Known learning rules tend to fall near one of two extremes: single-pass associative learning with low complexity and capacity, and multi-pass iterative learning with high complexity and capacity. In this work we investigate the mathematical feasibility of learning rules that are both single-pass and achieve the theoretical upper bound on capacity. We consider a fairly broad family of learning rules we call “span rules,” which include known rules such as Hebbian learning, perceptron learning, and backpropagation as special cases. To our knowledge, previous work has not determined whether single-pass, full-capacity span rules exist, even in the most fundamental case of a linear threshold neuron with binary input vectors, which is the focus of this study. We derive a necessary condition for the existence of such learning rules, which takes the form of a linear program, and show that the linear program is infeasible. This establishes an impossibility result that span rules can not be both single-pass and full-capacity.

Falling is a critical problem for both people and robots, which may cause bodily harm to the elderly or prevent robots from executing issued orders. This motivates applications of machine learning to recognize and detect falls. Many datasets have been collected for this purpose, but primarily for detecting human falls after they occur. In this paper, we contribute simulated and real training data for robotic fall prediction in advance, based on egocentric video. We also compare an existing fall recognition model with a custom deep architecture we designed, to establish baseline performance on our datasets. We find that our architecture performs well for various prediction spans that can shift between training and testing.