Explaining Neural Networks in Preference Learning: a Post-hoc Inductive Logic Programming Approach

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.

Neurosymbolic AI combines neural networks with symbolic programs to create robust and explainable predictions. One such framework is NeurASP, which trains a neural network to predict concepts and reasons over them using rules written in answer set programming (ASP) to solve downstream tasks. Crucially, labels are only provided for the downstream prediction produced by the symbolic rules, not for the latent concepts themselves. Backpropagation through the non-differentiable ASP component requires expensive probability and gradient calculations, which has hindered scalability to more sophisticated tasks. In this paper, we address the current limitations of NeurASP by improving its computational performance through vectorization, batch processing and caching of intermediate computations during training. We compare computation speeds between the original and our new implementation of NeurASP and report speedups of multiple orders of magnitude for larger tasks. To this end, we propose a new dataset of difficult tasks involving playing cards, which we use to test the capabilities of NeurASP's enhanced learning function.

Current Large Language Model (LLM) preference learning methods such as Proximal Policy Optimization and Direct Preference Optimization learn from direct rankings or numerical ratings of model outputs, these rankings are subjective, and a single numerical rating chosen directly by a judge is a poor proxy for the quality of natural language, we introduce the What Is Missing (WIM) rating system to produce rankings from natural-language feedback, WIM integrates into existing training pipelines, can be combined with other rating techniques, and can be used as input to any preference learning method without changing the learning algorithm, to compute a WIM rating, a human or LLM judge writes feedback describing what the model output is missing, we embed the output and the feedback with a sentence embedding model and compute the cosine similarity between the resulting vectors, we empirically observe that, compared to discrete numerical ratings, WIM yields fewer ties and larger rating deltas, which improves the availability of a learning signal in pairwise preference data, we use interpretable in the following limited sense: for each scalar rating, we can inspect the judge's missing-information text that produced it, enabling qualitative debugging of the preference labels.