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新论文 · v1arXiv:2611.10487

GEAR: A GPU-Accelerated Global Solver for Bounded Continuous Nonlinear Programs via Linear Bound Propagation

Duo Zhou, Hesun Chen, Xiangru Zhong, Grani A. Hanasusanto, Huan Zhang

原文摘要

We present a novel GPU-accelerated global solver for constrained nonlinear programming (NLP) inspired by the efficient linear bound propagation framework in neural network (NN) verification. Existing work on NN verification, a problem that can be cast as feasibility detection for a nonlinear objective, demonstrated orders-of-magnitude speedups with the linear bound propagation-based framework when compared to traditional solvers. Extending this paradigm to global nonlinear programming requires addressing many challenges: a global constrained NLP solver must effectively exploit all, possibly unstructured, nonlinear constraints to improve the objective, whereas NN verification typically handles simple input box constraints over a well-structured NN and does not directly optimize an objective function. We address these challenges by fully exploiting the linear bounds produced by bound propagation: these linear bounds can be viewed as relaxations of nonlinear constraints and used to provide lower bounds, check infeasibility, and guide the search for a primal solution. In addition, we propose tighter linear relaxations for bilinear, quotient, and other commonly used nonlinear functions in NLP problems, and a projected augmented Lagrangian method tightly coupled to our dual solving procedure to produce primal solutions. Our method solves 421 of 505 bounded and continuous NLP problems in the GAMS and MINLPLib benchmarks under a 180-second limit, more than each of the six global solvers we compare with, including Gurobi and BARON (commercial), and SCIP (open-source). Sixteen of these problems are certified by none of the six global solvers; all of them contain exponential, logarithmic, or trigonometric terms, which are often challenging for traditional approaches. Project webpage is at https://verified-intelligence.github.io/GEAR.

math.OC · cs.LG · cs.MS · math.NA

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首次观测 · 记录 #1ACL Anthology · ACL 2026:acl:2026.acl-long.1974ACL Anthology · ACL 2026

AdaFuse: Adaptive Ensemble Decoding for Large Language Models

Chengming Cui University of Illinois at Urbana-Champaign, Tianxin Wei, Ziyi Chen, Ruizhong Qiu University of Illinois Urbana-Champaign, Zhichen Zeng University of Illinois Urbana-Champaign, Zhining Liu, Xuying Ning, Duo Zhou University of Illinois at Urbana-Champaign 等 9 位作者

原文摘要

Large language models (LLMs) exhibit complementary strengths arising from differences in pretraining data, model architectures, and decoding behaviors. Inference-time ensembling provides a practical way to combine these capabilities without retraining. However, existing ensemble approaches suffer from fundamental limitations. Most rely on fixed fusion granularity, which lacks the flexibility required for mid-generation adaptation and fails to adapt to different generation characteristics across tasks. To address these challenges, we propose AdaFuse, an adaptive ensemble decoding framework that dynamically selects semantically appropriate fusion units during generation. Rather than committing to a fixed granularity, AdaFuse adjusts fusion behavior on the fly based on the decoding context, with words serving as basic building blocks for alignment. To be specific, we introduce an uncertainty-based criterion to decide whether to apply ensembling at each decoding step. Under confident decoding states, the model continues generation directly. In less certain states, AdaFuse invokes a diversity-aware scaling strategy to explore alternative candidate continuations and inform ensemble decisions. This design establishes a synergistic interaction between adaptive ensembling and test-time scaling, where ensemble decisions guide targeted exploration, and the resulting diversity in turn strengthens ensemble quality. Experiments on open-domain QA, arithmetic reasoning, and machine translation demonstrate that AdaFuse consistently outperforms strong ensemble baselines, achieving an average relative improvement of 6.88%.

cs.CL

Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表