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Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as Knowledgebra. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, SemE, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective. 

Were astronauts forced to land on the surface of Mars using manual control of their vehicle, they would not have familiar gravitational cues because Mars’ gravity is only 0.38 g. They could become susceptible to spatial disorientation, potentially causing mission ending crashes. In our earlier studies, we secured blindfolded participants into a Multi-Axis Rotation System (MARS) device that was programmed to behave like an inverted pendulum. Participants used a joystick to stabilize around the balance point. We created a spaceflight analog condition by having participants dynamically balance in the horizontal roll plane, where they did not tilt relative to the gravitational vertical and therefore could not use gravitational cues to determine their position. We found 90% of participants in our spaceflight analog condition reported spatial disorientation and all of them showed it in their data. There was a high rate of crashing into boundaries that were set at ± 60 ° from the balance point. Our goal was to see whether we could use deep learning to predict the occurrence of crashes before they happened. We used stacked gated recurrent units (GRU) to predict crash events 800 ms in advance with an AUC (area under the curve) value of 99%. When we prioritized reducing false negatives we found it resulted in more false positives. We found that false negatives occurred when participants made destabilizing joystick deflections that rapidly moved the MARS away from the balance point. These unpredictable destabilizing joystick deflections, which occurred in the duration of time after the input data, are likely a result of spatial disorientation. If our model could work in real time, we calculated that immediate human action would result in the prevention of 80.7% of crashes, however, if we accounted for human reaction times (∼400 ms), only 30.3% of crashes could be prevented, suggesting that one solution could be an AI taking temporary control of the spacecraft during these moments.