Holographic Reduced Representations (HRR) are a method for performing symbolic AI on top of real-valued vectors \cite{Plate1995} by associating each vector with an abstract concept, and providing mathematical operations to manipulate vectors as if they were classic symbolic objects. This method has seen little use outside of older symbolic AI work and cognitive science. Our goal is to revisit this approach to understand if it is viable for enabling a hybrid neural-symbolic approach to learning as a differentiable component of a deep learning architecture. HRRs today are not effective in a differentiable solution due to numerical instability, a problem we solve by introducing a projection step that forces the vectors to exist in a well behaved point in space. In doing so we improve the concept retrieval efficacy of HRRs by over $100\times$. Using multi-label classification we demonstrate how to leverage the symbolic HRR properties to develop an output layer and loss function that is able to learn effectively, and allows us to investigate some of the pros and cons of an HRR neuro-symbolic learning approach.

We propose a Bi-Directional Manifold Alignment (BDMA) that learns a non-linear mapping between two manifolds by explicitly training it to be bijective. We demonstrate BDMA by training a model for a pair of languages rather than individual, directed source and target combinations, reducing the number of models by 50%. We show that models trained with BDMA in the "forward" (source to target) direction can successfully map words in the "reverse" (target to source) direction, yielding equivalent (or better) performance to standard unidirectional translation models where the source and target language is flipped. We also show how BDMA reduces the overall size of the model.

Evolving cybersecurity threats are a persistent challenge for systemadministrators and security experts as new malwares are continu-ally released. Attackers may look for vulnerabilities in commercialproducts or execute sophisticated reconnaissance campaigns tounderstand a targets network and gather information on securityproducts like firewalls and intrusion detection / prevention systems(network or host-based). Many new attacks tend to be modificationsof existing ones. In such a scenario, rule-based systems fail to detectthe attack, even though there are minor differences in conditions /attributes between rules to identify the new and existing attack. Todetect these differences the IDS must be able to isolate the subset ofconditions that are true and predict the likely conditions (differentfrom the original) that must be observed. In this paper, we proposeaprobabilistic abductive reasoningapproach that augments an exist-ing rule-based IDS (snort [29]) to detect these evolved attacks by (a)Predicting rule conditions that are likely to occur (based on existingrules) and (b) able to generate new snort rules when provided withseed rule (i.e. a starting rule) to reduce the burden on experts toconstantly update them. We demonstrate the effectiveness of theapproach by generating new rules from the snort 2012 rules set andtesting it on the MACCDC 2012 dataset [6].