Related papers: Using Bounded Model Checking to Focus Fixpoint Ite…

Fixed-point iterations are at the heart of numerical computing and are often a computational bottleneck in real-time applications that typically need a fast solution of moderate accuracy. We present neural fixed-point acceleration which…

A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow…

We propose a construction for joint feature learning and clustering of multichannel extracellular electrophysiological data across multiple recording periods for action potential detection and discrimination ("spike sorting"). Our…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…

Spatial confounding is how is called the confounding between fixed and spatial random effects. It has been widely studied and it gained attention in the past years in the spatial statistics literature, as it may generate unexpected results…

Compilers for statically typed functional programming languages are notorious for generating confusing type error messages. When the compiler detects a type error, it typically reports the program location where the type checking failed as…

In continual learning, where task data arrives in a sequence, fine-tuning on later tasks will often lead to performance degradation on earlier tasks. This is especially pronounced when these tasks come from diverse domains. In this setting,…

This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…

In the era of large language models, model merging is a promising way to combine multiple task-specific models into a single multitask model without extra training. However, two challenges remain: (a) interference between different models…

Model merging provides a compelling paradigm for integrating specialized expertise into a unified multi-task model, a goal that aligns naturally with the sequential knowledge acquisition in continual learning (CL). However, the requirement…

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…

Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…

SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition…

Previous papers have shown the impact of partial convergence of discretized PDE on the accuracy of tangent and adjoint linearizations. A series of papers suggested linearization of the fixed point iteration used in the solution process as a…

Supervised fine-tuning (SFT) is a crucial step for adapting large language models (LLMs) to downstream tasks. However, conflicting objectives across heterogeneous SFT tasks often induce the "seesaw effect": optimizing for one task may…

This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…