Certified Access: Test-Time Compute on Conservative Physics-Structured AI Memory
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 CT) resolves reach failures at detJ=1 exactly. We verify this certificate stack on a designed analytic testbed. Reaching just beyond CT 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.
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BibTeX
@misc{jawahar2026certified,
title = {{Certified Access: Test-Time Compute on Conservative Physics-Structured AI Memory}},
author = {Pratik Jawahar and Riccardo Maggioni and Jonas Petersen and Matteo Cozzi and Gian-Alessandro Lombardi and Marek Gajewski and Camilla Mazzoleni and Federico Martelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39073},
eprint = {2610.39073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39073},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Certified Access: Test-Time Compute on Conservative Physics-Structured AI Memory
AU - Pratik Jawahar
AU - Riccardo Maggioni
AU - Jonas Petersen
AU - Matteo Cozzi
AU - Gian-Alessandro Lombardi
AU - Marek Gajewski
AU - Camilla Mazzoleni
AU - Federico Martelli
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39073
UR - https://arxiv.org/abs/2610.39073
AB - 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.
ER -