Language-encoded network topology enables large language models to reason about complex networks

Networks describe systems in biology and beyond, from protein interactions and social relationships to power grids and citation records. Reasoning about such systems requires understanding their structure: which elements are central, which connections bridge separate communities, and how it changes when elements are removed. Although large language models (LLMs) excel at natural language, they struggle with such questions when networks are given as edge lists, sentences or measurement tables, because their structural meaning must be inferred. Here we introduce BioGlyph, which compiles network topology into an interpretable and transferable language of structural roles. BioGlyph combines graph partitioning and structural measurements to identify roles such as hubs, community cores and cross-community connectors, and fixed rules to translate them into a universal vocabulary. The representation describes each element through its structural role, supporting evidence and semantic consequences, leaving both the network and the LLM unchanged. Across twenty networks spanning five domains, BioGlyph substantially improves open LLMs' ability to answer structural reasoning questions, outperforming edge-based, numerical and learned representations by up to 26 percentage points in system accuracy. Ablations show that the gain comes from explicitly encoding structural roles in semantically interpretable terms. The gain is more prominent in dense, community-structured networks and diminishes in sparse networks whose topology is more readily inferred from text. In a budding-yeast protein-interaction network, BioGlyph exposes biological organization: cross-community connectors are enriched for essential genes, whereas peripheral proteins are depleted. BioGlyph thus provides an interpretable representation for both language models and scientists to reason about network structure.

A Comparative Study of Graph Representations for GNN-Based Power Grid Control in L2RPN

Graph construction is a critical but underexamined design choice in deep reinforcement learning for power grid control. We present a controlled experimental comparison of different graph representations, including physical topology, electrical-sensitivity, and hybrid variants for topology control in the Learning to Run a Power Network (L2RPN) environment. Our findings indicate that matching graph complexity to task granularity is more important than maximizing representational richness, and highlight the importance of controlled representation studies at scale.

Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization

Bilevel mixed-integer linear optimization problems model hierarchical decision processes in which a leader anticipates the optimal response of a follower. Although expressive, these problems are computationally challenging because lower-level optimality is embedded in the leader's feasible region. Value-function reformulations replace the nested follower optimization with a constraint involving the follower's optimal value, but evaluating this value function exactly can itself be expensive. This paper introduces Graph4BiLO, a graph neural network (GNN) approach for learning bilevel value functions from variable--constraint graph representations. In contrast to fixed-length multilayer perceptron (MLP) representations, the GNN uses shared message-passing parameters and can therefore be applied across multiple problem sizes with a single trained model. The learned ReLU network is encoded exactly as mixed-integer linear constraints and embedded in an approximate single-level formulation. A repair step subsequently re-solves the follower problem for the selected leader decision to recover a bilevel-feasible follower response. We evaluate Graph4BiLO on knapsack interdiction instances with 20--100 items against the exact MibS solver and the learning-based Neur2BiLO method. Graph4BiLO obtains objective values comparable to Neur2BiLO across all tested sizes while avoiding size-specific neural networks. An additional out-of-distribution experiment demonstrates zero-shot transfer from 20-item training instances to previously unseen 40- and 60-item instances. However, embedding message passing at every graph node substantially increases the resulting mixed-integer formulation size and solve time. These results identify a central tradeoff between size-generalizable graph representations and the computational cost of embedding GNNs within optimization models.

Personalized Auto-Research: Towards a True AI Co-Scientist

AI co-scientists that generate hypotheses, retrieve related work, design experiments, execute code, and draft full papers are beginning to change how research is carried out. Despite this rapid progress, state-of-the-art systems remain researcher-agnostic: given a research goal, they optimize novelty, validity, or reviewer score while ignoring the individual scientist who will use the output. This overlooks a fundamental fact about research, namely, that what counts as novel, valuable, or feasible depends on the researcher, including their prior work, methodological repertoire, and the collaborators and communities in which they are embedded. In this work, we introduce the problem of personalized auto-research, which conditions every stage of the research process on a representation of the individual researcher. We argue that personalization is not a convenience layer, but rather the fundamental property that allows an AI system to serve as a genuine co-scientist rather than a generic instrument. To address this problem, we propose a general and flexible framework that threads a graph-grounded researcher context through retrieval, hypothesis search, experimentation, writing, and review. The framework consists of three fundamental components: (i) graph-grounded researcher representations, (ii) personalization across the full research pipeline, and (iii) evaluation grounded in the individual. Notably, we highlight a one-size-fits-all failure mode where distinct researchers issuing the same goal receive essentially the same research, erasing the tacit knowledge through which novel ideas arise. Finally, we discuss fundamental open problems and challenges.

