Derives fluctuation-dissipation relations for SGD, linking hyperparameters and measurable quantities.
problem Understanding and optimizing the training process of machine learning models.
method Derives stationary fluctuation-dissipation relations for stochastic gradient descent.
result Stationary fluctuation-dissipation relations hold for any stationary state and can be used to adaptively set training schedules.
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian…
In this study, the fluctuation-dissipation theory is invoked to shed light on input-output interindustrial relations at a macroscopic level by its application to IIP (indices of industrial production) data for Japan. Statistical noise arising from finiteness of the time series data is carefully removed by making use of…
On curved spaces, viscous fluids reach equilibrium quickly.
problem Thermalization of viscous fluids on negatively curved manifolds.
method Stochastic Navier-Stokes equations with kinematically selected deformation Laplacian.
result Exponential thermalization rate of $2νλ_\Def$.
Framework predicts nonlinear system responses using GFDT and generative models.
problem Predicting higher-order moments of nonlinear stochastic systems to small perturbations.
method Combining GFDT with generative modeling to estimate score function directly from data.
result Accurately captures nonlinear and non-Gaussian features of system responses.
Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.
problem Stochastic dynamics of rigid inclusions on curved surfaces.
method Cartan's method of moving frames, Hamiltonian equations, intrinsic Langevin equations, Fokker-Planck equation.
result Extracted overdamped equations for accurate simulations of diffusion processes.
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationa…
In this paper we compare market price fluctuations with the response to fundamental price drops within the Lux-Marchesi model which is able to reproduce the most important stylized facts of real market data. Major differences can be observed between the decay of spontaneous fluctuations and of changes due to external p…
A new method called MCLMC avoids dissipation in sampling from canonical distributions.
problem Sampling from canonical distributions without dissipation.
method Microcanonical Langevin Monte Carlo (MCLMC) as a dissipation-free system of SDE.
result MCLMC converges faster than HMC for lattice φ^4 models.
We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportun…
Stochastic Gradient Descent introduces noise in training, affecting model decision boundaries.
problem Understanding the impact of noise in SGD on model decision boundaries.
method Characterized SGD and persistent SGD dynamics in a neural network model, measuring noise magnitude in both under- and over-parametrized regimes.
result Noisier algorithms lead to wider decision boundaries in constraint satisfaction problems.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
Defines relations between Dirac structures and spinors using Courant algebroid relations.
problem Defines relations between Dirac structures and spinors using Courant algebroid relations.
method Uses Courant algebroid relations to define relations between Dirac structures and spinors.
result Proves existence results for T-dual structures and demonstrates compatibility with Type II supergravity equations.
A new model improves relation extraction accuracy through relation-gated adversarial learning.
problem Relation extraction from sentences is challenging due to expensive human annotation and noisy distant supervision.
method Proposes relation-gated adversarial learning for relation extraction, extending domain adaptation methods.
result The model outperforms previous domain adaptation methods and improves accuracy of distance supervised relation extraction.
Method discovers nonlinear relations from time series data.
problem Identifying directional relations from nonlinear interactions in time series.
method Minimum predictive information regularization method for deep learning.
result Substantially outperforms other methods for learning nonlinear relations.
Paper uses knowledge bases to discover new relations from text.
problem Discover new relations from text without annotated data.
method Construct constraints based on knowledge base embeddings and incorporate into variational auto-encoder for relation discovery.
result Improves relation discovery performance significantly.
SARN improves relational reasoning with less computation.
problem Efficiently perform relational reasoning with reduced computation.
method Introduces SARN, a sequential attention relational network.
result SARN achieves high accuracy on relational questions.
Abstractor enhances Transformers for relational reasoning, improving sample efficiency and performance.
problem Improving sample efficiency and performance in relational tasks.
method Introduces Abstractor module with relational cross-attention to enable explicit relational reasoning.
result Dramatic improvements in sample efficiency and performance on various relational tasks.
