Papers

Field

Top tools here

Open problems in Neural operators

Stable and efficient online reinforcement learning for diffusion models3 papers raise it · 3 address it
Current methods are either inefficient due to poor credit assignment or unstable without careful tuning, limiting practical deployment.
- DiffusionART: Efficient, Stable and Scalable Reinforcement of Diffusion Modelsraises · addresses
- Routing Policy Optimization for Online Diffusion Reinforcement Learningraises · addresses
- MEND: RL For Flow Models via Proximal Velocity Matchingraises · addresses
Scalable minibatch optimal transport for flow matching1 paper raises it · 1 addresses it
Small minibatches limit benefits of optimal transport, while large minibatches are computationally prohibitive, and theoretical gaps remain in gradient and integration stability.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Benchmarking System One models on graph tasks1 paper raises it · 1 addresses it
Capabilities of fast, choice-based models on graph-related tasks are unclear, and existing evaluations lack standardized, diagnostic benchmarks.
- GraphDecisionBench: Benchmarking System One Models on Graph Tasksraises · addresses
Efficient edge sparsification for graph neural networks1 paper raises it · 1 addresses it
Reusing a fixed sparse graph locks training to a fixed topology, while dynamic sparsification is computationally expensive.
- EDiS: Edge Disjoint Subgraph Sparsification Framework for Graph Neural Networksraises · addresses

Named by an AI from these papers' abstracts.

Open problems

Recently funded

Topics in this field

neural operators · physics informed neural · informed neural networks367 papers27 this week
graph neural · graph learning · graph neural networks307 papers25 this week
relu networks · gradient descent · deep neural157 papers20 this week
deep neural · neural networks · neural network157 papers16 this week
flow matching · normalizing flows · flow201 papers14 this week
bayesian neural · bayesian networks · amortized bayesian103 papers14 this week

