Latent Dynamics · 2026-10-30
Certified Access: Test-Time Compute on Conservative Physics-Structured AI Memory
Pratik Jawahar, Riccardo Maggioni, Jonas Petersen, Matteo Cozzi, Gian-Alessandro Lombardi, Marek Gajewski, Camilla Mazzoleni, Federico Martelli
AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.
TL;DR
The authors propose a framework for test-time compute on a Latent Dynamics Model used as memory, where latent access is implemented by structure-preserving symplectic dynamics. For two access mechanisms (a Lorentz squeeze and a gated canonical translation), they provide “certificate stacks” covering exact phase-volume Jacobians, bounded energy change, and latch-transport laws—validated on a designed analytic testbed. They also evaluate calibrated compute rationing and non-local routing limits against a physics-free baseline.
Why it matters
The work links additional inference compute to explicit, theorem-backed changes in a model’s latent dynamics rather than treating retries/routing/halting as black-box additions. By defining conditional certificates (volume, energy, latch transport) and showing where they stop (e.g., BIBO stability needs coercive-component screening), the authors clarify both what extra access buys and what safety/stability guarantees require.
Method
- Define “certified access” for a conservative latent dynamics memory: an encoder state (q,p) is advanced by a damped symplectic (velocity-Verlet) step of a learned separable Hamiltonian.
- Split reachability failures into escape vs reach; use a Lorentz squeeze to resolve escape failures and a gated canonical translation channel to resolve reach failures, each with explicit Jacobian/energy/latch-transport certificates.
- Verify the certificate stack on an analytic testbed, then evaluate on learned physics-structured memory: calibrated compute rationing and scaling limits of non-local routing vs a physics-free router baseline.
Limitation
The authors’ certificates are conditional: the volume certificate holds for damping frozen within a step (not for the state-dependent governor), the latch law holds at the jump only, and energy statements hold on the stated testbed potentials. They also do not bound trajectories; BIBO stability requires coercive-component screening (not guaranteed by det J=1 with zero energy change).
Abstract (from arXiv)
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.
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Publication record
Bibliographic evidence describes where and when a record appeared. It does not validate scientific claims.
First public release: 2026-10-29 · Indexed by Pub-AI: 2026-10-30 UTC
Certified Access: Test-Time Compute on Conservative Physics-Structured AI Memory
Preprint posted: 2026-10-29 · Original record ↗
- arxiv
- 2610.39073
Explicit source versions (1)
- v1 · 2026-10-29
- Preprint available
Source date: 2026-10-29 · First detected: 2026-10-30 UTC · Historical baseline
Source evidence (2)
- Official evidence ↗ · RSS guid=oai:arXiv.org:2610.39073v1; arxiv:announce_type=new; item pubDate (official metadata)
- Official evidence ↗ · atom:published (official metadata)
Abstract · arxiv
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.