An Integer Programming Approach to Compute Lower Bounds for Ramsey Numbers Using Circulant Graphs
本文提出了一种整数规划方法，通过限制搜索范围到循环图来计算Ramsey数的下界，并利用分支切割算法求解，提高了25个R(3,n)值的下界。
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Capacitated power dominating set problem: a solution approach based on forbidden propagation sets
This study addresses the optimal placement of measurement devices in power systems under capacity constraints, formalized as the capacitated power dominating set problem. The authors introduce a novel combinatorial structure termed the "forbidden propagation set," derive its structural properties, valid inequalities, and redundancy-elimination conditions, and formulate an integer linear programming model that avoids big-M constraints. By integrating infection variables with exponentially many constraints, they design an efficient delayed separation algorithm based on graph-theoretic cycle detection. Evaluated on benchmark instances with up to 14,000 nodes, the proposed approach achieves an average speedup of 1.7× over existing methods, demonstrating that performance is jointly influenced by network size and device capacity, thereby significantly enhancing scalability and computational efficiency for large-scale power systems.
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Variational Approximations for Robust Bayesian Inference via Rho-Posteriors
This work addresses the computational intractability of ρ-posteriors in Bayesian robust inference, which arises from optimizing over a reference distribution. To resolve this issue, the authors develop a PAC-Bayesian framework that restores theoretical guarantees by introducing a temperature-tuned Gibbs posterior, while enabling scalable inference through variational approximations. The proposed method is the first to simultaneously ensure robustness against contaminated data, computational feasibility, and rigorous finite-sample theoretical guarantees—including oracle inequalities with explicit convergence rates. Numerical experiments demonstrate the practical effectiveness and robustness of the approach in real-world settings.
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Empirical PAC-Bayes bounds for Markov chains
Existing PAC and PAC-Bayes generalization bounds for time-dependent data rely on unknown process parameters—such as mixing coefficients or spectral gaps—rendering them impractical for real-world applications. Method: We propose the first fully empirical PAC-Bayes bound for Markov chains: we replace the intractable spectral gap with an estimable “pseudo-spectral gap” and provide a data-driven estimator for it under finite state spaces. The bound is constructed solely from observed trajectories, requiring no prior knowledge of the underlying Markov process. Contribution/Results: Our theoretical analysis establishes statistical validity, while simulations demonstrate that the empirical bound achieves tightness comparable to its non-empirical counterpart. This work delivers the first practical, assumption-free PAC-Bayes generalization guarantee for Markovian settings—eliminating reliance on unknown process parameters—and significantly enhances the operationality of learning theory for dependent data.
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Can LLMs Help Improve Analogical Reasoning For Strategic Decisions? Experimental Evidence from Humans and GPT-4
Strategic analogical reasoning—particularly the “source-target matching” stage—has been overlooked as a distinct cognitive process, and the comparative capabilities of large language models (LLMs) versus humans remain poorly understood. Method: We propose a causal-structure-mapping framework that moves beyond superficial similarity to rigorously evaluate analogical alignment. Using controlled behavioral experiments and causal alignment assessments, we compare GPT-4 and human performance in strategic analogy generation and evaluation. Contribution/Results: GPT-4 exhibits high recall but low precision—prone to surface-level matches—whereas humans show the inverse pattern. Their error profiles are complementary: LLMs lack causal modeling capacity, while humans often misinterpret underlying mechanisms. Building on this, we introduce a novel human-AI collaboration paradigm wherein AI generates candidate analogies and humans perform causal validation. Empirical results demonstrate that this division of cognitive labor significantly improves strategic analogy quality, offering a practical, cognitively grounded pathway for AI-augmented organizational decision-making.
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An Integer Programming Approach to Compute Lower Bounds for Ramsey Numbers Using Circulant Graphs
本文提出了一种整数规划方法，通过限制搜索范围到循环图来计算Ramsey数的下界，并利用分支切割算法求解，提高了25个R(3,n)值的下界。
0 citationsRead paper
Capacitated power dominating set problem: a solution approach based on forbidden propagation sets
This study addresses the optimal placement of measurement devices in power systems under capacity constraints, formalized as the capacitated power dominating set problem. The authors introduce a novel combinatorial structure termed the "forbidden propagation set," derive its structural properties, valid inequalities, and redundancy-elimination conditions, and formulate an integer linear programming model that avoids big-M constraints. By integrating infection variables with exponentially many constraints, they design an efficient delayed separation algorithm based on graph-theoretic cycle detection. Evaluated on benchmark instances with up to 14,000 nodes, the proposed approach achieves an average speedup of 1.7× over existing methods, demonstrating that performance is jointly influenced by network size and device capacity, thereby significantly enhancing scalability and computational efficiency for large-scale power systems.
0 citationsRead paper
Variational Approximations for Robust Bayesian Inference via Rho-Posteriors
This work addresses the computational intractability of ρ-posteriors in Bayesian robust inference, which arises from optimizing over a reference distribution. To resolve this issue, the authors develop a PAC-Bayesian framework that restores theoretical guarantees by introducing a temperature-tuned Gibbs posterior, while enabling scalable inference through variational approximations. The proposed method is the first to simultaneously ensure robustness against contaminated data, computational feasibility, and rigorous finite-sample theoretical guarantees—including oracle inequalities with explicit convergence rates. Numerical experiments demonstrate the practical effectiveness and robustness of the approach in real-world settings.
0 citationsRead paper
Empirical PAC-Bayes bounds for Markov chains
Existing PAC and PAC-Bayes generalization bounds for time-dependent data rely on unknown process parameters—such as mixing coefficients or spectral gaps—rendering them impractical for real-world applications. Method: We propose the first fully empirical PAC-Bayes bound for Markov chains: we replace the intractable spectral gap with an estimable “pseudo-spectral gap” and provide a data-driven estimator for it under finite state spaces. The bound is constructed solely from observed trajectories, requiring no prior knowledge of the underlying Markov process. Contribution/Results: Our theoretical analysis establishes statistical validity, while simulations demonstrate that the empirical bound achieves tightness comparable to its non-empirical counterpart. This work delivers the first practical, assumption-free PAC-Bayes generalization guarantee for Markovian settings—eliminating reliance on unknown process parameters—and significantly enhances the operationality of learning theory for dependent data.
0 citationsRead paper
Can LLMs Help Improve Analogical Reasoning For Strategic Decisions? Experimental Evidence from Humans and GPT-4
Strategic analogical reasoning—particularly the “source-target matching” stage—has been overlooked as a distinct cognitive process, and the comparative capabilities of large language models (LLMs) versus humans remain poorly understood. Method: We propose a causal-structure-mapping framework that moves beyond superficial similarity to rigorously evaluate analogical alignment. Using controlled behavioral experiments and causal alignment assessments, we compare GPT-4 and human performance in strategic analogy generation and evaluation. Contribution/Results: GPT-4 exhibits high recall but low precision—prone to surface-level matches—whereas humans show the inverse pattern. Their error profiles are complementary: LLMs lack causal modeling capacity, while humans often misinterpret underlying mechanisms. Building on this, we introduce a novel human-AI collaboration paradigm wherein AI generates candidate analogies and humans perform causal validation. Empirical results demonstrate that this division of cognitive labor significantly improves strategic analogy quality, offering a practical, cognitively grounded pathway for AI-augmented organizational decision-making.
0 citationsRead paper