Topics in this field

Active contributors · 90 days

Active contributors

Activity · 12 weeks

Activity

Recent papers

All papers in Research

arXiv cs.LGOct 29
Composing and Steering Diffusion Models with Generalized Feynman-Kac Correctors
Wael Mattar, Daniel Freedman
Diffusion models have become the leading paradigm in generative modeling, yet many applications require sampling from distributions that are not those of any single pretrained model, but are instead defined through combinations of several models, possibly tilted toward high values of a downstream reward. Naively combining the scores of the models yields incorrect samples, while existing corrections are restricted to specific families of targets. In this work, we introduce the generalized Feynman-Kac correctors (GFKC), a principled framework for sampling from an arbitrary target function of several pretrained diffusion models. We show that the geometric interpolation between an arbitrary initial function and the target function of the models satisfies a Feynman--Kac partial differential equation, and derive its potential in closed form. To evaluate this potential during generation, we further generalize the log-probability ODE to track the density of each model along trajectories driven by a different velocity field. The resulting algorithm operates entirely in the log domain, incorporates reward-based steering at no additional conceptual cost, and corrects the generation on the…
PDF arXiv
arXiv cs.AIOct 29
Bridging Semantics and Structure: A Theoretically Grounded Framework for Link Prediction on TAGs
Chen Shao, Ruirui Wang, Tobias Kafer, Danai Koutra
Link prediction on text-attributed graphs (TAGs) is a fundamental problem with applications in knowledge discovery, recommendation and beyond. Recent progress has highlighted the promise of combining Graph Neural Networks (GNNs) with Language Models (LMs) in order to leverage the complementary structural and semantic signals. However, due to the distinct inductive biases of GNNs and LMs, the design of an optimal fusion strategy remains an open research question. In this work, we present Bridge-LP, an intuitive, simple, efficient and theoretically grounded framework that unifies graph and language representations. It is built around three theoretically-justified design components: (D1) jumping connection of textual proximity, which enables robust LM training; (D2) compressed embedding, which encodes neighborhood information long exploited by classical link prediction heuristics, thereby enriching structural signals in a learnable way; and (D3) cache embedding training strategy, which reduces computational complexity. Together, these mechanisms establish an end-to-end cross-modal framework that scales to large graphs while capturing richer graph-text interactions. We conduct an…
PDF arXiv
arXiv cs.LGOct 29
Mode Dynamics: A Framework for Neural Network Learning
Hossein Honarvar
We introduce Mode Dynamics, a framework that connects coordinated parameter motion during neural network learning to changes in model outputs. Starting from a recorded parameter trajectory, we decompose its updates into collective modes and map each mode to its state-dependent output effect. The framework organizes this link through three mechanisms. Decomposition identifies collective modes in parameter motion and their time-varying amplitudes. Reconstruction tests whether the effects induced by those modes recover local and accumulated output change. Concentration quantifies how behavioral contribution is distributed across modes. Controlled scalar regression and next-token experiments directly test these mechanisms. They show that small sets of leading modes reconstruct behavior, induced effects depend on the training path, and modal complexity varies with task and data. We then evaluate the framework on held-out image and language-model outputs using CIFAR-100 autoencoding and a public Pythia-70M pretraining trajectory. Across these settings, the results connect compact modal subspaces of recorded parameter motion to evolving behavior.
PDF arXiv
arXiv cs.LGOct 29
FIDE: Fiber-Informed Differentiable Experimental Design for Reference-Relative Law Dynamics
Pietro Zanotta, Ján Drgoňa
Aggregate measurements generally leave an evolving population law underdetermined, so different measurement systems can be equally adequate for a scientific task while constraining different aspects of the law. We study how to resolve this residual design freedom in baseline-preserving settings, where an existing dynamical model remains the working baseline outside quantities explicitly valued by the task. \textbf{F}iber-\textbf{I}nformed \textbf{D}ifferentiable \textbf{E}xperimental Design (\textbf{FIDE}) completes each candidate's aggregate constraints by information projection relative to a common frozen reference, then ranks scientifically adequate designs by the dynamical revision required to realize the resulting completed paths. The resulting \emph{Full action} is the minimum mean-squared velocity correction needed to realize a completed path; equivalently, its square root is the sharp reference-relative expectation-rate discrepancy over a gradient-normalized Sobolev class. This defines a conditional minimum-revision principle for baseline-preserving design rather than a generic truth-recovery objective. Experiments show that this preference changes sensor selection, can…
PDF arXiv
arXiv cs.AIOct 29
Efficient Learning of Mechanism Designs and Compositionality
João Pedro Gandarela, Thiago Rios, Stefan Menzel, André Freitas
Learning mechanism behaviour requires a representation of how connected parts jointly constrain motion. We study whether exposing reusable constraint subassemblies improves prediction from limited data. Assur-KB represents planar mechanisms through irreducible modules, boundary interfaces, and solve dependencies while retaining source geometry. Our theoretical results characterize transfer through module interfaces and establish physical limits arising from missing interface information and accumulated sensitivity. To test the representation claim directly, the experimental design compares matched mechanism-curve pairs across training budgets within the same multilayer-perceptron family. This controlled comparison establishes the utility of the complete representation in the evaluated learning setting. Assur-derived features provide a geometric-mean $1.8\times$ advantage in sample efficiency over flattened adjacency and position inputs across budgets of 50-10,000 mechanisms. Separate experiments establish invariance under tested joint relabelings, higher valid-generation rates under dyadic composition, and a coarser structural index over 10.02 million mechanisms. In summary, the…
PDF arXiv
arXiv cs.LGOct 29
Data-driven Random-feature Approximation of Koopman Generators of Nonlinear Continuous-time Systems
Ana Čukarska, Maximilian Gollwitzer, Viola Muning Li, Vladyslav Fediukov, Zahra Monfared +1
Learning continuous-time dynamical systems from data is an active area of research. The Koopman formalism is often used here, because it is a flexible approach that is informative about the system's fundamental properties. The formalism represents dynamical systems through linear operators acting on a suitable function space. A practical difficulty arising in the numerical approximation of Koopman operators is the choice of a ``dictionary'', meaning an effective finite-dimensional representation of the function space. In this paper, we focus on learning dynamical systems in continuous-time, and so we consider numerical approximations of the Koopman generator instead of the Koopman operator. Our main contribution is a data-driven random-feature method to obtain a parsimonious and effective function representation for Galerkin approximation methods such as gEDMD. The representation we construct is data-informed, which allows us to improve upon data-agnostic methods. We empirically demonstrate the suitability of our method for forecasting tasks and system analysis. The numerical experiments show that our approach is accurate, and faster than iterative optimization. Further, we prove…
PDF arXiv

Papers

Topics in this field

neural operators · physics informed neural · informed neural networks367 papers27 this week
graph neural · graph learning · graph neural networks307 papers25 this week
relu networks · gradient descent · deep neural157 papers20 this week
deep neural · neural networks · neural network157 papers16 this week
flow matching · normalizing flows · flow201 papers14 this week
bayesian neural · bayesian networks · amortized bayesian103 papers14 this week

Active contributors · 90 days

Activity · 12 weeks

Fields · AI · updated 12m ago

Neural operators

Found by the topic model: neural operators, graph neural, flow matching.

