The code and demo are available online.

Leveraging planning during learning and decision-making is central to the long-term development of intelligent agents.

Pre-trained large language models based on Transformers have demonstrated remarkable in-context learning (ICL) abilities. With just a few demonstration examples, the models can implement new tasks without any parameter updates. However, it is still an open question to understand the mechanism of ICL.

These extensions have seen a wide degree of empirical success [26, 28, 3].

However, there is a large gap between its delay-dependent part, i.e.,

The integration of the PDE into a loss function endows PINNs with a distinctive feature to require computing derivatives of model up to the PDE order.

The matrix completion problem seeks to recover a d d ground truth matrix of low rank r d from observations of its individual elements. Real-world matrix completion is often a huge-scale optimization problem, with d so large that even the simplest full-dimension vector operations with O ( d) time complexity become prohibitively expensive. Stochastic gradient descent (SGD) is one of the few algorithms capable of solving matrix completion on a huge scale, and can also naturally handle streaming data over an evolving ground truth. Unfortunately, SGD experiences a dramatic slow-down when the underlying ground truth is ill-conditioned; it requires at least O ( κ log(1 /ϵ)) iterations to get ϵ -close to ground truth matrix with condition number κ. In this paper, we propose a preconditioned version of SGD that preserves all the favorable practical qualities of SGD for huge-scale online optimization while also making it agnostic to κ. For a symmetric ground truth and the Root Mean Square Error (RMSE) loss, we prove that the preconditioned SGD converges to ϵ -accuracy in O (log(1 /ϵ)) iterations, with a rapid linear convergence rate as if the ground truth were perfectly conditioned with κ = 1 . In our experiments, we observe a similar acceleration for item-item collaborative filtering on the MovieLens25M dataset via a pair-wise ranking loss, with 100 million training pairs and 10 million testing pairs.

Moreover, most prior works on neural kernels have focused on the ReLU activation, mainly due to its popularity but also due to the difficulty of computing such kernels for general activations.