Deep neural networks are starting to show their potential for solving partial differential equations (PDEs)inavarietyofproblemdomains,includingturbulentflow,heattransfer,elastodynamics,and many more [1, 2, 3, 4, 5]. Thanks to their smooth and analytically-differentiable nature, implicit neural representations with periodic activation functions are emerging as a particularly attractive and powerful option in this context [4].

We discover that the recurrent update of these modelsresembles amonoid,leading ustoreformulate existing models using anovel monoid-based framework that we callmemoroids.

Thispaperproposes animplicit model-based multi-agent reinforcement learning method based onvalue decomposition methods. Under this method, agents can interact with thelearned virtual environment and evaluate thecurrent state value according to imagined future states in the latent space, making agents have the foresight. Our approach can be applied toanymulti-agent value decomposition method.

In this material, we will give more technical details as well as additional experiments to support the main paper. The overview of the proposed framework, DeWave, is illustrated in Figure 6. The dataset is split into training (80%), development (10%), and testing (10%) sets, comprising 10,874, 1,387, and 1,387 unique sentences, respectively, with no overlap. We release our implementation code through GitHub to contribute to this area. Section 3.3, where a 6-layer CNN encoder slides through the whole wave and gets the embedding The codex encoder shares the same structure with word-level features.

The translation of brain dynamics into natural language is pivotal for brain-computer interfaces (BCIs).