In this applied paper, we address the difficult open problem of when to discharge patients from the Intensive Care Unit. This can be conceived as an optimal stopping scenario with three added challenges: 1) the evaluation of a stopping strategy from observational data is itself a complex causal inference problem, 2) the composite objective is to minimize the length of intervention and maximize the outcome, but the two cannot be collapsed to a single dimension, and 3) the recording of variables stops when the intervention is discontinued. Our contributions are two-fold. First, we generalize the implementation of the g-formula Python package, providing a framework to evaluate stopping strategies for problems with the aforementioned structure, including positivity and coverage checks. Second, with a fully open-source pipeline, we apply this approach to MIMIC-IV, a public ICU dataset, demonstrating the potential for strategies that improve upon current care.

Precision medicine aims to tailor therapeutic decisions to individual patient characteristics. This objective is commonly formalized through dynamic treatment regimes, which use statistical and machine learning methods to derive sequential decision rules adapted to evolving clinical information. In most existing formulations, these approaches produce a single optimal treatment at each stage, leading to a unique decision sequence. However, in many clinical settings, several treatment options may yield similar expected outcomes, and focusing on a single optimal policy may conceal meaningful alternatives. We extend the Q-learning framework for retrospective data by introducing a worst-value tolerance criterion controlled by a hyperparameter $\varepsilon$, which specifies the maximum acceptable deviation from the optimal expected value. Rather than identifying a single optimal policy, the proposed approach constructs sets of $\varepsilon$-optimal policies whose performance remains within a controlled neighborhood of the optimum. This formulation shifts Q-learning from a vector-valued representation to a matrix-valued one, allowing multiple admissible value functions to coexist during backward recursion. The approach yields families of near-equivalent treatment strategies and explicitly identifies regions of treatment indifference where several decisions achieve comparable outcomes. We illustrate the framework in two settings: a single-stage problem highlighting indifference regions around the decision boundary, and a multi-stage decision process based on a simulated oncology model describing tumor size and treatment toxicity dynamics.

Recent efforts for developing general-purpose estimators with broader coverage, incorporating thefront-door adjustment (FD) (Pearl, 2000) andothers, are not scalable due to the high computational cost of summing over a highdimensional set of variables.

We are grateful to the discussants, Levis and Kennedy [2025], Luo and Geng [2025], Wang and van der Laan [2025], and Yang and Kim [2025], for their thoughtful comments on our paper (Nabi et al., 2025). In this rejoinder, we summarize our main contributions and respond to each discussion in turn.

Watermarking generative content serves as a vital tool for authentication, ownership protection, and mitigation of potential misuse. Existing watermarking methods face the challenge of balancing robustness and concealment. They empirically inject a watermark that is both invisible and robust and passively achieve concealment by limiting the strength of the watermark, thus reducing the robustness. In this paper, we propose to explicitly introduce a watermark hiding process to actively achieve concealment, thus allowing the embedding of stronger watermarks. To be specific, we implant a robust watermark in an intermediate diffusion state and then guide the model to hide the watermark in the final generated image.

Scientific discovery is driven by the iterative process of background research, hypothesis generation, experimentation, and data analysis. Despite recent advancements in applying artificial intelligence to scientific discovery, no system has yet automated all of these stages in a single workflow. Here, we introduce Robin, the first multi-agent system capable of fully automating the key intellectual steps of the scientific process. By integrating literature search agents with data analysis agents, Robin can generate hypotheses, propose experiments, interpret experimental results, and generate updated hypotheses, achieving a semi-autonomous approach to scientific discovery. By applying this system, we were able to identify a novel treatment for dry age-related macular degeneration (dAMD), the major cause of blindness in the developed world. Robin proposed enhancing retinal pigment epithelium phagocytosis as a therapeutic strategy, and identified and validated a promising therapeutic candidate, ripasudil. Ripasudil is a clinically-used rho kinase (ROCK) inhibitor that has never previously been proposed for treating dAMD. To elucidate the mechanism of ripasudil-induced upregulation of phagocytosis, Robin then proposed and analyzed a follow-up RNA-seq experiment, which revealed upregulation of ABCA1, a critical lipid efflux pump and possible novel target. All hypotheses, experimental plans, data analyses, and data figures in the main text of this report were produced by Robin. As the first AI system to autonomously discover and validate a novel therapeutic candidate within an iterative lab-in-the-loop framework, Robin establishes a new paradigm for AI-driven scientific discovery.

We extend the existing work on Hopfield network state classification, employing more complex models that remain interpretable, such as densely-connected feed-forward deep neural networks and support vector machines. The states of the Hopfield network can be grouped into several classes, including learned (those presented during training), spurious (stable states that were not learned), and prototype (stable states that were not learned but are representative for a subset of learned states). It is often useful to determine to what class a given state belongs to; for example to ignore spurious states when retrieving from the network. Previous research has approached the state classification task with simple linear methods, most notably the stability ratio. We deepen the research on classifying states from prototype-regime Hopfield networks, investigating how varying the factors strengthening prototypes influences the state classification task. We study the generalizability of different classification models when trained on states derived from different prototype tasks -- for example, can a network trained on a Hopfield network with 10 prototypes classify states from a network with 20 prototypes? We find that simple models often outperform the stability ratio while remaining interpretable. These models require surprisingly little training data and generalize exceptionally well to states generated by a range of Hopfield networks, even those that were trained on exceedingly different datasets.