147papers this week−38.2% vs last week

All papers · 1.7k With code · 11

Newest Most relevant

1.1k papers this month

Open problems in Neural operators

Stable and efficient online reinforcement learning for diffusion models3 papers raise it · 3 address it
Current methods are either inefficient due to poor credit assignment or unstable without careful tuning, limiting practical deployment.
- DiffusionART: Efficient, Stable and Scalable Reinforcement of Diffusion Modelsraises · addresses
- Routing Policy Optimization for Online Diffusion Reinforcement Learningraises · addresses
- MEND: RL For Flow Models via Proximal Velocity Matchingraises · addresses
Scalable minibatch optimal transport for flow matching1 paper raises it · 1 addresses it
Small minibatches limit benefits of optimal transport, while large minibatches are computationally prohibitive, and theoretical gaps remain in gradient and integration stability.
- Scaling Online Optimal Transport Minibatches for Flow Matchingraises · addresses
Benchmarking System One models on graph tasks1 paper raises it · 1 addresses it
Capabilities of fast, choice-based models on graph-related tasks are unclear, and existing evaluations lack standardized, diagnostic benchmarks.
- GraphDecisionBench: Benchmarking System One Models on Graph Tasksraises · addresses
Efficient edge sparsification for graph neural networks1 paper raises it · 1 addresses it
Reusing a fixed sparse graph locks training to a fixed topology, while dynamic sparsification is computationally expensive.
- EDiS: Edge Disjoint Subgraph Sparsification Framework for Graph Neural Networksraises · addresses

Named by an AI from these papers' abstracts.

