Large Language Models have proved surprisingly effective at solving a wide range of tasks from just a handful of examples. However, their lack of reliability and modularity limits their capacity to tackle large problems that require many steps of reasoning. In response, researchers have proposed advanced pipelines that leverage domain-specific knowledge to chain smaller prompts, provide intermediate feedback and improve performance through search. However, the current complexity of writing, tuning, maintaining and improving such pipelines has limited their sophistication. We propose oracular programming, a foundational paradigm for building LLM-enabled applications that lets domain experts express high-level problem-solving strategies as programs with unresolved choice points. These choice points are resolved at runtime by LLMs, which generalize from user-provided examples of correct and incorrect decisions. An oracular program is composed of three orthogonal components: a strategy that consists in a nondeterministic program with choice points that can be reified into a search tree, a policy that specifies how to navigate this tree with the help of LLM oracles, and a set of demonstrations that describe successful and unsuccessful search tree navigation scenarios across diverse problem instances. Each component is expressed in a dedicated programming language and can be independently improved or substituted. We address the key programming language design challenges of modularly composing oracular programs and enforcing consistency between their components as they evolve.

Weaknesses: The paper only shows proxy task complicated search space may not work as well as using a simple search task without much approximation. It doesn't really tell us what happens if a complicated search space can be efficiently explored on the real task. In this sense, this paper is only a reflection of current practice, without providing a clear direction forward. In fact, the simplification of this paper (reducing the search space to number of op to apply, and the shared magnitude of ops) seems like an over-kill. By doing that, it misses an opportunity to answer some interesting question, such as: "Does assigning a different magnitude to different ops useful at all in auto data augmentation"?

This paper got mixed reviews. The original ratings are 6,5,5,6. On the positive side, reviewers think the paper solves an important problem. Data augmentation is recognized to be an important step for improving machine learning model performance. However, existing auto data augmentation methods are typically very costly.

Weaknesses: The search space is not the same as the google publications but similar to once-for-all. The se-ratio is 0.25 in this paper's code, the expansion rates are {4,6} in this paper and the maximum depth is 5 in every stage, slightly different. Thus, please report #params in Tab. 1. L120. In this paper, the author uses 2K images as the validation set (L212) and use the validation loss to train the meta-network M. I'm curious that the author claim that this step is time-consuming (L159), then how many iterations in total are used for updating M in this paper? The Kendall rank is important, and I prefer more results.

SUMMARY The paper introduces a principled approach to generate a diverse set of relevant object proposals. This is formulated as optimizing a function F defined on sets of bounding boxes. This function is defined as a sum of a relevance term (which encourages individual bounding boxes to be likely to contain an object) and a diversity term. For optimization they commit to a greedy approach which iteratively adds the most promising bounding box, until the desired number of proposals was generated. The greedy procedure was motivated by existing theoretical guarantees on the obtained solution when F is submodular and monotone.

Fitness landscapes in test-based program synthesis are known to be extremely rugged, with even minimal modifications of programs often leading to fundamental changes in their behavior and, consequently, fitness values. Relying on fitness as the only guidance in iterative search algorithms like genetic programming is thus unnecessarily limiting, especially when combined with purely syntactic search operators that are agnostic about their impact on program behavior. In this study, we propose a semantics-aware search operator that steers the search towards candidate programs that are valuable not only actually (high fitness) but also only potentially, i.e. are likely to be turned into high-quality solutions even if their current fitness is low. The key component of the method is a graph neural network that learns to model the interactions between program instructions and processed data, and produces a saliency map over graph nodes that represents possible search decisions. When applied to a suite of symbolic regression benchmarks, the proposed method outperforms conventional tree-based genetic programming and the ablated variant of the method.

The performance of Variational Quantum Algorithms (VQAs) strongly depends on the choice of the parameterized quantum circuit to optimize. One of the biggest challenges in VQAs is designing quantum circuits tailored to the particular problem and to the quantum hardware. This article proposes a gradient-free Monte Carlo Tree Search (MCTS) technique to automate the process of quantum circuit design. It introduces a novel formulation of the action space based on a sampling scheme and a progressive widening technique to explore the space dynamically. When testing our MCTS approach on the domain of random quantum circuits, MCTS approximates unstructured circuits under different values of stabilizer R\'enyi entropy. It turns out that MCTS manages to approximate the benchmark quantum states independently from their degree of nonstabilizerness. Next, our technique exhibits robustness across various application domains, including quantum chemistry and systems of linear equations. Compared to previous MCTS research, our technique reduces the number of quantum circuit evaluations by a factor of 10 to 100 while achieving equal or better results. In addition, the resulting quantum circuits have up to three times fewer CNOT gates.

Additional Feedback: Algorithm 2. X_t is never defined. I assumed that X_t is defined by Equation 2 like Algorithm 1. Authors mentioned the same computational budget for acquisition function optimization. What is the optimizer though? Constrained optimization of the acquisition function inside H_t (Equation 3) does not seem trivial. It isn't mentioned anywhere how the acquisition funciton was optimized.

The paper has been discussed after the rebuttal that the reviewers found useful and actionable (e.g., concerns about the confidence bound). The paper is recommended for acceptance. All reviewers have acknowledged that the paper is well motivated, well written and establishes a nice interplay between theory and a practical problem of interest.

AI methods, such as generative models and reinforcement learning, have recently been applied to combinatorial optimization (CO) problems, especially NP-hard ones. This paper compares such GPU-based methods with classical CPU-based methods on Maximum Independent Set (MIS). Experiments on standard graph families show that AI-based algorithms fail to outperform and, in many cases, to match the solution quality of the state-of-art classical solver KaMIS running on a single CPU. Some GPU-based methods even perform similarly to the simplest heuristic, degree-based greedy. Even with post-processing techniques like local search, AI-based methods still perform worse than CPU-based solvers. We develop a new mode of analysis to reveal that non-backtracking AI methods, e.g. LTFT (which is based on GFlowNets), end up reasoning similarly to the simplest degree-based greedy approach, and thus worse than KaMIS. We also find that CPU-based algorithms, notably KaMIS, have strong performance on sparse random graphs, which appears to refute a well-known conjectured upper bound for efficient algorithms from Coja-Oghlan & Efthymiou (2015).