IRGNN: Efficient Invariant Radar Graph Neural Network for Radar Point Cloud Object Detection

Perception is a fundamental component of autonomous driving systems. While LiDAR-based methods have achieved remarkable progress in object detection, their reliability can degrade under adverse weather conditions. Radar point clouds provide a robust alternative due to their resilience to bad weather and low-illumination scenarios. However, radar point clouds are typically sparse, unordered, and less informative than LiDAR data, making it challenging to directly apply existing LiDAR-based perception methods. To address these challenges, we propose IRGNN, an Invariant Radar Graph Neural Network for radar point cloud object detection. IRGNN first reconstructs radar point clouds into graph representations using translation- and rotation-invariant feature designs, enabling robust modeling of sparse radar measurements. It then employs an improved message passing neural network (MPNN) with residual connections and a virtual node layer to enhance local feature propagation and global context modeling. Finally, task-specific heads are applied to the learned graph representations for object classification and bounding box prediction. Experimental results on the RadarScenes dataset show that IRGNN outperforms existing radar-based object detection methods and achieves competitive performance. In addition, IRGNN significantly reduces computational cost and memory usage during inference, demonstrating its effectiveness and practical potential for efficient radar-based perception in autonomous driving.

LLM-based Vulnerability Discovery in Business Process Documentation

Just like software and hardware, business processes are susceptible to vulnerabilities that can lead to product quality issues, delays, and increased costs. Business process vulnerabilities can arise from a variety of sources, including conflicting requirements, ambiguous documentation, invalid measurement spec-ifications, omission of quality checks, or implementations that differ from speci-fications. MIRABELLE is a system that identifies and characterizes business logic (BL) vulnerabilities from available business process representations, in-cluding ISO 9000/9001 documentation, user guides, work instructions, and pro-cess execution logs. MIRABELLE leverages recent advances in AI/ML to pro-cess available business process documentation and generate attributed graph rep-resentations of the business logic that can be processed using both graph and for-mal logic approaches for identifying potential vulnerabilities. However, extract-ing the business logic (e.g., operation execution sequences, decisions, input/out-put resources) from mostly natural language artifacts is challenging due to the required domain expertise, inherent process complexity, and the sometimes very large volumes of information. This paper focuses on our experimentation with Large Language Models (LLMs) and their role within MIRABELLE. We report on the performance of several LLMs across vital stages of vulnerability detection, from grammatical and technical error-flagging in short phrasings, to complete process structure recovery and extraction.

The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression

Over-parameterized linear regression has been widely studied over the last decade. However, most existing works assume that the covariates are independent and that their covariance matrices are non-degenerate. In this paper, we relax both assumptions and derive deterministic equivalents for the prediction risk in a vanishing-ridge regime. We show that degeneracy of the covariance matrices and dependence can lead to multiple descent, and characterize where the corresponding peaks can occur. Our proofs use a novel graph representation of the variance profile. We show that maximum matchings and the Dulmage--Mendelsohn decomposition of the associated bipartite graph identify the configurations at which the variance becomes singular.

Dependency-Guided Code Generation: Structured Matrix Decomposition and Consistency-Guided Refinement

The increasing complexity of modern software systems has made automated code generation a fundamental task in software engineering. However, existing approaches often fail to adequately capture the intricate, multi-level dependencies among code entities, leading to generated code that is logically incomplete or difficult to integrate into real-world systems. To address this limitation, we propose a dependency-aware code generation framework that explicitly models interactions among code entities through a graph-based representation. We decompose dependencies into two complementary components: a quantized matrix that captures strong, explicit relations, and a sparse low-rank factorization that models weaker, implicit interactions. The decomposition is efficiently learned via an alternating optimization procedure. During code generation, the learned dependency structure is incorporated as a constraint, ensuring both semantic coherence and structural consistency of the generated code. Furthermore, we introduce a sparse triplet representation for strong dependencies, significantly improving storage efficiency and computational scalability. Extensive experiments demonstrate that our approach consistently produces code with superior semantic alignment and structural fidelity compared to existing methods.

