Disentanglement with Holographic Reduced Representations

Disentanglement, the separation of factors of variation in data using neural networks, remains a long-standing challenge in machine learning. Prior work has addressed this problem with variational autoencoders and generative adversarial networks that incorporate ideas from variational inference and information-theoretic constraints. In contrast to methods that rely on continuous representations, we propose a design that treats disentangled representations as symbolic structures, motivated by the compositional relationships among the concepts that make up samples from a distribution. However, learning discrete symbolic structures with neural networks while maintaining differentiability is difficult and often requires complex architectures. To address this, we introduce an unsupervised learning algorithm that uses holographic reduced representations (HRR) for neural disentanglement. We show that the HRR unbinding operation provides an inductive bias for separating factors and yields competitive results against baselines, as measured by latent traversals and disentanglement metrics. We complement these empirical findings with an information-theoretic analysis of the HRR unbinding channel. We prove that unbinding induces approximately independent symbol-value pairs and derive a per-slot capacity bound that quantifies how many distinct symbolic concepts can be reliably encoded, giving a quantitative account of the inductive bias toward disentanglement. The resulting representations differ from standard autoencoder-based models, in that their latent units are vectors that are summed together, rather than scalar dimensions of a low-dimensional latent vector. We show that this HRR representation is more robust to noise than other disentangled representations and maintains reconstruction quality across a range of SNRs.

Neurosymbolic Learning for Advanced Persistent Threat Detection under Extreme Class Imbalance

The growing deployment of Internet of Things (IoT) devices in smart cities and industrial environments increases vulnerability to stealthy, multi-stage advanced persistent threats (APTs) that exploit wireless communication. Detection is challenging due to severe class imbalance in network traffic, which limits the effectiveness of traditional deep learning approaches and their lack of explainability in classification decisions. To address these challenges, this paper proposes a neurosymbolic architecture that integrates an optimized BERT model with logic tensor networks (LTN) for explainable APT detection in wireless IoT networks. The proposed method addresses the challenges of mobile IoT environments through efficient feature encoding that transforms network flow data into BERT-compatible sequences while preserving temporal dependencies critical for APT stage identification. Severe class imbalance is mitigated using focal loss, hierarchical classification that separates normal traffic detection from attack categorization, and adaptive sampling strategies. Evaluation on the SCVIC-APT2021 dataset demonstrates an operationally viable binary classification F1 score of 95.27% with a false positive rate of 0.14%, and a 76.75% macro F1 score for multi-class attack categorization. Furthermore, a novel explainability analysis statistically validates the importance of distinct network features. These results demonstrate that neurosymbolic learning enables high-performance, interpretable, and operationally viable APT detection for IoT network monitoring architectures.