The aim of 4D A* is to find the shortest path between two four-dimensional (4D) nodes of a 4D search space - a starting node and a target node - as long as there is a path. It achieves both optimality and completeness. The former is because the path is shortest possible, and the latter because if the solution exists the algorithm is guaranteed to find it.

**TILDEv2** is a [BERT](https://paperswithcode.com/method/bert)-based re-ranking method that stems from [TILDE](https://dl.acm.org/doi/abs/10.1145/3404835.3462922) but that addresses its limitations. It relies on contextualized exact term matching with expanded passages. This requires to only store in the index the score of tokens that appear in the expanded passages (rather than all the vocabulary), thus producing indexes that are 99% smaller than those of the original.

Specifically, TILDE is modified in the following aspects:

- **Exact Term Matching**. The query likelihood matching originally employed in TILDE, expands passages into the BERT vocabulary size, resulting in large indexes. To overcome this issue, estimating relevance scores is achieved with contextualized exact term matching. This allows the model to index tokens only present in the passage, thus reducing the index size. In addition to this, we replace the query likelihood loss function, with the Noise contrastive estimation (NCE) loss that allows to better leverage negative training samples. 
 
- **Passage Expansion**. To overcome the vocabulary mismatch problem that affects exact term matching methods, passage expansion is used to expand the original passage collection. Passages in the collection are expanded using deep LMs with a limited number of tokens. This requires TILDEv2 to only index a few extra tokens in addition to those in the original passages.

TILDEv2

Fast Passage Re-ranking with Contextualized Exact Term Matching and Efficient Passage Expansion

4D A*

Artificial Intelligence Control in 4D Cylindrical Space for Industrial Robotic Applications

The **Multiplex Molecular Graph Neural Network (MXMNet)** is an approach for the representation learning of molecules. The molecular interactions are divided into two categories: local and global. Then a two-layer multiplex graph $G = \\{ G_{l}, G_{g} \\}$ is constructed for a molecule. In $G$, the local layer $G_{l}$ only contains the local connections that mainly capture covalent interactions, and the global layer $G_{g}$ contains the global connections that cover non-covalent interactions. MXMNet uses the Multiplex Molecular (MXM) module that contains a novel angle-aware message passing operated on $G_{l}$ and an efficient message passing operated on $G_{g}$.

Source	Artificial Intelligence Control in 4D Cylindrical Space for Industrial Robotic Applications
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com