Related papers: Compilation and Fast Model Counting beyond CNF
We investigate conjunctive normal form (CNF) encodings of a function represented with a decomposable negation normal form (DNNF). Several encodings of DNNFs and decision diagrams were considered by (Abio et al. 2016). The authors…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Safety constraints of nonlinear control systems are commonly enforced through the use of control barrier functions (CBFs). Uncertainties in the dynamic model can disrupt forward invariance guarantees or cause the state to be restricted to…
Time, cost, and energy efficiency are critical considerations in Deep-Learning (DL), particularly when processing long texts. Transformers, which represent the current state of the art, exhibit quadratic computational complexity relative to…
Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…
Learning the cumulative distribution function (CDF) of an outcome variable conditional on a set of features remains challenging, especially in high-dimensional settings. Conditional transformation models provide a semi-parametric approach…
Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based on Pfaffians. In particular, they…
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA '14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit…
Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…
Fixed-parameter tractable (FPT) algorithms have been successfully applied to many intractable problems -- with a focus on decision and optimization problems. Their aim is to confine the exponential explosion to some parameter, while the…
The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for…
Control Barrier Functions (CBFs) offer a framework for ensuring set invariance and designing constrained control laws. However, crafting a valid CBF relies on system-specific assumptions and the availability of an accurate system model,…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
During the last decade, deep neural networks (DNN) have demonstrated impressive performances solving a wide range of problems in various domains such as medicine, finance, law, etc. Despite their great performances, they have long been…
Conformal prediction (CP) constructs prediction sets with marginal coverage guarantees under the assumption that the calibration and test distributions are identical. However, under distribution shift, existing approaches primarily align…
Several `edge-discovery' applications over graph-based data models are known to have worst-case quadratic time complexity in the nodes, even if the discovered edges are sparse. One example is the generic link discovery problem between two…
In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer…