pLogicNet combines logic rules and embeddings for efficient knowledge graph reasoning.
problem Efficiently predicting missing facts in knowledge graphs.
method Combines Markov Logic Networks with knowledge graph embeddings using variational EM algorithm.
result pLogicNet outperforms traditional methods on multiple knowledge graphs.
Paper introduces a new framework combining deep learning and logic for relational data.
problem Scalability and flexibility of deep learning methods for relational data.
method Combines auto-encoding principle with first-order logic and logic programs.
result Latent representations are more accurate, flexible, and interpretable.
Graphs improve theorem proving in higher-order logic.
problem Challenges in converting higher-order logic formulas into graph-based representations.
method Used graph neural networks (GNNs) to represent and search higher-order logic.
result GNNs outperform state-of-the-art methods in higher-order theorem proving.
Quantum methods speed up inference in Markov logic networks.
problem Efficient inference in Markov logic networks (MLNs).
method Analysis of graph structures and application of quantum protocols to Gibbs sampling.
result Exponential speedup in approximate probabilistic inference using quantum methods.
Paper augments neural nets with logic for improved performance.
problem Training neural networks with declarative knowledge without extra parameters.
method Systematically compiles logical statements into computation graphs that augment neural networks.
result Knowledge-augmented networks significantly improve performance, especially in low-data scenarios.
Paper introduces techniques to learn higher-order programs, improving predictive accuracy and reducing learning times.
problem Expressing and learning complex programs in ILP.
method Extending meta-interpretive learning to support higher-order definitions as background knowledge.
result Learning higher-order programs reduces hypothesis space and sample complexity, improving predictive accuracy and reducing learning times.
RWTNs improve NTN performance in SRL tasks.
problem Improving NTN performance in SRL tasks.
method Randomly weighted, untrained tensors in NTN encoder network.
result RWTNs outperform LTNs in SII tasks.
Two scalable methods for PSL structure learning improve runtime and AUC.
problem Efficiently learning clauses for probabilistic soft logic models.
method Greedy search and a novel optimization method combining data-driven clause generation and PPLL objective.
result PPLL achieves up to 15% AUC gains and an order of magnitude runtime speedup.
Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop…
RelNN models object properties alongside relations for relational learning.
problem Combining deep learning with first-order logic for noisy domains.
method Developed RelNNs by adding hidden layers to relational logistic regression, learning latent properties for objects.
result Initial experiments show RelNNs are promising models for relational learning.
LYRICS integrates deep learning and logic inference for complex decision-making.
problem Combining deep learning with symbolic logic for intelligent decision-making.
method LYRICS provides a generic interface layer that integrates TF models with FOL knowledge, converting constraints into optimization problems.
result LYRICS enables learning under logical constraints, improving model performance and decision-making.
Paper formalizes analogy between data sets and models using Hoare logic.
problem Lack of formal criteria for transferring machine learning models between data domains.
method Formalization of analogy using first-order logic and Hoare logic, rigorous theorem proving.
result Rigorous formalization of analogy in knowledge transfer between machine learning models.
New rack invariants detect geometric properties of Legendrian knots.
problem Detecting geometric properties of Legendrian knots.
method Introducing Legendrian racks, a generalization of quandle invariants.
result These invariants form a natural generalization of quandle invariants.
The paper explains deep neural network predictions using logical proxies.
problem Creating understandable explanations for deep neural network predictions.
method Randomized propositionalization and Bayes-like approach to identify logical proxies.
result Models in first-order logic can approximate DRM's predictions in local regions.
NMLNs use neural networks to learn relational structure from data.
problem Learning implicit rules from data without explicit logic rules.
method Combines Markov logic with neural networks to learn relational structure.
result NMLNs can predict in settings without explicit logic rules.
Determining when two knots are equivalent (more precisely isotopic) is a fundamental problem in topology. Here we formulate this problem in terms of Predicate Calculus, using the formulation of knots in terms of braids and some basic topological results. Concretely, Knot theory is formulated in terms of a language with…
Unified approach tackles logical constraints in mixed-integer optimization.
problem Logical constraints in mixed-integer optimization problems.
method Express logical constraints non-linearly, reformulate as convex binary optimization, solve using outer-approximation.
result Solves problems faster and at larger scale than existing methods.
