PROTOtypical Logic Tensor Networks (PROTO-LTN) for Zero Shot Learning
This work addresses zero-shot learning for semantic image interpretation by integrating logical axioms to compensate for lack of labeled data, representing an incremental improvement over existing neuro-symbolic methods.
The authors tackled the problem of zero-shot learning by proposing PROTOtypical Logic Tensor Networks (PROTO-LTN), which combine neural networks with logical reasoning using a common predicate based on class prototypes, reducing parameters and enabling effective training in few- and zero-shot scenarios. Experiments on Generalized Zero Shot Learning benchmarks showed it as a competitive alternative to traditional embedding-based approaches.
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 \texttt{isOfClass} 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 \texttt{isOfClass} 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.