Predicting stock returns requires modeling persistent company relations and time-varying market signals. Graph Neural Network (GNN) approaches combine static priors with dynamic relational graphs, but treat every extracted edge as a trustworthy binary fact, ignoring heterogeneous reliability across relational sources. We propose LENS (LLM-Extracted priors and News-driven Semantics), a static--dynamic graph framework for stock return prediction and ranking that models relational reliability as a first-class signal across the pipeline. On the static side, we extract a multi-relational company graph from a Large Language Model and aggregate it over multiple runs with confidence weighting to downweight low-consistency edges. On the dynamic side, we build a news-driven semantic graph with exponential-decay temporal aggregation to capture changing market context under uneven coverage. A context-dependent gated fusion module rebalances the two graphs at the per-stock, per-day level. On S&P 500, LENS improves AR@5 by 16.4% and SR@5 by 22.6% over the strongest baseline, and on NASDAQ 100 it achieves comparable improvements (15.5% and 20.9% respectively). Ablations isolate each component's contribution, and a human-validation study of sampled relations supports that the aggregation is grounded, providing evidence that reliability-aware LLM relations and news-based semantic graphs carry complementary information for graph-based financial prediction.
Reinforcement learning (RL) has become a dominant paradigm for enhancing LLMs' reasoning capabilities. Yet long-horizon autoregressive rollouts introduce a fundamental limitation: local policy mismatch can compound into severe state distribution shift over trajectories. Existing LLM RL methods, such as GRPO and GSPO, control policy mismatch at the token or sequence level, but overlook this trajectory-induced shift, causing training instability and eventual collapse as the horizon grows. To close the state distribution gap, we propose Trajectory-Aware Policy Optimization (TAPO), a principled framework that theoretically derives the state-distribution correction from the off-policy policy gradient and incorporates it into the RL objective. TAPO further employs a geometric-mean estimator for variance reduction, together with a length-aware dynamic clipping that prevents overly deviated updates across the trajectory. Extensive experiments demonstrate that TAPO significantly surpasses existing LLM RL algorithms across eight competition-level benchmarks, achieving up to 48% and 12% improvement over GRPO on mathematical reasoning and algorithmic coding, with substantially enhanced training stability.
Lean is increasingly used to verify mathematical proofs and software produced by LLM agents, but writing formal proofs remains hard. Existing prover systems take a divide-and-conquer approach that recursively decomposes hard proof goals into easier lemmas and splits again any lemma that resists proof. However, a lemma can resist proof for different reasons, including insufficient guidance, a false statement, or a flaw in the decomposition that produced it. Existing systems cannot tell these apart as a failed attempt reports little beyond its failure, and responses are confined to the failing node without considering the rest of the proof or revising the plan above it. The system may thus keep decomposing obligations along a flawed proof direction until the budget runs out, causing the whole proof attempt to fail. We introduce Maestro, a Lean prover harness that handles failures through global coordination. Provers report why they failed, not just that they failed, and a coordinator that sees the whole proof chooses an appropriate response, such as guiding a stuck prover, correcting a false lemma, or retracting a flawed subtree and replanning it. The same harness extends to verified code synthesis, where a checked counterexample sends the code back for repair. We evaluate Maestro with four frontier LLMs on seven mathematics and three software verification benchmarks. It proves more targets than each model's native coding agent (Claude Code or Codex) on every benchmark the agent has not already saturated, with the largest gains on research-level mathematics. With Claude Opus 5, it discovers its own proofs of 34 of the 48 theorems in the June 2026 release of arXivLean, against 19 for the native agent. It also outperforms all published prover systems on every benchmark they share, solving 669/672 PutnamBench, 59/60 Lean-IMO-Bench, and 6/6 IMO 2026.