5 papers
High-Dimensional Interpolators Can Be Fragile: Heavy Tails and High-Dimensional Large Deviations
Youheng Zhu, Yiping Lu
High-dimensional interpolation is common in modern machine learning, but its tail risk is less understood than its expected prediction risk. Existing theory shows that interpolatin…
An AI-Assisted Solution to the Signed BAR Conjecture: Uniqueness in the Harrison--Reiman Class and a Completely- Class Obstruction
Yiping Lu, Youheng Zhu
For a multidimensional reflected diffusion, determining whether the associated basic adjoint relationship (BAR) uniquely characterizes the stationary distribution is a basic unique…
On the Power of (Approximate) Reward Models for Inference-Time Scaling
Youheng Zhu, Yiping Lu
Inference-time scaling has recently emerged as a powerful paradigm for improving the reasoning capability of large language models. Among various approaches, Sequential Monte Carlo…
What is a Sketch-and-Precondition Derivation for Low-Rank Approximation? Inverse Power Error or Inverse Power Estimation?
Ruihan Xu, Yiping Lu
Randomized sketching accelerates large-scale numerical linear algebra by reducing computational complexity. While the traditional sketch-and-solve approach reduces the problem size…
Randomized Iterative Solver as Iterative Refinement: A Simple Fix Towards Backward Stability
Ruihan Xu, Yiping Lu
Iterative sketching and sketch-and-precondition are well-established randomized algorithms for solving large-scale, over-determined linear least-squares problems. In this paper, we…