Additional Feedback: Response to author feedback: From the informal discussion about the cross-component counters, I'm getting that it's somehow bad if different components have been explored unevenly and therefore encouraging more balanced exploration (pairwise) reduces overall variance in the amount of exploration between components. I'm sure there's a lot I'm not getting, but that helps a bit. I think it should be the case that you recover an object when you multiply its factors together (for the appropriate definition of "multiply"). There are papers (well, just one I can think of) that deal with truly factored MDPs that are the product of simpler MDPs. They correctly call their MDPs factored.

While this paper initially had some mild divergence of opinion among the reviewers, after the author response and some detailed discussion, it was agreed that this paper makes a solid contribution (please see the revised reviews). It is certainly is of relevance to NeuRIPS. After discussion, there was agreement on the significance of the conceptual contribution, namely the treatment of the cross-component bonuses. Several reviewers note that the mathematics is fairly "standard" (Bernstein-bound machinery), though in the end that should not be considered a drawback. At least one reviewer notes that the 31pp appendix means that it is not possible to verify the mathematical results during the review period.

Weaknesses: While the general idea of the paper is appealing and has been evaluated extensively, the presentation of the methodology is lacking in clarity at times. After reading section 3, some issues could have been addressed more clearly: • Regarding line 171/172: what do the authors mean by "regret reaches the plateau"? Consider the case of the 1D sine function and we have data points only at increments of pi. K-means would result in two clusters, i.e., the points with values 1 and -1, respectively. What would be the resulting domain for TuRBO then?

The paper contains some interesting ideas of partitioning the search space in Bayesian optimization. Experimental studies are good, although the paper could benefit from another round of editing for the camera ready. Reviewers were not overly excited about the paper, but also did not identify any fundamental flaws. As such, it is recommended for acceptance as a poster. We strongly encourage the authors to take the feedback from the reviews into account when preparing the camera-ready version.

This paper still considers the only resolution, depth and width dimensions, which have been studied in EfficientNet. Although the discovery in this paper that "resolution and depth are more important than width for tiny networks" is different from the conclusion in EfficientNet, I feel this point is not significant enough and it seems like just a supplement for EfficientNet. I'm not saying that this kind of method is not good, but I think the insights and intuitions why resolution and depth are more important than width for small networks (derived from this way) are still not clear. In my opinion, this paper is basically doing random search by shrinking the EfficientNet-B0 structure configurations on the mentioned three dimensions, I believe the derived observation is useful but the method itself contains very limited value to the community. Even some simple searching method like evolutionary searching can achieve similar or the same purpose through a more efficient way.

The paper received mixed ratings: two reviewers recommend acceptance, and two reviewers consider the paper is marginally below the threshold. All reviewers agree that the paper provides useful insights, e.g., the observation that resolution and depth are more important than width for tiny networks. The main concerns raised by the reviewers were (i) novelty is not highly significant/the method is too heuristic (ii) issues with experiments and lack of analysis on other tasks, such as object detection. The rebuttal helped clarify several other questions raised by the reviewers, and included new experiments on COCO object detection using Faster-RCNN. All reviewers actively participated in the discussion phase.

The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules. This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

Multimodal large language models (MLLMs) exhibit impressive capabilities but still face challenges in complex visual reasoning. While recent efforts attempt to enhance MLLMs' reasoning by incorporating OpenAI o1-like structured thinking through explicit search structures or teacher-guided distillation, they often struggle to balance performance and efficiency. A critical limitation is their heavy reliance on extensive data and search spaces, resulting in low-efficiency implicit insight extraction and data utilization. To address this, we propose AStar, an Automated Structured thinking paradigm for multimodal reasoning via Monte Carlo Tree Search (MCTS). AStar automatically derives high-level cognitive reasoning patterns from limited data using MCTS-powered hierarchical structures. Building on these explicit patterns, we design a unified reasoning framework that seamlessly integrates models' internal reasoning capabilities and external reasoning guidelines, enabling efficient inference with minimal tree iterations. This novel paradigm strikes a compelling balance between performance and efficiency. Extensive experiments demonstrate AStar's effectiveness, achieving superior accuracy (54.0$\%$) on the MathVerse benchmark with a 7B backbone, surpassing GPT-4o (50.2$\%$) while maintaining substantial data and computational efficiency.

With the advent of large multimodal language models, science is now at a threshold of an AI-based technological transformation. Recently, a plethora of new AI models and tools has been proposed, promising to empower researchers and academics worldwide to conduct their research more effectively and efficiently. This includes all aspects of the research cycle, especially (1) searching for relevant literature; (2) generating research ideas and conducting experimentation; generating (3) text-based and (4) multimodal content (e.g., scientific figures and diagrams); and (5) AI-based automatic peer review. In this survey, we provide an in-depth overview over these exciting recent developments, which promise to fundamentally alter the scientific research process for good. Our survey covers the five aspects outlined above, indicating relevant datasets, methods and results (including evaluation) as well as limitations and scope for future research. Ethical concerns regarding shortcomings of these tools and potential for misuse (fake science, plagiarism, harms to research integrity) take a particularly prominent place in our discussion. We hope that our survey will not only become a reference guide for newcomers to the field but also a catalyst for new AI-based initiatives in the area of "AI4Science".