# Exact Discrete Stochastic Simulation with Deep-Learning-Scale Gradient Optimization

arXiv: https://arxiv.org/abs/2602.19775 · HTML: https://mlsanity.com/paper/2602.19775/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Breaking the Curse of Dimensionality with Convex Neural Networks](https://mlsanity.com/paper/1412.8690/) (2014)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [REBAR: Low-variance, unbiased gradient estimates for discrete latent variable models](https://mlsanity.com/paper/1703.07370/) (2017)
- [Dynamics-informed deconvolutional neural networks for super-resolution identification of regime changes in epidemiological time series](https://mlsanity.com/paper/2209.07802/) (2022)
- [GenAI-Net: A Generative AI Framework for Automated Biomolecular Network Design](https://mlsanity.com/paper/2601.17582/) (2026)

## Built on by (most cited first, 2 of 2)

- [Gradient estimators for parameter inference in discrete stochastic kinetic models](https://mlsanity.com/paper/2604.02121/) (2026)
- [Propensity Straight-Through Gradients for Discrete Stochastic Systems](https://mlsanity.com/paper/2608.25631/) (2026)

## Abstract (arXiv)

Exact stochastic simulation of continuous-time Markov chains (CTMCs) is essential when discreteness and noise drive system behavior, but the hard categorical event selection in Gillespie-type algorithms blocks gradient-based learning. We eliminate this constraint by decoupling forward simulation from backward differentiation, with hard categorical sampling generating exact trajectories and gradients propagating through a continuous massively-parallel Gumbel-Softmax straight-through surrogate. Our approach enables accurate optimization at parameter scales over four orders of magnitude beyond existing simulators. We validate for accuracy, scalability, and reliability on a reversible dimerization model (0.09% error), a genetic oscillator (1.2% error), a 203,796-parameter gene regulatory network achieving 98.4% MNIST accuracy (a prototypical deep-learning multilayer perceptron benchmark), and experimental patch-clamp recordings of ion channel gating (R^2 = 0.987) in the single-channel regime. Our GPU implementation delivers 1.9 billion steps per second, matching the scale of non-differentiable simulators. By making exact stochastic simulation massively parallel and autodiff-compatible, our results enable high-dimensional parameter inference and inverse design across systems biology, chemical kinetics, physics, and related CTMC-governed domains.