See and Copy Generation of complex compositional movements from modular and geometric RNN representations

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See and Copy: Generation of complex compositional

movements from modular and geometric RNN

representations

Sunny Duan†sunnyd@mit.edu

Mikail Khona†mikail@mit.edu

Adrian Bertagnoli†ab @mit.edu

Sarthak Chandra sarthakc@mit.edu

Ila Fiete fiete@mit.edu

[†] Denotes co-ﬁrst authors

Abstract

A hallmark of biological intelligence and control is combinatorial generalization: animals

are able to learn various things, then piece them together in new combinations to produce

appropriate outputs for new tasks. Inspired by the ability of primates to readily imitate

seen movement sequences, we present a model of motor control using a realistic model of

arm dynamics, tasked with imitating a guide that makes arbitrary two-segment drawings.

We hypothesize that modular organization is one of the keys to such ﬂexible and general-

izable control. We construct a modular control model consisting of separate encoding and

motor RNNs and a scheduler, which we train end-to-end on the task. We show that the

modular structure allows the model to generalize not only to unseen two-segment trajec-

tories, but to new drawings consisting of many more segments than it was trained on, and

also allows for rapid adaptation to perturbations. Finally, our model recapitulates exper-

imental observations of the preparatory and execution-related processes unfolding during

motor control, providing a normative explanation for functional segregation of preparatory

and execution-related activity within the motor cortex.

Keywords: Modularity, Motor Control, Neural Representational Geometry

1. Introduction

Animal behavior is believed to be atomic: composed of a discrete set of “syllables” or motifs

which together form a “grammar” Wiltschko et al. (2015); Markowitz et al. (2018). Ac-

tion sequences are then generated by combining syllables and executing them sequentially.

The compositional structure inherent in this scheme allows animals to ﬂexibly recombine

motor primitives to generate novel, ecologically relevant movement patterns. This system

aﬀords animals a combinatorially large movement repertoire built of out simpler compo-

nents. However, the specialized structures in the motor system required to implement this

scheme eﬃciently remain unknown.

Existing experiments in the motor cortices of non-human primates performing reaching

movements have indicated that the process of movement generation is comprised of three

interdependent stages: a preparatory stage, a trigger signal and action execution. During

the preparatory stage, the parameters for a motion are able to be decoded from the motor

cortex Churchland et al. (2010) indicating that the planned trajectory is present in the

arXiv:2210.02521v1 [q-bio.NC] 5 Oct 2022

motor cortex despite the lack of motion production. After the onset of the trigger signal,

the motor cortex exhibits dynamics which produce downstream muscle activations leading

to the desired motion.

In order to combine multiple motor primitives into complex sequences, there must be

additional structure to support these longer sequences. Recent work studying the neural

dynamics of rhesus macaques performing skilled, practiced compound reaches has indi-

cated that conjunctive movement consists of separate independent chains of motor pro-

cesses sharing the same underlying neural substrate Zimnik and Churchland (2021). In

order to skillfully and smoothly execute a sequence of movements, the motor cortex needs

to simultaneously prepare for an upcoming movement while current motor commands are

being executed. This multi-tasking capability requires functional segregation preparatory

activity and execution within the underlying motor cortical circuitry. Existing research

suggests that this is implemented in biological systems by separating preparatory activity

and execution into orthogonal subspaces.

We demonstrate that a task-optimized neural network is able to implement arbitrary

motor subroutines in a ﬂexible and reusable manner. Our model demonstrates remark-

able generalization capabilities due to its structure. Through learning, our model exhibits

emergent self-organization of its latent representation which facilitates robust production

of movement patterns. Furthermore, our model is able to continuously produce sequences

of motion interference, demonstrating properties of functional segregation exhibited in bio-

logical neural circuits.

2. Methods

Our model architecture resembles the sequence-to-sequence models used in natural language

processing Sutskever et al. (2014). The input data (from the observed “guide”) consists of

procedurally generated movements consisting of up to two straight segments, represented by

a sequence of x,y coordinates. The agent constructs an embedding by sequentially ingesting

the x,y coordinates of the guide sequence into an encoder implemented as a recurrent

neural network (RNN) consisting of continuous-time neurons. The encoder produces a single

(static) readout, or embedding, at the end of each segment. These embeddings are fed into

the motor RNN at pre-speciﬁed times by a scheduler, which modulates the embedding by

a ramping function such that motion onset is triggered by the falling edge of the ramping

signal Hennequin et al. (2014). The beginning of the ramp signal was timed such that the

embedding signal was provided 7 steps before the end of the previous segment such that

the go signal aligns with the end of the previous segment. This temporal overlap forced the

network to simultaneously process both the future motor command while completing the

current segment.

The motor RNN takes in the ramp-modulated static encoder embedding and produces

a sequence of muscle activation commands which are implemented by a realistic simula-

tion of an over-actuated two-link arm moving in two dimensional space Kalidindi et al.

(2021), Lillicrap and Scott (2013). The entire system is trained end-to-end on one or two

segment motions using stochastic gradient descent and supervised learning with additional

biologically relevant loss terms penalizing neural activity and simultaneous activation of

antagonistic muscle pairs.

Segment 1

Demonstrated Trajectory

MLP

CT-RNN

Encoder

Scheduler

MLP

CT-RNN

Motor RNN

Arm Dynamics

MLP

CT-RNN

Sensory feedback

Training trajectories

Segment 2

Model

Target

Complex evaluated trajectories Distribution of preferred angles

Peak neural activity vs reach

direction

AgentWorld Body

d e

/2 2

3 /2 3 /2

7 /4

5 /4

3 /4

Figure 1: a) Schematic of encoder-decoder training setup b) Example trajectories used for

training the model, consisting of procedurally generated single and 2-segment tra-

jectories of various length and angles. c) Examples of complex, out-of-distribution

sequences generated by the trained model. d) Polar histogram of the number of

neurons which ﬁre preferentially in a given direction. e) Distribution of pre-

ferred reach direction for diﬀerent starting locations within the drawing board,

computed by ﬁnding the reach direction which minimized error.

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摘要：

SeeandCopy:GenerationofcomplexcompositionalmovementsfrommodularandgeometricRNNrepresentationsSunnyDuanysunnyd@mit.eduMikailKhonaymikail@mit.eduAdrianBertagnoliyab@mit.eduSarthakChandrasarthakc@mit.eduIlaFietefiete@mit.edu[y]Denotesco-rstauthorsAbstractAhallmarkofbiologicalintelligenceandcontrolisco...

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