We introduce neural Markov logic networks (NMLNs), a statistical relational learning system that borrows ideas from Markov logic. Like Markov logic networks (MLNs), NMLNs are an exponential-family model for modelling distributions over possible worlds, but unlike MLNs, they do not rely on explicitly specified first-ord…
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48 results for “Markov logic networks”
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference …
Combining logic and probability has been a long stand- ing goal of AI research. Markov Logic Networks (MLNs) achieve this by attaching weights to formulas in first-order logic, and can be seen as templates for constructing features for ground Markov networks. Most techniques for learning weights of MLNs are domain-size…
Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is th…
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.
Effectively combining logic reasoning and probabilistic inference has been a long-standing goal of machine learning: the former has the ability to generalize with small training data, while the latter provides a principled framework for dealing with noisy data. However, existing methods for combining the best of both w…
Statistical relational frameworks such as Markov logic networks and probabilistic soft logic (PSL) encode model structure with weighted first-order logical clauses. Learning these clauses from data is referred to as structure learning. Structure learning alleviates the manual cost of specifying models. However, this be…
Proposes PRMs for interpreting financial risk concept drift.
problem Concept drift in high-stakes predictions like credit risk.
method Probabilistic Rule Models (PRMs) using Markov Logic Networks.
result Interpretable rules explain borrower risk changes.
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…
Explaining neural network computation in terms of probabilistic/fuzzy logical operations has attracted much attention due to its simplicity and high interpretability. Different choices of logical operators such as AND, OR and XOR give rise to another dimension for network optimization, and in this paper, we study the o…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the ability of logical reasoning. However, the concrete ability of logical reas…
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.
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.
Deep reinforcement learning under signal temporal logic constraints using Lagrangian relaxationstat.ML
Study uses DRL with Lagrangian relaxation to solve temporal control tasks with STL constraints.
problem Optimal control problems with temporal logic constraints.
method Extended CMDP formulation, Lagrangian relaxation, two-phase constrained DRL algorithm.
result Demonstrated learning performance of the proposed algorithm through simulations.
Neural Logic Reasoning integrates deep learning and symbolic logic for better prediction tasks.
problem Lack of cognitive reasoning in deep neural networks limits their ability to solve complex prediction tasks.
method Proposes Logic-Integrated Neural Network (LINN) that learns logical operations and conducts propositional logical reasoning.
result LINN significantly outperforms state-of-the-art recommendation models in Top-K recommendation.
Logical neural networks solve mazes by filling dead ends, but not all methods generalize well.
problem Understanding how logical neural networks extrapolate solutions to mazes.
method Examined recurrent and implicit neural networks trained on maze-solving tasks.
result Models fail to generalize well to diverse maze sizes, suggesting limitations in learning scalable algorithms.
We propose a method for efficient training of Q-functions for continuous-state Markov Decision Processes (MDPs) such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a modal logic, can express a wide range of time-dependent logical properties (including "safety") that…
Transformers learn to predict temporal logic solutions from classical solver outputs.
problem Training neural networks on logic problem solutions for verification.
method Training a Transformer on generated training data from classical solvers, focusing on one solution per formula.
result Transformers can predict correct solutions to temporal logic problems, even to unseen benchmarks.
Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian classifiers, DNN suffer from bad interpretability where we understand by interpr…
ENN neural network learns logical syllogisms using Euler diagrams.
problem Traditional neural networks struggle with logical reasoning, especially syllogisms.
method ENN represents logical relations as Euler diagrams, optimizing syllogism structures with a novel back-propagation algorithm.
result ENN can precisely represent and reason with all 24 syllogism structures.
We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifier…
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…
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.
Unified tensor network formalism for combining neural and symbolic AI.
problem Combining neural and symbolic AI approaches remains a challenge.
method Introduces a tensor network formalism capturing sparsity principles.
result Unified treatment identifies tensor network contractions as a fundamental inference class.
Deep networks can be understood as logical circuits, improving interpretability and generalization.
problem Lack of interpretability in deep neural networks.
method Hierarchical decomposition of DNN discrete classification map into logical combinations of intermediate classifiers.
result Deep networks can be interpreted as logical circuits with improved generalization.