LP Mining with LP2Graph: A Use Case for Railway Rescheduling

Like many optimization-driven domains, railway rescheduling relies on Mixed-Integer Linear Programming (MILP), yet the field's modeling knowledge is scattered across hundreds of papers in incompatible notations, and narrative surveys organize it subjectively: they classify models by vocabulary rather than by structure, and reproduce neither. We present LP Mining with LP2Graph, a method that mines the structure of published LP and MILP formulations into a reproducible dataset and an induced taxonomy. Its core, LP2Graph, represents each formulation admitted by its canonical grammar as a typed variable--equation graph derived from a single canonical model; once a source is extracted into that model, everything downstream is deterministic. Each source is parsed into this model, homologized, and clustered bottom-up (over variables, then constraints and the objective, then whole-model structure) and, separately, by application domain and solution approach; the resulting groups are labeled by a rule-seeded, self-updating classifier. We validate the representation rather than assume it: per-cluster representatives are regenerated as independent LaTeX and re-solved across CBC, HiGHS and Gurobi against the optimum reported in the source paper. The outcome is an objective, repeatable taxonomy of variables, constraints and model types: the principled foundation on which our raiLPminer line of automated railway-rescheduling model development builds.

Instruction Set and Language for Hypergraphs

We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $Σ_{\mathrm{HG}}$. The encoding is executed by a small virtual machine comprising a sparse hypergraph, a circular doubly-linked list (CDLL) of node references, and $k$ traversal pointers, where $k$ bounds the hyperedge arity. Instructions either move a pointer through the CDLL or insert a hyperedge, optionally together with new nodes, into the hypergraph. Every string over $Σ_{\mathrm{HG}}$ decodes to a valid hypergraph; the alphabet is closed. A greedy \emph{HypergraphToString} (h2s) algorithm encodes any connected hypergraph into a string; a backtracking variant seeded at nodes of lexicographically maximal structural tuple produces a \emph{canonical string} $w^{*}$, which we conjecture to be a complete isomorphism invariant. Canonical-string equality then decides hypergraph isomorphism natively, without the standard reduction to the Levi incidence graph followed by a graph-isomorphism engine. We verify the round-trip property $s2h(h2s(H)) \cong H$ on 150 connected random uniform hypergraphs and on named combinatorial designs, and we benchmark the canonical algorithm against the three practically available exact baselines -- nauty, Traces, and bliss operating on the 2-coloured Levi graph -- across a $(n, c)$ grid with ten seeds per cell. All four methods agree on every one of 600 isomorphism verdicts, consistent with the completeness conjecture. On wall-clock time the Levi baselines dominate every tested cell by three to five orders of magnitude (geometric-mean ratio $311\times$ to $117{,}672\times$), which we report as measured. We contribute the representation framework, a conjecture of canonical completeness, and the first native-versus-Levi benchmark for hypergraph isomorphism.

GRADE: Graph Representation of LLM Agent Dependency and Execution

Can one graph represent every kind of LLM agent's run? A trace records what each step did, never what it relied on, the state it read, and the results it reused. GRADE recovers that missing layer: it models any run as one graph over its step nodes with two edge layers, execution edges (what ran in what order) read from the trace for free, and dependency edges (what each step relied on) rarely logged, so each is graded by how it is known, observed, declared, or inferred. One representation, and each layer earns its place. Across six corpora of LLM agents spanning tool use, coding, and the web, the dependency layer can predict failure where run size is weak and, under leave-one-corpus-out transfer, stays above chance on every held-out class while run size fails. Meanwhile, the execution layer localizes the faulting step in a failed multi-agent run. This work also provides a more in-depth analysis of why generic graph neural networks may misread the dependency layer, unlike our feature-based alternative. The same graph representation opens further uses, carrying from failure diagnosis in a single run to efficiency and robustness optimization at scale.

Accurate Legal Reasoning at Scale: Neuro-Symbolic Offloading and Structural Auditability for Robust Legal Adjudication

Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning errors and the high cost of inference. We propose Amortized Intelligence, a neuro-symbolic approach where we use an LLM once to translate a legal text into Deterministic Autonomous Contract Language (DACL): a typed graph intermediate representation. Adjudication then relies on deterministic graph executions with a visually auditable trace. In comparison against runtime LRM baselines (including GPT-5.2 and Gemini 3 Pro), our DACL-based Agent achieves near-perfect consistency and mitigates the "reasoning cliff" observed in probabilistic models. The system reduces compute costs by over 90% in high-volume workflows while satisfying the strict auditability requirements of legal adjudication.