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New lower bounds for binary constant-weight codes: $A(23,6,10)\geq 2979$ and $A(24,6,10)\geq 4214$

Jul 21, 2026

This work addresses the long-standing open problem of constructing optimal binary constant-weight codes by introducing a novel coordinate decomposition approach. The method fixes half of the coordinates using known codewords and selects the remaining half from a fully cross-compatible pool, then employs the CHILS algorithm to solve a maximum-weight independent set problem to construct larger codes. The maximality of the resulting codes is verified using two exact solvers, and symmetry analysis of prime-order permutation-invariant codes eliminates redundant structures. This strategy breaks the lower bound records that had remained unimproved since 1990, establishing new results: $A(23,6,10) \geq 2979$ and $A(24,6,10) \geq 4214$, while also improving the known lower bounds for $A(23,6,11)$ and $A(24,6,8)$. All new bounds have been incorporated into Brouwer’s online table.

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A Causal Markov Condition for Value

Jul 18, 2026

This work formalizes the independence of utility within causal structures, establishing a systematic link between causal inference and decision theory. It introduces the value causal Markov condition (v-CMC) along with its local, global, and factorization forms, and proves their equivalence. A v-separation criterion is defined and shown to be complete. The Bellman recursion is generalized to arbitrary causal directed acyclic graphs (DAGs). Leveraging a probability–utility duality, the paper develops a comprehensive causal utility framework that enables modular representation, inference, and transfer of utilities across causal contexts. Furthermore, it proposes a structured utility heuristic and an automated method for constructing influence diagrams, offering efficient tools for decision modeling.

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A Divergence-Based Method for Weighting and Averaging Model Predictions

Apr 27, 2026

This work addresses the challenge of combining probabilistic predictions from multiple models in few-shot settings by proposing a general weighted averaging method grounded in a minimum divergence framework. Applicable to models constructed via frequentist, Bayesian, or other fitting paradigms, the approach employs a dual-motivation weighting scheme that simultaneously minimizes the divergence between the aggregated predictive distribution and the true data-generating distribution while accounting for model complexity. Theoretical analysis elucidates the source of its advantage under limited data regimes, and empirical evaluations demonstrate that the method consistently matches or significantly outperforms conventional model averaging strategies—such as Akaike weights and stacking—in terms of predictive accuracy, exhibiting robust performance across diverse scenarios.

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Latest Papers

New lower bounds for binary constant-weight codes: $A(23,6,10)\geq 2979$ and $A(24,6,10)\geq 4214$

Jul 21, 2026

This work addresses the long-standing open problem of constructing optimal binary constant-weight codes by introducing a novel coordinate decomposition approach. The method fixes half of the coordinates using known codewords and selects the remaining half from a fully cross-compatible pool, then employs the CHILS algorithm to solve a maximum-weight independent set problem to construct larger codes. The maximality of the resulting codes is verified using two exact solvers, and symmetry analysis of prime-order permutation-invariant codes eliminates redundant structures. This strategy breaks the lower bound records that had remained unimproved since 1990, establishing new results: $A(23,6,10) \geq 2979$ and $A(24,6,10) \geq 4214$, while also improving the known lower bounds for $A(23,6,11)$ and $A(24,6,8)$. All new bounds have been incorporated into Brouwer’s online table.

0 citationsRead paper

A Causal Markov Condition for Value

Jul 18, 2026

This work formalizes the independence of utility within causal structures, establishing a systematic link between causal inference and decision theory. It introduces the value causal Markov condition (v-CMC) along with its local, global, and factorization forms, and proves their equivalence. A v-separation criterion is defined and shown to be complete. The Bellman recursion is generalized to arbitrary causal directed acyclic graphs (DAGs). Leveraging a probability–utility duality, the paper develops a comprehensive causal utility framework that enables modular representation, inference, and transfer of utilities across causal contexts. Furthermore, it proposes a structured utility heuristic and an automated method for constructing influence diagrams, offering efficient tools for decision modeling.

0 citationsRead paper

A Divergence-Based Method for Weighting and Averaging Model Predictions

Apr 27, 2026

This work addresses the challenge of combining probabilistic predictions from multiple models in few-shot settings by proposing a general weighted averaging method grounded in a minimum divergence framework. Applicable to models constructed via frequentist, Bayesian, or other fitting paradigms, the approach employs a dual-motivation weighting scheme that simultaneously minimizes the divergence between the aggregated predictive distribution and the true data-generating distribution while accounting for model complexity. Theoretical analysis elucidates the source of its advantage under limited data regimes, and empirical evaluations demonstrate that the method consistently matches or significantly outperforms conventional model averaging strategies—such as Akaike weights and stacking—in terms of predictive accuracy, exhibiting robust performance across diverse scenarios.

0 citationsRead paper