Study logical generalization in GNNs using a new benchmark.
problem Understanding how GNNs adapt to new logical tasks.
method Developed GraphLog benchmark suite for logical tasks, evaluated GNNs in supervised, pretraining, and continual learning settings.
result Logical diversity during training affects GNNs' ability to generalize.
GraIL predicts relations by reasoning over subgraphs, outperforming embeddings.
problem Relation prediction in knowledge graphs using latent representations is limited.
method Graph neural network with inductive bias to learn entity-independent relational semantics.
result GraIL outperforms existing rule-induction baselines in the inductive setting.
Framework predicts logical queries on incomplete knowledge graphs.
problem Complex logical queries involving multiple unobserved edges and entities.
method Low-dimensional embeddings and learned geometric operations.
result Efficient predictions with linear time complexity in query variables.
Novel semi-supervised method for online structure learning in noisy data streams.
problem Discovering complex relations in noisy data streams with limited labelled data.
method Combines graph-cut minimization and first-order logic for online, single-pass label completion.
result Improves accuracy of structure learning system by completing missing labels.
End-to-end model detects emotions and predicts Facebook reactions.
problem Detecting emotions and predicting reactions on Facebook posts.
method Jointly learns emotions and reactions using neural model with logic formulas as constraints.
result Model improves both emotion classification and reaction prediction.
Combines neural networks and logic circuits for interpretable, accurate, and cost-effective learning.
problem Lack of generalizability and interpretability in neural networks and high hardware cost in logic circuits.
method Trains a neural network, then translates it to random forests, and finally to AND-Inverter logic.
result The pipeline maintains greater accuracy and minimizes logic complexity.
DA-MLNs improve MLNs by scaling feature weights based on domain size.
problem Extreme probabilities in MLNs when testing on different domain sizes.
method DA-MLNs divide ground feature weights by a scaling factor that depends on the number of connections.
result DA-MLNs achieve significantly higher accuracy on domains with different sizes compared to standard MLNs.
Transformers improve logical reasoning on longer proofs but struggle with length.
problem Understanding systematic generalization in neural proof generation.
method Soft theorem-proving using Transformer models, evaluating logical consistency and inference accuracy.
result Transformers improve generalization with longer proofs but have difficulty with length.
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.
Paper proposes using logic networks to inject prior knowledge for better reinforcement learning.
problem Improving reinforcement learning agents with prior knowledge of object and event semantics.
method Integrates first-order logic grounded in deep neural networks as prior knowledge into reinforcement learning algorithms.
result Demonstrates that combining symbolic and image layers in a single decision module improves learning efficiency.
Study on topological order on fractal geometries, proving no-go theorem and fault-tolerant gates.
problem Investigating topological order on fractal geometries embedded in n dimensions.
method Using quantum error-correcting codes and systolic geometry to diagnose topological order.
result Proves no-go theorem for topological order on 2D fractals, survival on higher dimensions, and construction of fault-tolerant gates.
Paper improves robustness certification by integrating ML and logical reasoning.
problem Limited robustness certification under perturbation radius.
method Integrates statistical ML models with logical reasoning using Markov logic networks.
result First certified robustness bound for MLN derived and experimentally validated.
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.
We show that the Kuratowski imbedding of a Riemannian manifold in L^\infty, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every C>0. Our key tool is the first variation formula thought of…
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
problem Characterize polyhedrally-complete intermediate logics.
method Developed Nerve Criterion to characterize polyhedrally-complete logics combinatorially.
result Nerve Criterion provides a necessary and sufficient condition for polyhedrally-completeness.
Unified model learns concepts across domains like left and right.
problem Limited generalization of language concepts in inference-only models.
method Logic-Enhanced Foundation Model (LEFT) with a differentiable, domain-independent program executor.
result LEFT flexibly learns and reasons with concepts across 2D images, 3D scenes, human motions, and robotic manipulation.
