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:
Providing feedback, both assessing final work and giving hints to stuck students, is difficult for open-ended assignments in massive online classes which can range from thousands to millions of students. We introduce a neural network method to encode programs as a linear mapping from an embedded precondition space to an embedded postcondition space and propose an algorithm for feedback at scale using these linear maps as features. We apply our algorithm to assessments from the Code.org Hour of Code and Stanford University's CS1 course, where we propagate human comments on student assignments to orders of magnitude more submissions.

Cited Abstract(s):
[1]: Recursive neural network models and their accompanying vector representations for words have seen success in an array of increasingly semantically sophisticated tasks, but almost nothing is known about their ability to accurately capture the aspects of linguistic meaning that are necessary for interpretation or reasoning. To evaluate this, I train a recursive model on a new corpus of constructed examples of logical reasoning in short sentences, like the inference of "some animal walks" from "some dog walks" or "some cat walks," given that dogs and cats are animals. This model learns representations that generalize well to new types of reasoning pattern in all but a few cases, a result which is promising for the ability of learned representation models to capture logical reasoning.

[2]: In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a set of grammar rules we build trees that combine different rules, looking for branches which yield compositions that are analytically equivalent to a target expression, but of lower computational complexity. However, as the size of the trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neural-network. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation.

[3]: We introduce a novel machine learning framework based on recursive autoencoders for sentence-level prediction of sentiment label distributions. Our method learns vector space representations for multi-word phrases. In sentiment prediction tasks these representations outperform other state-of-the-art approaches on commonly used datasets, such as movie reviews, without using any pre-defined sentiment lexica or polarity shifting rules. We also evaluate the model's ability to predict sentiment distributions on a new dataset based on confessions from the experience project. The dataset consists of personal user stories annotated with multiple labels which, when aggregated, form a multinomial distribution that captures emotional reactions. Our algorithm can more accurately predict distributions over such labels compared to several competitive baselines.

[4]: Semantic word spaces have been very useful but cannot express the meaning of longer phrases in a principled way. Further progress towards understanding compositionality in tasks such as sentiment detection requires richer supervised training and evaluation resources and more powerful models of composition. To remedy this, we introduce a Sentiment Treebank. It includes fine grained sentiment labels for 215,154 phrases in the parse trees of 11,855 sentences and presents new challenges for sentiment compositionality. To address them, we introduce the Recursive Neural Tensor Network. When trained on the new treebank, this model outperforms all previous methods on several metrics. It pushes the state of the art in single sentence positive negative classification from 80 up to 85.4 . The accuracy of predicting fine-grained sentiment labels for all phrases reaches 80.7 , an improvement of 9.7 over bag of features baselines. Lastly, it is the only model that can accurately capture the effects of negation and its scope at various tree levels for both positive and negative phrases.
Embedding programs has many crossovers with embedding natural language artifacts, given the similarity between the AST representation and parse trees. Our models are related to recent work from the NLP and deep learning communities on recursive neural networks, particularly for modeling semantics in sentences or symbolic expressions [4] [3] [2] [1] .