A Solvable Molecular Switch Model for Stable Temporal Information Processing

2025-08-21

AI Summary

Addressing the dual challenge of biological plausibility and mathematical stability in temporal data processing for neuromorphic computing, this paper proposes a synapse-inspired monostable differential-equation-based molecular switch model. The model integrates linear state dynamics with a nonlinear input-driven mechanism, ensuring analytical tractability, global asymptotic convergence, and exponential-decay memory. Leveraging dynamical systems theory, we rigorously prove the unification of brain-like behaviors—including threshold-triggered responses and short-term memory—with mathematical robustness. Experimental evaluation demonstrates its efficacy as a universal computational unit across deep feedforward and recurrent architectures for sequence learning tasks. Our work establishes a novel paradigm for constructing analytically solvable, formally verifiable, brain-inspired temporal modeling frameworks.

Technology Category

Cognitive Modeling & Cognitive Systems: Neural Spike CodingMachine Learning: Bio-inspired LearningHumans and AI: Brain-Sensing and Analysis

Application Category

Web Mining and Content Analysis: Models for Web evolutionGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This paper studies an input-driven one-state differential equation model initially developed for an experimentally demonstrated dynamic molecular switch that switches like synapses in the brain do. The linear-in-the-state and nonlinear-in-the-input model is exactly solvable, and it is shown that it also possesses mathematical properties of convergence and fading memory that enable stable processing of time-varying inputs by nonlinear dynamical systems. Thus, the model exhibits the co-existence of biologically-inspired behavior and desirable mathematical properties for stable learning on sequential data. The results give theoretical support for the use of the dynamic molecular switches as computational units in deep cascaded/layered feedforward and recurrent architectures as well as other more general structures for neuromorphic computing. They could also inspire more general exactly solvable models that can be fitted to emulate arbitrary physical devices which can mimic brain-inspired behaviour and perform stable computation on input signals.

Problem

• Modeling molecular switches for stable temporal information processing
• Analyzing solvable nonlinear dynamics with convergence and memory properties
• Enabling neuromorphic computing with biologically-inspired computational units

Innovation

• Exactly solvable molecular switch differential equation model
• Linear-in-state nonlinear-in-input with convergence properties
• Enables stable temporal processing in neuromorphic architectures