Solving the chemical master equation for stochastic biochemical systems: A variational autoencoder approach with effective reactions
Bibliographic record
Abstract
The stochasticity of biochemical reactions at mesoscopic scale presents significant challenges to our understanding of the underpinnings. The Chemical Master Equation (CME) serves as a crucial tool for describing the dynamics of biochemical reactions, but solving the CME is notoriously difficult and often faces the curse of dimensionality. In this paper, we propose an efficient CME solver for stochastic biochemical dynamics leveraging the power of Variational Autoencoder (VAE). VAE is employed to find effective reactions from a group of elementary reactions, reducing the complexity of the system. By using VAE to find equivalent propensity for a set of complex reactions, we simplify the intermediate reactions, reducing the sample size and time for training. The trained VAE can predict the distributions of unseen time points, different reaction structures and unobserved species. We show a robust method that simplifies the resolution of CME, providing a powerful tool for analyzing stochastic biochemical systems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".