Dependency Graph

Multi-turn agent trajectories often contain redundant rounds (failed tool calls, parallel sub-queries, verification-only steps) that inflate both training and inference cost. We propose viewing each trajectory as a \emph{round-level dependency DAG} that exposes which rounds are globally load-bearing for the final answer, and fine-tune agents on trajectories refined through this DAG. Given an LLM-annotated DAG, these edits are deterministic and interpretable, with optional rephrasing. Models trained on these refined trajectories consistently outperform those trained on the original trajectories at lower inference cost. Specifically, across four multi-modal QA benchmarks, our refinements improve downstream accuracy by up to $1.7$,pp over vanilla SFT (and $5.7$,pp over an LLM-deletion baseline) while reducing per-sample inference messages by up to approximately $40\%$ and inference tokens by up to approximately $48\%$, translating to substantial savings in compute and serving cost. Code is available.

Large language model (LLM) agent failures often contain multiple related errors rather than a single mistake. Existing attribution methods usually identify a responsible agent, step, or root cause, but do not explicitly model dependency between errors. We introduce EDGE, an Error Dependency Graph-guided multi-Error attribution framework. EDGE constructs an error dependency graph from observed error events and validates a reliable causal subset through counterfactual rollout. The inference graph guides a two-stage LLM-as-judge detector for error attribution, and the intervention-validated subgraph provides a more reliable basis for explanation and repair analysis. Experiments on TRAIL and MAST show that EDGE improves category-level multi-error attribution across most evaluated models and settings. Experiments with adapted Who&When-style prompts show that the graph helps across prompting strategies. These results suggest that dependency structure is a useful diagnostic prior for agent failures beyond isolated root-cause prediction.

Comprendia is an Eclipse plugin that integrates structural dependency visualization with LLM-powered code explanation on a shared interactive graph for Java program comprehension. The tool rests on four pillars: (1) a multi-edge-type dependency graph with live search and multiple layouts; (2) LLM explanations grounded in Graph-Aware Callee Pruning (GACP), an auditable strategy that selects relevant callees using the same graph the developer navigates; (3) a clone-detection overlay that highlights duplication and suggests extract-to-parent refactoring opportunities; and (4) a CVE risk overlay powered by OSV.dev. GACP uses graph distance, inheritance collapse, and edge-type weighting to produce prompts that are reproducible across LLM families and traceable to visible graph nodes. We demonstrate Comprendia on a Java project containing known clones and vulnerabilities, showing how the unified graph substrate supports comprehension while keeping the developer in control. Screencast: https://youtu.be/1wlh_RYehzA

The increasing complexity of enterprise business scenarios has promoted the widespread adoption of long SKILL documents in agent systems, posing new challenges for compliance detection: large models incur substantial inference costs, while small models may fail to maintain detection accuracy. To address this gap, we propose SkillCDG, a graph-based framework for long SKILL compliance detection. SkillCDG represents complex business policies as a two-layer constraint dependency graph, where the upper layer indexes SKILL descriptions for scenario routing and the lower layer captures dependencies among atomic constraints within each SKILL. During inference, two-level retrieval followed by dependency closure supports compliance judgment and source traceability. We comprehensively evaluate the framework on three enterprise datasets and two controlled public benchmark variants. Experimental results demonstrate that SkillCDG outperforms baseline methods by up to 12.8 percentage points in detection F1 score, while reducing token consumption by a maximum 64.3%. Moreover, we further investigate the inherent relationships among policy-graph complexity, model scale, and detection performance. Comparative experiments conducted on four checkpoints from a single model family validate a concise and effective scaling trend: end-to-end detection correctness exhibits a complexity-differentiated scaling pattern, and the complexity metric derived from the constraint dependency graph can effectively quantify instance difficulty and the performance improvement potential of models. Leveraging this insightful scaling trend, we conduct adaptive training sample selection and adopt on-policy distillation to efficiently enhance the compliance detection capability of small-scale models.

