Implicit Regularization of Mini-Batch Training in Graph Neural Networks

Mini-batch training of Graph Neural Networks (GNNs) is fundamentally different from training on i.i.d. data: sampling a subgraph alters the topology and introduces boundary effects, leading prior work to develop structure-aware samplers that preserve local connectivity and reduce embedding variance. Surprisingly, we demonstrate that the simplest possible scheme, Random Node Sampling (RNS), training on the induced subgraph of uniformly sampled nodes, matches or outperforms full-graph training on 8 of 10 datasets at a fraction of the wall-clock time and memory. To explain this, we apply backward error analysis to graph mini-batch Stochastic Gradient Descent (SGD) and show that it implicitly minimizes the sampled loss plus a regularizer proportional to the mini-batch gradient variance, a quantity directly shaped by the sampler. Although RNS discards local structure, it produces mini-batches whose expected loss is closer to the full-graph loss, and whose per-batch gradients have lower variance, yielding a better implicit objective. Our analysis reframes the choice of graph sampler as a form of implicit regularization, and identifies RNS as a strong, theoretically grounded method for scalable GNN training.

On the Identifiability of Semi-Blind Estimation in Cell-Free Massive MIMO Networks

Semi-blind joint channel estimation and data detection (JCD) is a promising approach to mitigate pilot contamination in cell-free massive multiple-input multiple-output (CF-MaMIMO) networks. The effectiveness of such methods fundamentally depends on identifiability, i.e., the ability to unambiguously recover the unknown channel coefficients and transmitted data signals from the received uplink observations. In this work, we investigate the identifiability of semi-blind JCD from a large-scale system design perspective. We consider a CF-MaMIMO network in which access points (APs) and user equipments (UEs) are spatially distributed according to Poisson point processes (PPPs). The resulting network topology is modeled as bipartite random geometric graph (BRGG) that captures local connectivity induced by wireless propagation. To enable a tractable analysis, the spatially dependent graph model is approximated by a surrogate independent-edge random graph with matched degree distributions. Building on this model, we develop a recursive probabilistic analysis that characterizes the conditions under which semi-blind recovery succeeds with high probability. The proposed analysis reveals an identifiability region as a function of key system parameters, including AP and UE densities and the connectivity radius beyond which channel coefficients are assumed negligible. Monte Carlo simulations validate the predicted identifiability region and assess the accuracy of the proposed graph approximation. The proposed framework provides system level insights into how network density and connectivity affect identifiability in large-scale CF-MaMIMO systems and offers guidelines for selecting deployment parameters and pilot sequence lengths that enable reliable semi-blind recovery.

AgentCo-op: Retrieval-Based Synthesis of Interoperable Multi-Agent Workflows

Designing multi-agent workflows is especially difficult in open-ended scientific settings where tasks lack curated training sets, reliable scalar evaluation metrics, and standardized interfaces between existing tools and agents. We propose AgentCo-op, a retrieval-based synthesis framework that composes reusable skills, tools, and external agents into executable workflows through typed artifact handoffs, then applies bounded self-guided local repair to implicated components when execution evidence indicates failure. In two open-world genomics case studies, AgentCo-op composes independently developed scientific agents and external tool repositories into auditable workflows without redesigning them or running global topology search. It coordinates specialized agents for spatial transcriptomics and gene-set interpretation to enable collaborative discovery from spatial transcriptomics data, and builds a parallel workflow for cross-modality marker analysis on single-cell multiome data. AgentCo-op can also import a searched workflow as a structural prior and improve it by grounding nodes with retrieved components and applying local repair, showing that synthesis and search are complementary. On six coding, math, and question-answering benchmarks, AgentCo-op achieves the best result on four benchmarks and the best average score under a unified backbone setting, while consistently reducing per-task cost relative to multi-agent baselines. Together, these results suggest that retrieval-based synthesis can extend automated agentic workflow design beyond benchmark-optimized agent graphs to open-world workflows built from existing agents, tools, and typed artifacts.