Reinforcement Learning (RL) is a widely employed machine learning architecture that has been applied to a variety of control problems. However, applications in safety-critical domains require a systematic and formal approach to specifying requirements as tasks or goals. We propose a model-free RL algorithm that enables…
AI in finance uses quantum logic for better decision-making.
problem Improving financial decision-making models using AI.
method Application of quantum logic in machine learning techniques.
result Advantages of quantum-inspired neural networks in finance.
Tensor logic aims to unify AI types with scalable and transparent features.
problem Lack of a unified AI programming language with scalability and transparency.
method Introduces tensor logic, a new AI language based on tensor equations.
result Tensor logic enables key AI forms like transformers, formal reasoning, and graphical models.
Enhances neural networks with logical knowledge for better performance.
problem Improving neural network performance with logical knowledge.
method Integrating logical knowledge into neural networks through a new final layer with learnable clause weights.
result KENN outperforms other methods in collective classification tasks with relational data.
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.
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take consistent and robust decisions in complex environments. The integration of deep learn…
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,…
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.
Refines neural network predictions using background knowledge for improved accuracy.
problem Compensate for lack of labeled data in neural networks.
method Introduces differentiable refinement functions and Iterative Local Refinement (ILR) algorithm to refine predictions efficiently and accurately.
result ILR finds competitive results in MNIST addition task and refines predictions on complex SAT formulas.
Structure Learning of Markov Random Fields through Grow-Shrink Maximum Pseudolikelihood Estimationstat.ML
Learning the structure of Markov random fields (MRFs) plays an important role in multivariate analysis. The importance has been increasing with the recent rise of statistical relational models since the MRF serves as a building block of these models such as Markov logic networks. There are two fundamental ways to learn…
RDLI integrates domain logic and context grounding to detect crypto anomalies under scarce labels.
problem Extreme label scarcity and evasion strategies in crypto networks.
method Relational Domain Logic Integration (RDLI) with Retrieval Grounded Context (RGC).
result RDLI outperforms GNN baselines by 28.9% in F1 score under 0.01% label scarcity.
This paper presents a stochastic logic time delay reservoir design. The reservoir is analyzed using a number of metrics, such as kernel quality, generalization rank, performance on simple benchmarks, and is also compared to a deterministic design. A novel re-seeding method is introduced to reduce the adverse effects of…
Paper tackles interpretability issues in deep learning models.
problem Lack of understanding of deep learning models' decision-making processes.
method Integrates concepts from machine learning, quantum computation, and quantum field theory.
result Demonstrates a many valued quantum logic system in Convolutional Deep Belief Networks.
Real artificial intelligence always has been focused on by many machine learning researchers, especially in the area of deep learning. However deep neural network is hard to be understood and explained, and sometimes, even metaphysics. The reason is, we believe that: the network is essentially a perceptual model. There…
The paper explores how different network architectures learn logical functions under GOTU, finding that a min-degree-interpolator is learned.
problem Learning logical functions with a focus on generalization on the unseen.
method Study of different network architectures trained by SGD under GOTU.
result For sparse functions and certain network models, a min-degree-interpolator is learned on the unseen.
Paper investigates differentiable fuzzy implications and their suitability for learning.
problem Analyzing differentiable fuzzy implications and their suitability for learning.
method Investigates the properties of fuzzy implications in a differentiable setting and introduces a new family of fuzzy implications.
result Various fuzzy implications are unsuitable for differentiable learning, and a new family of fuzzy implications is introduced.
Combines neural networks and STL for multi-class time-series classification.
problem Lack of interpretability in neural networks for time-series data.
method Proposes a method that uses neural networks to classify time-series data using STL specifications, introducing margin for multi-class classification and STL-based attributes for interpretability.
result Evaluations show improved interpretability and performance compared to state-of-the-art baselines.
Our interest in this paper is in the construction of symbolic explanations for predictions made by a deep neural network. We will focus attention on deep relational machines (DRMs, first proposed by H. Lodhi). A DRM is a deep network in which the input layer consists of Boolean-valued functions (features) that are defi…
New algebra counts components of arborescent knots and links.
problem Counting components of arborescent knots and links.
method Developed a new algebra called the crossing algebra.
result The crossing algebra counts the number of components for arborescent knots and links.
Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple un…
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.
Deep neural networks have achieved impressive performance and become the de-facto standard in many tasks. However, troubling phenomena such as adversarial and fooling examples suggest that the generalization they make is flawed. I argue that among the roots of the phenomena are two geometric properties of common deep l…