Inclusion dependency is a relation between attributes of tables that indicates possible Primary Key-Foreign Key references. Automatic discovery of inclusion dependencies is a relevant problem for both academic and industrial communities. The core concern for this problem is the efficiency of discovery process, since it is a computationally expensive task. However, existing studies only address the algorithmic side, while leaving out the implementation aspect. At the same time, engineering details are at least as important as the algorithmic ones for achieving good performance. In this paper, we describe techniques for efficient implementation of two algorithms for discovery of inclusion dependencies - Spider and Faida. The first one is a classic algorithm whose ideas lie in the foundation of many other inclusion dependency discovery algorithms. We propose an efficient parallelization technique, which greatly speeds up the algorithm while simultaneously reducing its memory consumption. The second one is the state-of-the-art approximate algorithm, which we approach by applying four types of optimizations: data buffering, SIMD-enabled execution, careful hash-table selection and parallelization. In order to experimentally evaluate our techniques, we have implemented these algorithms in Desbordante - an open-source science-intensive data profiler written in C++. For Spider, we have evaluated several different options, and in case of Faida we have demonstrated that all our optimization techniques yield results. We also compared our implementations with Metanome - a Java-based data profiler. Overall, we report up to 5x improvement in terms of run time reduction for Spider and up to 8x for Faida.

LLM-based repository-level code generation aims to generate code using the context available in a software repository, requiring LLMs to reason over complex code dependencies. Due to limited context windows and insufficient repository-specific understanding, LLMs typically rely on retrieval-augmented generation (RAG) to incorporate relevant code. Early RAG approaches primarily employ similarity-based retrieval, which often fails to retrieve code snippets that the target function depends on. Recent work introduces graph-based retrieval to model such dependencies, but typically relies on manually designed rules and static global graphs, leading to limited flexibility and high construction and maintenance costs. In contrast, human developers collect helpful context by implicitly constructing a partial dependency graph and iteratively inspecting along it. Inspired by this behavior, we propose DyRetriever, an efficient context retrieval method via partial dependency graphs. DyRetriever uses an LLM to first select a set of entry-point functions and then perform multi-hop reasoning along the code dependency graph. During multi-hop reasoning, it uses the LLM's semantic understanding to validate whether a function can help generate the target function, eliminating manually designed rules and enabling flexibility across scenarios. Instead of statically constructing a global dependency graph, DyRetriever builds a partial graph on demand and discards it after use, reducing construction and maintenance costs. We integrate DyRetriever with a similarity-based code retriever to build DyCoder and evaluate it on CoderEval and DevEval. Experimental results show that DyCoder achieves relative Pass@1 improvements of 25.63% and 59.73% on CoderEval and DevEval, respectively, compared with existing RAG-based methods, while being 7.4x faster than baselines based on static dependency graph construction.

LLM-based Lean proving systems increasingly organize a proof as a blueprint: a dependency graph of formal statements. We introduce BlueprintRepair, a repair interface that lets a model change this graph through ten schema-checked local operations. An operation names the node it edits, so the target theorem cannot be changed. Lean checks every applied change, and an accepted repair must declare every blueprint lemma its proof uses. We also construct BlueprintTrace, a benchmark of 142 controlled failures with complete accepted and rejected repair trajectories. We compare typed edits, exact source patches, and complete module rewrites under matched source, feedback, model, and budget, one episode per state and interface. With DeepSeek-V4-Flash, the three interfaces solve almost the same number of the benchmark's localized failures. Typed repair is the cheapest per solved state (patching is 1.30x as expensive, rewriting 2.06x), and within 10,000 completion tokens per task it reaches almost all of its final coverage, while both free-form interfaces are well behind. A second model, Qwen3.6-Flash, solves fewer states but keeps typed repair cheapest, puts it ahead on the proof-authoring states, and repeats the localized pattern.

Large language models (LLMs) generate code from natural-language prompts, yet real-world prompts rarely provide complete specifications. When prompts leave input formats, error handling, or design decisions unspecified, LLMs fill these gaps with implicit assumptions that shape the generated code's behavior and correctness. Because these assumptions remain hidden, generated code may satisfy tests while violating developer intent. We present AssumptionMiner, a framework that makes implicit assumptions a first-class artifact of LLM-based code generation. In addition to code, AssumptionMiner produces an explicit assumption layer, a structured representation of inferred constraints and design decisions that developers can inspect, confirm, or revise. An AST-based dependency graph enables targeted regeneration of only the code affected by a revised assumption. We also introduce a benchmark of 180 ambiguous programming tasks with 676 annotated assumptions, including a human-verified subset for evaluating code localization. We evaluate assumption extraction, code localization, and assumption-guided regeneration. Across open-source LLMs, a confidence-weighted ensemble achieves an F1 score of 0.816 for assumption extraction, improving on the strongest offline baseline by 3.6x. On the human-verified localization benchmark, AST-guided localization identifies more precise code regions than keyword-based and whole-file baselines. During assumption revision, targeted regeneration modifies less code than non-targeted alternatives while exposing challenges in handling cascading edits. These results demonstrate that making assumptions explicit improves the transparency and controllability of LLM-based code generation.

