4arXiv cs.LG (Machine Learning)·
Deep Gaussian Processes on Directed Acyclic Graphs: theory and structured variational inference
A new arXiv preprint introduces Deep Gaussian Processes (DGPs) defined over directed acyclic graphs (DAGs), providing a principled probabilistic framework for compositional function estimation in causal models, multi-fidelity simulations, and gene-regulatory networks. The authors derive theoretical results on prior-collapse behavior and information preservation as a function of graph topology, and propose a structured variational approximation that respects graph dependencies and collider explaining-away effects. Empirical validation covers a protein signalling network and a multi-fidelity heavy-ion collision emulation task, claiming state-of-the-art performance. The work is a methodological contribution at the intersection of probabilistic ML and structured graphical models.
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GaP: Graph-as-Policy multi-agent harness for reliable robot automation via self-learning computation graphs
Researchers introduce Graph-as-Policy (GaP), a multi-agent coding harness that generates directed computation graphs combining perception, planning, and control nodes for robotic 'Variational Automation' tasks — those with high variation in object geometry and pose. GaP uses an internal simulation environment to rehearse and iteratively refine graph structures in parallel, improving success rates without relying solely on model-free policies. Evaluation across 8 new benchmarks (4 simulated, 4 real-world) shows significant outperformance over baselines. The work bridges agentic coding systems with interpretable robot programming and Task and Motion Planning.
Graph Sparse Sampling (GSS) breaks exponential horizon dependence in continuous MDP planning
Researchers introduce Graph Sparse Sampling (GSS), an online planning algorithm for continuous Markov Decision Processes that shares sampled futures across candidate decisions rather than branching separately per action, eliminating the tree structure of methods like MCTS. The approach exposes large GPU-friendly batches and uses heuristics to focus computation, with finite-sample performance guarantees showing polynomial (rather than exponential) dependence on planning horizon under suitable conditions. Empirical results on continuous-control tasks show GSS substantially outperforms tree-based planners at long horizons. The work formalizes when shared-future graph planning can avoid the curse of the horizon that afflicts sparse sampling trees.
KGRL: Neuro-symbolic reinforcement learning for parametrized action spaces using Datalog knowledge bases
A new arXiv preprint introduces KGRL (Knowledge- and Gradient-Guided Reinforcement Learning), a neuro-symbolic algorithm for Parametrized Action Markov Decision Processes (PAMDPs) where each decision involves both a symbolic action and continuous numerical parameters. KGRL uses a Datalog knowledge base to prune infeasible actions and constrain parameter spaces, then applies gradient-based refinement to estimate optimal parameters during training and deployment. The approach improves sample efficiency and episodic return over state-of-the-art PAMDP baselines, and provides local procedural explanations for its decisions.
Graph Convolutional Attention: Spectral perspective improves graph denoising and diffusion
A new arXiv preprint introduces Spectral Attention and its practical realization, Graph Convolutional Attention (GCA), motivated by a theoretical analysis showing that linear attention is suboptimal for graph denoising tasks. The authors prove that standard linear attention can only learn an average spectral filter over the training distribution, while GCA provably outperforms it by a margin tied to spectral diversity. Empirically, GCA improves graph denoising and diffusion on synthetic and real datasets, and in the DiGress graph diffusion model it matches standard graph-transformer performance without expensive structural feature computation, enabling faster inference when combined with PEARL positional encodings.
PTL-Diffusion: Diffusion framework with periodic terminal laws for manifold-aware generation
PTL-Diffusion is a new diffusion modeling framework that replaces the standard single Gaussian terminal distribution with a periodic family of Gaussian terminal laws, embedding phase structure directly into the forward noising dynamics rather than only in the denoising network. The authors derive closed-form forward marginals and reverse posteriors for a periodically forced Ornstein-Uhlenbeck process, enabling standard noise-prediction training. Experiments on torus, cylinder, and face datasets show improvements in manifold-level distributional matching over DDPM baselines. The work is a proof-of-concept motivating structured terminal reference laws as a direction for geometry-aware generative modeling.
Large Language Gibbs: MCMC-based structured probabilistic inference using LLM conditionals
Researchers propose Large Language Gibbs, a structured inference scheme that uses an LLM's conditional token distributions as transition operators in a Gibbs sampling (MCMC) loop, iteratively resampling individual variables rather than generating outputs in a single autoregressive pass. The approach targets order-dependent biases in standard generation and aims to produce a stationary distribution reflecting a coherent compromise across all local conditionals. It is evaluated on synthetic distributions, consistent reasoning tasks, and Bayesian structure learning, showing MCMC-based inference is a practical alternative to one-pass generation for structured probabilistic tasks.
Unified framework for Riemannian deep learning: modules, architectures, and geometries
A doctoral thesis proposes a unified framework for deep learning on manifold-valued representations, addressing limitations of existing approaches tied to specific manifolds or relying on Euclidean approximations. The work generalizes batch normalization to Lie groups and gyrogroups, extends multinomial logistic regression to SPD and general Riemannian manifolds, and introduces new architectures for hyperbolic space and correlation matrices. It also contributes adaptive, computationally efficient Riemannian metrics including learnable Log-Euclidean and Cholesky-based geometries, validated across vision, signal processing, graph learning, and genomics tasks.
P-K-GCN: Physics-augmented Koopman-enhanced Graph Convolutional Network for spatiotemporal super-resolution
Researchers propose P-K-GCN, a framework combining graph convolutional networks, Koopman operator theory, and physics-informed loss functions for spatiotemporal super-resolution on irregular geometries. The method linearizes nonlinear dynamics in a latent space and enforces physical constraints to improve reconstruction fidelity. Theoretical analysis claims guaranteed error reduction via Rademacher complexity bounds. The framework is evaluated on reconstructing high-resolution cardiac electrodynamics from sparse 3D heart geometry measurements.