WoundFormer: Multi-Scale Spatial Feature Fusion for Multi-Class Wound Tissue Segmentation

Chronic wounds such as diabetic foot ulcers and pressure injuries require accurate tissue-level assessment to guide treatment planning and monitor healing progression. While deep learning methods have advanced automated wound analysis, most existing approaches focus on binary segmentation and inadequately model heterogeneous tissue composition due to high intra-class variability and limited annotated data. Multi-class wound tissue segmentation, therefore, remains a challenging and clinically relevant problem. We propose WoundFormer, a transformer-based framework that enhances hierarchical spatial feature fusion for multi-class wound tissue segmentation. Specifically, we replace the standard SegFormer decoder with a spatially-preserving multi-scale aggregation head that maintains feature topology during cross-scale integration and strengthens contextual interactions through convolutional fusion. This design improves boundary localization and discrimination between visually similar tissue categories while preserving transformer efficiency. We evaluate WoundFormer on the WoundTissueSeg dataset (147 images, six tissue classes) and a second benchmark (DFUTissue dataset). The proposed method achieves an overall Dice score of 81.9%, outperforming strong CNN- and transformer-based baselines by up to 4.3 Dice points on the WoundTissueSeg benchmark, with consistent improvements across minority tissue classes. These results indicate that explicit modeling of hierarchical spatial interactions enhances transformer representations for heterogeneous wound tissue segmentation and supports more reliable quantitative wound assessment.

A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations

Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered, and data-driven systems. This work provides a unified perspective on such systems by connecting continuous formulations based on the Helmholtz-Hodge decomposition with discrete and data-driven representations. We review the recently proposed Graph Vector Field (GVF) framework, which enables a decomposition of complex dynamics into gradient, curl, and harmonic components on simplicial complexes, offering both expressivity and interpretability. We then introduce a hierarchy of alternative modeling approaches, including parametric conditional models, linear graph dynamical systems, and reduced Hodge representations, which trade expressive power for computational tractability and reduced data requirements. A key contribution of this work is a cross-domain validation strategy that leverages datasets from well-understood physical systems to verify model correctness and assess robustness independently of the target application domain. This approach enables a systematic evaluation of the trade-offs between model complexity, interpretability, and predictive performance. The resulting framework supports an iterative modeling methodology in which highly expressive models are used as diagnostic tools to identify dominant mechanisms, guiding the construction of simplified models tailored to practical constraints. This work highlights the broad applicability of structured flow modeling and provides a foundation for scalable and interpretable analysis of complex dynamical systems.

ToMAToMP: Robust and Multi-Parameter Topological Clustering

Topological clustering, and its main algorithm ToMATo, is a clustering method from Topological Data Analysis (TDA) which has been applied successfully in several applications during the last few years. This is due to its high versatility, as clusters are detected from the persistent components in the sublevel sets of any user-defined function (gene expression, pixel values, etc), and efficiency, as topological clustering enjoys robustness guarantees. However, ToMATo is also limited in several ways. First, a graph on the data points needs to be provided as a hyper-parameter of the method (whose fine-tuning is left to the user). Second, ToMATo is known to be very sensitive to outlier values in the function range. Finally, and most importantly, ToMATo can only handle one function at a time, whereas it is critical to use several functions in various applications. In this article, we introduce ToMAToMP: the first topological clustering method able to handle several functions at the same time with theoretical guarantees. More specifically, we leverage a recent tool from multi-parameter persistent homology, called MMA decomposition, to design our clustering algorithm, and prove that it enjoys robustness properties. As corollaries, we show that it can be used to make ToMATo independent of graph tuning, and robust to outliers. Finally, we provide a set of numerical experiments showcasing the efficiency and quality of the clusterings produced by ToMAToMP, by showing strong improvement over non-topological and topological baselines for various datasets.

