You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
The procedural generation of video game levels has existed for at least 30 years, but only recently have machine learning approaches been used to generate levels without specifying the rules for generation. A number of these have looked at platformer levels as a sequence of characters and performed generation using Markov chains. In this paper we examine the use of Long Short-Term Memory recurrent neural networks (LSTMs) for the purpose of generating levels trained from a corpus of Super Mario Brothers levels. We analyze a number of different data representations and how the generated levels fit into the space of human authored Super Mario Brothers levels.

Cited Abstract(s):
[1]: In this paper we outline a method of procedurally generating maps using Markov Chains. Our method attempts to learn what makes a “good” map from a set of given human-authored maps, and then uses those learned patterns to generate new maps. We present an empirical evaluation using the game Super Mario Bros., showing encouraging results.

[2]: In this paper we describe a hierarchical method for procedurally generating 2D game maps using multi-dimensional Markov chains (MdMCs). Our method takes a collection of 2D game maps, breaks them into small chunks and performs clustering to find a set of chunks that correspond to high-level structures (high-level tiles) in the training maps. This set of high-level tiles is then used to re-represent the training maps, and to fit two sets of MdMC models: a high-level model captures the distribution of high-level tiles in the map, and a set of low-level models capture the internal structure of each highlevel tile. These two sets of models can then be used to hierarchically generate new maps. We test our approach using two classic games, Super Mario Bros. and Loderunner, and compare the results against other existing map generators.

[3]:
Snodgrass and Onta n ' o n ( [1] [3] ) have used tile-to-tile transitions for the placement of tiles. Because of this, they do not have the problems of the vertical slice approach, but this brings a host of other issues. Namely, it can be far too likely for the system to generate sequences of tiles that violate implicit semantic constraints, such as generating ground tiles at the top of the level. Multiple attempts were made to reduce such problems via learning different chains for varying heights, or learning a hierarchical Markov chain ( [2] ). We build on the tile-to-tile approach for the work we report here as it is better able to generalize over a larger collection of levels. With the column based approach it is very easy to imagine that a new level might have a column that has never been seen before and so the system will be unable to generalize, but it is much harder to imagine a single-tile-to-tile transition that has never been seen (unless it is one that should never be seen like an enemy embedded inside a pipe).