Deposon offers auditable energy-conserving checks on AI reasoning paths
Deposon: An Auditable, Conservation-Guaranteed, Game-Theoretically Tested Scattering Layer over LLM Reasoning Paths
Artificial IntelligenceMachine Learning
Summary
AI systems that think through multi-step problems often lose track of discarded steps, making it hard to check their reasoning later. The authors introduce Deposon, a method that tracks and verifies parts of an AI's thought process with very precise mathematical guarantees. They tested it on artificial puzzles and real tasks, showing it records verifiable reasoning without improving task accuracy. They also explored theoretical properties of their approach but found some expected game-theory connections only approximate.
What this means in practice
- •For ai system engineers: Verify and audit internal reasoning steps of multi-step AI models without changing their output accuracy.
- •For software verification teams: Maintain a mathematically verified record of decision paths inside AI-driven reasoning components for security audits.
Authors
Qihao Yuan
Abstract
Multi-step LLM reasoning lacks a machine-recheckable ledger: discarded reasoning paths leave no auditable record. We propose the Deposon scattering layer, which binds each node of an LLM-generated concept-decomposition graph to a two-parameter Deposon state; paths undergo three-channel scattering -- transmission, reflection, irreversible dissipation -- obeying T+R+A=1 for arbitrary parameters, with a maximum per-path energy-audit deviation of 2.2E-16 (machine epsilon). We report all three evidence tiers honestly. On synthetic trap benchmarks the path-filtering gain is closed (pre-registered): unified reaches 100% versus a decoy-capture baseline at 7%/10%. On real benchmarks the layer is indistinguishable from a trivial six-keyword rule filter (GSM8K 0.87 >= 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899); no difference is detected here, so we sharpen the claim to "the differential value lies solely in machine verifiability." Fusion yields a second negative result: convex combinations with a semantic prior never improve (physics 0.484 -> 0.452), and the apparent lambda=2 gain is an anti-field artifact; any fusion gain must be nonlinear. Modeling the reverse dynamics as a potential game on the graph, we evidence an auditable scalar's monotonicity and near-gradientness and quantify the empirical coordination ratio (ECR). The three formalized dynamical-equivalence propositions (P1a/P1b/T-P1c) are falsified under the pre-registered kill protocol, and the potential-game claim is downgraded to approximate (cyclic-graph median residual 0.669): only consistency-level evidence survives at the dynamical level. Code: github.com/zeroandcat/Deposon.