Recent papers

All papers in Research

arXiv cs.LGOct 29
Composing and Steering Diffusion Models with Generalized Feynman-Kac Correctors
Wael Mattar, Daniel Freedman
Diffusion models have become the leading paradigm in generative modeling, yet many applications require sampling from distributions that are not those of any single pretrained model, but are instead defined through combinations of several models, possibly tilted toward high values of a downstream reward. Naively combining the scores of the models yields incorrect samples, while existing corrections are restricted to specific families of targets. In this work, we introduce the generalized Feynman-Kac correctors (GFKC), a principled framework for sampling from an arbitrary target function of several pretrained diffusion models. We show that the geometric interpolation between an arbitrary initial function and the target function of the models satisfies a Feynman--Kac partial differential equation, and derive its potential in closed form. To evaluate this potential during generation, we further generalize the log-probability ODE to track the density of each model along trajectories driven by a different velocity field. The resulting algorithm operates entirely in the log domain, incorporates reward-based steering at no additional conceptual cost, and corrects the generation on the…
PDF arXiv
arXiv cs.AIOct 29
Bridging Semantics and Structure: A Theoretically Grounded Framework for Link Prediction on TAGs
Chen Shao, Ruirui Wang, Tobias Kafer, Danai Koutra
Link prediction on text-attributed graphs (TAGs) is a fundamental problem with applications in knowledge discovery, recommendation and beyond. Recent progress has highlighted the promise of combining Graph Neural Networks (GNNs) with Language Models (LMs) in order to leverage the complementary structural and semantic signals. However, due to the distinct inductive biases of GNNs and LMs, the design of an optimal fusion strategy remains an open research question. In this work, we present Bridge-LP, an intuitive, simple, efficient and theoretically grounded framework that unifies graph and language representations. It is built around three theoretically-justified design components: (D1) jumping connection of textual proximity, which enables robust LM training; (D2) compressed embedding, which encodes neighborhood information long exploited by classical link prediction heuristics, thereby enriching structural signals in a learnable way; and (D3) cache embedding training strategy, which reduces computational complexity. Together, these mechanisms establish an end-to-end cross-modal framework that scales to large graphs while capturing richer graph-text interactions. We conduct an…
PDF arXiv
arXiv cs.LGOct 29
Mode Dynamics: A Framework for Neural Network Learning
Hossein Honarvar
We introduce Mode Dynamics, a framework that connects coordinated parameter motion during neural network learning to changes in model outputs. Starting from a recorded parameter trajectory, we decompose its updates into collective modes and map each mode to its state-dependent output effect. The framework organizes this link through three mechanisms. Decomposition identifies collective modes in parameter motion and their time-varying amplitudes. Reconstruction tests whether the effects induced by those modes recover local and accumulated output change. Concentration quantifies how behavioral contribution is distributed across modes. Controlled scalar regression and next-token experiments directly test these mechanisms. They show that small sets of leading modes reconstruct behavior, induced effects depend on the training path, and modal complexity varies with task and data. We then evaluate the framework on held-out image and language-model outputs using CIFAR-100 autoencoding and a public Pythia-70M pretraining trajectory. Across these settings, the results connect compact modal subspaces of recorded parameter motion to evolving behavior.
PDF arXiv
arXiv cs.LGOct 29
FIDE: Fiber-Informed Differentiable Experimental Design for Reference-Relative Law Dynamics
Pietro Zanotta, Ján Drgoňa
Aggregate measurements generally leave an evolving population law underdetermined, so different measurement systems can be equally adequate for a scientific task while constraining different aspects of the law. We study how to resolve this residual design freedom in baseline-preserving settings, where an existing dynamical model remains the working baseline outside quantities explicitly valued by the task. \textbf{F}iber-\textbf{I}nformed \textbf{D}ifferentiable \textbf{E}xperimental Design (\textbf{FIDE}) completes each candidate's aggregate constraints by information projection relative to a common frozen reference, then ranks scientifically adequate designs by the dynamical revision required to realize the resulting completed paths. The resulting \emph{Full action} is the minimum mean-squared velocity correction needed to realize a completed path; equivalently, its square root is the sharp reference-relative expectation-rate discrepancy over a gradient-normalized Sobolev class. This defines a conditional minimum-revision principle for baseline-preserving design rather than a generic truth-recovery objective. Experiments show that this preference changes sensor selection, can…
PDF arXiv
arXiv cs.AIOct 29
Efficient Learning of Mechanism Designs and Compositionality
João Pedro Gandarela, Thiago Rios, Stefan Menzel, André Freitas
Learning mechanism behaviour requires a representation of how connected parts jointly constrain motion. We study whether exposing reusable constraint subassemblies improves prediction from limited data. Assur-KB represents planar mechanisms through irreducible modules, boundary interfaces, and solve dependencies while retaining source geometry. Our theoretical results characterize transfer through module interfaces and establish physical limits arising from missing interface information and accumulated sensitivity. To test the representation claim directly, the experimental design compares matched mechanism-curve pairs across training budgets within the same multilayer-perceptron family. This controlled comparison establishes the utility of the complete representation in the evaluated learning setting. Assur-derived features provide a geometric-mean $1.8\times$ advantage in sample efficiency over flattened adjacency and position inputs across budgets of 50-10,000 mechanisms. Separate experiments establish invariance under tested joint relabelings, higher valid-generation rates under dyadic composition, and a coarser structural index over 10.02 million mechanisms. In summary, the…
PDF arXiv
arXiv cs.LGOct 29
Data-driven Random-feature Approximation of Koopman Generators of Nonlinear Continuous-time Systems
Ana Čukarska, Maximilian Gollwitzer, Viola Muning Li, Vladyslav Fediukov, Zahra Monfared +1
Learning continuous-time dynamical systems from data is an active area of research. The Koopman formalism is often used here, because it is a flexible approach that is informative about the system's fundamental properties. The formalism represents dynamical systems through linear operators acting on a suitable function space. A practical difficulty arising in the numerical approximation of Koopman operators is the choice of a ``dictionary'', meaning an effective finite-dimensional representation of the function space. In this paper, we focus on learning dynamical systems in continuous-time, and so we consider numerical approximations of the Koopman generator instead of the Koopman operator. Our main contribution is a data-driven random-feature method to obtain a parsimonious and effective function representation for Galerkin approximation methods such as gEDMD. The representation we construct is data-informed, which allows us to improve upon data-agnostic methods. We empirically demonstrate the suitability of our method for forecasting tasks and system analysis. The numerical experiments show that our approach is accurate, and faster than iterative optimization. Further, we prove…
PDF arXiv