The paper introduces a generative graph model that combines mechanistic interpretability with amortized inference by formulating both the generative process and parameter recovery in function space. It extends step graphons to a multifractal construction, enabling a neural inverse operator that can infer parameters for unseen graph sizes. Experiments show the model outperforms a pretrained graph foundation model on zero‑shot generation and matches instance‑specific methods on single‑observation networks, while also sensitively tracking brain state changes in an EEG study.
arXiv:2510. 03690v4 Announce Type: replace Abstract: Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions.
arXiv:2609.06093v1 Announce Type: new Abstract: Connectomes, graph-level maps of neurons and their synaptic connections, provide a structural basis for understanding how brain circuits support functi...
The paper introduces RGC‑Net, a Reservoir‑Based Graph Convolutional Network that combines fixed‑random reservoir dynamics with a structured convolutional framework for graph learning. It addresses limitations of existing reservoir‑based GNNs by adding a leaky integrator for better feature retention and a robust, adaptable architecture for graph classification and generation. Experiments demonstrate state‑of‑the‑art performance on classification and generative tasks, including dynamic brain connectivity, with faster convergence and reduced over‑smoothing.
The paper introduces xVGAE, a hierarchical variational graph autoencoder designed for exchangeable graphs. Leveraging the Aldous-Hoover theorem, the model uses a graph-level latent variable, exchangeable node-specific latent variables, and a graphon function to learn and generate graph distributions efficiently. Experiments demonstrate that xVGAE produces high-quality graphs quickly while capturing key structural properties of the training data.
arXiv:2509. 24256v2 Announce Type: replace-cross Abstract: The pretrain-transfer paradigm, which underpins the success of large language models (LLMs), has demonstrated the immense power of creating foundation models that learn generalizable representations from vast datasets.
The paper introduces adVersarial Parameter Decomposition (VPD), a method that splits a language model’s parameters into simple subcomponents, each responsible for a small part of the model’s algorithm. VPD optimizes these decompositions so that the model’s input‑output behavior remains intact even when many subcomponents are removed, including adversarially chosen ones. This approach enables a new form of circuit analysis by tracing how sequences of parameter subcomponents interact to produce outputs for specific inputs.
The paper proposes a mathematical framework to infer canonical distributed computations from large‑scale neural activity. It combines normative assumptions that the brain learns a structured internal model of its environment with an algorithmic view that inference is a nonlinear message‑passing process on a graph‑structured model. Using time‑series neural data from a perceptual inference task, the framework identifies latent variables, their neural representations, the interactions defining the brain’s internal model, and the message functions governing inference, demonstrating its feasibility on simulated neural recordings.
arXiv:2507. 10005v2 Announce Type: replace Abstract: In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention.
The paper introduces MS‑WDRO, a multi‑source Wasserstein distributionally robust optimization framework for reconstructing complex network topologies from scarce target‑domain data and abundant heterogeneous source data. It fuses sources via a weighted Wasserstein barycenter, builds an ambiguity set around it, and solves a regularized Laplacian estimator using a provably convergent ADMM scheme. The authors provide finite‑sample guarantees, demonstrate that naive aggregation is suboptimal, and show through experiments on synthetic data and the ABIDE I neuroimaging dataset that MS‑WDRO outperforms seven baselines in graph recovery, sample efficiency, and diagnostic utility, especially when target samples are limited.
arXiv:2607. 03039v1 Announce Type: new Abstract: Neural networks are increasingly used to infer hidden physical structure from dynamical observations, yet it remains unclear whether their out-of-distribution performance reflects transferable physical rule learning.
arXiv:2607. 07425v1 Announce Type: cross Abstract: Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data.
arXiv:2609.06668v1 Announce Type: new Abstract: Multimodal graphs couple node attributes in different modalities, such as text and images, with relational structure, enabling topological structure an...