Representation and Invariance in Reinforcement Learning

Source: cs.GT updates on arXiv.org — https://arxiv.org/abs/2112.07752 Date read: 2026-09-02 Connected to: L-005, L-011 Kind: content Escalation: store-only Escalation rationale:

What this is

A theoretical paper formalizing the conditions under which RL agents can be mapped between different formal frameworks while preserving relative intelligence. The core contribution is a sufficiency criterion for framework-agnostic agent portability, with a proof that this criterion cannot be universally met across all framework pairs.

What I took from it

The paper directly engages the mechanical problem underlying L-011 (Causal Detachment as Stable Protocol Equilibrium) and L-005 (Gall Generalization): when you formalize an agent's behavior in one representational system, can that formalization survive intact when ported to a different representational substrate?

The negative result — that the sufficiency criterion "cannot be met" — is the key finding here. It suggests that framework conversion necessarily introduces a representation gap that cannot be closed by any single mapping rule. This aligns with L-005's claim that complex functional systems resist restructuring: an RL agent optimized within one framework's reward/state abstraction cannot be naively transplanted without degradation. The paper does not develop the why behind this irreducibility, but the finding itself is mechanically sound for the protocol ossification inventory.

However, this remains a domain-specific mathematical result. It does not establish whether the barrier is fundamental to all protocol migration, whether it generalizes to non-RL adaptive systems, or whether it has predictive or exploratory power beyond framework theory.

Research connections

L-005: The unmappability result confirms Gall's intuition that complex functional systems resist clean restructuring — here instantiated in the formalism of agent representation across framework boundaries.
L-011: Touches the causal detachment question: operational functionality in one framework may not survive formalization in another, suggesting that "stable functional configurations" are substrate-dependent rather than portable.
seed-062 (Formalization Opacity Collapse): The paper hints at a deeper motif — that formalization itself introduces irreversible abstraction loss, a candidate mechanism for why transparency does not guarantee portability.

Seed

Seed title: Representation Gap as Irreducible Protocol Boundary Seed type: observation Seed text: When a protocol agent or decision rule is formalized in one representational system (reward structure, state abstraction, action space), a sufficient mapping into an alternative formal framework cannot be guaranteed to preserve relative performance or functional integrity. The gap is not a gap in clarity or completeness — it is a structural feature of framework incommensurability. This may generalize beyond RL: any protocol migration that requires re-encoding an agent's optimization target into a new legible substrate risks introducing a floor below which performance cannot be recovered without redesign at the agent level, not the framework level.