WHY RARE EVENTS MATTER
A small probability can carry a large consequence.
Sampling systems are often judged by how well they reproduce the outcomes seen most often. But some decisions depend on the far edge of a distribution: an uncommon failure, an extreme state, or the chance that a critical threshold will be crossed. A sampler can describe the center convincingly and still be wrong where the decision is actually made.
WHAT WE ARE TESTING
Whether looking stable is the same as being right.
We are placing simulated thermodynamic samplers in controlled probability landscapes, including systems that are difficult to move through or contain competing states. Where an exact reference is available, we can compare what the sampler reports with what the probability should actually be. We then introduce controlled, hardware-inspired imperfections and ask whether familiar diagnostics notice when the rare-event estimate begins to drift.
METHODS + RESEARCH STACK
Built to compare the answer with something we can inspect.
The study separates a clear reference implementation from the accelerated system being evaluated. That gives us a known point of comparison before speed, scale, or hardware-inspired effects enter the picture.
NumPy + exact enumeration
Small cases use inspectable NumPy kernels and exact probability calculations so the expected distribution is known rather than estimated.
JAX + CUDA 13
Batched sampler chains run in 64-bit numerical mode through JAX on an NVIDIA RTX 3090 Ti, after agreement with the reference layer is established.
SciPy, ArviZ, Xarray + Polars
These libraries support statistical checks, diagnostic summaries, labeled experiment data, and the larger tables produced across repeated trials.
Python 3.12 + sealed telemetry
A locked software environment, hashed source records, checkpoints, and synchronized machine telemetry preserve the conditions behind each result.
THE DISTINCTION
Three views of the same sampler.
The common states
The outcomes a sampler visits frequently can make its behavior appear stable and well mixed.
The rare tail
Low-probability outcomes receive fewer observations, making consequential errors harder to see.
The decision
A small error in the tail can change whether a risk limit, reliability target, or other threshold is crossed.
WHAT IT COULD MEAN
Better evidence before we trust the answer.
If ordinary checks can miss consequential tail errors, emerging sampling systems may need a different standard of evaluation—one that can detect uncertainty, bound the risk of a wrong estimate, and decline to offer confidence when the evidence is not strong enough. This study focuses on simulation so those failures can be introduced and measured under controlled conditions.