Watermarking generative content serves as a vital tool for authentication, ownership protection, and mitigation of potential misuse.

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.

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. We employ an adversarial optimization algorithm to produce the optimal hiding prompt guiding signal for each watermark. The prompt embedding is optimized to minimize artifacts in the generated image, while the watermark is optimized to achieve maximum strength. The watermark can be verified by reversing the generation process. Experiments on various diffusion models demonstrate the watermark remains verifiable even under significant image tampering and shows superior invisibility compared to other state-of-the-art robust watermarking methods.

Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with multi-valued and time-varying treatments. In this paper, we use machine learning together with recent developments in semiparametric efficiency theory for longitudinal studies to propose such an estimator. The proposed estimator is based on a study of the non-parametric identifying functional, including first order von-Mises expansions as well as the efficient influence function and the efficiency bound. We show conditions under which the proposed estimator is efficient, asymptotically normal, and sequentially doubly robust in the sense that it is consistent if, for each time point, either the outcome or the treatment mechanism is consistently estimated. We perform a simulation study to illustrate the properties of the estimators, and present the results of our motivating study on a COVID-19 dataset studying the impact of mobility on the cumulative number of observed cases.