LIBRE learns interpretable Boolean rules from data.
problem Creating interpretable classifiers in imbalanced settings.
method Ensemble of weak learners on random feature subsets, combined with a simple union.
result Efficiently balances prediction accuracy and interpretability.
Estimates overlap in observational studies for causal effect estimation.
problem Overlap between treatment groups is crucial for causal effect estimation.
method Formalizes overlap estimation as a binary classification problem with Boolean rule classifiers.
result Rules provide interpretable explanations for causal conclusions.
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 …
This paper explores how boolean formulas can be learned by deep neural networks.
problem Understanding the learnability of boolean formulas by deep neural networks.
method Analysis of boolean formulas associated with model-sampling benchmarks, combinatorial optimization problems, and random 3-CNFs.
result Neural networks outperform rule-based systems and pure symbolic approaches in learning boolean formulas.
Data discretization is an important step in the process of machine learning, since it is easier for classifiers to deal with discrete attributes rather than continuous attributes. Over the years, several methods of performing discretization such as Boolean Reasoning, Equal Frequency Binning, Entropy have been proposed,…
In this technical report we presented a novel approach to machine learning. Once the new framework is presented, we will provide a simple and yet very powerful learning algorithm which will be benchmark on various dataset. The framework we proposed is based on booleen circuits; more specifically the classifier produced…
Study examines noise sensitivity of DNNs for binary classification.
problem Understanding non-robustness of DNN classifiers under noise.
method Defined and extended noise sensitivity and stability concepts for Boolean functions, applied to DNN models.
result Sorted out the relation between definitions and properties of DNN architectures under noise.
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate scalable sampling-based posterior inference by exploitation of the combinatorial…
Neural networks favor Boolean functions with low entropy.
problem Understanding the inductive bias of neural networks.
method Analyzing a single-layer perceptron with random initial weights.
result There is a strong intrinsic bias towards low entropy Boolean functions.
There is a growing body of literature showing that deep neural networks are vulnerable to adversarial input modification. Recently this work has been extended from image classification to malware classification over boolean features. In this paper we present several new methods for training restricted networks in this …
Boolean logic used for neural network training and inference, with convergence analysis.
problem Discrete optimization in neural networks with Boolean logic.
method Boolean logic backpropagation with convergence analysis.
result First convergence analysis for Boolean logic in neural networks.
Improved bounds on combining hypothesis classes for binary functions.
problem Understanding how to combine hypothesis classes for binary functions.
method Established upper bounds on Littlestone and threshold dimensions for combined classes.
result Upper bounds are nearly tight and give exponential improvements.
New approach to certifiably robust neural networks using Boolean function perspective.
problem Lack of principled understanding and certified robustness for ℓ∞ perturbations. method New perspective on Boolean functions, deriving impossibility results, and developing a unified Lipschitz network.
result Unified Lipschitz network that bypasses expressive power limitations and achieves better certified robustness.
Study on functions computed by deep-layered machines finds same distribution in neural networks and Boolean circuits.
problem Understanding the space of functions computed by deep-layered machines.
method Investigation of Boolean functions on random-layered machines, including neural networks and Boolean circuits.
result The space of functions computed at large depth limit is characterized and the macroscopic entropy of Boolean functions is either monotonically increasing or decreasing with depth.
We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the algorithm succeeds with respect to {\em any} distribution on the unit ball in n …
New Fourier analysis method for non-uniform Boolean hypercube.
problem Non-uniform probability measures on the Boolean hypercube.
method ANOVA-based decomposition, explicit basis, least squares problem.
result Generalization of Fourier analysis for arbitrary probability measures.
A new deep learning method using Boolean logic reduces training and inference energy.
problem High computational and energy costs in deep learning training and inference.
method Introduces Boolean weights and inputs for efficient training using Boolean logic.
result Achieves full-precision accuracy in ImageNet classification and surpasses state-of-the-art results in semantic segmentation.
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…
Motivation: Thanks to digitization, we often have access to large databases, consisting of various fields of information, ranging from numbers to texts and even boolean values. Such databases lend themselves especially well to machine learning, classification and big data analysis tasks. We are able to train classifier…
New Boolean algebra method shows knot unknotting number is (c+1)/2.
problem Finding the minimum number of region crossing changes to unknot a knot.
method Boolean algebra applied to region crossing changes.
result Region unknotting number is (c+1)/2 for any knot with crossing number c.
A new method relaxes Boolean Matrix Factorization to make it more efficient.
problem High computational cost of solving NP-hard combinatorial optimization problems in Boolean Matrix Factorization.
method Proposes a proximal gradient algorithm using an elastic-binary regularizer to relax BMF.
result Demonstrates improved runtime and better recall, loss, and interpretability on real-world data.
Probabilistic learning for binary classification with categorical variables.
problem Binary classification with categorical covariates.
method Probabilistic analysis and two algorithms for learning boolean functions.
result Effective learning of boolean functions from binary data.
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…
New machine learning method uses algorithmic complexity for non-differentiable spaces.
problem Machine learning on non-differentiable spaces.
method Introduces complexity theory in machine learning, using algorithmic complexity for regression and classification.
result More generalizable and resilient to random attacks compared to traditional methods.
Survey on learning Boolean functions in computational theory.
problem Learning Boolean function classes in computational theory.
method Overview of known results in PAC and related models.
result Discussion of various learning results for Boolean functions.
SigD2 reduces noisy rules in rule-based classifiers for better accuracy and readability.
problem Redundant and noisy rules in rule-based classifiers reduce model accuracy and readability.
method Two-stage pruning strategy and ensemble methods (bagging and boosting) to reduce noise and improve model performance.
result SigD2 and ACboost ensemble models outperform state-of-the-art classifiers in terms of accuracy and rule count.
