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The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the…
This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in…
Differentially private empirical risk minimization (DP-ERM) is a fundamental problem in private optimization. While the theory of DP-ERM is well-studied, as large-scale models become prevalent, traditional DP-ERM methods face new…
Efficient text embedding is crucial for large-scale natural language processing (NLP) applications, where storage and computational efficiency are key concerns. In this paper, we explore how using binary representations (barcodes) instead…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
Context: Large Language Models (LLMs) are increasingly used in modern software development, aiding in code generation, code completion, and refactoring through AI-powered assistants. While they accelerate development workflows, they often…
We propose a novel Branch-and-Bound method for reachability analysis of neural networks in both open-loop and closed-loop settings. Our idea is to first compute accurate bounds on the Lipschitz constant of the neural network in certain…
In this paper we study syntactic branching programs of bounded repetition representing CNFs of bounded treewidth. For this purpose we introduce two new structural graph parameters $d$-pathwidth and clique preserving $d$-pathwidth denoted by…
In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by…
Partially Observable Markov Decision Processes (POMDPs) offer a promising world representation for autonomous agents, as they can model both transitional and perceptual uncertainties. Calculating the optimal solution to POMDP problems can…
Kernelization is a significant topic in parameterized complexity. Turing kernelization is a general form of kernelization. In the aspect of kernelization, an impressive hardness theory has been established [Bodlaender etc. (ICALP 2008,…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
Hierarchical beam search in mmWave communications incurs substantial training overhead, necessitating deep learning-enabled beam predictions to effectively leverage channel priors and mitigate this overhead. In this study, we introduce a…
We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. First, we propose novel bounding algorithms based on Lagrangian Decomposition. Previous works have used…
Background: Combinatorial optimization problems (COPs) are central to Logistics and Supply Chain decision making, yet their NP-hardness prevents exact optimal solutions in reasonable time. Methods: This work addresses that limitation by…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
In this paper, we consider online planning in partially observable domains. Solving the corresponding POMDP problem is a very challenging task, particularly in an online setting. Our key contribution is a novel algorithmic approach,…