Related papers: BOSPHORUS: Bridging ANF and CNF Solvers

The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and…

Activation functions (AFs) are an important part of the design of neural networks (NNs), and their choice plays a predominant role in the performance of a NN. In this work, we are particularly interested in the estimation of flexible…

We devise an autoencoder based strategy to facilitate anomaly detection for boosted jets, employing Graph Neural Networks (GNNs) to do so. To overcome known limitations of GNN autoencoders, we design a symmetric decoder capable of…

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Faugere's F4 is a well-known Grobner bases algorithm to solve this problem. However, a serious drawback exists in the Grobner bases based…

Given a CNF formula and a weight for each assignment of values to variables, two natural problems are weighted model counting and distribution-aware sampling of satisfying assignments. Both problems have a wide variety of important…

Collaborative Filtering (CF) based recommendation methods have been widely studied, which can be generally categorized into two types, i.e., representation learning-based CF methods and matching function learning-based CF methods.…

Quantized Neural Networks (QNNs) use low bit-width fixed-point numbers for representing weight parameters and activations, and are often used in real-world applications due to their saving of computation resources and reproducibility of…

Graph data is becoming increasingly prevalent due to the growing demand for relational insights in AI across various domains. Organizations regularly use graph data to solve complex problems involving relationships and connections. Causal…

We introduce a novel generalization of Counterexample-Guided Inductive Synthesis (CEGIS) and instantiate it to yield a novel, competitive algorithm for solving Quantified Boolean Formulas (QBF). Current QBF solvers based on…

The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches…

Despite enjoying desirable efficiency and reduced reliance on domain expertise, existing neural methods for vehicle routing problems (VRPs) suffer from severe robustness issues -- their performance significantly deteriorates on clean…

A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation…

Foundational optimization embeddings have recently emerged as powerful pre-trained representations for mixed-integer programming (MIP) problems. These embeddings were shown to enable cross-domain transfer and reduce reliance on…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

We solve the normal ordering problem for (A* A)^n where A* (resp. A) are one mode deformed bosonic creation (resp. annihilation) operators satisfying [A,A*]=[N+1]-[N]. The solution generalizes results known for canonical and q-bosons. It…

Recent advancement in generative models have demonstrated remarkable performance across various data modalities. Beyond their typical use in data synthesis, these models play a crucial role in distribution matching tasks such as latent…

Quaternionic polynomials occur naturally in applications of quaternions in science and engineering, and normalization of quaternionic polynomials is a basic manipulation. Once a Groebner basis is certified for the defining ideal I of the…

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Grobner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Grobner bases based…

Methods of solving big Boolean equations can be broadly classified as algebraic, tabular, numerical and map methods. The most prominent among these classes are the algebraic and map methods. This paper surveys and compares these two types…

Artificial and biological neural networks (ANNs and BNNs) can encode inputs in the form of combinations of individual neurons' activities. These combinatorial neural codes present a computational challenge for direct and efficient analysis…