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Title: Deep neuroethology of a virtual rodent

Paper content:
Parallel developments in neuroscience and deep learning have led to mutually productive exchanges, pushing our understanding of real and artificial neural networks in sensory and cognitive systems.
However, this interaction between fields is less developed in the study of motor control.
In this work, we develop a virtual rodent as a platform for the grounded study of motor activity in artificial models of embodied control.
We then use this platform to study motor activity across contexts by training a model to solve four complex tasks.
Using methods familiar to neuroscientists, we describe the behavioral representations and algorithms employed by different layers of the network using a neuroethological approach to characterize motor activity relative to the rodent's behavior and goals.
We find that the model uses two classes of representations which respectively encode the task-specific behavioral strategies and task-invariant behavioral kinematics.
These representations are reflected in the sequential activity and population dynamics of neural subpopulations.
Overall, the virtual rodent facilitates grounded collaborations between deep reinforcement learning and motor neuroscience.
Animals have nervous systems that allow them to coordinate their movement and perform a diverse set of complex behaviors.
Mammals, in particular, are generalists in that they use the same general neural network to solve a wide variety of tasks.
This flexibility in adapting behaviors towards many different goals far surpasses that of robots or artificial motor control systems.
Hence, studies of the neural underpinnings of flexible behavior in mammals could yield important insights into the classes of algorithms capable of complex control across contexts and inspire algorithms for flexible control in artificial systems (Merel et al., 2019b) .
Recent efforts at the interface of neuroscience and machine learning have sparked renewed interest in constructive approaches in which artificial models that solve tasks similar to those solved by animals serve as normative models of biological intelligence.
Researchers have attempted to leverage these models to gain insights into the functional transformations implemented by neurobiological circuits, prominently in vision (Khaligh-Razavi & Kriegeskorte, 2014; Yamins et al., 2014; Kar et al., 2019) , but also increasingly in other areas, including audition (Kell et al., 2018) and navigation (Banino et al., 2018; Cueva & Wei, 2018) .
Efforts to construct models of biological locomotion systems have informed our understanding of the mechanisms and evolutionary history of bodies and behavior (Grillner et al., 2007; Ijspeert et al., 2007; Ramdya et al., 2017; Nyakatura et al., 2019) .
Neural control approaches have also been applied to the study of reaching movements, though often in constrained behavioral paradigms (Lillicrap & Scott, 2013) , where supervised training is possible (Sussillo et al., 2015; Michaels et al., 2019) .
While these approaches model parts of the interactions between animals and their environments (Chiel & Beer, 1997) , none attempt to capture the full complexity of embodied control, involving how an animal uses its senses, body and behaviors to solve challenges in a physical environment.
Equal contribution.
The development of models of embodied control is valuable to the field of motor neuroscience, which typically focuses on restricted behaviors in controlled experimental settings.
It is also valuable for AI research, where flexible models of embodied control could be applicable to robotics.
Here, we introduce a virtual model of a rodent to facilitate grounded investigation of embodied motor systems.
The virtual rodent affords a new opportunity to directly compare principles of artificial control to biological data from real-world rodents, which are more experimentally accessible than humans.
We draw inspiration from emerging deep reinforcement learning algorithms which now allow artificial agents to perform complex and adaptive movement in physical environments with sensory information that is increasingly similar to that available to animals (Peng et al., 2016; Heess et al., 2017; Merel et al., 2019a; .
Similarly, our virtual rodent exists in a physical world, equipped with a set of actuators that must be coordinated for it to behave effectively.
It also possesses a sensory system that allows it to use visual input from an egocentric camera located on its head and proprioceptive input to sense the configuration of its body in space.
There are several questions one could answer using the virtual rodent platform.
Here we focus on the problem of embodied control across multiple tasks.
While some efforts have been made to analyze neural activity in reduced systems trained to solve multiple tasks (Song et al., 2017; Yang et al., 2019) , those studies lacked the important element of motor control in a physical environment.
Our rodent platform presents the opportunity to study how representations of movements as well as sequences of movements change as a function of goals and task contexts.
To address these questions, we trained our virtual rodent to solve four complex tasks within a physical environment, all requiring the coordinated control of its body.
We then ask "Can a neuroscientist understand a virtual rodent?" -a more grounded take on the originally satirical "Can a biologist fix a radio?" (Lazebnik, 2002) or the more recent "Could a neuroscientist understand a microprocessor?" (Jonas & Kording, 2017) .
We take a more sanguine view of the tremendous advances that have been made in computational neuroscience in the past decade, and posit that the supposed 'failure' of these approaches in synthetic systems is partly a misdirection.
Analysis approaches in neuroscience were developed with the explicit purpose of understanding sensation and action in real brains, and often implicitly rooted in the types of architectures and processing that are thought relevant in biological control systems.
