  The existence of a universal learning architecture in human cognition is a
widely spread conjecture supported by experimental findings from neuroscience.
While no low-level implementation can be specified yet, an abstract outline of
human perception and learning is believed to entail three basic properties: (a)
hierarchical attention and processing, (b) memory-based knowledge
representation, and (c) progressive learning and knowledge compaction. We
approach the design of such a learning architecture from a system-theoretic
viewpoint, developing a closed-loop system with three main components: (i) a
multi-resolution analysis pre-processor, (ii) a group-invariant feature
extractor, and (iii) a progressive knowledge-based learning module.
Multi-resolution feedback loops are used for learning, i.e., for adapting the
system parameters to online observations. To design (i) and (ii), we build upon
the established theory of wavelet-based multi-resolution analysis and the
properties of group convolution operators. Regarding (iii), we introduce a
novel learning algorithm that constructs progressively growing knowledge
representations in multiple resolutions. The proposed algorithm is an extension
of the Online Deterministic Annealing (ODA) algorithm based on annealing
optimization, solved using gradient-free stochastic approximation. ODA has
inherent robustness and regularization properties and provides a means to
progressively increase the complexity of the learning model i.e. the number of
the neurons, as needed, through an intuitive bifurcation phenomenon. The
proposed multi-resolution approach is hierarchical, progressive,
knowledge-based, and interpretable. We illustrate the properties of the
proposed architecture in the context of the state-of-the-art learning
algorithms and deep learning methods.
