# On Improving Neurosymbolic Learning by Exploiting the Representation Space

arXiv: https://arxiv.org/abs/2602.07973 · HTML: https://mlsanity.com/paper/2602.07973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 8 Feb 2026.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [LXMERT: Learning Cross-Modality Encoder Representations from Transformers](https://mlsanity.com/paper/1908.07490/) (2019)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Scallop: A Language for Neurosymbolic Programming](https://mlsanity.com/paper/2304.04812/) (2023)
- [Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcuts](https://mlsanity.com/paper/2305.19951/) (2023)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [Augmenting Neural Networks with First-order Logic](https://mlsanity.com/paper/1906.06298/) (2019)
- [Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2110.12911/) (2021)
- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)
- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [Structured Prediction with Partial Labelling through the Infimum Loss](https://mlsanity.com/paper/2003.00920/) (2020)
- [VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming](https://mlsanity.com/paper/2202.04178/) (2022)
- [Learning from Aggregate Observations](https://mlsanity.com/paper/2004.06316/) (2020)
- [Neuro-Symbolic Entropy Regularization](https://mlsanity.com/paper/2201.11250/) (2022)
- [MUGEN: A Playground for Video-Audio-Text Multimodal Understanding and GENeration](https://mlsanity.com/paper/2204.08058/) (2022)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [LASER: A Neuro-Symbolic Framework for Learning Spatial-Temporal Scene Graphs with Weak Supervision](https://mlsanity.com/paper/2304.07647/) (2023)
- [On Learning Latent Models with Multi-Instance Weak Supervision](https://mlsanity.com/paper/2306.13796/) (2023)
- [Mapping the Neuro-Symbolic AI Landscape by Architectures: A Handbook on Augmenting Deep Learning Through Symbolic Reasoning](https://mlsanity.com/paper/2410.22077/) (2024)
- [Towards Effective Visual Representations for Partial-Label Learning](https://mlsanity.com/paper/2305.06080/) (2023)
- [Data-Efficient Learning with Neural Programs](https://mlsanity.com/paper/2406.06246/) (2024)
- [Relational Programming with Foundation Models](https://mlsanity.com/paper/2412.14515/) (2024)
- [Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning](https://mlsanity.com/paper/2410.03348/) (2024)
- [Local Branching Relaxation Heuristics for Integer Linear Programs](https://mlsanity.com/paper/2212.08183/) (2022)

## Built on by (most cited first, 1 of 1)

- [Rule-Based Languages for Neurosymbolic AI](https://mlsanity.com/paper/2610.07313/) (2026)

## Abstract (arXiv)

We study the problem of learning neural classifiers in a neurosymbolic setting where the hidden gold labels of input instances must satisfy a logical formula. Learning in this setting proceeds by first computing (a subset of) the possible combinations of labels that satisfy the formula and then computing a loss using those combinations and the classifiers' scores. One challenge is that the space of label combinations can grow exponentially, making learning difficult. We propose a technique that prunes this space by exploiting the intuition that instances with similar latent representations are likely to share the same label. While this intuition has been widely used in weakly supervised learning, its application in our setting is challenging due to label dependencies imposed by logical constraints. We formulate the pruning process as an integer linear program that discards inconsistent label combinations while respecting logical structure. Our approach, CLIPPER, is orthogonal to existing training algorithms and can be seamlessly integrated with them. Across 16 benchmarks over complex neurosymbolic tasks, we demonstrate that CLIPPER boosts the performance of state-of-the-art neurosymbolic engines like Scallop, Dolphin, and ISED by up to 48%, 53%, and 8%, leading to state-of-the-art accuracies.