We present an efficient online learning scheme for non-negative sparse coding in autoencoder neural networks. It comprises a novel synaptic decay rule that ensures non-negative weights and an intrinsic self-adaptation rule that optimizes sparseness of the non-negative encoding. We show that non-negativity constrains the space of solutions such that overfitting is prevented and very similar encodings are found irrespective of the network initialization and size. We benchmark the novel method on real-world datasets of handwritten digits and faces. The autoencoder yields higher sparseness and lower reconstruction errors than related batch algorithms based on matrix factorization. It generalizes to new inputs both accurately and without costly computations, which is fundamentally different from the classical matrix factorization approaches.
The data-driven approximation of vector fields that encode dynamical systems is a persistently hard task in machine learning. If data is sparse and given in form of velocities derived from few trajectories only, state-space regions exists, where no information on the vector field and its induced dynamics is available. Generalization towards such regions is meaningful only if strong biases are introduced, for instance assumptions on global stability properties of the to-belearned dynamics. We address this issue in a novel learning scheme that represents vector fields by means of neural networks, where asymptotic stability of the induced dynamics is explicitly enforced through utilizing knowledge from Lyapunov's stability theory, in a predefined workspace. The learning of vector fields is constrained through point-wise conditions, derived from a suitable Lyapunov function candidate, which is first adjusted towards the training data. We point out the significance of optimized Lyapunov function candidates and analyze the approach in a scenario where trajectories are learned and generalized from human handwriting motions. In addition, we demonstrate that learning from robotic data obtained by kinesthetic teaching of the humanoid robot iCub leads to robust motion generation.
Feed-forward model-based control relies on models of the controlled plant, e.g., in robotics on accurate knowledge of manipulator kinematics or dynamics. However, mechanical and analytical models do not capture all aspects of a plant's intrinsic properties and there remain unmodeled dynamics due to varying parameters, unmodeled friction or soft materials. In this context, machine learning is an alternative suitable technique to extract non-linear plant models from data. However, fully data-based models suffer from inaccuracies as well and are inefficient if they include learning of well known analytical models. This paper thus argues that feed-forward control based on hybrid models comprising an analytical model and a learned error model can significantly improve modeling accuracy. Hybrid modeling here serves the purpose to combine the best of the two modeling worlds. The hybrid modeling methodology is described and the approach is demonstrated for two typical problems in robotics, i.e., inverse kinematics control and computed torque control. The former is performed for a redundant soft robot and the latter for a rigid industrial robot with redundant degrees of freedom, where a complete analytical model is not available for any of the platforms.
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