Hypergraph Enterprise Agentic Reasoner over Heterogeneous Business Systems

Applying Large Language Models (LLMs) to heterogeneous enterprise systems is hindered by hallucinations and failures in multi-hop, n-ary reasoning. Existing paradigms (e.g., GraphRAG, NL2SQL) lack the semantic grounding and auditable execution required for these complex environments. We introduce HEAR, an enterprise agentic reasoner built on a Stratified Hypergraph Ontology. Its base Graph Layer virtualizes provenance-aware data interfaces, while the Hyperedge Layer encodes n-ary business rules and procedural protocols. Operating an evidence-driven reasoning loop, HEAR dynamically orchestrates ontology tools for structured multi-hop analysis without requiring LLM retraining. Evaluations on supply-chain tasks, including order fulfillment blockage root cause analysis (RCA), show HEAR achieves up to 94.7% accuracy. Crucially, HEAR demonstrates adaptive efficiency: utilizing procedural hyperedges to minimize token costs, while leveraging topological exploration for rigorous correctness on complex queries. By matching proprietary model performance with open-weight backbones and automating manual diagnostics, HEAR establishes a scalable, auditable foundation for enterprise intelligence.

It's not the Language Model, it's the Tool: Deterministic Mediation for Scientific Workflows

Language models can produce convincing scientific analyses, but repeated generations on the same data do not guarantee the same result. A researcher may regenerate an identical query and receive a different fit, a different peak position or a different analysis procedure, without an obvious way to decide which output to trust. We propose typed mediation, a pattern in which the model orchestrates deterministic tools rather than generating analytical code. Each tool encodes one researcher's exact procedure for one instrument, ported through structured interviews. The model selects which tool to call and with what parameters. The tool produces the result. Regeneration does not change it. We evaluate this claim by running the same photoluminescence analysis on four platforms, including three commercial foundation models, four times each with the same prompt. The typed tool produces identical results across all runs. The commercial platforms either vary in numerical output and analytical methodology across runs, or fail to produce valid results on the task. We deploy this pattern on two instruments serving users over approximately six months, with very positive user feedback. Both cases are very challenging: they involve proprietary binary formats and per-seat licensed software, which force the tool to remain on local infrastructure alongside the data and the instrument it operates. We argue that deployment topology is not just a preference, but a structural requirement of scientific tool mediation. The result is a practical pattern for deploying language models in scientific workflows where reproducibility is mandatory, reducing analysis time from weeks to minutes while guaranteeing identical outputs across runs.

A Resampling-Based Framework for Network Structure Learning in High-Dimensional Data

RSNet is an open-source R package that provides a resampling-based framework for robust and interpretable network inference, designed to address the limited-sample-size challenges common in high-dimensional data. It supports both the estimation of partial correlation networks modeled as Gaussian networks and conditional Gaussian Bayesian networks for mixed data types that combine continuous and discrete variables. The framework incorporates multiple resampling strategies, including bootstrap, subsampling, and cluster-based approaches, to accommodate both independent and correlated observations. To enhance interpretability, RSNet integrates graphlet-based topology analysis that captures higher-order connectivity and edge sign information, enabling single-node and subnetwork-level insights. Notably, RSNet is the first R package to efficiently construct signed graphlet degree vector matrices (GDVMs) in near-constant time for sparse networks, providing scalable analysis of higher-order network structure. Collectively, RSNet offers a versatile tool for statistically reliable and interpretable network inference in high-dimensional data.

A Hybrid Framework for Natural Language Querying of IFC Models with Relational and Graph Representations

Building Information Modeling (BIM) is widely used in the Architecture, Engineering, and Construction (AEC) industry, but the complexity of Industry Foundation Classes (IFC) limits accessibility for non-expert users. To address this, we introduce IfcLLM, a hybrid framework for natural language interaction with IFC-based BIM models. It transforms IFC models into complementary representations: a relational representation for structured element properties and geometry, and a graph representation for topological relationships. These representations are integrated through iterative retry-and-refine LLM reasoning. We implement the framework using an open-weight LLM (GPT OSS 120B), supporting reproducible and deployment-oriented workflows. Evaluation on three IFC models with queries derived from 30 scenarios shows first-attempt accuracy of 93.3%-100%, with all failures recovered using a fallback LLM. The results show that combining complementary representations with iterative reasoning enables more accessible natural language querying of IFC data while supporting routine BIM analysis tasks.