Teacher education faces persistent challenges, including limited access to authentic field experiences and a disconnect between theoretical instruction and classroom practice. While virtual reality (VR) simulations offer an alternative, most are constrained by inflexible design and lack scalability, failing to mirror the complexity of real teaching environments. This study introduces TeacherGen@i, a generative AI (GenAI)-enhanced VR simulation designed to provide pre-service teachers with immersive, adaptive teaching practice through realistic GenAI agents. Using an explanatory case study with a mixed-methods approach, the study examines the simulation’s usability, design challenges, and instructional utility within a university-based teacher preparation course. Data sources included usability surveys and reflective journals, analyzed through thematic coding and computational linguistic analysis using LIWC. Findings suggest that TeacherGen@i facilitates meaningful development of teaching competencies such as instructional decision-making, classroom communication, and student engagement, while also identifying notable design limitations related to cognitive load, user interface design, and instructional scaffolding. This exploratory research offers preliminary insights into the integration of generative AI in teacher simulations and its potential to support responsive and scalable simulation-based learning environments.

Diffusion models generate high-resolution images through iterative stochastic processes. In particular, the denoising method is one of the most popular approaches that predicts the noise in samples and denoises it at each time step. It has been commonly observed that the resolution of generated samples changes over time, starting off blurry and coarse, and becoming sharper and finer. In this paper, we introduce "resolution chromatography" that indicates the signal generation rate of each resolution, which is very helpful concept to mathematically explain this coarse-to-fine behavior in generation process, to understand the role of noise schedule, and to design time-dependent modulation. Using resolution chromatography, we determine which resolution level becomes dominant at a specific time step, and experimentally verify our theory with text-to-image diffusion models. We also propose some direct applications utilizing the concept: upscaling pre-trained models to higher resolutions and time-dependent prompt composing. Our theory not only enables a better understanding of numerous pre-existing techniques for manipulating image generation, but also suggests the potential for designing better noise schedules.

Mirror descent is an elegant optimization technique that leverages a dual space of parametric models to perform gradient descent. While originally developed for convex optimization, it has increasingly been applied in the field of machine learning. In this study, we propose a novel approach for using mirror descent to initialize the parameters of neural networks. Specifically, we demonstrate that by using the Hopfield model as a prototype for neural networks, mirror descent can effectively train the model with significantly improved performance compared to traditional gradient descent methods that rely on random parameter initialization. Our findings highlight the potential of mirror descent as a promising initialization technique for enhancing the optimization of machine learning models.

This chapter examines how data analytics can be leveraged to enhance immersive teacher simulations, situating this inquiry within the broader learning sciences discourse on embodied cognition, data-informed feedback, and teacher professional learning. It explores both conceptual foundations and empirical cases to illustrate how analytics serve as mediational tools that connect immersive experiences with reflective teaching practice. The chapter unfolds in multiple sections: (1) The Innovation Journey: An Overview of Immersive Teacher Simulations outlines the evolution from traditional simulations to XR-based environments, highlighting the need for professional decision-making under realistic constraints. (2) Innovation in Existing Research and Practice situates teacher analytics within the trajectory from descriptive observation to multimodal and predictive modeling. (3) Study Approach and Design details how multimodal data-discourse, behavior, and gaze-from the TeacherGen@i simulation were collected and organized to reveal cognitive distribution of pedagogical discourse and interaction patterns. (4) Findings present the cognitive distribution of preservice teachers' pedagogical discourse and the sequential interaction patterns that emerge in exchange, illustrating how multimodal analytics make pedagogical reasoning processes visible within immersive simulations. (5) Understanding Innovative Practices in Teacher Education examines teaching analytics to enhance immersive teacher simulation based on the findings of the study. (6) Key Takeaways of the Innovation Journey identifies research challenges and design implications for scalable, analytics-enhanced teacher education. Together, these sections position immersive teacher simulations as a pivotal testbed for aligning learning analytics, professional learning, and next-generation immersive learning environment design.