Research

My research uses probability and numerical analysis to study how machine learning systems behave. These are six projects with faculty in Computer Science and Mathematics at Iowa State. The first to reach a preprint is Inside the Trap, written with Ali Jannesari. It explains why an LLM serving engine can stay stuck after a burst of agent traffic, even at a load it handled before, and how a session cap gets it out. The other five look at Langevin samplers, rare events in load-balancing queues, the stability of neural PDE solvers, forecast calibration and the reliability of LLM agents.

The preprint and the three manuscripts are listed at the bottom of this page.

A large pastel whirl fills the frame: broad curved bands wind inward from peach, pink and lilac at the edges, through violet and blue, to a small navy comma near the centre.

Preprint

Inside the Trap

A Renewal Law for Prefix-Cache Collapse in LLM Agent Serving

A flat contour map of two wells seen from above: a dark purple figure-eight runs diagonally across the frame, its two lobes touching at a single point, with warm bands of coral, pink, peach and apricot rippling outward to cream at the corners.

Advisor review

Langevin Sampling

Discretization Bias and Transport Coefficients

A regular grid of white cubes on a gray floor, seen from above at an angle. Almost every cube stands alone, and in the centre one stack of ten blue cubes rises far above the rest.

Paused

Rare Events

Large Deviations and Importance Sampling for Mean-Field Queues

Fifteen tall rounded columns on a purple background, their heights rising and falling in one smooth, symmetric mound. Each glows coral low down and warms to pale apricot at its tip.

In preparation

Learned PDE Solvers

Von Neumann Stability Analysis for Cell-Average Neural Networks

On a dark slate background, a pale gray staircase climbs from the lower left to the right edge. A white line crosses the image just below the middle, and the steps above the line are blue.

In development

Early-Feedback Calibration

Online Calibration of Volatility Forecasts with Early, One-Sided Feedback

Three thick concentric arcs with rounded ends on a pink-to-violet background, all starting from the same point and running clockwise for different distances. The middle arc, pale blue deepening to indigo, stops before half way, and a pale band marks the rest of its lap.

In development

Agent Reliability

Restarting Stalled Agents and Estimating Rare Failures

Publications

arXiv 2026

Inside the Trap: A Renewal Law for Prefix-Cache Collapse in LLM Agent Serving [Paper] [PDF] [Code] [Project]
Akshat Valse and Ali Jannesari

Manuscript

Langevin Dynamics and Transport-Coefficient Estimation for Molecular Systems
Akshat Valse, D. Herzog, O. Smith and D. Wu Draft in advisor review

Manuscript

Stability Certificates for Cell-Average-Based Neural Network Solvers: von Neumann Analysis of Trained Flux Networks
Akshat Valse, M. Yang and J. Yan In preparation

Manuscript

Large-Deviation-Guided Importance Sampling for Rare Events in the Mean-Field Join-the-Shortest-Queue Model
Akshat Valse and R. Wu Paused during the advisor's sabbatical