The Handbook of Combinatorial Designs catalogs many types of combinatorial designs, together with lists of open instances for which existence has not yet been determined. We develop a constructive protocol CPro1, which uses Large Language Models (LLMs) to generate code that constructs combinatorial designs and resolves some of these open instances. The protocol starts from a definition of a particular type of design, and a verifier that reliably confirms whether a proposed design is valid. The LLM selects strategies and implements them in code, and scaffolding provides automated hyperparameter tuning and execution feedback using the verifier. Most generated code fails, but by generating many candidates, the protocol automates exploration of a variety of standard methods (e.g.

Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying quantum algorithms to real-world problems remains challenging. Hybrid quantum-classical techniques have been explored to bridge this gap, but they often face limitations in expressiveness, trainability, or scalability. In this work, we introduce conditional Generative Quantum Eigensolver (conditional-GQE), a context-aware quantum circuit generator powered by an encoder-decoder Transformer. Focusing on combinatorial optimization, we train our generator for solving problems with up to 10 qubits, exhibiting nearly perfect performance on new problems. By leveraging the high expressiveness and flexibility of classical generative models, along with an efficient preference-based training scheme, conditional-GQE provides a generalizable and scalable framework for quantum circuit generation. Our approach advances hybrid quantum-classical computing and contributes to accelerate the transition toward fault-tolerant quantum computing.

We present COS(M+O)S, a System 2-inspired framework for open-ended plot development that systematically explores the vast space of possible story expansions, enabling a 3B-parameter language model to approach the plot quality of a 70B model on select short-story tasks. The method accomplishes this by combining Monte Carlo Tree Search (MCTS), guided by a step-level value model that rewards moderate surprisal (curiosity) while penalizing incoherence, and Odds Ratio Preference Optimization (ORPO) to fine-tune the policy on high-value plot expansions. This iterative reinforcement learning loop systematically explores multiple candidate plot branches, backpropagates quality signals, and adapts the policy for faster convergence, notably shifting the policy from puzzle-based Chain-of-Thought to more character-driven storytelling. In small-scale tests with short-story prompts, 67%-77% of participants favored COS(M+O)S's highest-rated expansions over lower-rated ones, suggesting that our learned value function aligns. GPT-4o ratings further show that COS(M+O)S surpasses naive single-pass decoding from Llama 3.2 3B by 0.59 SD, coming within 0.06 SD of Llama 3.1 70B (no significant difference, p=0.93). Pairwise comparisons with o1 place COS(M+O)S 1.5 SD above the 3B baseline and find no statistically significant gap from 70B. Nevertheless, absolute story quality remains modest, constrained by the small model's capacity and limited training data.

Post-rebuttal: I am satisfied with the rebuttal. I am interested to know more about "One reason why such rates are common in online learning is the connection of the sequential Rademacher complexity with uniform convergence of martingale difference sequences in the corresponding Banach space (see [2] for details)." If the paper is accepted and space is allowed, I suggest to elaborate on this more thoroughly.

One of the main issues of this paper is clarity, however. We trust that you will work very hard to improve clarity for the final submission, as suggested in the reviews.

In particular, the gap in the analysis is due to my mis-reading the formula, and the response convinced me. However, the paper overall looks incremental, so it is a paper nice to have, but its acceptance seems to be depending on the quality of other papers.] The paper studies the bandit combinatorial optimization problem and improve the lower bound of the problem from \Omega(\sqrt{dk 3T/log T}) in the prior work [8] to \Omega(\sqrt{dk 3T}), removing a factor of 1/\sqrt{\log T} . This makes the regret dependency on T and k, d tight up to a logarithmic factor. The analysis is built upon prior work [2,8], with the major innovation being a design of new distribution of loss vectors (given in Eq.(8)) that leads to a better lower bound.

The reviewers all agree that this is a fine result.

Applying Bayesian optimization to expensive black-box problems needs to specify the bound of search space. However, when tackling a completely new problem, there is no prior knowledge to guarantee that the specified search space contains the global optimum. The paper proposes an approach to deal with this situation. In the approach, the user first specifies an initial search space; then the bound of search space automatically expands as the iteration proceeds; finally the algorithm will return a solution achieving \epsilon-accuracy. The key is how to expand the search space.

This paper proposes an algorithm to expand the search space for Bayesian optimization. The reviewers thought the work tackles an important problem and would be of interest to the community. The claims are well supported by empirical evidence and the paper is clearly written. There were concerns about the practicality of the method and that the work is a combination of well-known techniques. Because the paper presents a relatively novel approach and substantiates the claims with strong supporting evidence, it seems to be above the bar of acceptance.

Post-feedback update: Thank you for your update. Your additional results will strengthen this paper, and I still think it should be accepted. Specifically, it combines the basic overall framework for SPEN training using a reward signal introduced by [1] with the idea of adding in random search to find reward scoring violations, which has been used in the past by various papers (which are cited appropriately in this work). However, this exact combination is novel. Quality: The motivation behind using random search to augment the generation of labels to use for training the model is sound and verified empirically. Numerous appropriate baselines are included, ranging from beam search-type approaches to more directly comparable approaches such as [1], and the introduced approach outperforms all of them.