arXiv research

Boolean logic used for neural network training and inference, with convergence analysis.

A new method relaxes Boolean Matrix Factorization to make it more efficient.

Paper proposes algorithms for BMF using integer programming.

This paper explores how boolean formulas can be learned by deep neural networks.

New findings show that common optimization algorithms struggle with random problems.

The paper develops algorithms for Boolean matrix factorization using IP and heuristics.

Efficiently optimizes boolean functions using multilinear polynomials and exponential weight updates.

Paper improves variational inference on Boolean hypercube using quantum methods.

Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the non-convex objective and the combinatorial constraints. We propose Binary Matching P…

Study on functions computed by deep-layered machines finds same distribution in neural networks and Boolean circuits.

Decision Machines embeds decision trees into vector spaces for improved optimization.

New Fourier analysis method for non-uniform Boolean hypercube.

A new deep learning method using Boolean logic reduces training and inference energy.

Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message p…

New Boolean algebra method shows knot unknotting number is (c+1)/2.

As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive normal form (OR-of-ANDs). A principled objective function is proposed to trade …

Probabilistic learning for binary classification with categorical variables.

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic genera…

Survey on learning Boolean functions in computational theory.

New algorithm learns halfspaces over hypercube with random bit flips.

A Bayesian Boolean Matrix Factorization for cancer genomics

Minimalist softmax attention learns constrained Boolean functions with supervision.

The ability to compose learned skills to solve new tasks is an important property of lifelong-learning agents. In this work, we formalise the logical composition of tasks as a Boolean algebra. This allows us to formulate new tasks in terms of the negation, disjunction and conjunction of a set of base tasks. We then sho…

New framework reduces LLM complexity by directly finetuning in Boolean domain.

GETF efficiently decomposes large-scale Boolean tensors.

This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in w…

We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning. The underlying computation is given by a looped Boolean circuit whose graph is a perfect $ν$-ary tree ($ν\ge 2$), with outputs recursively fed back as inputs across computation ro…

We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively bypassing the problem of learning in large RBMs, and creating a system able to mod…

Transformers learn sparse Boolean functions through RL and SFT, revealing distinct learning behaviors.

Boolean matrix factorization (BMF) is a popular and powerful technique for inferring knowledge from data. The mining result is the Boolean product of two matrices, approximating the input dataset. The Boolean product is a disjunction of rank-1 binary matrices, each describing a feature-relation, called pattern, for a g…

Study examines noise sensitivity of DNNs for binary classification.

We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.

This paper introduces the combinatorial Boolean model (CBM), which is defined as the class of linear combinations of conjunctions of Boolean attributes. This paper addresses the issue of learning CBM from labeled data. CBM is of high knowledge interpretability but naïve learning of it requires exponentially large compu…

Theory of ends of spaces using linear algebra.

Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matri…

The study optimizes polynomial regression for learning under Gaussian distributions.

It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed to solve Boolean satisfiability (SAT), it remains a mystery of GNN-based solvers for more complex predicate logic formulae. In this work,…

Study links neural network inductive bias, feature learning, and generalization on Boolean functions.

The study explores how Matrix Product States can represent boolean and continuous functions.

During the past few years Boolean matrix factorization (BMF) has become an important direction in data analysis. The minimum description length principle (MDL) was successfully adapted in BMF for the model order selection. Nevertheless, a BMF algorithm performing good results from the standpoint of standard measures in…

Cube category simplifies set modeling.

Efficiently estimate Boolean product distribution parameters from truncated samples.

Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean satisfiability. Our…

Extends quantum learning theory to multiclass and online settings.

Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world applications.This study proposed a new probabilistic algorithm free of assumptions of lat…

The degree-$d$ Chow parameters of a Boolean function $f: \{-1,1\}^n \to \mathbb{R}$ are its degree at most $d$ Fourier coefficients. It is well-known that degree-$d$ Chow parameters uniquely characterize degree-$d$ polynomial threshold functions (PTFs) within the space of all bounded functions. In this paper, we prove …

The study explores the compressive power of Boolean threshold autoencoders, finding that seven layers are necessary but three are not.

We show a connection between the Fourier spectrum of Boolean functions and the REINFORCE gradient estimator for binary latent variable models. We show that REINFORCE estimates (up to a factor) the degree-1 Fourier coefficients of a Boolean function. Using this connection we offer a new perspective on variance reduction…