Neuro-symbolic neural networks have been extensively studied to integrate
symbolic operations with neural networks, thereby improving systematic
generalization. Specifically, Tensor Product Representation (TPR) framework
enables neural networks to perform differentiable symbolic operations by
encoding the symbolic structure of data within vector spaces. However,
TPR-based neural networks often struggle to decompose unseen data into
structured TPR representations, undermining their symbolic operations. To
address this decomposition problem, we propose a Discrete Dictionary-based
Decomposition (D3) layer designed to enhance the decomposition capabilities of
TPR-based models. D3 employs discrete, learnable key-value dictionaries trained
to capture symbolic features essential for decomposition operations. It
leverages the prior knowledge acquired during training to generate structured
TPR representations by mapping input data to pre-learned symbolic features
within these dictionaries. D3 is a straightforward drop-in layer that can be
seamlessly integrated into any TPR-based model without modifications. Our
experimental results demonstrate that D3 significantly improves the systematic
generalization of various TPR-based models while requiring fewer additional
parameters. Notably, D3 outperforms baseline models on the synthetic task that
demands the systematic decomposition of unseen combinatorial data.

通过引入离散字典分解层，我们改进了 Tensor Product Representation（TPR）框架，增强了神经网络的分解能力，提高了各种基于 TPR 的模型的系统推广能力。

基于离散字典的结构化表示学习分解层

Discrete Dictionary-based Decomposition Layer for Structured  Representation Learning

Machine reading comprehension (MRC) that requires discrete reasoning
involving symbolic operations, e.g., addition, sorting, and counting, is a
challenging task. According to this nature, semantic parsing-based methods
predict interpretable but complex logical forms. However, logical form
generation is nontrivial and even a little perturbation in a logical form will
lead to wrong answers. To alleviate this issue, multi-predictor -based methods
are proposed to directly predict different types of answers and achieve
improvements. However, they ignore the utilization of symbolic operations and
encounter a lack of reasoning ability and interpretability. To inherit the
advantages of these two types of methods, we propose OPERA, an
operation-pivoted discrete reasoning framework, where lightweight symbolic
operations (compared with logical forms) as neural modules are utilized to
facilitate the reasoning ability and interpretability. Specifically, operations
are first selected and then softly executed to simulate the answer reasoning
procedure. Extensive experiments on both DROP and RACENum datasets show the
reasoning ability of OPERA. Moreover, further analysis verifies its
interpretability.

提出了一种基于操作的离散推理框架 OPERA，通过使用轻量级符号操作作为神经模块来实现推理能力和可解释性，该方法在多个数据集上进行了广泛实验并取得了不错的成果。

OPERA: 基于操作中心的离散文本推理

OPERA:Operation-Pivoted Discrete Reasoning over Text

Recent neural models for data-to-text generation are mostly based on
data-driven end-to-end training over encoder-decoder networks. Even though the
generated texts are mostly fluent and informative, they often generate
descriptions that are not consistent with the input structured data. This is a
critical issue especially in domains that require inference or calculations
over raw data. In this paper, we attempt to improve the fidelity of neural
data-to-text generation by utilizing pre-executed symbolic operations. We
propose a framework called Operation-guided Attention-based
sequence-to-sequence network (OpAtt), with a specifically designed gating
mechanism as well as a quantization module for operation results to utilize
information from pre-executed operations. Experiments on two sports datasets
show our proposed method clearly improves the fidelity of the generated texts
to the input structured data.

本文提出了一种利用预先执行的符号操作来改善神经数据到文本生成保真度的框架 (OpAtt)，并在两个体育数据集上进行实验，证明该方法显著提高了生成文本的保真度。