The HIPE-2026 shared task introduces person-place relation extraction from multilingual historical newspapers as a new evaluation track, classifying the at and isAt relations between pre-annotated person and location mentions in English, French, and German. Motivated by the cost of processing historical archives at scale, our team (DS@GT HIPE, team 2 in the official results) investigates how far a lightweight, interpretable system can go without any pretrained language model at the relation classification stage. Our approach builds a document-level graph from dependency parses, extracts proximity-based and part-of-speech features for each entity pair, and classifies them with small scikit-learn ensembles or compact Graph Attention Networks, keeping every submitted run under 847K parameters. On the official evaluation (Test A, the newspaper test set), our best run reached a macro recall of 0.5142, ranking 3rd on the Efficiency profile while placing mid-table on Accuracy among the 17 participating teams. Two findings stand out. First, minimum character distance alone captures most of the classification signal; adding further engineered features yields inconsistent gains and sometimes degrades performance, echoing prior evidence that argument distance dominates relation extraction. Second, document-grouped cross-validation is essential on this corpus: pair-level splits inflate scores by 25-37 percentage points because entity mentions recur across documents, a data-leakage effect that grouped cross-validation removes.

Matching dependency is a generalization of the functional dependency concept, which allows users to apply custom similarity functions for matching individual attributes. Matching dependencies have a wide range of applications for solving various data quality problems, such as entity resolution, data deduplication, data integration, schema matching, and many more. However, their discovery is a very computationally intensive problem, which limits their practical application. In this paper, we describe a number of optimization techniques for HyMD - currently the state-of-the-art algorithm for the discovery of matching dependencies. These optimizations belong to both technical and scientific domains. The most important of them are: 1) a new sampling technique, 2) a faster generalization lookup technique, and 3) an improved representation of a dependency. The first one aims to raise the efficiency of inference from record pairs, while the last two are designed to speed up lattice-related operations. To evaluate our optimizations, we implemented our version of HyMD in Desbordante, an open-source high-performance data profiler. Experiments demonstrated that they allow for a speedup of more than 40x over the state-of-the-art implementation on average, reaching a speedup greater than 170x in some cases. Finally, the improved version of HyMD is ready to use by anyone. It comes with bidirectional Python integration, which allows calling the C++ algorithm implementation from Python programs while allowing users to supply their custom matching functions.

Conditional functional dependencies (CFDs) are functional dependencies with a restricted scope: they specify the context in which a dependency holds and are useful for data-quality tasks, specifying complex integrity constraints, and extracting valuable insights from data. We study the CFD discovery problem, which is computationally demanding. We build on the state-of-the-art CFDFinder algorithm and introduce a set of algorithmic and engineering improvements, including a parallelization strategy, to produce ParCFDFinder. Our implementation is integrated into Desbordante - a high-performance open-source data profiler written in C++ that exposes a Python interface, enabling CFD discovery to be invoked from any Python program. Experimental results show that our enhancements speed up the algorithm by up to $318\times$ ($118\times$ on average) and reduce memory usage by up to $23\times$ ($14\times$ on average) compared with the existing Java-based implementation of Metanome. Integrating ParCFDFinder into Desbordante makes it possible, for the first time, to conveniently discover CFDs on datasets with hundreds of thousands of rows on a commodity machine within a reasonable time.

