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.
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 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.
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.
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 …
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
New neural network model with rectified edges for classification.
problem Classifying data with monotone properties.
method Introduces rectified wire networks with a novel learning algorithm.
result Demonstrates SDA algorithm achieving zero loss for correct classification.
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.
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 show how to incorporate ethical principles into machine learning models.
problem Machine-learned systems often violate deontological ethical principles.
method Add shape constraints to models to ensure positive responses to relevant inputs.
result Shape constraints help produce more ethical AI by avoiding penalties on good attributes.
Efficiently optimizes boolean functions using multilinear polynomials and exponential weight updates.
problem Optimizing boolean functions over the boolean hypercube with high computational cost.
method Proposes a computationally efficient algorithm using multilinear polynomials and exponential weight updates.
result Improves computational time up to several orders of magnitude compared to state-of-the-art algorithms.
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.
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.
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.
The paper explores how neural networks learn logical functions and their generalization error.
problem Learning logical functions with neural networks and understanding generalization error.
method Gradient descent on neural networks, analyzing noise-stability and Boolean influence.
result Gradient descent on certain neural architectures tends to favor low-degree representations, impacting generalization error.
Paper proposes an iterative NAS technique inspired by Boolean function learning.
problem Challenges in Neural Architecture Search (NAS).
method Inspired by algorithms for learning low-degree sparse Boolean functions.
result Validated on DARTs and NAS-Bench-201, providing theoretical analysis.
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.
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.
Paper computes link determinants using Fourier-Hadamard transforms.
problem Computing determinants of complex link structures.
method Fourier-Hadamard transforms of Boolean functions.
result Determinant of centrally symmetric links with even components equals zero.
Paper shows how to identify and reconstruct degree-d PTFs robustly from their Fourier coefficients.
problem Identifying and reconstructing degree-d polynomial threshold functions (PTFs) from their Fourier coefficients.
method Proves a robust version of the theorem that degree-d Chow parameters uniquely characterize degree-d PTFs, and uses this to develop efficient algorithms.
result Boolean degree-d PTFs are robustly identifiable from their degree-d Chow parameters.
Neural networks can learn Boolean circuits with local correlation.
problem Learning Boolean circuits with neural networks is computationally hard.
method Observing local correlation between input patterns and target labels, focusing on tree-structured Boolean circuits.
result Local correlation determines the success or failure of optimization in learning Boolean circuits.
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…
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.
Fourier analysis improves REINFORCE for binary models.
problem Improving gradient estimation for binary latent variable models.
method Connecting Fourier spectrum of Boolean functions to REINFORCE and developing low-variance unbiased gradient estimators.
result REINFORCE estimates degree-1 Fourier coefficients of a Boolean function.
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 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.
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
The paper explores the difficulty of robust machine learning models.
problem Understanding the vulnerability of machine learning models to adversarial attacks.
method The study uses computational learning theory to analyze the feasibility of robust learning from both sample and computational complexity perspectives.
result No non-trivial concept class can be robustly learned in the distribution-free setting against a single-bit adversary, and the class of monotone conjunctions cannot be robustly learned under the uniform distribution against an adversary that can perturb ω(logn) bits. 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.
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.
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…
This study shows neural nets can approximate Turing machines with meaningful statistical properties.
problem Theoretical limitations in approximating Turing machines with neural networks.
method Formal definition of statistically meaningful approximation, analysis of boolean circuits and Turing machines using neural nets.
result Transformers can statistically meaningfully approximate Turing machines with polynomial sample complexity.
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.
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.
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.