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.
Neurosymbolic predictors fail to model uncertainty under independence assumption.
problem Neurosymbolic predictors' reliance on independence assumption limits their ability to model uncertainty.
method Formal analysis of NeSy predictors under independence assumption.
result Assuming independence among symbolic concepts prevents NeSy predictors from representing uncertainty.
VERAFI improves financial AI by verifying calculations and compliance.
problem Financial AI systems generate errors and violations during reasoning.
method VERAFI combines dense retrieval, reranking, and automated reasoning policies.
result VERAFI achieves 94.7% factual correctness, 81% relative improvement.
A-NeSI scales approximate inference for probabilistic neurosymbolic learning.
problem Combining neural networks with symbolic reasoning for scalable inference.
method A-NeSI: a new framework for PNL using neural networks for approximate inference.
result A-NeSI achieves scalable approximate inference without semantic changes.
Cosmos models scenes using neural encodings and symbolic attributes for compositional generalization.
problem Modeling scenes with high performance on unseen input scenes composed of known visual elements.
method Neurosymbolic grounding with neurosymbolic scene encodings and attention mechanisms.
result Establishes a new state-of-the-art for compositional generalization in world modeling.
Survey of neurosymbolic AI methods for reasoning over knowledge graphs.
problem Combining symbolic reasoning with deep learning for graph data.
method Logically-informed embedding, embedding with logical constraints, and rule learning approaches.
result A novel taxonomy for classifying neurosymbolic reasoning methods on knowledge graphs.
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.
Revel tackles safe exploration in RL with verified symbolic policies.
problem Computational infeasibility of verifying neural networks in RL learning loops.
method Two policy classes: neurosymbolic with approximate gradients and symbolic policies for efficient verification. Mirror descent over policies to safely update and project policies.
result Revel discovers policies that outperform prior approaches to verified exploration.
Study characterizes and mitigates imbalances in neurosymbolic learning.
problem Characterizing and mitigating class-specific risks in neural classifiers.
method Theoretical analysis and practical techniques including estimating marginal gold labels and mitigating imbalances at training and testing time.
result Learning imbalances can be greatly impacted by the symbolic component σ, unlike in supervised and weakly supervised learning.
Novel framework for uncertainty quantification in neurosymbolic programs.
problem Lack of correctness guarantees in neurosymbolic programs due to machine learning model fallibility.
method Adapting conformal prediction to neurosymbolic programs using abstract interpretation.
result Framework provides probabilistic guarantees for correctness, compositionality, and structured values.
SATNet solves the Symbol Grounding Problem, enabling self-supervised learning.
problem Mapping visual inputs to symbolic variables without explicit supervision.
method Self-supervised pre-training pipeline and proofreading method.
result SATNet achieves full accuracy with no label leakage, surpassing state-of-the-art.
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.
Study improves self-driving safety in dynamic environments.
problem Safe self-driving in non-stationary urban settings.
method Neurosymbolic Meta-Reinforcement Lookahead Learning (NUMERLA).
result Self-driving agents can adapt safely in real-time.
Significant strides have been made toward designing better generative models in recent years. Despite this progress, however, state-of-the-art approaches are still largely unable to capture complex global structure in data. For example, images of buildings typically contain spatial patterns such as windows repeating at…
We present a neurosymbolic framework for the lifelong learning of algorithmic tasks that mix perception and procedural reasoning. Reusing high-level concepts across domains and learning complex procedures are key challenges in lifelong learning. We show that a program synthesis approach that combines gradient descent w…
Overview of integrable systems with symmetries, focusing on toric and semitoric systems.
problem Classifying and understanding integrable systems with symmetries.
method Using decorated polygons and controlled bifurcations in one-parameter families of systems.
result Construction of explicit semitoric systems with prescribed invariants.
New method to derive integrable systems from existing Lax systems.
problem Deriving new integrable systems from existing ones.
method Systematic method of deriving new integrable systems from a given one.
result Examples of new integrable systems derived, including the dispersionless Hirota equation, the general heavenly equation, and the web equations.
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.
Discrete-time systems can be characterized by simple flat coordinates and their shifts.
problem Characterizing flatness of discrete-time systems.
method Developed a map from flat coordinates and their shifts to system state and input, fulfilling system equations identically.
result Derived necessary conditions for a system to be flat, without requiring differential geometry methods.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.
problem High sample complexity for learning partially observed linear dynamical systems in high dimensions.
method Introduces an ℓ1-regularized estimation method that reduces sample complexity from linear to logarithmic with system dimension. result Markov parameters can be learned with logarithmic number of samples relative to system dimension, improving sample complexity.
