It is still unknown how associative biological memories operate. Hopfield networks are popular models of associative memory, but they suffer from spurious memories and low efficiency. Here, we present a new model of an associative memory that overcomes these deficiencies. We call this model sparse associative memory (SAM) because it is based on sparse projections from neural patterns to pattern-specific neurons. These sparse projections have been shown to be sufficient to uniquely encode a neural pattern. Based on this principle, we investigate theoretically and in simulation our SAM model, which turns out to have high memory efficiency and a vanishingly small probability of spurious memories. This model may serve as a basic building block of brain functions involving associative memory.

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.