# STL-based Optimization of Biomolecular Neural Networks for Regression and Control

arXiv: https://arxiv.org/abs/2509.05481 · HTML: https://mlsanity.com/paper/2509.05481/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 5 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics](https://mlsanity.com/paper/1904.11611/) (2019)
- [Safe Control under Uncertainty](https://mlsanity.com/paper/1510.07313/) (2015)
- [Programming molecular systems to emulate a learning spiking neuron](https://mlsanity.com/paper/2206.02519/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic](https://mlsanity.com/paper/2607.08899/) (2026)

## Abstract (arXiv)

Biomolecular Neural Networks (BNNs), artificial neural networks with biologically synthesizable architectures, achieve universal function approximation capabilities beyond simple biological circuits. However, training BNNs remains challenging due to the lack of target data. To address this, we propose leveraging Signal Temporal Logic (STL) specifications to define training objectives for BNNs. We build on the quantitative semantics of STL, enabling gradient-based optimization of the BNN weights, and introduce a learning algorithm that enables BNNs to perform regression and control tasks in biological systems. Specifically, we investigate two regression problems in which we train BNNs to act as reporters of dysregulated states, and a feedback control problem in which we train the BNN in closed-loop with a chronic disease model, learning to reduce inflammation while avoiding adverse responses to external infections. Our numerical experiments demonstrate that STL-based learning can solve the investigated regression and control tasks efficiently.