HyDI: A hybrid Deep Learning-Inductive Logic Programming ensemble for multi-label classification

Although concept-based models promise interpretability by explaining predictions with human-understandable concepts, they typically rely on exhaustive annotations and treat concepts as flat and independent. To circumvent this, recent work has introduced Hierarchical Concept Embedding Models (HiCEMs) to explicitly model concept relationships, and Concept Splitting to discover sub-concepts using only coarse annotations. However, both HiCEMs and Concept Splitting are restricted to shallow hierarchies. We overcome this limitation with Multi-Level Concept Splitting (MLCS), which discovers multi-level concept hierarchies from only top-level supervision, and Deep-HiCEMs, an architecture that represents these discovered hierarchies and enables interventions at multiple levels of abstraction. Experiments across multiple datasets show that MLCS discovers human-interpretable concepts absent during training and that Deep-HiCEMs maintain high accuracy while supporting test-time concept interventions that can improve task performance.

Deep learning has become the dominant approach for creating high capacity, scalable models across diverse data modalities. However, because these models rely on a large number of learned parameters, tightly couple feature extraction with task objectives, and often lack explicit reasoning mechanisms, it is difficult for humans to understand how they arrive at their predictions. Understanding what representations emerge and why they arise from the training data remains an open challenge. We introduce Deep Arguing, a novel neurosymbolic approach that integrates deep learning with argumentation construction and reasoning for interpretable classification with different data modalities. In our approach deep neural networks construct an argumentation structure wherein data points support their assigned label and attack different ones. Using differentiable argumentation semantics for reasoning, the model is trained end-to-end to jointly learn feature representation and argumentative interactions. This results in argumentation structures providing faithful case-based explanations for predictions. Structure constraints over the argumentation graph guide learning, improving both interpretability and predictive performance. Experiments with tabular and imaging datasets show that Deep Arguing achieves performance competitive with standard baselines whilst offering interpretable argumentative reasoning.

Segment-based explanation methods such as LIME return a single explanation for each prediction, computed from one fixed image segmentation. This hides two important facts: a prediction can be supported by many different sets of image segments, and the segmentation itself shapes which explanations can be found. We introduce MOXIE (Multi-Objective eXplanation Imaging Engine), an evolutionary framework that searches for segment subsets that preserve the classifier's confidence while keeping as little of the image as possible. Instead of one explanation, MOXIE returns a Pareto front of alternative explanations that range from compact to highly faithful. We evaluate MOXIE with NSGA-II and four segmentation methods (SLIC, Felzenszwalb, Watershed and Voronoi) on BloodMNIST and HAM10000 datasets, using the same evaluation budget as LIME. Results show that MOXIE achieves a higher hypervolume than LIME on every image. LIME's explanations often appear convincing, yet the classifier's confidence collapses when only the highlighted segments are shown. MOXIE's fronts reveal how much of the image is needed to preserve the model's confidence and which contextual regions influence it. We also find that segmentation strongly affects evaluation: methods with unequal segment sizes appear most compact when segments are counted. These results show that alternative explanations provide a more complete view of a model's decision than a single explanation.