The sim-to-real gap remains a critical challenge in robotics, hindering the deployment of algorithms trained in simulation to real-world systems. This paper introduces a novel Real-Sim-Real (RSR) loop framework leveraging differentiable simulation to address this gap by iteratively refining simulation parameters, aligning them with real-world conditions, and enabling robust and efficient policy transfer. A key contribution of our work is the design of an informative cost function that encourages the collection of diverse and representative real-world data, minimizing bias and maximizing the utility of each data point for simulation refinement. This cost function integrates seamlessly into existing reinforcement learning algorithms (e.g., PPO, SAC) and ensures a balanced exploration of critical regions in the real domain. Furthermore, our approach is implemented on the versatile Mujoco MJX platform, and our framework is compatible with a wide range of robotic systems. Experimental results on several robotic manipulation tasks demonstrate that our method significantly reduces the sim-to-real gap, achieving high task performance and generalizability across diverse scenarios of both explicit and implicit environmental uncertainties.

Vector quantization is a technique in machine learning that discretizes continuous representations into a set of discrete vectors. It is widely employed in tokenizing data representations for large language models, diffusion models, and other generative models. Despite its prevalence, the characteristics and behaviors of vector quantization in generative models remain largely underexplored. In this study, we investigate representation collapse in vector quantization - a critical degradation where codebook tokens or latent embeddings lose their discriminative power by converging to a limited subset of values. This collapse fundamentally compromises the model's ability to capture diverse data patterns. By leveraging both synthetic and real datasets, we identify the severity of each type of collapses and triggering conditions. Our analysis reveals that restricted initialization and limited encoder capacity result in tokens collapse and embeddings collapse. Building on these findings, we propose potential solutions aimed at mitigating each collapse. To the best of our knowledge, this is the first comprehensive study examining representation collapsing problems in vector quantization.

Large pretrained language models (LLMs) have shown surprising In-Context Learning (ICL) ability. An important application in deploying large language models is to augment LLMs with a private database for some specific task. The main problem with this promising commercial use is that LLMs have been shown to memorize their training data and their prompt data are vulnerable to membership inference attacks (MIA) and prompt leaking attacks. In order to deal with this problem, we treat LLMs as untrusted in privacy and propose a locally differentially private framework of in-context learning (LDP-ICL) in the settings where labels are sensitive. Considering the mechanisms of in-context learning in Transformers by gradient descent, we provide an analysis of the trade-off between privacy and utility in such LDP-ICL for classification. Moreover, we apply LDP-ICL to the discrete distribution estimation problem. In the end, we perform several experiments to demonstrate our analysis results.