Agent skills package reusable operational knowledge for Large Language Model (LLM) agents, yet as they grow in scope, they become dependency-bearing artifacts whose identities, versions, and provenance remain implicit. This opacity already causes duplicated dependencies and inconsistent installations, exposing a gap that dependency management has yet to close. We introduce Agent Skill Supply Chains (ASSCs) to characterize mixed skill-package-service dependency graphs and help close this gap. Borrowing from Software Bill of Materials (SBOMs), we design SkillDepAnalyzer to capture natural-language dependency evidence and model skills as dependency-bearing artifacts. On the SKILL-DEP benchmark, SkillDepAnalyzer recovers skill metadata and dependency graphs accurately and comprehensively, substantially outperforming an LLM-based baseline and package-centric SBOM tools. Applying SkillDepAnalyzer to over 1.43 million skills, we obtain ASSCs and explore their structural diversity and security signals. We find four structural patterns: skill metadata is activation-ready but governance-poor; dependency graphs span skill, package, and service dependencies with concentrated reuse; recursive skill reuse expands dependency graphs and creates hidden package inventory; and skill dependency clusters form around related workflows. We also find that inspecting a skill alone misses security-relevant signals hiding in its dependencies. By analyzing ASSCs, we identify and report known malicious skills persisting in ASSCs to their developers. Based on these findings, we recommend typed dependency manifests, first-class dependency-cluster management, risk-warning audit commands for skill infrastructure maintainers, and lockfile-like records for skill developers.

Mathematical knowledge is organized around statements and their dependencies, but this structure is exposed unevenly: informal papers cite mostly at the document level, while formal libraries record fine-grained dependencies over a much smaller body of mathematics. We introduce TheoremGraph, a unified statement-level dependency graph spanning both informal and formal mathematics. On the informal side, we parse 11.7M theorem-like environments from mathematics arXiv and recover 18.3M candidate directed dependencies, each labeled by the extractor that proposed it so downstream users can trade coverage for precision. On the formal side, we release LeanGraph, a Lean 4 elaborator-level extractor producing 388,105 declaration nodes and 11.3M typed edges across 25 Lean projects. We bridge the two graphs by embedding generated natural-language slogans into a shared semantic space, linking related statements across papers and across the informal/formal divide; an LLM judge affirms 47,952 such matches above a 0.8 cosine floor, with the judge-acceptance rate rising from 48% across the floor to 87% in the >=0.9 tier. On formal concept retrieval, our name-and-signature representation with graph expansion comes within 0.5pp of LeanSearch v2's reranked Recall@10 (0.775 vs. 0.780) without an LM reranker. We release the dataset, extractors, HTTP API, and MCP interface as infrastructure for mathematical search, attribution, and retrieval-augmented reasoning, available at theoremsearch.com and huggingface.co/datasets/uw-math-ai/theorem-matching.

We introduce LEDGER to tackle the novel context engineering challenge of agentic document editing, where localized edits to long, structured documents must be applied efficiently without breaking cross-references or semantic consistency. LEDGER constructs a lightweight dependency graph that explicitly models document structure, including hierarchical organization, explicit references, implicit dependencies, and semantic relationships. For each edit, graph-guided retrieval selects only the necessary context, avoiding full-document processing while preserving consistency. We evaluate LEDGER on a curated benchmark of 1.9k test cases with various document types and lengths, spanning six state-of-the-art models: LEDGER improves consistency from 56% to 76% across all six models and test scenarios while reducing token usage. Notably, LEDGER with low reasoning effort matches baseline performance at high reasoning effort using fewer tokens, showing that explicit dependency representations can partially substitute for expensive internal reasoning in agentic document editing.

Mainstream relational databases ship a uniform feature set across deployments, although individual workloads exercise only a fraction of the available subsystems. We investigate whether a database can instead be generated on demand with a feature set matched to the target workload. We present SpecDB, a system that uses large language models (LLMs) to synthesize customized relational databases. We survey 9 production systems and decompose them into 10 functional modules, each further divided into implementation variants. To capture cross-module dependencies, including cases where implementations in disjoint subtrees must be co-designed, we adopt the FODA feature model and extend it with a cooperate edge, yielding a dependency graph DBGraph. SpecDB operationalizes DBGraph through a layered module-construction pipeline in which each module is generated, validated, and integrated by a dedicated subagent (driven by three inner agents: Main, Tester, Architect), and a Refining Agent that iteratively repairs and tunes the assembled database against a user-supplied refining harness with read-only access to existing database source code. A companion selection component translates a natural-language workload description into a set of implementation variants, providing an end-to-end pipeline from workload description to deployable database. We evaluate SpecDB on TPC-C with BenchmarkSQL. The generated database (23,779 lines of Rust) completes 60-minute TPC-C at 1 and 10 warehouses with zero errors. At 10 warehouses it reaches tpmC=130, compared to 128 for PostgreSQL and 127 for MySQL, with comparable latency at ~3% of their code size. Because the agent operates at module-specification level rather than product source, it can in principle combine techniques across system boundaries. Paired with falling LLM costs, generating a purpose-built database for a target workload is becoming straightforward.

