# Markov Chain Monte Carlo

AMARA splits MCMC sampling over discrete probabilistic graphical models into an intermediate representation the compiler can process, then maps it onto a programmable ASIC. Previously CPUs and GPUs raised throughput by replicating independent Markov chains, but replicating 4096 chains yielded only about a 270-fold gain, while specialized accelerators often assumed a fixed topology or update schedule. Evaluated on grid-structured and irregular energy-based models and causal inference networks, AMARA achieves an average (up to) higher sampling throughput than a JAX-GPU baseline on irregular workloads and supports a broader range of discrete models than state-of-the-art accelerators.

AMARA splits MCMC sampling over discrete probabilistic graphical models into an intermediate representation the compiler can process, then maps it onto a programmable ASIC. Previously CPUs and GPUs raised throughput by replicating independent Markov chains, but replicating 4096 chains yielded only about a 270-fold gain, while specialized accelerators often assumed a fixed topology or update schedule. Evaluated on grid-structured and irregular energy-based models and causal inference networks, AMARA achieves an average (up to) higher sampling throughput than a JAX-GPU baseline on irregular workloads and supports a broader range of discrete models than state-of-the-art accelerators.

Geological uncertainty in subsurface flow systems is often hierarchical: a set of geological metaparameters controls overall statistics while cell-by-cell property fields vary, and both must be estimated from observations. An adaptive-tempered sequential Monte Carlo method estimates metaparameters and Gaussian latent variables jointly within one likelihood framework, with surrogate models supplying all forward evaluations. Across four synthetic true models, its posterior metaparameter distributions and flow predictions agree closely with reference MCMC results, while single-GPU data assimilation is 2.5–7.0 times faster and needs fewer function evaluations.

Geological uncertainty in subsurface flow systems is often hierarchical: a set of geological metaparameters controls overall statistics while cell-by-cell property fields vary, and both must be estimated from observations. An adaptive-tempered sequential Monte Carlo method estimates metaparameters and Gaussian latent variables jointly within one likelihood framework, with surrogate models supplying all forward evaluations. Across four synthetic true models, its posterior metaparameter distributions and flow predictions agree closely with reference MCMC results, while single-GPU data assimilation is 2.5–7.0 times faster and needs fewer function evaluations.

PowerMH must decide each accept/reject before it can generate the next proposal; PreSTO prefetches several future proposals in one batched call, giving a median 1.71× speedup over PowerMH across seven datasets and five base LLMs while leaving its transition kernel unchanged.

PowerMH must decide each accept/reject before it can generate the next proposal; PreSTO prefetches several future proposals in one batched call, giving a median 1.71× speedup over PowerMH across seven datasets and five base LLMs while leaving its transition kernel unchanged.

Galaxy rotation curves have long favored cored dark-matter halos over the steeply rising cusps predicted by cold dark matter simulations. Fitting five SPARC galaxies with Bayesian inference while modeling correlated errors between neighboring radii largely closes that gap. In DDO 154 the reduced chi-square moves from 2.40 versus 9.41 to 0.94 versus 1.04, leaving one-dimensional rotation curves unable to separate the two halo shapes.

Galaxy rotation curves have long favored cored dark-matter halos over the steeply rising cusps predicted by cold dark matter simulations. Fitting five SPARC galaxies with Bayesian inference while modeling correlated errors between neighboring radii largely closes that gap. In DDO 154 the reduced chi-square moves from 2.40 versus 9.41 to 0.94 versus 1.04, leaving one-dimensional rotation curves unable to separate the two halo shapes.

MCMC and SMC samplers for the power distribution fail to converge under realistic compute budgets, and their reasoning gains are largely recreated by simple Best-of-N selection; Power-RLOO, which fine-tunes directly toward the power distribution, helps only when the base model is already aligned with the task.

MCMC and SMC samplers for the power distribution fail to converge under realistic compute budgets, and their reasoning gains are largely recreated by simple Best-of-N selection; Power-RLOO, which fine-tunes directly toward the power distribution, helps only when the base model is already aligned with the task.

The work interprets several evolutionary algorithms as approximate Markov Chain Monte Carlo (MCMC) and, on that basis, introduces Distribution Matching Evolutionary Algorithms (DME), a class of search methods that sample from a global target distribution without updating model weights and that empirically shows higher sample efficiency than existing methods on problems requiring many samples to find a solution.

The work interprets several evolutionary algorithms as approximate Markov Chain Monte Carlo (MCMC) and, on that basis, introduces Distribution Matching Evolutionary Algorithms (DME), a class of search methods that sample from a global target distribution without updating model weights and that empirically shows higher sample efficiency than existing methods on problems requiring many samples to find a solution.