With this philosophy, we use analysis approaches common in neuroscience to explore the types of representations and dynamics that the virtual rodent's neural network employs to coordinate multiple complex movements in the service of solving motor and cognitive tasks.
We implemented a virtual rodent body (Figure 1 ) in MuJoCo (Todorov et al., 2012) , based on measurements of laboratory rats (see Appendix A.1).
The rodent body has 38 controllable degrees of freedom.
The tail, spine, and neck consist of multiple segments with joints, but are controlled by tendons that co-activate multiple joints (spatial tendons in MuJoCo).
The rodent will be released as part of dm control/locomotion.
The virtual rodent has access to proprioceptive information as well as "raw" egocentric RGB-camera (64×64 pixels) input from a head-mounted camera.
The proprioceptive inputs include internal joint angles and angular velocities, the positions and velocities of the tendons that provide actuation, egocentric vectors from the root (pelvis) of the body to the positions of the head and paws, a vestibular-like upright orientation vector, touch or contact sensors in the paws, as well as egocentric acceleration, velocity, and 3D angular velocity of the root.
For many computational neuroscientists and artificial intelligence researchers, an aim is to reverseengineer the nervous system at an appropriate level of abstraction.
In the motor system, such an effort requires that we build embodied models of animals equipped with artificial nervous systems capable of controlling their synthetic bodies across a range of behavior.
Here we introduced a virtual rodent capable of performing a variety of complex locomotor behaviors to solve multiple tasks using a single policy.
We then used this virtual nervous system to study principles of the neural control of movement across contexts and described several commonalities between the neural activity of artificial control and previous descriptions of biological control.
A key advantage of this approach relative to experimental approaches in neuroscience is that we can fully observe sensory inputs, neural activity, and behavior, facilitating more comprehensive testing of theories related to how behavior can be generated.
Furthermore, we have complete knowledge of the connectivity, sources of variance, and training objectives of each component of the model, providing a rare ground truth to test the validity of our neural analyses.
With these advantages in mind, we evaluated our analyses based on their capacity to both describe the algorithms and representations employed by the virtual rodent and recapitulate the known functional objectives underlying its creation without prior knowledge.
To this end, our description of core and policy as respectively representing value and motor production is consistent with the model's actor-critic training objectives.
But beyond validation, our analyses provide several insights into how these objectives are reached.
RSA revealed that the cell activity of core and policy layers had greater similarity with behavioral and postural features than with short-timescale actuators.
This suggests that the representation of behavior is useful in the moment-to-moment production of motor actions in artificial control, a model that has been previously proposed in biological action selection and motor control (Mink, 1996; Graziano, 2006) .
These behavioral representations were more consistent across tasks in the policy than in the core, suggesting that task context and value activity in the core engaged task-specific behavioral strategies through the reuse of shared motor activity in the policy.
Our analysis of neural dynamics suggests that reused motor activity patterns are often organized as sequences.
Specifically, the activity of policy units uniformly tiles time in the production of several stereotyped behaviors like running, jumping, spinning, and the two-tap sequence.
This finding is consistent with reports linking sequential neural activity to the production of stereotyped motor and task-oriented behavior in rodents (Berke et al., 2009; Rueda-Orozco & Robbe, 2015; Dhawale et al., 2019) , including during task delay periods (Akhlaghpour et al., 2016) , as well as in singing birds (Albert & Margoliash, 1996; Hahnloser et al., 2002) .
Similarly, by relating rotational dynamics to the virtual rodent's behavior, we found that different behaviors were seemingly associated with distinct rotations in neural activity space that evolved at different timescales.
These findings are consistent with a hierarchical control scheme in which policy layer dynamics that generate reused behaviors are activated and modulated by sensorimotor signals from the core.
This work represents an early step toward the constructive modeling of embodied control for the purpose of understanding the neural mechanisms behind the generation of behavior.
Incrementally and judiciously increasing the realism of the model's embodiment, behavioral repertoire, and neural architecture is a natural path for future research.
Our virtual rodent possesses far fewer actuators and touch sensors than a real rodent, uses a vastly different sense of vision, and lacks integration with olfactory, auditory, and whisker-based sensation (see Zhuang et al., 2017) .
While the virtual rodent is capable of locomotor behaviors, an increased diversity of tasks involving decision making, memory-based navigation, and working memory could give insight into "cognitive" behaviors of which rodents are capable.
Furthermore, biologically-inspired design of neural architectures and training procedures should facilitate comparisons to real neural recordings and manipulations.
We expect that this comparison will help isolate residual elements of animal behavior generation that are poorly captured by current models of motor control, and encourage the development of artificial neural architectures that can produce increasingly realistic behavior.

assistant: text: We built a physical simulation of a rodent, trained it to solve a set of tasks, and analyzed the resulting networks.