Standard sequential decision-making paradigms aim to maximize the cumulative reward when interacting with the unknown environment., i.e., maximize $\sum_{h = 1}^H r_h$ where $H$ is the planning horizon. However, this paradigm fails to model important practical applications, e.g., safe control that aims to maximize the lowest reward, i.e., maximize $\min_{h= 1}^H r_h$. In this paper, based on techniques in sketching algorithms, we propose a novel planning algorithm in deterministic systems which deals with a large class of objective functions of the form $f(r_1, r_2, ... r_H)$ that are of interest to practical applications. We show that efficient planning is possible if $f$ is symmetric under permutation of coordinates and satisfies certain technical conditions. Complementing our algorithm, we further prove that removing any of the conditions will make the problem intractable in the worst case and thus demonstrate the necessity of our conditions.

Inverse halftoning is a technique used to recover realistic images from ancient prints (\textit{e.g.}, photographs, newspapers, books). The rise of deep learning has led to the gradual incorporation of neural network designs into inverse halftoning methods. Most of existing inverse halftoning approaches adopt the U-net architecture, which uses an encoder to encode halftone prints, followed by a decoder for image reconstruction. However, the mainstream supervised learning paradigm with element-wise regression commonly adopted in U-net based methods has poor generalization ability in practical applications. Specifically, when there is a large gap between the dithering patterns of the training and test halftones, the reconstructed continuous-tone images have obvious artifacts.

We kindly thank the reviewers for their detailed reviews, valuable feedback and suggestions for improvement. Indeed, our proof of the new SW theorem relies on an "ordering" of the coordinates of arbitrary equivariant SW theorem under arbitrary finite group action would be desirable, however the proof is out of our reach as of today. In a way, this limitation is similar to the distinction between "point clouds" (which in We will add this discussion in the paper, and mention it in the abstract. In its "deep" original version, it covers all type of "Message-Passing" GNNs, but not spectral GNNs which use powers of the adjacency matrix. We will clarify this in the final version.

We thank the reviewers for all of these valuable comments. We provide point-by-point responses below. Re: generalize to other applications. Cooperative Navigation problem (Lowe et al. '17) and achieved a competitive mean reward (-4.8) against MADDPG Specifically, the stochastic target selection will make the executor inefficient to learn. We will further discuss the factors of each component in the next revision.

We thank the reviewers for their constructive and positive comments. They will improve the quality of the paper. As an instance in RL, we mention the problem of "active exploration in MDPs" (see [28]), where the Reiterating the discussion in Section 2.3, let us consider the small-budget regime, and We will provide a footnote in page 7 to clarify this. This is indeed a nice remark. As a result, the theorem is valid even if irreducibility and aperiodicity are dropped.

We kindly thank the reviewers for their detailed reviews, valuable feedback and suggestions for improvement. Indeed, our proof of the new SW theorem relies on an "ordering" of the coordinates of arbitrary equivariant SW theorem under arbitrary finite group action would be desirable, however the proof is out of our reach as of today. In a way, this limitation is similar to the distinction between "point clouds" (which in We will add this discussion in the paper, and mention it in the abstract. In its "deep" original version, it covers all type of "Message-Passing" GNNs, but not spectral GNNs which use powers of the adjacency matrix. We will clarify this in the final version.

--Special tags such as AprilT ags that facilitate image processing and pattern recognition are useful in practical applications. In close and private environments, identity security is unlikely to be an issue because all involved AprilT ags can be completely regulated. However, in open and public environments, identity security is no longer an issue that can be neglected. T o handle potential harm caused by adversarial attacks, this note advocates utilization of adjustable AprilT ags instead of fixed ones. Special tags that facilitate image processing and pattern recognition are useful in practical applications.

MSC 804 5 - 0020 - 10 St. Louis, MO 63110 Financial Support: P30 - AR073752 Conflict of interest: No conflicts declared. Page 2 of 13 Roberson 2025 - LLMs in medicine Abstract The medical ecosystem consists of the training of new clinicians and researchers, the practice of clinical medicine, and areas of adjacen t research. There are many aspects of these domains that could benefit from the application of task automation and programmatic assistance. Machine learning and artificial intelligence techniques, including large language models ( LLMs), have been promised to deliver on healthcare innovation, improving care speed and accuracy, and reducing the burden on staff for manual interventions . However, LLMs have no understanding of objective truth that is based in reality. They also represent real risks to the disclo sure of protected information when used by clinicians and researchers. The use of AI in medicine in general, and the deployment of LLMs in particular, therefore requires careful consideration and thoughtful application to reap the benefits of these technol ogies while avoiding the dangers in each context. Page 3 of 13 Roberson 2025 - LLMs in medicine Abbreviations AI: Artificial intelligence CSP: Constrained solution problems EHR: Electronic health records GPT: Generative pre - trained transformer LLM: Large language model ML: Machine learning RAG: Retrieval - augmented generation Page 4 of 13 Roberson 2025 - LLMs in medicine What is a large language model? Large language models are one of the most hyped artificial intelligence technologies of the past few years. Buzz terms associated with them include artificial intelligence, machine learning, a nd deep learning.

Standard sequential decision-making paradigms aim to maximize the cumulative reward when interacting with the unknown environment., i.e., maximize \sum_{h 1} H r_h where H is the planning horizon. However, this paradigm fails to model important practical applications, e.g., safe control that aims to maximize the lowest reward, i.e., maximize \min_{h 1} H r_h . In this paper, based on techniques in sketching algorithms, we propose a novel planning algorithm in deterministic systems which deals with a large class of objective functions of the form f(r_1, r_2, ... r_H) that are of interest to practical applications. We show that efficient planning is possible if f is symmetric under permutation of coordinates and satisfies certain technical conditions. Complementing our algorithm, we further prove that removing any of the conditions will make the problem intractable in the worst case and thus demonstrate the necessity of our conditions.