Automated survey generation systems increasingly rely on flat retrieval over document collections, limiting their ability to capture the evolutionary structure of research fields. We present SurveyGraph, a framework centered on a Methods-Entity Knowledge Graph (MEKG) that encodes method-level follow-on, competition, and shared-resource relations across papers. The MEKG serves as a unified backbone for core-paper discovery, graph-aware retrieval, hybrid outline generation, and evolutionary narrative synthesis.

We evaluate SurveyGraph through a multi-level protocol spanning retrieval benchmarks, semantic-edge validation, citation grounding audits, benchmark-facing collection probes, and same-backend generation-stage diagnostics. In a controlled seven-method equal-budget benchmark, MEKG-anchored fusion achieves the best balance of recall and structural density among all tested methods, demonstrating that typed graph structure provides a complementary signal to simpler retrieval approaches. On the archived graph-native core diagnostic, graph-aware retrieval nearly doubles recall over flat lexical baselines across all eight runs (p = 0.004). A semantic evidence gate with AUC = 0.75 filters noisy edges, and citation-grounding audits over 160 generated sentences confirm 80.6% anchored-or-partial support with evidence-level contrasts validating genuine alignment. Human validation over 108 stratified semantic edges (Cohen’s κ = 0.64 for the binary support decision) confirms 68.5% supported-or-partial after adjudication, with improves relations strongest at 80.6% and extends weakest at 52.8%. A SurveyBench-facing collection probe reaches 0.521 mean reference coverage on four topics under an eight-paper budget; same-backend Qwen diagnostics over a 30-paper/74-relation MEKG further show that removing hybrid outlining lowers artifact organization signals. We report concurrent-system comparisons only as bounded diagnostics rather than same-backend end-to-end claims. Code and artifacts are available at: https://github.com/xzzvsxd/SurveyGraph.

Open-weight large language models (LLMs) can generate function-level programs from natural-language prompts, but plausible candidates still fail on hidden semantics and repeat mistakes across repair attempts. We present ReMCTS, an execution-grounded, memory-augmented, LLM-guided MCTS-style search framework. It organizes program candidates as tree states, retains branch-local debugging context, retrieves failure experience across branches, and distinguishes failed checks from unavailable evidence. On HumanEval and MBPP-Sanitized, visible-test ReMCTS improves over direct generation in 8 of 10 model–dataset pairs under held-out evaluation, whereas proxy-only search is less stable. Controlled tree-search, sampling, repair, and memory ablations characterize the source and limits of these gains. A 30-task HumanEval-X C++ pilot further demonstrates compatibility with compiler-backed execution, but does not constitute a broad multilingual evaluation.

Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib’s definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework. We introduce TaoAnalysisBench, an undergraduate-level benchmark derived from the exercises and definitional frameworks given in Terence Tao’s Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoAnalysisBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of 2.18x on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoAnalysisBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.

Large language models can repeat an instruction while failing to keep obeying it. We study this recall–compliance dissociation in long-horizon dialogue and define State Integrity Collapse: a model preserves a stated constraint in memory but stops applying it to later turns. We introduce StateTrack-Bench, a controlled suite of conversations covering numerical, format, role/persona, factual-memory, and logical-rule constraints. Across seven provider-pinned model snapshots and five dialogue-depth probes, strict joint retention ranges from 62.4% to 100.0%, with degradation concentrated in symbolic constraints and in one especially brittle model. A forked recall audit shows that 88.6% of observed failures are behavioral-drift failures rather than ordinary forgetting; excluding the brittle outlier preserves this diagnosis (84.4% of failures). Extended evaluations at depths up to 50 turns confirm that the dissociation persists beyond the core benchmark, while Structured State Anchoring recovers up to 24.4 points on immutable constraints. The results show that reliability cannot be inferred from single-turn instruction following alone; evaluation must track whether remembered constraints remain operational as dialogue state grows. Code and artifacts are available at: https://github.com/xzzvsxd/StateTrack.