A Bayesian Boolean Matrix Factorization for cancer genomics
problem Identifying coordinated feature changes in cancer
method Bayesian Boolean Matrix Factorization
result Captures widespread, near-simultaneous chromosome-number changes
Minimalist softmax attention learns constrained Boolean functions with supervision.
problem Learning k-bit Boolean functions, especially AND and OR. method Minimalist single-head softmax-attention mechanism with teacher forcing.
result Minimalist attention can solve Boolean tasks with supervision, but not without.
Study classifies ruled surfaces critical to Dirichlet energy.
problem Identifying ruled surfaces critical to Dirichlet energy.
method Explicit parametrization of ruled surfaces.
result Classification of ruled surfaces as critical points of Dirichlet energy.
Novel approach for creating interpretable classifiers using bilevel optimization of split-rules in NLDTs.
problem Creating highly accurate and easily interpretable classifiers for practical applications.
method Representing classifiers as assemblies of simple mathematical rules using NLDTs with evolutionary bilevel optimization.
result The approach ensures interpretability while achieving high accuracy on various classification problems.
New framework reduces LLM complexity by directly finetuning in Boolean domain.
problem Reducing the complexity of large language models (LLMs) while maintaining performance.
method Proposes a novel framework using multi-kernel Boolean parameters for direct finetuning in the Boolean domain.
result Significantly reduces complexity during both finetuning and inference, outperforming recent techniques.
GETF efficiently decomposes large-scale Boolean tensors.
problem Efficiently factorizing large-scale Boolean tensors.
method Geometric Expansion for all-order Tensor Factorization (GETF).
result GETF significantly improves reconstruction accuracy and efficiency.
We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of M arbitrary training classifiers. If the classifiers are consistent, then so is the aggregation rule. Moreover, asymptotically the aggregation rule b…
Rule-based classifiers quantify uncertainty using Bernoulli random variables.
problem Quantifying the uncertainty of precision estimates for rule-based text classifiers.
method Treat partitions of sub-strings as Bernoulli random variables, compare means using statistical tests, and combine classifiers using Dempster-Shafer theory.
result The approach can be used to combine binary classifiers into a multi-label classifier.
Paper classifies ruled surfaces in Lorentz-Minkowski space for a specific flow.
problem Classifying ruled surfaces in Lorentz-Minkowski space.
method Examining homothetic self-similar solutions of the inverse mean curvature flow.
result Existence of two classes of non-cylindrical homothetic solitons.
Transformers learn sparse Boolean functions through RL and SFT, revealing distinct learning behaviors.
problem Learning sparse Boolean functions with Transformers.
method Reinforcement Learning (RL) with process rewards and Supervised Fine-Tuning (SFT).
result RL learns the whole CoT chain simultaneously, while SFT learns step by step.
CIfly simplifies causal inference tasks with linear-time reachability primitives.
problem Efficiently solving complex causal inference problems.
method Formalizes reachability as a core operation, builds on state-space graphs, and uses rule tables.
result CIfly algorithms run in linear time, outperforming existing methods.
Graph neural networks struggle with proving unsatisfiability in complex logical formulas.
problem Proving unsatisfiability in complex logical formulas.
method Investigating the limitations of graph neural networks in logical reasoning tasks.
result Graph neural networks may fail in certifying unsatisfiability in Boolean formulae.
Paper improves variational inference on Boolean hypercube using quantum methods.
problem Improving variational inference for pairwise Markov random fields on the Boolean hypercube.
method Quantum relaxations of the Kullback-Leibler divergence for upper-bounds, primal-dual optimization, and greedy selection of hierarchies.
result Efficient algorithm and improved bounds for variational inference.
A Boolean algebra formalizes task composition for reinforcement learning.
problem Formalizing task composition for efficient learning and problem-solving.
method Formalized tasks as a Boolean algebra, learning goal-oriented value functions, and composing them to solve new tasks.
result Agents can solve new tasks without additional learning by composing value functions in specific ways.
The paper classifies ruled surfaces in a specific space that move in a special way.
problem Understanding how surfaces move in a special space.
method Classifying ruled surfaces as translating solitons of inverse mean curvature flow.
result Existence of non-cylindrical ruled translating solitons.
Develops a fast BMF approach for binary matrices.
problem Finding patterns in binary matrices for various applications.
method MEBF (Median Expansion for Boolean Factorization) using geometric segmentation and heuristic submatrix identification.
result Superior performance in reconstruction error and computational efficiency compared to existing methods.
Subdivision rules create sequences of nested cell structures on CW-complexes, and they frequently arise from groups. In this paper, we develop several tools for classifying subdivision rules. We give a criterion for a subdivision rule to represent a Gromov hyperbolic space, and show that a subdivision rule for a hyperb…
SESSC clusters fuzzy rules for TSK classifiers, improving performance with label info.
problem Lack of supervised clustering for TSK fuzzy classifiers.
method SESSC integrates within-cluster compactness, between-cluster separation, and label information.
result SESSC initialization outperforms other clustering methods, especially for small rule numbers.
Paper proposes algorithms for BMF using integer programming.
problem Approximating binary input matrix as product of two smaller binary factors.
method Alternating optimization strategy using integer programming to solve subproblems and combine solutions.
result Proposed algorithms outperform state of the art on medium-scale problems.
The paper develops algorithms for Boolean matrix factorization using IP and heuristics.
problem Approximating binary input matrices as products of smaller binary factors.
method Alternating optimization with integer programming and greedy/local-search heuristics.
result Proposed methods improve scalability and performance compared to existing techniques.
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…
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.