Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations

TLDR

Neural modeling must explain how continuous, multimodal input streams can be processed in real time by stereotypical recurrent integrate‑and‑fire circuits, a challenge supported by rigorous mathematical results that predict universal computational power under idealized conditions yet remain unaddressed in biologically realistic scenarios. The authors propose a new computational model for real‑time processing of time‑varying input that offers an alternative to Turing‑machine and attractor‑neural‑network paradigms. Their model relies on high‑dimensional dynamical systems and statistical learning, using transient dynamics of large heterogeneous recurrent circuits as universal analog fading memory, with readout neurons extracting current and past input information and producing stable outputs without requiring task‑dependent circuit construction or discrete internal states, as embodied in a liquid‑state‑machine framework. The study demonstrates that the transient dynamics of such circuits provide universal analog fading memory and that this framework yields new insights into neural coding, experimental design, data analysis, and applications in robotics and neurotechnology.

Abstract

A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.