There are two primary ways of incorporating new information into a language model (LM): changing its prompt or changing its parameters, e.g. via fine-tuning. Parameter updates incur no long-term storage cost for model changes. However, for many model updates, prompting is significantly more effective: prompted models can generalize robustly from single examples and draw logical inferences that do not occur under standard fine-tuning. Can models be modified so that fine-tuning does emulate prompting? This paper describes a method for meta-training LMs such that gradient updates emulate the effects of conditioning on new information. Our approach uses tools from gradient-based meta-learning but uses an LM's own prompted predictions as targets, eliminating the need for ground-truth labels. Subsequent gradient descent training recovers some (and occasionally all) of prompted model performance -- showing improvement on the ``reversal curse'' tasks, and answering questions about text passages after a single gradient update. These results suggest that, with appropriate initialization, gradient descent can be surprisingly expressive. Our results suggest new avenues for long-context modeling and offer insight into the generalization capabilities of gradient-based learning.

Recent advances in deep learning for physics have focused on discovering shared representations of target systems by incorporating physics priors or inductive biases into neural networks. While effective, these methods are limited to the system domain, where the type of system remains consistent and thus cannot ensure the adaptation to new, or unseen physical systems governed by different laws. For instance, a neural network trained on a mass-spring system cannot guarantee accurate predictions for the behavior of a two-body system or any other system with different physical laws. In this work, we take a significant leap forward by targeting cross domain generalization within the field of Hamiltonian dynamics. We model our system with a graph neural network and employ a meta learning algorithm to enable the model to gain experience over a distribution of tasks and make it adapt to new physics. Our approach aims to learn a unified Hamiltonian representation that is generalizable across multiple system domains, thereby overcoming the limitations of system-specific models. Our results demonstrate that the meta-trained model not only adapts effectively to new systems but also captures a generalized Hamiltonian representation that is consistent across different physical domains. Overall, through the use of meta learning, we offer a framework that achieves cross domain generalization, providing a step towards a unified model for understanding a wide array of dynamical systems via deep learning. Deep learning has succeeded in many application areas such as image classification, image generation, natural language processing, and so on (Reed et al., 2016; Tan & Le, 2019; Raffel et al., 2020; Gu et al., 2022). One of the major roles of such accomplishment was capable of parameterizing useful representations from data with neural networks (Chen et al., 2020; Van Den Oord et al., 2017; Hamilton et al., 2017). However, grafting deep learning onto physics is yet another problem. They struggle to learn conservation laws or implicit physical geometries or symmetries.

This work developed a meta-learning approach that adapts the control policy on the fly to different changing conditions for robust locomotion. The proposed method constantly updates the interaction model, samples feasible sequences of actions of estimated the state-action trajectories, and then applies the optimal actions to maximize the reward. To achieve online model adaptation, our proposed method learns different latent vectors of each training condition, which are selected online given the newly collected data. Our work designs appropriate state space and reward functions, and optimizes feasible actions in an MPC fashion which are then sampled directly in the joint space considering constraints, hence requiring no prior design of specific walking gaits. We further demonstrate the robot's capability of detecting unexpected changes during interaction and adapting control policies quickly. The extensive validation on the SpotMicro robot in a physics simulation shows adaptive and robust locomotion skills under varying ground friction, external pushes, and different robot models including hardware faults and changes.