Paper solves low-rank Boolean matrix approximation using integer programming.
problem Finding low-rank approximations to Boolean matrices.
method Integer programming formulation with polynomial variables and constraints.
result First computationally tractable integer programming approach.
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.
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…
The paper introduces false discovery rate control for BMF to avoid noisy patterns.
problem No guarantees exist for BMF patterns being real, not just noise.
method Proposes false discovery rate (FDR) to control BMF patterns, proving bounds on FDR.
result Improved BMF algorithms using theoretical FDR bounds for rank selection.
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 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…
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.
Bayesian model learns optimal number of latent dimensions for Boolean data.
problem Optimal number of latent dimensions in Boolean data models.
method Indian Buffet Process prior over factor matrices for non-parametric Boolean factorisation.
result Posterior inference is efficient and the number of latent dimensions is transparently inferred.
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
New algorithm uses random matrices for neural network training without synaptic weight symmetries.
problem Training neural networks efficiently and without synaptic weight symmetries.
method Contrastive Hebbian learning with random feedback weights.
result Random contrastive Hebbian learning achieves better computational models for learning.
Decision Machines embeds decision trees into vector spaces for improved optimization.
problem Overfitting and difficulty in finding optimal decision tree structure.
method Embedding Boolean tests into a binary vector space and representing tree structure as matrices.
result Optimized decision trees with enhanced predictive power.
Paper proposes continual learning for sentence encoders.
problem Optimize sentence encoders for new corpora while maintaining old corpus accuracy.
method Initialize encoders with corpus-independent features, update using Boolean operations of conceptor matrices.
result Proposed sentence encoder can continually learn features from new corpora.
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
problem Finding a symmetric factorization of a given matrix into a sparse, Boolean matrix.
method Polynomial-time algorithm based on bootstrapping higher-order information and tensor decomposition.
result A matrix with full column rank can be recovered with high probability when the matrix size is sufficiently large.
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.
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.
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.
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.
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.
GRAB efficiently learns combinatorial Boolean models from data.
problem Learning combinatorial Boolean models from labeled data is computationally expensive.
method GRAB algorithm, using L1-regularized loss minimization and frequent itemset mining. result GRAB efficiently learns CBM with reduced computational time and improved accuracy.
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.
New algorithm for robust Boolean matrix factorization handles noise and missing data.
problem Robust probabilistic Boolean matrix factorization in the presence of noise and missing values.
method Probabilistic Expectation Maximization algorithm without latent factor assumptions.
result Outperforms state-of-the-art probabilistic algorithms on real data.
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.
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.
Efficiently decomposes tensors with Boolean factors using BMP.
problem Tensor decomposition with Boolean factors is challenging due to non-convexity and combinatorial constraints.
method Binary Matching Pursuit (BMP) iteratively searches for atoms in a greedy fashion, solving the greedy atom search step via MAXCUT-like boolean quadratic program.
result BMP converges sublinearly to the optimal solution and recovers factors under mild conditions.
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.
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.
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 new BMF algorithm outperforms existing methods using MDL.
problem Developing a BMF algorithm that performs well across multiple metrics.
method From-below Boolean matrix factorization algorithm based on MDL principle.
result The proposed algorithm outperforms existing methods in various experiments.
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.
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.
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.
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.
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.
Theory of ends of spaces using linear algebra.
problem Understanding ends of spaces at infinity.
method Developing a theory using scale, sub-Boolean algebras, and linear algebra.
result All known types of ends are special cases of a linear algebraic process.
Probabilistic Boolean tensor decomposition improves accuracy and scalability.
problem Approximating multi-way binary data with interpretable low-rank factors.
method Scalable sampling-based posterior inference exploiting combinatorial structure.
result Maximum a posteriori decompositions outperform existing techniques.
New findings show that common optimization algorithms struggle with random problems.
problem Finding near-optimal solutions to random optimization problems.
method Low-degree polynomials, Boolean circuits, and Langevin dynamics.
result These algorithms fail to produce nearly optimal solutions with high probability.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
problem Understanding how neural networks learn and generalize on Boolean data.
method End-to-end analysis of depth-2 discrete fully connected networks and DNF formulas, using Monte Carlo learning.
result Predictable training dynamics and interpretable features emerge, linking inductive bias and generalization.
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.
New approach uses Boolean circuits to optimize neural networks.
problem Improving efficiency of neural network implementations on hardware accelerators.
method Formalized neural networks as Boolean circuits, showing binarized networks are functionally complete.
result Binarized neural networks are functionally complete, suggesting new possibilities for neural network accelerators.
The study explores how Matrix Product States can represent boolean and continuous functions.
problem Representing arbitrary boolean and continuous functions using Matrix Product States.
method Developed a construction method for MPS to represent boolean gates and proved density in continuous function space.
result MPS can accurately represent arbitrary boolean functions and continuous functions densely.
Cube category simplifies set modeling.
problem Modeling set operations efficiently.
method Introducing interval-preserving monotone functions between finite Boolean lattices.
result Cube category facilitates model structures equivalent to simplicial sets.
Efficiently estimate Boolean product distribution parameters from truncated samples.
problem Estimating parameters of Boolean product distributions from truncated samples.
method Introducing fatness of truncation set, using membership queries, and adapting Stochastic Gradient Descent.
result Efficiently learn Boolean product distributions from truncated samples with small sample complexity.
Extends quantum learning theory to multiclass and online settings.
problem Quantum learning theory for batch and online learning.
method Adapts classical models to quantum settings, introduces new online learning model.
result Quantum and classical sample complexities have the same form for various learning scenarios.
New methods protect malware classification networks from adversarial attacks.
problem Adversarial perturbations compromise malware classification networks.
method Training restricted networks with non-negative weight restrictions and relaxing constraints.
result Improved classifier accuracy while maintaining resistance to adversarial attacks.
Paper verifies properties of binarized neural networks using SAT solvers.
problem Verifying properties of deep neural networks.
method Exact Boolean encoding of binarized neural networks, SAT solvers, counterexample-guided search.
result Demonstrates scalability to medium-size deep neural networks for robustness verification.