AI & Agents
Compositional Intelligence: Bisimulation Equivalence Classes, HML, and Practical Implications for LLMs
“From behavior comparison to behavior classification.” — Lucius Meredith (Oct 2024)
In brief: This essay extends the bisimulation framework into classification. Bisimulation groups computations into equivalence classes; for computational ‘sense-makers,’ this becomes an upper bound on how finely they can discriminate phenomena. Viewing an LLM as computing a representative of an equivalence class plus a distribution opens a different angle on interpretability and safety.
Key takeaways
- Bisimulation classifies computations into equivalence classes; for computational ‘sense-makers,’ this becomes an upper bound on how finely they can discriminate phenomena.
- An LLM can be viewed as computing a representative of a bisimulation equivalence class plus a distribution — opening a different angle on interpretability and safety.
- Hennessy–Milner logic characterizes bisimulation: two computations are bisimilar iff they satisfy the same HML formulae.
Key questions
- How does this classification framework apply when the model itself is continuously updated?
- Can HML-based probes become a practical interpretability tool for production systems?
- What are the limits of behavior-first classification for safety-critical applications?
Why it matters for developers
This framing pushes toward behavior-first methods: define what must be true of the system’s behavior, then test and compare using repeatable probes. That’s a concrete engineering discipline, not a philosophical stance.
bisimulation
equivalence classes
HML
LLM interpretability
safety
behavior classification