AIarXiv
Ranked by formulaVerdict: NotableCertified Access: Test-Time Compute on Conservative Physics-Structured AI Memory
Test-time compute mechanisms, such as retries, confidence-based escalation and non-local routing, are conventionally deployed as black-box additions to trained models.
VerdictWorth a reader's time today.
Abstract
Test-time compute mechanisms, such as retries, confidence-based escalation and non-local routing, are conventionally deployed as black-box additions to trained models. They typically add forward passes or halting heads, but give no structural account of what the extra compute buys or what it costs against the model's stability guarantees. We therefore propose a theoretical and empirical framework for test-time compute on a Latent Dynamics Model used as the memory. When an encoder's latent state (q,p) is advanced by a damped symplectic (velocity-Verlet) step of a learned Hamiltonian, every mechanism that expands access has an exact phase-volume Jacobian, a bounded energy change and an exact latch-transport law. We split reachability failures into escape failures and reach failures. A Lorentz squeeze resolves escape failures by injecting bounded, re-absorbable energy. A gated canonical translation (a one-step channel across C_T) resolves reach failures at detJ=1 exactly. We verify this certificate stack on a designed analytic testbed. Reaching just beyond C_T with the squeeze requires energy that grows quadratically in the excess distance. The gated channel's energy cost equals the potential difference between its endpoints, which is zero on the matched channel measured here, and so does not grow with distance in this testbed. An untrained state-replacing map annihilates phase volume and erases stored charge, while the gated channel transports it. On a learned physics-structured memory, we show calibrated compute rationing and evaluate the scaling limits of non-local routing against a physics-free baseline. The main contribution is the formalization and verification of the certificate stack, not benchmark performance.
The editor's rubric
- Leverage3 / 5
- A method or resource many groups across the field will adopt within a year.
- Magnitude2 / 5
- Solid incremental gain on a meaningful problem.
- Evidence3 / 5
- Solid: multiple benchmarks or cohorts, ablations, fair baselines, released code or data.
- Novelty3 / 5
- A genuinely new approach to an open problem.
- Trajectory2 / 5
- Some room to improve with obvious engineering.
- Stakes2 / 5
- Benefits a professional community (practitioners, clinicians, engineers).
Editor’s rationale
Heuristic triage from title and abstract text only, not a reading of the paper. Cues found: method (we report); scale (scalable); stakes (energy).
How the score was computed
Desks place stronger verdicts first, then use this score to order work within the same verdict.
- Merit
- 5.2 / 10
- Adjusted merit
- 5.2 / 10
- Attention
- 0%
- Freshness
- 0%