Animals and robots exist in a physical world and must coordinate their bodies to achieve behavioral objectives. With recent developments in deep reinforcement learning, it is now possible for scientists and engineers to obtain sensorimotor strategies (policies) for specific tasks using physically simulated bodies and environments. However, the utility of these methods goes beyond the constraints of a specific task; they offer an exciting framework for understanding the organization of an animal sensorimotor system in connection to its morphology and physical interaction with the environment, as well as for deriving general design rules for sensing and actuation in robotic systems. Algorithms and code implementing both learning agents and environments are increasingly available, but the basic assumptions and choices that go into the formulation of an embodied feedback control problem using deep reinforcement learning may not be immediately apparent. Here, we present a concise exposition of the mathematical and algorithmic aspects of model-free reinforcement learning, specifically through the use of \textit{actor-critic} methods, as a tool for investigating the feedback control underlying animal and robotic behavior.

The significant resource requirements associated with Large-scale Language Models (LLMs) have generated considerable interest in the development of techniques aimed at compressing and accelerating neural networks. Among these techniques, Post-Training Quantization (PTQ) has emerged as a subject of considerable interest due to its noteworthy compression efficiency and cost-effectiveness in the context of training. Existing PTQ methods for LLMs limit the optimization scope to scaling transformations between pre- and post-quantization weights. In this paper, we advocate for the direct optimization using equivalent Affine transformations in PTQ (AffineQuant). This approach extends the optimization scope and thus significantly minimizing quantization errors. Additionally, by employing the corresponding inverse matrix, we can ensure equivalence between the pre- and post-quantization outputs of PTQ, thereby maintaining its efficiency and generalization capabilities. To ensure the invertibility of the transformation during optimization, we further introduce a gradual mask optimization method. This method initially focuses on optimizing the diagonal elements and gradually extends to the other elements. Such an approach aligns with the Levy-Desplanques theorem, theoretically ensuring invertibility of the transformation. As a result, significant performance improvements are evident across different LLMs on diverse datasets. To illustrate, we attain a C4 perplexity of 15.76 (2.26 lower vs 18.02 in OmniQuant) on the LLaMA2-7B model of W4A4 quantization without overhead. On zero-shot tasks, AffineQuant achieves an average of 58.61 accuracy (1.98 lower vs 56.63 in OmniQuant) when using 4/4-bit quantization for LLaMA-30B, which setting a new state-of-the-art benchmark for PTQ in LLMs.