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Out-of-distribution (OOD) detection is important for deploying reliable machine learning models on real-world applications. Recent advances in outlier exposure have shown promising results on OOD detection via fine-tuning model with…
In this review we present hyper-dual numbers as a tool for the automatic differentiation of computer programs via operator overloading. We start with a motivational introduction into the ideas of algorithmic differentiation. Then we…
Pointer analysis is foundational for many static analysis tasks, yet its effectiveness is often hindered by imprecise modeling of heap allocations, particularly in C/C++ programs where custom allocation functions (CAFs) are pervasive.…
The convergence of deep learning and formal mathematics has spurred research in formal verification. Statement autoformalization, a crucial first step in this process, aims to translate informal descriptions into machine-verifiable…
We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD)…
The deployment and application of Large Language Models (LLMs) is hindered by their memory inefficiency, computational demands, and the high costs of API inferences. Traditional distillation methods, which transfer the capabilities of LLMs…
Agentic Variation Operators (AVO) are a new family of evolutionary variation operators that replace the fixed mutation, crossover, and hand-designed heuristics of classical evolutionary search with autonomous coding agents. Rather than…
Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations.…
In real world scenarios, out-of-distribution (OOD) datasets may have a large distributional shift from training datasets. This phenomena generally occurs when a trained classifier is deployed on varying dynamic environments, which causes a…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
Modern data workflows are inherently adaptive, repeatedly querying the same dataset to refine and validate sequential decisions, but such adaptivity can lead to overfitting and invalid statistical inference. Adaptive Data Analysis (ADA)…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN)…
Koopman operator theory has been gaining momentum for model extraction, planning, and control of data-driven robotic systems. The Koopman operator's ability to extract dynamics from data depends heavily on the selection of an appropriate…
We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference operator onto the test function. The main advantage of this…
The concept of linearity plays a central role in both mathematics and computer science, with distinct yet complementary meanings. In mathematics, linearity underpins functions and vector spaces, forming the foundation of linear algebra and…
Automatic translation of natural language mathematics into faithful Lean 4 code is hindered by the fundamental dissonance between informal set-theoretic intuition and strict formal type theory. This gap often causes LLMs to hallucinate…
Out-of-distribution (OOD) detection aims to detect test samples that do not fall into any training in-distribution (ID) classes. Prior efforts focus on regularizing models with ID data only, largely underperforming counterparts that utilize…
Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be…
Ptychography is a lensless imaging method that allows for wavefront sensing and phase-sensitive microscopy from a set of diffraction patterns. Recently, it has been shown that the optimization task in ptychography can be achieved via…