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Simple and Effective Transfer Learning for Neuro-Symbolic Integration

Alessandro Daniele, Tommaso Campari, Sagar Malhotra, Luciano Serafini

TL;DR

The paper addresses the bottleneck in Neuro-Symbolic Integration where weak supervision from symbolic reasoning leads to slow convergence and local minima. It proposes a simple, effective transfer-learning strategy: pretrain a neural model on the downstream task and then transfer its perception encoder to NeSy models, freezing it so that only the embedding-to-symbol mapping is learned. Across multiple NeSy methods and tasks, this approach yields faster convergence, reduced local minima issues, and expanded capability to handle complex perception inputs, with modest preprocessing overhead. The findings demonstrate improved accuracy and scalability, suggesting a practical path to more reliable and generalizable NeSy systems in real-world reasoning tasks.

Abstract

Deep Learning (DL) techniques have achieved remarkable successes in recent years. However, their ability to generalize and execute reasoning tasks remains a challenge. A potential solution to this issue is Neuro-Symbolic Integration (NeSy), where neural approaches are combined with symbolic reasoning. Most of these methods exploit a neural network to map perceptions to symbols and a logical reasoner to predict the output of the downstream task. These methods exhibit superior generalization capacity compared to fully neural architectures. However, they suffer from several issues, including slow convergence, learning difficulties with complex perception tasks, and convergence to local minima. This paper proposes a simple yet effective method to ameliorate these problems. The key idea involves pretraining a neural model on the downstream task. Then, a NeSy model is trained on the same task via transfer learning, where the weights of the perceptual part are injected from the pretrained network. The key observation of our work is that the neural network fails to generalize only at the level of the symbolic part while being perfectly capable of learning the mapping from perceptions to symbols. We have tested our training strategy on various SOTA NeSy methods and datasets, demonstrating consistent improvements in the aforementioned problems.

Simple and Effective Transfer Learning for Neuro-Symbolic Integration

TL;DR

The paper addresses the bottleneck in Neuro-Symbolic Integration where weak supervision from symbolic reasoning leads to slow convergence and local minima. It proposes a simple, effective transfer-learning strategy: pretrain a neural model on the downstream task and then transfer its perception encoder to NeSy models, freezing it so that only the embedding-to-symbol mapping is learned. Across multiple NeSy methods and tasks, this approach yields faster convergence, reduced local minima issues, and expanded capability to handle complex perception inputs, with modest preprocessing overhead. The findings demonstrate improved accuracy and scalability, suggesting a practical path to more reliable and generalizable NeSy systems in real-world reasoning tasks.

Abstract

Deep Learning (DL) techniques have achieved remarkable successes in recent years. However, their ability to generalize and execute reasoning tasks remains a challenge. A potential solution to this issue is Neuro-Symbolic Integration (NeSy), where neural approaches are combined with symbolic reasoning. Most of these methods exploit a neural network to map perceptions to symbols and a logical reasoner to predict the output of the downstream task. These methods exhibit superior generalization capacity compared to fully neural architectures. However, they suffer from several issues, including slow convergence, learning difficulties with complex perception tasks, and convergence to local minima. This paper proposes a simple yet effective method to ameliorate these problems. The key idea involves pretraining a neural model on the downstream task. Then, a NeSy model is trained on the same task via transfer learning, where the weights of the perceptual part are injected from the pretrained network. The key observation of our work is that the neural network fails to generalize only at the level of the symbolic part while being perfectly capable of learning the mapping from perceptions to symbols. We have tested our training strategy on various SOTA NeSy methods and datasets, demonstrating consistent improvements in the aforementioned problems.
Paper Structure (14 sections, 2 equations, 4 figures, 5 tables)

This paper contains 14 sections, 2 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Method
  4. Experiments
  5. Implementation Details.
  6. Evaluation Metrics.
  7. MNISTSum
  8. CIFARSum
  9. MNISTMultiOp
  10. Visual Parity
  11. MNISTMultiDigitSum
  12. Limitations and Future Works.
  13. Conclusions
  14. Acknowledgments

Figures (4)

  • Figure 1: Training procedure overview: in the first phase, a neural network model is trained on the downstream task; in the second phase, the NeSy method is trained starting from the previously learned perception model.
  • Figure 2: An example of our learning strategy on the MNISTSum task: on the first phase (left), we train a neural model for the downstream task; on the second phase (right), we use the pretrained weights of the neural network $f_e$ as a starting point for the NeSy architecture, which learns the mapping from embeddings to symbols ($f_m$) and, in case of DSL, the symbolic function $g$.
  • Figure 3: t-SNE applied to embeddings of $f_e$ learned by the neural model on the MNISTSum (left) and CIFARSum (right) tasks. Colours represent different digits.
  • Figure 4: Minimum and maximum (transparent boundaries) and average accuracies (solid lines) obtained while training the RNN (on 2 or 3 digits) and DSL$^{\text{PR}}$. DSL convergence is slower but can generalize to longer sequences with higher results. The results are obtained across ten runs.