This thesis aims to bridge the gap between data-driven models and symbolic learning through the lens of Concept-Based Learning, a paradigm that guides model learning through high-level, human-understandable concepts. Here, models first learn a set of concepts, subsequently using them to perform a task of interest. Prior work on concept-based models has largely focused on relatively simple classification settings, where classes are linear combinations of pre-specified concepts; treating concepts largely as tools to increase interpretability, rather than as fundamental building blocks of the learning process itself. In contrast, this thesis explores the broader potential of concepts, as the core units of representation and reasoning in neural network models, capable of shaping how models learn and generalize.

Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring predictions as a linear combination of semantic concepts. However, a linear combination is inherently limiting. So we propose the enhancement of concept-based learning models through propositional logic. We introduce a logic module that is carefully designed to connect the learned concepts from CBMs through differentiable logic operations, such that our proposed LogicCBM can go beyond simple weighted combinations of concepts to leverage various logical operations to yield the final predictions, while maintaining end-to-end learnability. Composing concepts using a set of logic operators enables the model to capture inter-concept relations, while simultaneously improving the expressivity of the model in terms of logic operations. Our empirical studies on well-known benchmarks and synthetic datasets demonstrate that these models have better accuracy, perform effective interventions and are highly interpretable1.

Concept-based methods have emerged as a promising direction to develop interpretable neural networks in standard supervised settings. However, most works that study them in incremental settings assume either a static concept set across all experiences or assume that each experience relies on a distinct set of concepts. In this work, we study concept-based models in a more realistic, dynamic setting where new classes may rely on older concepts in addition to introducing new concepts themselves. We show that concepts and classes form a complex web of relationships, which is susceptible to degradation and needs to be preserved and augmented across experiences. We introduce new metrics to show that existing concept-based models cannot preserve these relationships even when trained using methods to prevent catastrophic forgetting, since they cannot handle forgetting at concept, class, and concept-class relationship levels simultaneously. To address these issues, we propose a novel method - MuCIL - that uses multimodal concepts to perform classification without increasing the number of trainable parameters across experiences. The multimodal concepts are aligned to concepts provided in natural language, making them interpretable by design. Through extensive experimentation, we show that our approach obtains state-of-the-art classification performance compared to other concept-based models, achieving over 2x the classification performance in some cases. We also study the ability of our model to perform interventions on concepts, and show that it can localize visual concepts in input images, providing post-hoc interpretations.