Paper uses subjective logic to estimate uncertainty in multi-armed bandit problems.
problem Estimating uncertainty in multi-armed bandit problems.
method Formalism of subjective logic applied to multi-armed bandits, proposing new algorithms.
result Subjective logic quantities enable useful assessment of uncertainty.
New theory of co~events resolves debates between Bayesianists and frequentists.
problem Fierce debates between Bayesianists and frequentists over Bayesian scheme.
method Developed new co~event axiomatics and theory to study experience and chance as a single co~event.
result Demonstrated effectiveness of new theory in resolving debates over Bayesian scheme.
Unified framework for hierarchical image classification with epistemic uncertainty.
problem Overconfident predictions and lack of logical consistency in deep learning models.
method Neurosymbolic approach with epistemic deep learning, using focal set reasoning and differentiable fuzzy logic.
result Maintains accuracy on par with transformer baselines while providing more calibrated and interpretable predictions.
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.
CoT-UQ improves LLM uncertainty quantification by integrating reasoning steps.
problem LLMs' overconfidence and lack of response-wise uncertainty quantification.
method Integrates LLMs' reasoning steps into uncertainty estimation.
result Significantly improves uncertainty quantification accuracy (5.9% AUROC improvement).
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 …
This paper improves STL inference reliability under covariate shift.
problem Ensuring correct STL formulas in real-world settings with distribution shift.
method Proposes a conformalized STL inference framework that addresses covariate shift.
result Significantly improves symbolic learning reliability at deployment time.
Paper uses RL to synthesize control policies for LTL objectives in uncertain environments.
problem Control policies for uncertain, probabilistic environments with temporal logic specifications.
method Model-free RL algorithm, LTL to LDBA translation, synchronous reward function, asymptotic satisfaction probability.
result RL algorithm maximizes satisfaction probability of LTL objectives in PL-MDPs.
Hybrid models are reinterpreted as Neuro-Symbolic AI designs to quantify uncertainty and variability.
problem Limited semantic interface for comparing hybrid models across domains.
method Reinterpret hybrid models as Neuro-Symbolic AI, translating them into explicit inference function and logic-belief decomposition.
result Metrics SVR and BD quantify uncertainty and variability in hybrid models.
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.
New research challenges the independence assumption in neurosymbolic learning, leading to overconfident predictions and unrepresentable uncertainty.
problem The independence assumption in neurosymbolic learning systems can lead to overconfident predictions and hinder uncertainty quantification.
method The study proves the limitations of the independence assumption and introduces new loss functions that are non-convex and difficult to optimise.
result Neurosymbolic learning systems using the independence assumption are prone to overconfidence and cannot represent uncertainty over multiple valid options.
NLM combines neural networks and logic programming for complex reasoning.
problem Complex reasoning tasks involving logic and properties.
method Neural-symbolic architecture combining neural networks and logic programming.
result NLM achieves perfect generalization on various tasks.
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.
Logical scaffolds enhance AI software quality.
problem Improving AI component quality in software.
method Logical scaffolds as a method to improve AI components.
result Logical scaffolds can improve AI beyond perception systems.
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.
Graph neural networks improve logic reasoning for large datasets.
problem Combining logic reasoning and probabilistic inference for large datasets.
method Exploring Graph Neural Networks (GNNs) for Markov Logic Networks (MLN) to improve probabilistic logic inference.
result ExpressGNN, a more expressive variant of GNN, can perform effective probabilistic logic inference and scale to large datasets.
A new Bayesian optimization method tackles constrained optimization with uncertainties.
problem Optimizing functions with uncertain constraints.
method Bayesian optimization with a new acquisition criterion.
result The new criterion optimizes both objective function improvement and constraint reliability.
Develops deep learning for logical code segmentation.
problem Lack of logically segmented source code.
method Novel deep learning approach to generate logical code segments.
result Improves software analysis tasks like commenting, bug detection, and code synthesis.
Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains ignorant to its prediction confidence. Orthogonally to Bayesian neural nets that indi…
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.
Review of uncertainty representation methods in risk management.
problem Inadequate consideration of uncertainty in risk management.
method Systematic literature review of 370 publications.
result Probabilistic methods are predominant, but fuzzy and evidence-based approaches are also useful.
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.
The paper quantifies and attributes uncertainty in complex system simulations.
problem Uncertainty in complex system simulations due to unknown or approximated subprocesses.
method Developed a framework for quantifying and attributing submodel uncertainty using bootstrapping, Bayesian model averaging, and tree-based methods.
result Individual submodels contribute to overall uncertainty, and their importance can be quantified.
Driving styles have a great influence on vehicle fuel economy, active safety, and drivability. To recognize driving styles of path-tracking behaviors for different divers, a statistical pattern-recognition method is developed to deal with the uncertainty of driving styles or characteristics based on probability density…
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.
FPGA-based logic architecture speeds up GBDT training 259x.
problem Training efficiency and power consumption in GBDT models.
method Implemented logic architecture on FPGA, compared with software libraries.
result Training speed 26-259x faster, power efficiency 90-1,104x higher.
Integrates deep learning and logic reasoning for intelligent agents.
problem Combining deep learning and logic reasoning for robust decision-making.
method Deep Logic Models integrating deep learners and logic reasoning.
result Proposed models outperform other approaches in joint learning and inference.
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams, knot-logical diagrams and an arrow of reference that elucidates self-reference and G…
Kernel for STL formulae enables machine learning in temporal logic.
problem Lack of a kernel for STL formulae.
method Define a kernel for STL formulae and embed them into a Hilbert space.
result Kernel-based machine learning algorithms can now be applied to STL formulae.
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.
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.
A new PLL method uses class activation values to improve robustness.
problem Weakly supervised learning with noisy data and adversarial perturbations.
method Subjective logic with class activation values for uncertainty representation and label weight re-distribution.
result More robust predictions under high noise levels, out-of-distribution examples, and adversarial perturbations.
2-simplicial Transformer enhances logical reasoning in reinforcement learning.
problem Logical reasoning in reinforcement learning.
method Introduces 2-simplicial Transformer with higher-dimensional attention and tensor product updates. result Shows effectiveness of 2-simplicial Transformer for logical reasoning. Proposes NLRL for enhancing neural networks' interpretability.
problem Deep neural networks lack interpretability for humans.
method Introduces neural logic rule layers (NLRL) to represent arbitrary logic rules.
result NLRL-enhanced neural networks can learn complex logic and arithmetic.
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.
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.
Responds to comments on Bayesian Logic Regression algorithm, provides extensions and tutorial.
problem Improving Bayesian Logic Regression algorithm and its applications.
method Summarizes and responds to discussants' comments, provides extensions and tutorial.
result Extensions and tutorial for the Bayesian Logic Regression algorithm.
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.
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.
In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R^n with n >= 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot…
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.
No-knowledge alarms detect misaligned LLM judges without trusting them.
problem Monitoring LLM judges for consistency when ground truth is unknown.
method Formal logic and Linear Programming to detect disagreements.
result No false positives in detecting misaligned judges.
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.
SATNet integrates logical reasoning into deep learning with a differentiable MAXSAT solver.
problem Integrating logical reasoning into deep learning architectures.
method Differentiable MAXSAT solver based on fast coordinate descent for SDP.
result Minimally supervised learning of logical structures in deep learning systems.
Safe reinforcement learning with logical constraints for optimal policy synthesis.
problem Ensuring safety during reinforcement learning while maximizing goal satisfaction.
method Adaptive safe padding that synthesizes optimal control policies satisfying temporal logic formulas.
result The proposed method handles the trade-off between exploration and safety with theoretical guarantees.
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.