A plausible future mathematical claim must satisfy two constraints: it should follow the direction of prior work and respect the formal dependencies that constrain what can validly follow. Existing approaches typically model only one of these sources, producing claims that are either weakly grounded or insufficiently motivated. We introduce grounded future mathematical generation, where the goal is to generate a plausible future theorem-like claim for an anchor paper using two complementary sources of context: its scientific citation graph and aligned formal theorem dependency graph. To address this setting, we propose COMPOSE, a dual-graph framework that conditions a language model on both scientific citation context and formal theorem structure. To support this setting, we construct a dataset of 108K paired scientific-formal graph examples from arXiv and Mathlib, together with a benchmark of 47K future papers from 2024--2025. Experiments show that COMPOSE outperforms strong baselines on retrieval to real future papers and achieves the best overall performance under LLM-judge evaluation, producing more grounded and mathematically richer outputs. These results show that future mathematical generation benefits from combining scientific context with formal structure. Project page is available at https://david-busbib.github.io/COMPOSE-page/.

Tool-using LLM agents produce trajectories whose calls form a directed dependency graph: earlier tool outputs supply arguments to later calls. Whether this execution structure is represented inside the model is unknown; prior structural probes have targeted static code or chain-of-thought text, not an agent's run-time call graph. A low-capacity edge probe on the residual stream of Qwen3-32B decodes the tool-call dependency graph well above both a Hewitt--Liang random-label control and a positional baseline. A counterfactual contrast between value corruption and structural perturbation indicates the signal tracks abstract topology rather than identifier values, and replicates under an independent, non-substring oracle. The non-positional component replicates on three further interactive multi-hop benchmarks and attenuates as call order alone becomes a sufficient proxy for dependency, vanishing in single-shot planning. Per-layer activation patching shifts the probe at a later, non-patched boundary, evidence that the representation propagates rather than passively reads out, though the realised tool call does not move. To our knowledge this is the first structural probe of an LLM agent's runtime tool-call dependency graph. Our claims concern representation, not behavioural control, and span two model families and one primary domain.

Augmenting Transformers with linguistic structures effectively enhances the syntactic generalization performance of language models. Previous work in this direction focuses on syntactic tree structures of languages, in particular constituency tree structures. We propose Graph-Infused Layers Transformer Language Model (GiLT) which leverages dependency graphs for augmenting Transformer language models. Unlike most previous work, GiLT does not insert extra structural tokens in language modeling; instead, it injects structural information into language modeling by modulating attention weights in the Transformer with features extracted from the dependency graph that is incrementally constructed along with token prediction. In our experiments, GiLT with semantic dependency graphs achieves better syntactic generalization while maintaining competitive perplexity in comparison with Transformer language model baselines. In addition, GiLT can be finetuned from a pretrained language model to achieve improved downstream task performance. Our code is released at https://github.com/cookie-pie-oops/GiLT-LM.

Current autoformalization benchmarks are largely focused on olympiad or undergraduate mathematics, while graduate and research-level mathematics remains underexplored. In this paper, we introduce MathAtlas, the first large-scale autoformalization benchmark of in the wild graduate-level mathematics, containing ~52k theorems, definitions, exercises, examples, and proofs extracted from 103 graduate mathematics textbooks. MathAtlas is enriched with a mathematical dependency graph containing ~178k relations, and is the first autoformalization benchmark to include such relations, facilitating evaluation and development of dependency-aware autoformalization systems. Our extensive experiments show that MathAtlas is high quality but extremely challenging: strong baselines achieve at most 9.8% correctness on theorem statements and 16.7% on definitions. Furthermore, we find performance of state-of-the-art models degrades substantially with dependency depth: on MA-Hard, a subset of 700 entities with the deepest dependency trees, the best model achieves only 2.6% correctness for autoformalization on this challenging dataset. We release MathAtlas to the community as a benchmark set for large-scale autoformalization of graduate-level mathematics in the wild.

