Output-Oblivious Stochastic Chemical Reaction Networks
Bibliographic record
Abstract
We classify the functions $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN $\mathcal{C}$ becomes the input to a downstream CRN $\mathcal{C}'$, then $\mathcal{C}'$ could inadvertently consume too many outputs before $\mathcal{C}$ stabilizes. If, on the other hand, $\mathcal{C}$ is output-oblivious then $\mathcal{C}'$ may consume $\mathcal{C}$'s output as soon as it is available. In this work we prove that a semilinear function $f:\mathbb{N}^2 \rightarrow \mathbb{N}$ is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".