ML: Sampling

Machine-learning ideas tagged Sampling in the ML taxonomy of the Math2NN corpus.

✗ Mechanism failed 2026

ESS-Controlled Autoregressive CTMC Sampler

Generate discrete configurations globally with an autoregressive model and then refine them using a continuous-time Markov chain of local single-site replacement moves. Use importance weights and the paper's normalized ESS to adapt the CTMC refinement budget and to reject training batches in which the proposal has collapsed onto a few modes.

Useful7/10
Difficulty6/10
Novelty7/10
Paper: FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditions arXiv:2609.02948
✗ Failed on benchmark 2026

Persistent Hamiltonian categorical sampler

Replace independent categorical proposals or reversible Metropolis updates for discrete latent variables with a lifted sampler carrying persistent continuous edge momenta. Neighbor transitions are biased by the momentum and use a symmetric energy factor, so momentum reversal gives the required balance relation for the target Gibbs distribution while ordinary dynamics remain non-reversible. This should reduce random-walk behavior when sampling multimodal categorical latents or token sequences.

Useful7/10
Difficulty6/10
Novelty7/10
Paper: Hamiltonian dynamics for sampling on discrete spaces arXiv:2608.17961
✗ Failed on benchmark 2026

Cubic-Rate Third-Order Langevin Optimizer

Replace the usual parameter-plus-momentum Langevin state with a three-level chain consisting of parameters, velocity, and acceleration, while injecting Gaussian noise only into the highest auxiliary state. At a saddle, the escaping direction has a positive rate given by a cubic characteristic equation; use this rate to choose damping or adapt the temperature so that basin escape is accelerated without making the dynamics unstable.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: An Eyring--Kramers Law for the Hypoelliptic Third-Order Langevin Diffusion arXiv:2607.20882
Unverified 2026

Critical-Coupling Noise Controller

Add calibrated multiplicative noise to a binary energy-based model, Hopfield network, or discrete recurrent attractor system so that its effective coupling follows a chosen distance from the collective critical point. Unlike ordinary temperature annealing, the controller distinguishes microscopic channel noise from Gibbs or sampling noise and predicts when ordered attractors should disappear through a measurable susceptibility peak.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Decoherence-controlled collective criticality in a two-dimensional quantum Stag Hunt arXiv:2609.02957
Unverified 2026

Windowed Bouncy Particle Weight Sampler

Replace stepwise gradient evaluation in a Bouncy Particle sampler over neural-network parameters with deterministic windows. At the start of each window, compute one gradient and use smoothness to upper-bound the event intensity along the ballistic trajectory; candidate events are generated analytically from the integrated envelope and accepted using a gradient evaluation only at candidate locations. This gives an exact sampler under a certified global smoothness bound and a controllable…

Useful6/10
Difficulty6/10
Novelty7/10
Paper: Windowed thinning and query complexity for the bouncy particle and Zigzag samplers arXiv:2607.28413
✗ Mechanism failed 2026

KL-Budgeted Poisson-Race Sampling

Replace repeated rejection sampling from a neural proposal P with a Poisson race that selects one proposal candidate with exactly the target distribution Q. Candidate i receives a Poisson arrival time A_i and race score A_i divided by Q(X_i)/P(X_i); the smallest score wins. When Q is close to P in KL divergence, the selected index has low expected logarithmic rank, providing an adaptive compute budget instead of a fixed number of candidates.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: A note on shifting distributions via Poisson races arXiv:2608.26996
✗ Failed on benchmark 2026

Uniformly Mixing Coulomb Particle Bank

Represent a set of neural prototypes, mixture components, or latent particles by N points in R^2, and initialize or refresh them with Langevin dynamics targeting a quadratically confined logarithmic Coulomb gas. The logarithmic repulsion prevents particle collapse, while the paper's N-uniform logarithmic Sobolev inequality predicts that mixing need not degrade as the particle bank grows.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Uniform logarithmic Sobolev inequalities for the 2D Coulomb gas at the diffusive temperature scale arXiv:2608.24863
Unverified 2026

Even-Norm Group Diffusion Augmentation

Replace a fixed discrete augmentation distribution over a finite symmetry group by a continuous-time random walk driven by learnable symmetric Poisson jump rates. Use the resulting transformed-example distribution as a symmetry regularizer, with an even ℓ^{2m} distance to uniformity whose behavior is guaranteed to improve monotonically as the symmetric rates increase for the group families covered by the paper.

Useful5/10
Difficulty5/10
Novelty7/10
Paper: Proof of the Lyons--White Conjecture arXiv:2608.27708
Unverified 2026

Convex-mixture graph Langevin optimizer

Put a gradient-Gibbs prior on differences between connected neural parameters rather than on individual parameters, and evolve the parameters with Langevin steps generated from randomly selected strictly convex component energies. The aggregate regularizer may be non-convex, but every sampled component has controlled curvature and outward drift, providing a practical stability mechanism for noisy training.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Gradient Gibbs measures with non-convex potentials and the universality class of the Gaussian Free Field arXiv:2608.14526
Unverified 2026

Warm-start hit-and-run augmentation

Replace rejection sampling or short biased random walks inside a convex latent constraint set with hit-and-run. At each step, choose a uniformly random direction and sample uniformly along the entire chord through the current point; the paper's mixing result predicts that a chain initialized by a crude approximate sampler becomes close to uniform with only logarithmic dependence on initialization bias and target error.

Useful5/10
Difficulty5/10
Novelty7/10
Paper: Hit-and-Run Mixes as Fast as the Ball Walk arXiv:2608.13487
Unverified 2026

Certified partition-function reranking

Replace MAP scoring of discrete latent configurations by comparison of the total energy-model mass assigned to each candidate class. Estimate each class partition function with annealed importance sampling driven by identical random seeds, then return a prediction only when a paired bootstrap confidence interval certifies that its log-partition score exceeds every competitor.

Useful5/10
Difficulty6/10
Novelty6/10
Paper: Certified decoding of quantum LDPC codes arXiv:2608.25545
Unverified 2026

Conservative amortized collision layer

Add a learned stochastic pair-interaction layer to a particle graph neural network, with a conditional normalizing flow generating the post-interaction relative state. Parameterize the update in center-of-mass and invariant relative coordinates so every sampled interaction preserves pair momentum and kinetic energy exactly. The flow learns the transition law directly from observed scattering or trajectory data, replacing repeated numerical collision solves or unconstrained message-passing…

Useful5/10
Difficulty6/10
Novelty6/10
Paper: A particle method for the Boltzmann equation via amortized sampling from Green's function of the lifted linear operator arXiv:2608.22880