Research

Langevin dynamics: sampling, discretization bias, transport coefficients

David Herzog · Mathematics, Iowa State University · ongoing

The overdamped diffusion $d{X}_t=\nabla \log \pi (X_t)dt+\sqrt{2}d{W}_t$ leaves $\pi$ invariant, so discretizing it gives a sampler. That sampler is not a niche method. Stochastic gradient Langevin dynamics is its Euler–Maruyama discretization with a minibatch gradient; the inner loop of annealed Langevin sampling is the same chain at a fixed noise level; the corrector step of a predictor–corrector diffusion sampler is the same chain against a learned score. In all three the Metropolis correction is dropped, usually without comment, and the invariant law that results is ${\pi }_h\ne \pi$.

I measure that gap where it is computable rather than bounding it. On an anisotropic Gaussian the unadjusted chain is a coordinatewise AR(1) whose stationary variance solves exactly,

Large-deviation asymptotics for mean-field interacting systems

Ruoyu Wu · Mathematics, Iowa State University · ongoing

Large deviations sits underneath a good deal of learning theory. Sanov's theorem and the Donsker–Varadhan variational formula for relative entropy are the machinery behind PAC-Bayes generalization bounds and variational mutual-information estimators. Freidlin–Wentzell small-noise theory is how escape times from saddles and shallow basins are analyzed for SGD and for Langevin-based optimizers. And the empirical-measure LDP for a mean-field interacting particle system is structurally the same construction that sits one level above the mean-field limit of wide-network training.

I work on rate functionals and the variational characterization of rare events for the empirical measure ${\mu }_t^N=\frac{1}{N}{\sum }_i{\delta }_{X_t^{i,N}}$ of such a system, currently in the setting of load balancing. The object is a large-deviation principle on path space; the rate functional then supplies the change of measure for an importance-sampling estimator of rare events, benchmarked against the analytic rate function by exact and Monte Carlo numerics. The application domain is queueing, but the technique carries well past it.

The results are held back until the preprint is out. What the figure below shows instead is the mechanism the whole method rests on, on the one target where the answer is known to machine precision.

Stability of neural approximations to evolution equations

Jue Yan · Mathematics, Iowa State University · ongoing

A cell-average neural network solver learns a one-step finite-volume operator

A trained solver is still a numerical scheme: its weights are frozen once training ends, so what you have is a fixed deterministic update rule that happened to be fitted rather than derived. Numerical analysis has a long history of asking whether update rules of that kind are stable. I am adapting von Neumann analysis to this setting, deriving the linearised amplification factor of the learned time-stepping scheme and characterizing how perturbations propagate through it, toward a condition on the weights alone that can be checked before committing to an expensive rollout.

Joint with Mengyuan Yang. Approach and results held back pending submission.

Metastable failures in prefix-cached LLM agent serving

Ali Jannesari · SwaPP Lab, Computer Science, Iowa State University · ongoing

An agent works in a loop: model call, tool call, model call, re-sending the whole growing conversation each turn. Serving engines such as SGLang and vLLM keep that shared prefix in a GPU KV cache so a follow-up turn costs a fraction of the first. The cache is small, though. When enough agent sessions compete for it, a session evicted while it waits on a tool has to recompute everything on its next turn, and that extra work keeps the cache full and evicts the next session. The question is whether a short burst of traffic can push an otherwise healthy server into a self-sustaining all-miss, low-throughput state, a metastable failure, and which scheduling and admission mechanisms prevent it.

Three instruments. A discrete-event simulator of a continuous-batching engine with prefix caching, covering scheduling policies, eviction rules, memory-allocation modes and re-implementations of recently proposed mechanisms. A queueing-theoretic thrashing-curve model that connects the classical working-set and metastability literature to agent workloads and says when caching helps, when it collapses, and when admission control restores stability. And a load-testing harness that drives a production engine, SGLang serving a 7B-parameter model on NVIDIA A100s, on Iowa State's Nova cluster through SLURM, with the prediction for each run committed before the run and paired control arms under common random numbers. On the real engine, cache reuse collapses sharply once concurrent sessions exceed the cache's working set and throughput falls severalfold, which matches the simulator. Whether the collapse outlives the burst that caused it is the experiment in progress.

Public overview: Nova-Research-Overview. Code and data held back pending the preprint.

Online calibration of neural volatility forecasts with early, one-sided feedback

Hongyang Gao · Computer Science, Iowa State University · ongoing

A forecast of a cumulative quantity, the realized variance of an asset over the next day, say, is scored only when the horizon ends. Every online calibration method therefore learns one full horizon late, which is exactly when it is slowest to react to a shift. But the increments of such a quantity are non-negative, so the running sum is monotone, and if it crosses the issued upper bound before the horizon ends the miss is certain at once. Coverage is confirmed only at the end. The feedback is early, but one-sided.

The method is a model-agnostic layer on top of any quantile forecaster. It credits certain early misses to an online integrator as soon as they are confirmed, keeps explicit accounts of forecasts still pending so the eventual miss count is known to lie in an interval rather than treated as settled, and applies a bounded correction only when the accounting justifies it. The long-run coverage guarantee under early crediting, bounded correction and missing data is proved and checked numerically over tens of thousands of adversarial runs. Whether this recovers faster after a volatility jump than delayed-feedback conformal baselines, without widening the bounds the rest of the time, is the question, and the answer is being settled on a regime-shift simulation with exact oracle quantiles and on a sealed real-data test set, against pre-registered hypotheses.

Public overview: neural-forecasting-research-overview. Code, proofs and results held back pending submission.

Reliability of tool-using agents

Yang Li · Computer Science, Iowa State University · ongoing

Two questions about agents that run for a long time and sometimes fail. When one stalls, when is restarting it worth more than waiting, and what in the distribution of run times decides that? And how do you estimate the probability of a failure too rare for direct simulation to reach, the same problem as the rare-event work above with an agent in place of a queue? Two pilots on real agents, one on restart policies and one on rare failures, each with its kill criteria registered before any data, with the direction still being chosen between them.

Approach and results held back pending the choice of direction.