# A Solvable Molecular Switch Model for Stable Temporal Information Processing

arXiv: https://arxiv.org/abs/2508.15451 · HTML: https://mlsanity.com/paper/2508.15451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 39 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Temporal Information Processing on Noisy Quantum Computers](https://mlsanity.com/paper/2001.09498/) (2020)
- [On the stability properties of Gated Recurrent Units neural networks](https://mlsanity.com/paper/2011.06806/) (2020)
- [Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems](https://mlsanity.com/paper/1901.01653/) (2019)
- [Convergence Properties for Discrete-time Nonlinear Systems](https://mlsanity.com/paper/1612.05327/) (2016)
- [Modeling and Contractivity of Neural-Synaptic Networks with Hebbian Learning](https://mlsanity.com/paper/2204.05382/) (2022)
- [Stochastic Reservoir Computers](https://mlsanity.com/paper/2405.12382/) (2024)
- [Nonlinear Autoregression with Convergent Dynamics on Novel Computational Platforms](https://mlsanity.com/paper/2108.08001/) (2021)
- [Improving the Performance of Echo State Networks Through State Feedback](https://mlsanity.com/paper/2312.15141/) (2023)

## Abstract (arXiv)

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.