New method improves graph neural networks by considering different types of relations in sampling.
problem Current graph neural networks ignore relation types in biomedical graphs, leading to suboptimal performance.
method Proposes relation-dependent sampling for multi-relational graphs to balance relation frequency and importance.
result State-of-the-art graph neural networks achieve better accuracy and efficiency with relation-dependent sampling.
Temporal networks are ubiquitous and evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Although many relational datasets contain temporal information, the majority of existing techniques in relational learning focus on static snapshots and ignore the temporal dynamics. We propose…
Bayesian meta-learning on relation graphs improves few-shot relation extraction.
problem Predicting relations in sentences with limited labeled examples.
method Bayesian meta-learning on a global relation graph, using graph neural networks and Langevin dynamics.
result Framework effectively learns and generalizes to new relations.
Dilated DenseNets excel at relational reasoning without additional modules.
problem Deep neural networks struggle with relational reasoning.
method Dilated DenseNet architecture incorporating dilated convolutions.
result Dilated DenseNets surpass relational reasoning on Sort-of-CLEVR without additional modules.
Study improves CI tests for relational data to robustly discover causal structures.
problem Learning causal relationships from relational data.
method Conduct CI tests against relational data to robustly recover causal structure.
result Effective approach demonstrated through experiments.
Proves one-relator groups with negative immersions are hyperbolic and virtually special.
problem One-relator groups with negative immersions.
method Refinement of Magnus--Moldavanskii hierarchy and introduction of Z-stable HNN-extensions and hierarchies.
result One-relator groups with negative immersions are hyperbolic and virtually special, resolving a conjecture.
HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.
problem Modeling noisy, sparse, and heterogeneous relational data.
method Hierarchical Chinese restaurant process and Dirichlet process mixture for clustering and modeling relation values.
result HIRM generalizes standard models and discovers relational structure in real-world datasets.
Paper uses AC-GAN to generate high-quality relational sentences for relation extraction.
problem Limited training data for relation extraction models.
method Auxiliary Classifier Generative Adversarial Networks (AC-GANs).
result Significantly improved performance of relation extraction.
R-SQAIR adds relational bias to sequential object attention models for better object interactions.
problem Traditional sequential multi-object attention models struggle with relational inferences.
method Proposes R-SQAIR, a relational extension of SQAIR with a parallel pairwise interaction module.
result Demonstrates gains in object relations and combinatorial generalization over sequential mechanisms.
Introduces Relational Privacy (RP) to control relation memorization in question answering models.
problem Relation memorization in question answering models can lead to privacy issues.
method Formalizes Relational Privacy (RP) and Differential Relational Privacy (DrP), providing bounds on relation memorization.
result DrP allows effective learning of general properties of underlying concepts while preventing relation memorization.
Proposes a new method for predicting missing relations in knowledge graphs.
problem Predicting missing relations between entities in knowledge graphs.
method Relational message passing method considering only edge features without entity IDs.
result PathCon method outperforms state-of-the-art methods significantly.
Enhances social spam detection using multi-level dependency of relational sequences.
problem Social spam detection in multi-relation social networks.
method Developed the Multi-level Dependency Model (MDM) to exploit long-term and short-term dependencies in user relational sequences.
result MDM improves social spam detection accuracy on a real-world multi-relational social network.
The paper explores the pentagon relation and its algebraic forms.
problem Exploring the pentagon relation and its various forms.
method Starting with geometric form, then algebraic form as a family of equations, deriving equivalent forms using 6j-symbols, and extracting solutions from modular categories.
result Extracting a solution of the pentagon relation from any modular category.
In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which capture the relations among inputs. In many cases, more than two maps are strongly…
New model improves graph attention for relational data.
problem Improving graph attention models for relational data.
method Relational Graph Attention Networks (R-GAT) extending non-relational graph attention to relational data.
result R-GAT performs worse than expected, but some configurations marginally improve molecular property modeling.
