmODE, particularly feasible for digital computing. -LA ( algorithm) requires no prior knowledge number layers. Both gradient vanishing. Experimental results show comparable state-of-the-art methods.