Paper proposes a novel RRL framework that learns from images and incorporates expert knowledge.
problem Lack of effective methods to incorporate expert background knowledge and learn from non-relational data in RRL.
method Differentiable Inductive Logic Programming (ILP) for learning relational information from images and incorporating expert knowledge.
result Efficacy demonstrated on various environments and datasets, showing improved learning and generalization.
A fundamental challenge in developing high-impact machine learning technologies is balancing the need to model rich, structured domains with the ability to scale to big data. Many important problem areas are both richly structured and large scale, from social and biological networks, to knowledge graphs and the Web, to…
An ensemble approach learns vector-weighted formulae for RLR.
problem Learning Relational Logistic Regression (RLR) with vector-weighted features.
method Functional-gradient boosting methods for probabilistic logic models.
result Our approach outperforms other methods for learning RLR.
This paper introduces a new reward shaping method for average-reward reinforcement learning.
problem Speeding up convergence to an optimal policy in average-reward reinforcement learning tasks.
method Developed a temporal logic-based approach to automatically generate reward shaping functions.
result The optimal policy can be recovered using the proposed reward shaping framework.
Algorithm explains XGBoost models using LIME and ILP.
problem Explain XGBoost model behavior using logic programs.
method Use LIME to select features, then apply LIME-FOLD heuristic ILP to learn non-monotonic logic programs.
result Significant improvement in classification metrics with fewer rules.
A framework isolates VQA reasoning from perception for better model evaluation.
problem Improper separation of visual perception and reasoning in VQA models.
method Introducing a framework and a top-down calibration technique to decouple reasoning from perception.
result Improved evaluation of VQA models by separating reasoning from perception.
Intermediate logic of all convex polyhedra is axiomatized.
problem Defining and axiomatizing intermediate logic for convex polyhedra.
method Using Jankov-Fine formulas, classical polyhedral geometry, and p-morphic images to establish completeness.
result A finite axiomatisation of PL for all convex polyhedra.
Improves deep learning interpretability through logical network construction.
problem Difficulty in understanding and explaining deep neural networks, especially convolution neural networks.
method Proposes a method to construct a logical network based on fully connected layers to improve interpretability.
result Improves the interpretability of deep learning processes and models.
BOiLS optimizes circuit quality using Bayesian optimization.
problem Optimizing circuits with complex search spaces.
method Adapting Bayesian optimization to logic synthesis, using Gaussian process kernels and trust-region constrained acquisitions.
result Demonstrated superior performance in sample efficiency and QoR values.
DRUM discovers interpretable rules from knowledge graphs for unseen entities.
problem Inductive link prediction on unseen entities and lack of interpretability.
method Differentiable approach using bidirectional RNNs for low-rank tensor approximation.
result DRUM outperforms existing methods in inductive link prediction.
Study shows AI can learn to conform to logical restraining specifications.
problem Learning AI goals to match logical restraining specifications.
method Reinforcement learning with LTLf/LDLf specifications.
result AI can learn to conform to logical restraining specifications under general circumstances.
Paper tackles learning probabilistic logic programs for continuous data.
problem Learning meaningful symbolic representations from continuous data.
method Leverages piecewise polynomial function approximation theory for density function learning.
result First steps towards inducing probabilistic logic programs for continuous data.
AlphaLogics mines market logic to generate interpretable alpha factors.
problem Complex, opaque alpha factors from factor mining overlook market logic.
method Market Logic Mining, Factor Generation and Optimization, Market Logic Generation and Optimization.
result AlphaLogics improves predictive metrics and risk-adjusted returns over baselines.
NLN learns logical reasoning from neural networks.
problem Lack of logical reasoning in deep neural networks.
method Dynamic neural architecture that builds computational graph based on logical expressions, learns logical operations as neural modules, conducts propositional logical reasoning.
result NLN significantly outperforms state-of-the-art models on collaborative filtering and personalized recommendation tasks.
Paper studies a universal logical operator for deep networks, improving interpretability.
problem Learning a universal logical operator for deep convolution networks without manual prescription.
method Exploration of different logical operators (AND, OR, XOR) and learning a universal one.
result Insightful observations lead to a novel logical interpretation of deep convolution networks.