# PROTOtypical Logic Tensor Networks (PROTO-LTN) for Zero Shot Learning

arXiv: https://arxiv.org/abs/2207.00433 · HTML: https://mlsanity.com/paper/2207.00433/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 26 Jun 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Zero-Shot Learning -- A Comprehensive Evaluation of the Good, the Bad and the Ugly](https://mlsanity.com/paper/1707.00600/) (2017)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Learning a Deep Embedding Model for Zero-Shot Learning](https://mlsanity.com/paper/1611.05088/) (2016)
- [Generalized Zero-Shot Learning via Synthesized Examples](https://mlsanity.com/paper/1712.03878/) (2017)
- [Synthesized Classifiers for Zero-Shot Learning](https://mlsanity.com/paper/1603.00550/) (2016)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [From Statistical Relational to Neuro-Symbolic Artificial Intelligence](https://mlsanity.com/paper/2003.08316/) (2020)
- [Generative Dual Adversarial Network for Generalized Zero-shot Learning](https://mlsanity.com/paper/1811.04857/) (2018)
- [Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use cases](https://mlsanity.com/paper/2102.11965/) (2021)
- [Probabilistic Neural-symbolic Models for Interpretable Visual Question Answering](https://mlsanity.com/paper/1902.07864/) (2019)
- [Transductive Zero-Shot Learning with Visual Structure Constraint](https://mlsanity.com/paper/1901.01570/) (2019)
- [Progressive Ensemble Networks for Zero-Shot Recognition](https://mlsanity.com/paper/1805.07473/) (2018)
- [Generalized Zero-Shot Recognition based on Visually Semantic Embedding](https://mlsanity.com/paper/1811.07993/) (2018)
- [Calibrating Concepts and Operations: Towards Symbolic Reasoning on Real Images](https://mlsanity.com/paper/2110.00519/) (2021)
- [Compensating Supervision Incompleteness with Prior Knowledge in Semantic Image Interpretation](https://mlsanity.com/paper/1910.00462/) (2019)
- [Faster-LTN: a neuro-symbolic, end-to-end object detection architecture](https://mlsanity.com/paper/2107.01877/) (2021)

## Built on by (most cited first, 3 of 3)

- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [Fuzzy Logic Visual Network (FLVN): A neuro-symbolic approach for visual features matching](https://mlsanity.com/paper/2307.16019/) (2023)
- [Soft Symbol Grounding for Prototypical Concepts](https://mlsanity.com/paper/2609.12247/) (2026)

## Abstract (arXiv)

Semantic image interpretation can vastly benefit from approaches that combine sub-symbolic distributed representation learning with the capability to reason at a higher level of abstraction. Logic Tensor Networks (LTNs) are a class of neuro-symbolic systems based on a differentiable, first-order logic grounded into a deep neural network. LTNs replace the classical concept of training set with a knowledge base of fuzzy logical axioms. By defining a set of differentiable operators to approximate the role of connectives, predicates, functions and quantifiers, a loss function is automatically specified so that LTNs can learn to satisfy the knowledge base. We focus here on the subsumption or textttisOfClass predicate, which is fundamental to encode most semantic image interpretation tasks. Unlike conventional LTNs, which rely on a separate predicate for each class (e.g., dog, cat), each with its own set of learnable weights, we propose a common textttisOfClass predicate, whose level of truth is a function of the distance between an object embedding and the corresponding class prototype. The PROTOtypical Logic Tensor Networks (PROTO-LTN) extend the current formulation by grounding abstract concepts as parametrized class prototypes in a high-dimensional embedding space, while reducing the number of parameters required to ground the knowledge base. We show how this architecture can be effectively trained in the few and zero-shot learning scenarios. Experiments on Generalized Zero Shot Learning benchmarks validate the proposed implementation as a competitive alternative to traditional embedding-based approaches. The proposed formulation opens up new opportunities in zero shot learning settings, as the LTN formalism allows to integrate background knowledge in the form of logical axioms to compensate for the lack of labelled examples.