Related papers: Sharp Hybrid Zonotopes: Set Operations and the Ref…

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…

In recent years, mixup regularization has gained popularity as an effective way to improve the generalization performance of deep learning models by training on convex combinations of training data. While many mixup variants have been…

Mixed-precision quantization, where a deep neural network's layers are quantized to different precisions, offers the opportunity to optimize the trade-offs between model size, latency, and statistical accuracy beyond what can be achieved…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…

Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…

Mixup~\cite{zhang2017mixup} is a recently proposed method for training deep neural networks where additional samples are generated during training by convexly combining random pairs of images and their associated labels. While simple to…

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…

We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants…

Given a nonlinear, univariate, bounded, and differentiable function $f(x)$, this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of $f(x)$ and its…

The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…

Modern deep learning compilers rely on layout abstractions to manage the complex mapping between logical tensor structures and physical memory arrangements. CuTe layouts and Triton linear layouts are widely adopted industry standards.…

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…

The demand for long and accurate gravitational waveforms is increasing as we prepare for the next generation of detectors and seek to improve current waveform models. However, numerical relativity waveforms, while highly accurate, are often…

Hybrid systems play a crucial role in modeling real-world applications where discrete and continuous dynamics interact, including autonomous vehicles, power systems, and traffic networks. Safety verification for these systems requires…

A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XOR-ing a binary vector with a combination of other binary vectors called generators. Such a…

Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…

A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…

Neural network quantization is frequently used to optimize model size, latency and power consumption for on-device deployment of neural networks. In many cases, a target bit-width is set for an entire network, meaning every layer get…