Backpropagation is inherently sequential across depth, creating an $O(K)$-deep dependency chain that bottlenecks parallel training. While parallel-scan formulations theoretically reduce this depth to $O(\log K)$, they are computationally prohibitive for modern architectures due to the $O(d^3)$ cost of composing full-rank $d\times d$ Jacobians over the entire hidden state. We introduce Latent Bounded Interfaces (LBI), an algorithmic formulation that makes scan-based backpropagation tractable by restricting inter-region communication to a low-dimensional latent interface, $m_k \in \mathbb{R}^{r}$, where $r \ll d$. This reduces the adjoint recursion to a suffix scan over $r \times r$ Jacobians, cutting per-combine cost from $O(d^3)$ to $O(r^3)$ while preserving exact gradients under the bounded-interface model. We demonstrate that LBI maintains model quality across four architectures (Mamba-2, Mamba-3, Transformer, and a Mamba--Transformer hybrid) at 47--61M block parameters. Interfaces of dimension $r=16$ suffice to preserve training quality within 0.16--0.35 cross entropy of dense baselines. The resulting framework provides an algorithmic foundation for region-parallel training, reducing cross-device backward communication to a single scan over $K$ fixed-size matrices, of approximately 56 KB for our experimental configurations.

The security discussion around agentic AI focuses heavily on prompt injection. This paper argues that multi-agent systems also create a distinct authorization problem: maintaining authorization invariants as non-human principals retrieve data, delegate tasks, and synthesize results across changing boundaries. We call this problem authorization propagation. It is not reducible to prompt injection and is not fully addressed by classical access-control models such as RBAC, ABAC, or ReBAC. The paper formalizes authorization propagation as a workflow-level property, identifies three sub-problems (transitive delegation, aggregation inference, and temporal validity), and derives seven structural requirements for authorization architectures in multi-agent AI systems. Recent work on invocation-bound capability tokens, task-scoped authorization envelopes, dependency-graph policy enforcement, and execution-count revocation demonstrates that the field is converging on the problem, but not yet on a complete architecture. The central claim is that identity governance must be treated as infrastructure: evaluated continuously, enforced at every interaction boundary, and designed into the system before orchestration logic is allowed to scale. Preliminary implementation evidence from a production enterprise AI platform shows that ordinary system behavior, not only adversarial action, already produces the failures this model predicts.

Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their inability to synthesize new definitions. To tackle these issues, we present Aria (Agent for Retrieval and Iterative Autoformalization), a system for conjecture-level formalization in Lean that emulates human expert reasoning via a two-phase Graph-of-Thought process: recursively decomposing statements into a dependency graph and then constructing formalizations from grounded concepts. To ensure semantic correctness, we introduce AriaScorer, a checker that retrieves definitions from Mathlib for term-level grounding, enabling rigorous and reliable verification. We evaluate Aria on diverse benchmarks. On ProofNet, it achieves 91.6% compilation success rate and 68.5% final accuracy, surpassing previous methods. On FATE-X, a suite of challenging algebra problems from research literature, it outperforms the best baseline with 44.0% vs. 24.0% final accuracy. On a dataset of homological conjectures, Aria reaches 42.9% final accuracy while all other models score 0%.

Despite their widespread use, the principles governing the organisation of syntactic dependency trees remain poorly understood. I analyse dependency trees from 124 typologically, genetically, and geographically diverse languages. Their topology departs systematically from randomness. Relative to uniformly sampled random trees, dependency trees exhibit greater structural robustness and lower branching heterogeneity. I propose that these universal regularities emerge naturally from incremental grammatical encoding. I model this process using sublinear preferential attachment. The model accurately reproduces the observed topology. More generally, the results demonstrate how a universal statistical property of syntax can emerge from a simple, cognitively motivated generative process. They further illustrate a broader principle of efficiency by construction: communicatively efficient syntactic structures can emerge without direct optimisation for communication.