Fast social-like learning of complex behaviors based on motor motifs

TL;DR

Despite the huge variety of possible motif sequences it is shown that the learner, equipped with the provided learning model, can rewire "on the fly" its synaptic couplings in no more than (n-1) learning cycles and converge exponentially to the durations of the teacher's motifs.

Abstract

Social learning is widely observed in many species. Less experienced agents copy successful behaviors, exhibited by more experienced individuals. Nevertheless, the dynamical mechanisms behind this process remain largely unknown. Here we assume that a complex behavior can be decomposed into a sequence of $n$ motor motifs. Then a neural network capable of activating motor motifs in a given sequence can drive an agent. To account for $(n-1)!$ possible sequences of motifs in a neural network, we employ the winner-less competition approach. We then consider a teacher-learner situation: one agent exhibits a complex movement, while another one aims at mimicking the teacher's behavior. Despite the huge variety of possible motif sequences we show that the learner, equipped with the provided learning model, can rewire ``on the fly'' its synaptic couplings in no more than $(n-1)$ learning cycles and converge exponentially to the durations of the teacher's motifs. We validate the learning model on mobile robots. Experimental results show that indeed the learner is capable of copying the teacher's behavior composed of six motor motifs in a few learning cycles. The reported mechanism of learning is general and can be used for replicating different functions, including, for example, sound patterns or speech.

Figures (5)

• Figure 1: Implementation of motor behaviors as sequences of motor motifs. A) A Pioneer 3DX mobile robot used in experiments. B) Two examples of the robot's behaviors defined by graphs of six motor motifs (see main text). Depending on the order of the motifs and their durations the robot can move along different trajectories (color codifies the active motif).
• Figure 2: Behavior driving neural network. A) Schematic representation of the neural network (example for $n=6$). All neurons (circles) are mutually coupled by inhibitory synapses (black and red links). Red links mark couplings $\alpha= (0.6, 0.5, 0.7, 0.1, 0.8, 0.3)^T$ that define the activation sequence $N_1\to N_2\to N_3\to\cdots$, corresponding to the graph of motor motifs shown in Fig. \ref{['Fig_01']}B.1. The coupling strength of black links is equal to 2. B) WLC dynamics generated by the network. Each neuron switches between on (active) and off (inactive) states. Bottom colored stripe shows the activation intervals $T_1,\ldots,T_6$ of the corresponding neurons determined by $\alpha$.
• Figure 3: Representative example of exponentially fast learning of temporal patterns. A) Dynamics of the coupling strengths of the learner $\gamma(t)$ (solid curves) converging to the corresponding couplings of the teacher $\alpha$ (dashed lines). B) Exponentially fast convergence of the couplings. C) Synchronization (with a time shift) of oscillations in the learner with the teacher. D) Simulation of the robots' movements. The teacher (left) performs zigzag movements, while the learner (right) at the beginning moves in a circle, but after two learning cycle it starts replicating the teacher's behavior (color coding is the same as in C).
• Figure 4: Representative example of dynamical learning of the teacher's graph $1\to 10 \to 12 \to 4 \to 9 \to 13 \to 7 \to 8 \to 2 \to 6 \to 11 \to 3 \to 5 \to \cdots$ defining the sequence of motor motifs in the teacher's behavior. First panel shows in gray all possible connections. Iterations from 1 to 5 show correctly identified connections in red and the remaining ones in gray. A legend below each panel shows the learner's graph. Filled red triangles correspond to newly identified connections, open red triangles mark previously identified connections, and open black traingles label wrong connections.
• Figure 5: Experimental validation of learning. A) Robot-teacher implements the behavior composed of six motor motifs shown in Fig. \ref{['Fig_01']}B.2. The brightness of colors corresponds to time (the brighter, the closer to the present). B) Trajectory of the robot-learner. At the beginning it differs significant from the teacher's behavior. However, in only three cycles the robot learns the sequence of turns and then two more cycles are needed for final adjustment of the coupling strengths. Eventually the learner replicates almost exactly the behavior of the teacher. C) Quantification of the learning error (\ref{['Metric']}), defined as the distance between trajectories of the teacher and learner. Inset illustrates the trajectory curvature of the learner (blue curve) with superimposed curvatures of the teacher in three time windows marked by circles of different colors. The level of coincidence increases with time.

Theorems & Definitions (7)

• Definition 1
• Definition 2
• Theorem 1
• Theorem 2
• Theorem 3
• Lemma 1
• Corollary 1