Neuro-symbolic systems (NeSy), which claim to combine the best of both
learning and reasoning capabilities of artificial intelligence, are missing a
core property of reasoning systems: Declarativeness. The lack of
declarativeness is caused by the functional nature of neural predicates
inherited from neural networks. We propose and implement a general framework
for fully declarative neural predicates, which hence extends to fully
declarative NeSy frameworks. We first show that the declarative extension
preserves the learning and reasoning capabilities while being able to answer
arbitrary queries while only being trained on a single query type.

提出并实现了完全声明性的神经谓词的通用框架，从而扩展到完全声明性的 NeSy 框架。首先证明声明性扩展在保持学习和推理能力的同时，能够在仅通过单个查询类型进行训练的情况下回答任意查询。

走向完全声明性神经符号语言

Towards a fully declarative neuro-symbolic language

We address a key challenge for neuro-symbolic (NeSy) systems by leveraging
convex and bilevel optimization techniques to develop a general gradient-based
framework for end-to-end neural and symbolic parameter learning. The
applicability of our framework is demonstrated with NeuPSL, a state-of-the-art
NeSy architecture. To achieve this, we propose a smooth primal and dual
formulation of NeuPSL inference and show learning gradients are functions of
the optimal dual variables. Additionally, we develop a dual block coordinate
descent algorithm for the new formulation that naturally exploits warm-starts.
This leads to over 100x learning runtime improvements over the current best
NeuPSL inference method. Finally, we provide extensive empirical evaluations
across $8$ datasets covering a range of tasks and demonstrate our learning
framework achieves up to a 16% point prediction performance improvement over
alternative learning methods.

通过利用凸优化和双层优化技术，我们解决了神经符号系统的一个关键挑战，开发出一种基于梯度的通用框架，用于端到端神经和符号参数学习。我们的框架的适用性得到了 NeuPSL 的证明，这是一种最先进的神经符号体系结构。

神经符号推理与学习的凸二层优化

Convex and Bilevel Optimization for Neuro-Symbolic Inference and  Learning

Integrating logical reasoning and machine learning by approximating logical
inference with differentiable operators is a widely used technique in
Neuro-Symbolic systems.
However, some differentiable operators could bring a significant bias during
backpropagation and degrade the performance of Neuro-Symbolic learning.
In this paper, we reveal that this bias, named \textit{Implication Bias} is
common in loss functions derived from fuzzy logic operators.
Furthermore, we propose a simple yet effective method to transform the biased
loss functions into \textit{Reduced Implication-bias Logic Loss (RILL)} to
address the above problem.
Empirical study shows that RILL can achieve significant improvements compared
with the biased logic loss functions, especially when the knowledge base is
incomplete, and keeps more robust than the compared methods when labelled data
is insufficient.

本文提出了一种简单而有效的方法，即将有偏差的逻辑损失函数转化为 RILL 方法，以解决神经符号学习中的 Implication Bias 问题，并表明当知识库不完整或标注数据不足时，RILL 方法在与其他方法的比较中表现出更大的改进和更强的健壮性。