The Appendix is organized as follows.

Artificial intelligence is accelerating a new era of food innovation, connecting data from farm to consumer to improve formulation, processing, and health outcomes. Recent advances in deep learning, natural language processing, and multi-omics integration make it possible to understand and optimize food systems with unprecedented depth. However, AI adoption across the food sector remains uneven due to heterogeneous datasets, limited model and system interoperability, and a persistent skills gap between data scientists and food domain experts. To address these challenges and advance responsible innovation, the AI Institute for Next Generation Food Systems (AIFS) convened the inaugural AI for Food Product Development Symposium at University of California, Davis, in October 2025. This white paper synthesizes insights from the symposium, organized around five domains where AI can have the greatest near-term impact: supply chain; formulation and processing; consumer insights and sensory prediction; nutrition and health; and education and workforce development. Across the areas, participants emphasized the importance of interoperable data standards, transparent and interpretable models, and cross-sector collaboration to accelerate the translation of AI research into practice. The discussions further highlighted the need for robust digital infrastructure, privacy-preserving data-sharing mechanisms, and interdisciplinary training pathways that integrate AI literacy with domain expertise. Collectively, the priorities outline a roadmap for integrating AI into food manufacturing in ways that enhance innovation, sustainability, and human well-being while ensuring that technological progress remains grounded in ethics, scientific rigor, and societal benefit.

MNIST results) and white noise (finding homogeneous structure similar to scrambled classes, see Figure 1b). Despite this, we show in specific tasks that local structure of the units can still be informative. Beyond 3D, dimensionality reduction methods become difficult to visually interpret (the initial intended use). For continual learning, in appendix Fig. S4, S5 we show

The development of autonomous robotic systems offers significant potential for performing complex tasks with precision and consistency. Recent advances in Artificial Intelligence (AI) have enabled more capable intelligent automation systems, addressing increasingly complex challenges. However, this progress raises questions about human roles in such systems. Human-Centered AI (HCAI) aims to balance human control and automation, ensuring performance enhancement while maintaining creativity, mastery, and responsibility. For real-world applications, autonomous robots must balance task performance with reliability, safety, and trustworthiness. Integrating HCAI principles enhances human-robot collaboration and ensures responsible operation. This paper presents a bibliometric analysis of intelligent autonomous robotic systems, utilizing SciMA T and VOSViewer to examine data from the Scopus database. These insights are then projected onto the IBM MAPE-K architecture, with the goal of identifying how these research results map into actual robotic autonomous systems development efforts for real-world scenarios. In recent decades, robotics has made significant advancements across various sectors, including aviation, transportation, marine, and agriculture. According to the European strategy proposed by euRobotics in December 2024 [1], robotics is a complex integration of technologies that offers functional, economic, and societal benefits.

We thank the reviewers very much for their time and valuable feedback. Our MCMC method significantly outperforms the other MCMC methods. Monte Carlo (PMC) [35] which is an iterated importance sampling method with connections to SMC. SA-MCMC uses a "global" proposal distribution like IMH but unlike many MCMC methods. We will add the references and discuss future directions in our revision.

R3: "Unveiling these principles is a fundamental Hereafter, we respond to the reviewers' individual comments. R1: The assumption that patch likelihood is appropriately measured could use some more justification. This, in turn, allows likelihood evaluation [22]. R1: There could be more examples of similar phenomena explained by the model. Our paper focuses on a variety of lightness/color illusions, which "share some inherent properties, but are This is a major future direction.

R1: Title is too general: We will make the corresponding changes on the title. V -trace algorithm, they are from the original paper [17], and we do not make any additional assumptions. Our joint analysis of both is the key to our recursion (Proposition 2.1). Q-learning, and V -trace etc. can all be modeled by SA under contraction operator and martingale difference noise [5]. Thus our result is a broad tool to establish the finite-sample error bound of various RL algorithms.

We agree "biological plausibility" is subjective, but we did try to address some of your points and we'll elaborate