A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification

Standard cross-entropy is the default classification loss across virtually all of machine learning, yet it treats all misclassifications equally, ignoring the semantic distances that a class hierarchy encodes. We propose Hierarchy-Aware Cross-Entropy (HACE), a drop-in replacement for standard cross-entropy that incorporates a known class hierarchy directly into the loss. HACE combines two components: prediction aggregation, which propagates the model's probability mass upward through the class hierarchy to ensure that parent nodes accumulate the confidence of their children; and ancestral label smoothing, which distributes the ground-truth signal along the path from the true class to the root. We evaluate HACE on CIFAR-100, FGVC Aircraft, and NABirds in two regimes: end-to-end training across six architectures spanning convolutional and attention-based designs, and linear probing on frozen DINOv2-Large features. In end-to-end training, HACE improves accuracy over standard cross-entropy in 15 out of 18 architecture--dataset pairs, with a mean gain of 4.66%. In linear probing on frozen DINOv2-Large features, HACE outperforms all competing methods on all three datasets, with a mean improvement of 2.18% over the next best baseline.

Multimodal contrastive learning has enabled zero-shot visual classification by aligning images with textual categories. However, in hierarchically structured label spaces, existing methods often produce predictions that are inconsistent across taxonomic levels. For example, a model may predict a fine-grained category whose parent category contradicts its simultaneously predicted higher-level label. By analysis, the issue originates from false negative labels when contrastive comparison involves multiple taxonomic levels. To this end, we propose to restrict contrastive comparisons to categories within the same taxonomic level. In addition, we adopt a group-balanced design, ensuring each taxonomic level receives adequate optimization. As a result, the proposed framework improves both hierarchical consistency and classification accuracy from coarse to fine granularity. We train our model with TreeOfLife-10M based on BioCLIP and evaluate it across multiple hierarchical classification benchmarks, where the model demonstrates significantly improved hierarchical consistency in both Euclidean and hyperbolic spaces. Notably, on iNaturalist 2021 (iNat21), our method improves average accuracy across levels by 30.47% over the baseline, highlighting its effectiveness for hierarchical zero-shot classification.

Integrating domain knowledge into deep neural networks is a promising way to improve generalization. Existing methods either encode prior knowledge in the loss function or apply post-processing modules, but both depend on identifying useful symbolic knowledge to integrate. Since such rules are often unavailable in real-world vision tasks, we propose a method for targeted knowledge discovery. We propose a Differentiable Knowledge Unit (DKU) that enables modulating the classifier logits, yielding refined class probabilities. The DKU uses implication rules to represent relationships between task classes and implicit concepts learned entirely from the main task supervision, without requiring concept labels. Concepts are identified by dedicated classifiers, whose probabilities are passed to DKU alongside the primary class probabilities. DKU computes a logic-based adjustment vector via fuzzy inference, which modulates the primary class logits to yield refined class probabilities. When concept classifiers represent concepts that do not support the logical rule structure, the resulting adjustments to the class probabilities do not directly minimize the supervision loss. Consequently, optimizing the supervision loss on these adjusted class probabilities implicitly trains the concept classifiers. We construct the rule base so that bidirectional logical relations connect concepts and classes. We enforce the concepts to be distinct from each other and with respect to the classes. This design enforces a clean supervision signal for concept learning. We evaluate our methods on the PASCAL-VOC, COCO, and MedMNIST datasets. We demonstrate improvement through our knowledge integration across these datasets. We conduct domain generalization and hard-sample ablation studies and find that our implicit knowledge discovery and integration outperforms the baseline.