Nonreversible Metropolis uniform update
Algorithms AIMech:NonreversibleMetropolisUniformUpdate DRAFT
A Metropolis transition algorithm that retains a signed uniform acceptance variable, updates it by wrapped translation, and rescales it after an accepted state proposal to preserve a joint target distribution while changing the temporal dependence of acceptance decisions.
Identity Notes & Concept Scope
Compared both candidate identities with all 442 pinned AIO and 701 native IDs, names, aliases and generated synonyms of every scope using the repository Unicode-aware normalizer; no normalized collisions. All 1143 current record hashes were refreshed and verified unchanged from the assessed inventory immediately before this write. Full ignored- and hidden-inclusive searches of three checkouts were completed without access errors; the 52-group frontier follow-up and 6 fixed-string groups were read in full. The semantic assessment read all 359 selected definitions/identity fields (86 AIO, 273 native), 12 complete pinned AIO CLASS contexts and 15 full native neighbors. Root separately assessed the handoffs, retained byte-verified AIO contexts and documented primary pages. Signed threshold memory and previous/current state-pair memory define separate algorithms; neither is a general Markov-process model, hidden/observed pairwise model, Gibbs sampler or persistent contrastive-divergence training method. The mapping is related_match to AIO:MarkovChain, without equivalence or inherited network/hidden-layer assertions. Absence is bounded to this snapshot, maintained corpus and the documented searches.
Claims & Grounded Evidence
6 Claims
Mechanism
#joint-target-and-wrapped-update
In the maintained regular case, let pi be a proper target density that is positive on the state space used by the proposal. Retain the full state (x,v), with joint target pi(x) times Uniform(−1,1), and use u=abs(v) as the acceptance threshold. The equivalent height s=abs(v)*pi(x) is uniform between zero and pi(x), conditional on x. Replace v by v+delta+noise, wrapped modulo 2 into the signed interval. A fixed shift delta and a noise law independent of the current v preserve its conditional uniform distribution. The signed value, or equivalent direction information, must be retained; abs(v) alone does not determine the stated wrapped update.
Mechanism
#accepted-state-rescaling
For a symmetric stochastic proposal q(x,y)=q(y,x) whose distribution does not depend on v, propose y and accept when abs(v)<pi(y)/pi(x). On acceptance replace (x,v) by (y,v*pi(x)/pi(y)); on rejection retain both x and v for this accept/reject substep. The rescaling preserves the under-density height and is required for both lower-density and higher-density accepted moves. Together with the wrapped uniform update, this preserves the joint target. The target-density ratio alone is not a general acceptance rule for an asymmetric proposal.
Limitation
#composition-and-stationary-acceptance
Invariance of the joint target does not imply detailed balance or ergodicity. Reversibility of the threshold-update substep alone also does not determine reversibility of the full update: exact examples remain nonreversible after a half-period wrapped shift or after a full uniform refresh followed by accept/rescale. A fresh uniform before every proposal recovers ordinary Metropolis for the x process, but the augmented output includes the rescaled v. For repeated accept/rescale updates with zero shift, no noise and no other state updates, the under-density height remains fixed, providing no general ergodicity guarantee. At stationarity, using the same proposal kernel, the mean acceptance probability agrees with ordinary Metropolis because abs(v) is uniform and independent of x; temporal clustering can nevertheless change.
Scope
#augmented-momentum-and-interleaving-scope
The illustrated persistent-momentum application uses partial Gaussian momentum refresh, one leapfrog step with proposal momentum negation, accept/reject, and a final momentum negation. Its reversible, volume-preserving proposal acts on the joint position/momentum state, so acceptance and threshold rescaling use that joint density. This does not justify dropping the proposal correction from an arbitrary asymmetric position-only Langevin proposal. Other x updates preserving pi may be interleaved while leaving v alone when those updates ignore v, since the target factorizes. The threshold mechanism is not identical to the momentum method or to Hamiltonian Monte Carlo as a whole.
Scope
#exact-finite-boundary-checks
Curator calculations propagate piecewise constant signed-threshold densities with exact rational arithmetic. For target probabilities (1/3,2/3) and a symmetric state-flip proposal, accept/rescale preserves the product target. Omitting rescaling preserves the x marginal for one step but changes state 0 mass to 1/6 after the second step, instead of 1/3. Using the target ratio with the asymmetric proposal matrix with rows (1/2,1/2) and (1,0) gives state 0 mass 1/2. Further examples show unequal forward and reverse set fluxes for the half-period and full-refresh compositions. All 576 constructed positive-target, symmetric-proposal shift/noise cases preserve the joint density. These are exact finite examples with a continuous auxiliary variable, not author-code replication, a general convergence proof or a performance benchmark.
Limitation
#efficiency-and-source-limits
The source notes that noise may be needed when the target density takes only finitely many values; continuous variation is not a guarantee that a deterministic shift mixes. Its experiments concern particular Gaussian, mixed discrete/continuous and Bayesian neural-network targets, observables and tuning choices. They do not establish universal variance reduction, a higher stationary acceptance rate, or lower computational cost. The Bayesian neural-network result is preliminary. The appendix scripts were inspected as source text, without execution or benchmark reproduction.
⚠️ Curated Limitations & Negative Results
- The local label denotes this signed-threshold construction. Generic nonreversible MCMC, lifted MCMC, persistent learning particles and the full paper title are not asserted as exact aliases.
- The maintained target-ratio formula assumes a proper positive target and a symmetric proposal independent of v. Zero-support extensions and arbitrary asymmetric proposals require separate treatment.
- Threshold-substep reversibility cannot be promoted to full-composition reversibility. Neither the method name nor invariant marginals establish ergodicity for every tuning choice.
- The author-hosted 2020 report is the inspected version. Equivalence to arXiv PDF bytes was not established; other implementations and numerical reversibility were not audited.
- No author code, training, paid provider or benchmark replication was run. DRAFT remains.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:MarkovChain
Markov Chain
|
related_match | The algorithm constructs a Markov transition on an augmented state with a specified target marginal. The AIO target describes a stochastic process/model; this is a method-to-process relation, without equivalence, subclass status, or inheritance of its Network and ProbabilisticHiddenLayer assertions. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
neal2020
|
Radford M. Neal
|
author technical report
full_text
|
ID: arxiv:2001.11950
sha256:633fee302304…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-14T20:19:21Z
Updated: 2026-10-14T20:19:21Z