Explainability of Probabilistic Bisimilarity Distances for Labelled Markov Chains
Bibliographic record
Abstract
Abstract Probabilistic bisimilarity distances measure the similarity of behaviour of states of a labelled Markov chain. The smaller the distance between two states, the more alike they behave. Their distance is zero if and only if they are probabilistic bisimilar. Recently, algorithms have been developed that can compute probabilistic bisimilarity distances for labelled Markov chains with thousands of states within seconds. However, say we compute that the distance of two states is 0.125. How does one explain that 0.125 captures the similarity of their behaviour? In this paper, we address this question by returning to the definition of probabilistic bisimilarity distances proposed by Desharnais, Gupta, Jagadeesan, and Panangaden more than two decades ago. We use a slight variation of their logic to construct for each pair of states a sequence of formulas that explains the probabilistic bisimilarity distance of the states. Furthermore, we present an algorithm that computes those formulas and we show that each formula can be computed in polynomial time. We also prove that our logic is minimal. That is, if we leave out any operator from the logic, then the resulting logic no longer provides a logical characterization of the probabilistic bisimilarity distances.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".