arXiv AI June 9, 2026 By Rafael Cabral, Pang Zixi, Ziyi Shou, Shen Xin

Internalizing Geometric Law: Learning from Solver Residuals for Precision-Critical Generation

arXiv:2606. 09278v1 Announce Type: cross Abstract: Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

arXiv AI

Jun 29

Verifiable Geometry Problem Solving: Solver-Driven Autoformalization and Theorem Proposing

arXiv:2606. 27926v1 Announce Type: new Abstract: Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor.

By Can Li, Ting Zhang, Junbo Zhao, Hua Huang

agents reinforcement-learning multimodal

arXiv AI

Jul 21

Constraint-Anchored Reasoning Traces

arXiv:2607. 16727v1 Announce Type: new Abstract: Autoregressive multimodal large language models (MLLMs) suffer from error snowballing: a single incorrect inference early in a chainof-thought (CoT) trace corrupts all downstream reasoning.

By Zehua Cheng, Wei Dai, Jiahao Sun

llms fine-tuning multimodal benchmarks

arXiv AI

1d ago

Program Learning with Verifiable Rewards: Symbolic Backpropagation for Post-Training LLMs

arXiv:2608.28421v2 Announce Type: replace Abstract: Post training a language model to reason means updating its weights. Supervised finetuning and reinforcement learning both place the acquired capab...

By Vishvesh Bhat

llms reinforcement-learning fine-tuning benchmarks

arXiv AI

Aug 3

GeoRA: Geometry-Aware Low-Rank Adaptation for RLVR

arXiv:2601. 09361v4 Announce Type: replace-cross Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) is a key paradigm for improving large-scale reasoning models.

By Jiaying Zhang, Lei Shi, Jiguo Li, Jun Xu, Jiuchong Gao, Jinghua Hao, Renqing He

llms reinforcement-learning fine-tuning

arXiv AI

Jun 4

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems

arXiv:2606. 04816v1 Announce Type: new Abstract: Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code.

By Xizi Luo, Changhong He, Dongdong Geng, Chenggong Shi, Yu Mei

llms benchmarks

arXiv Machine Learning

Jun 9

TinyJudge: Unverifiable Constraint Alignment via Lightweight Specialist Ensembles

arXiv:2606. 07520v1 Announce Type: cross Abstract: Instruction Following (IF) is a core capability of LLMs, requiring strict adherence to diverse constraints, ranging from verifiable ones (e.

By Yirong Zeng, Yufei Liu, Xiao Ding, Yutai Hou, Yuxian Wang, Wu Ning, Haonan Song, Dandan Tu, Qixun Zhang, Yuxiang He, Bibo Cai, Ting Liu

llms reinforcement-learning benchmarks safety

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Related stories

Verifiable Geometry Problem Solving: Solver-Driven Autoformalization and Theorem Proposing

Constraint-Anchored Reasoning Traces

Program Learning with Verifiable Rewards: Symbolic Backpropagation for Post-Training LLMs

GeoRA: Geometry-Aware Low-Rank Adaptation for RLVR

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems

TinyJudge: Unverifiable Constraint Alignment via Lightweight Specialist Ensembles