Extends coherence results to one-relator products of locally indicable groups.
problem Coherence in one-relator products of locally indicable groups.
method Developed new methods to extend results of Helfer, Wise, Louder, Wilton, and Brodsky.
result New proof of a theorem by Brodsky.
Existing relation classification methods that rely on distant supervision assume that a bag of sentences mentioning an entity pair are all describing a relation for the entity pair. Such methods, performing classification at the bag level, cannot identify the mapping between a relation and a sentence, and largely suffe…
This work proposes a method to compose visual relations more faithfully.
problem Composing relations between objects in images is challenging due to their entanglement.
method Represent each relation as an unnormalized density (energy-based model) to compose relations factorizedly.
result The proposed method generates and edits scenes with multiple sets of relations more faithfully.
A new quantum relation connects exceptional Lie algebras and knots.
problem Understanding the relationship between exceptional Lie algebras and quantum invariants of knots.
method Developed a two-parameter skein relation on trivalent graphs that specializes to exceptional Lie algebras.
result Found a new quantum exceptional polynomial that agrees with classical computations for knots and links.
Enhances relational reasoning with multi-layer architecture.
problem Limited relational reasoning with shallow architectures.
method Multi-layer relation network architecture.
result Solved all 20 tasks in bAbI 20 QA dataset.
Proposes RT decomposition for better multi-relational link prediction.
problem Improving multi-relational link prediction in knowledge graphs.
method Relational Tucker3 (RT) decomposition, decouples entity and relation embeddings, allows parameter sharing, and learns sparsity patterns.
result RT decomposition can outperform existing sparse models in multi-relational link prediction.
RelEx explains relational models without gradient access.
problem Lack of explainability for relational models like GNNs and SRL.
method Model-agnostic explainer for relational models using only outputs.
result Comparable or better performance compared to GNN-Explainer.
Improves neural relational inference for dynamic multi-agent trajectories.
problem Limited accuracy of NRI in short output sequences for relational inference in multi-agent trajectories.
method Proposes DYnamic multi-AgentRelational Inference (DYARI) model to handle changing interactions over time.
result DYARI model outperforms NRI in dynamic relational inference tasks.
Method learns relational features for Gaifman models from knowledge bases.
problem Structure learning for Gaifman models.
method Relational tree distances to learn relational features.
result Empirical evaluation shows superiority over classical rule-learning.
Study super cluster algebras from super Plücker and Ptolemy relations.
problem Developing super cluster algebra structure in super Grassmannians.
method Analyzing super Plücker and Ptolemy relations, developing super cluster structure.
result New simple form of super Plücker relations for $\Gr_{r|1}(n|1)$.
Attention-based embeddings improve relation prediction in incomplete KGs.
problem Incomplete or missing relations in knowledge graphs.
method Attention-based feature embedding that captures entity and relation features in local neighborhoods.
result Marked performance gains on all datasets compared to state-of-the-art methods.
Proves a categorified relation in Khovanov homology.
problem None explicitly stated; focuses on categorification of a relation.
method Categorified analogue of Kontsevich's 4T relation on Khovanov homology.
result Proof of categorified 4T relation in Khovanov homology.
Introduces new algebraic structures for relational groupoids and proves a reduction theorem.
problem Developing algebraic tools for relational groupoids.
method Introduces relational groupoids and convolution algebras, provides examples, and proves a reduction theorem.
result Establishes a reduction theorem recovering the usual convolution of Lie groupoids.
CompGCN embeds nodes and relations in multi-relational graphs.
problem Handling multi-relational graphs with direction and labels.
method CompGCN uses entity-relation composition operations from KG embedding.
result CompGCN achieves superior results on node classification, link prediction, and graph classification.
The study categorizes knowledge graph relations and explains their embedding representations.
problem Understanding how knowledge graph relation representations capture semantic information.
method Categorizing knowledge graph relations into three types and deriving explicit requirements for their representations.
result Empirical properties of relation representations and the performance of methods are justified by the analysis.