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
problem Existence of Riemannian invariants for integrable systems of hydrodynamic type.
method Finding coordinates where the generator and all symmetries are diagonal.
result In integrable hydrodynamic systems, there exist coordinates where the generator and all symmetries are diagonal.
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Solves selecting the best optimizing system problems.
problem Selecting the best system among contenders with unknown performance.
method Adaptive algorithms integrating stochastic gradient descent and sequential elimination.
result Exponential rates of convergence to zero for false selection probability.
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…
Superintegrable systems on curved manifolds found to have Hessian structures.
problem Characterizing superintegrable systems on curved manifolds.
method Identifying and computing Hessian coordinates for superintegrable systems.
result Examples of superintegrable systems in 2D and 3D have natural Hessian coordinates.
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…
Researchers solve boundary and scattering rigidity problems for magnetic systems.
problem Recovering magnetic systems from boundary or scattering data.
method Reduced to magnetic systems and applied results from [DPSU07].
result Recovering MP-system up to a gauge. The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.
problem Finding general solutions for Lie systems.
method Develops mixed superposition rules for Lie systems with imprimitive Lie algebras and semidirect sums.
result Extends coalgebra method to Lie systems of partial differential equations.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
problem Reduction of controlled Lagrangian systems with symmetry and momentum map.
method Using Legendre transformation and Euler-Lagrange vector field, the paper extends symmetric reduction theory.
result Established regular reduction theory for RCL systems with symmetry and momentum map.
The paper studies connections in superintegrable systems, revealing geometric insights.
problem Understanding non- and semi-degenerate superintegrable systems.
method Analyzes two torsion-free connections associated with superintegrable systems.
result Semi-degenerate secondary structure tensor is the Ricci curvature of a natural torsion-free connection.
This paper proposes a system-agnostic policy for dynamic scheduling.
problem Dynamic scheduling in changing systems is challenging due to system-specific optimal policies.
method Descriptive policy that learns a system-agnostic scheduling principle.
result System-agnostic meta-learning enables adaptation to unseen system characteristics.
Learn dynamics of a system using auxiliary data from similar systems.
problem Learning dynamics of a linear system with limited data.
method Weighted least squares approach, incorporating auxiliary data.
result Auxiliary data can help reduce intrinsic error due to noise.
The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivativ…
Abstract reviews geometric theories of smooth and F-smooth systems.
problem Geometric theories of smooth and F-smooth systems.
method Reviews geometric theories of smooth and F-smooth systems.
result Discusses geometric theories of smooth and F-smooth systems.
New Lie systems derived from Goursat distributions with applications to differential equations.
problem Analyzing Lie systems associated with Goursat distributions and their applications.
method Analyzing bracket-generating distributions and their relation to Lie systems, focusing on reductions and reconstructions.
result Lie systems associated with Goursat distributions can be reduced and solutions reconstructed from reduced systems.
Elliptic systems are characterized by Darboux integrability.
problem Characterizing elliptic differential systems with holomorphic solutions.
method Using a complex manifold and associated holomorphic Pfaffian system.
result Elliptic systems are Darboux integrable under generic conditions.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.
Reduces multisymplectic Lie systems through symmetry analysis.
problem Solving multisymplectic Lie systems using symmetry reduction.
method Using momentum maps for reduction and reconstruction of multisymplectic Lie systems.
result Solves the original problem by analyzing simpler multisymplectic Lie systems.
Study integrable discretizations of cyclic systems with circular coordinate lines.
problem Integrable discretizations of 3D cyclic systems with circular coordinate lines.
method Investigate circle congruences and flat connections in the context of discrete cyclic systems.
result Characterization of circle congruences and existence of certain flat connections.
A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integer-order system. A discretization scheme is propo…
A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
This work extends reduction processes for nonholonomic discrete mechanical systems.
problem Nonholonomic discrete mechanical systems and their reductions.
method Introduces a category LDPd of discrete-time dynamical systems and a two-stage reduction process. result Two-stage reduction process produces systems isomorphic to one-stage reduction.
Unified approach to deform Lie-Hamilton systems using Poisson-Hopf algebra.
problem Deforming Lie systems with quantum algebras.
method Poisson-Hopf algebra deformations applied to Lie-Hamilton systems.
result Unified approach to deformations of Lie-Hamilton systems on the real plane.
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
Maps dBKP solutions to MS system solutions, defining Einstein-Weyl structures.
problem Constructing solutions and structures for dBKP and MS systems.
method Map construction and spectral characterisation of reductions.
result Defines Einstein-Weyl structures for dBKP and BMS systems.