## 50 Years Since the Marr, Ito, and Albus Models of the Cerebellum

Mitsuo Kawato, Shogo Ohmae, Huu Hoang and Terry Sanger (2021)

https://doi.org/10.1016/j.neuroscience.2020.06.019

[…]

Cerebellar internal models

Internal models in neuroscience are the neural networks

that simulate input–output relationships of some

processes, such as controlled objects in movement

execution. ‘‘Internal” implies that the neural network is

within the brain or the cerebellum. ‘‘Model” implies that

the neural network simulates a target dynamical

process. When humans move their bodies quickly, the

necessary computation is too difficult to be solved by

simple feedback controllers alone, and internal models

are necessary (Gomi and Kawato, 1996). Here, we

include both forward and inverse (see below) models as

possibilities. There is always feedback control, but except

very basic feedback control, model-predictive controllers

or precomputed ballistic movements include some forms

of internal models. When humans grow their bodies and

manipulate different objects, their dynamics change dras-

tically; thus, internal models cannot be genetically prepro-

grammed or fixed, and must be acquired through learning.

Ito (1970) proposed that internal models are acquired by

learning in the cerebellum (Table 1; Fig. 3A, B). Neither

Marr nor Albus mention internal models around 1970,

but Albus (1975) later proposed an artificial neural net-

work model called CMAC (cerebellar model articulation

controller), and one of its possible applications was to

learn inverse dynamics models of robots.Internal models are classified as either forward or

inverse. Forward models possess the same input–

output direction as controlled objects and simulate their

dynamics. For example, controlled objects such as

eyeballs or arms receive motor commands and

generate movement trajectories, that can be

represented as sensory feedback about the executed

trajectories. Forward models receive copies of motor

commands (corollary discharge or efference copy) and

predict movement trajectories or sensory feedback

(sensory consequence). In control engineering and

robotics, forward models have been and still are just

called ‘‘internal models.” Jordan and Rumelhart (1992)

coined this term to discriminate them from inverse mod-

els, and this terminology was soon adopted by cognitive

science and neuroscience. On the other hand, inverse

models simulate inverted input–output relationships of

controlled objects. In a sense, inverse models provide

inverse functions of modeled dynamical systems. Inverse

models of controlled objects can receive desired trajecto-

ries as inputs and can compute necessary motor com-

mands to realize the desired trajectories.[…]

In another interpretation based

on the forward model, part of the cerebellar

hemisphere provides a forward model of the controlled

object. It computes a predicted trajectory while receiving

the efference copy of the motor command. The difference

of the realized trajectory and the predicted trajectory pro-

vides a sensory prediction error that can be used as an

error signal to train the forward model.This forward model

can be used as an essential element for internal feedback

control, bypassing the long-loop through the external

world, reducing feedback delays and increasing control

performance.

## Neural Evidence of the Cerebellum as a State Predictor

Hirokazu Tanaka & Takahiro Ishikawa & Shinji Kakei (2019)

https://doi.org/10.1007/s12311-018-0996-4

Abstract

We here provide neural evidence that the cerebellar circuit can predict future inputs from present outputs, a hallmark of an internal forward model. Recent computational studies hypothesize that the cerebellum performs state prediction known as a forward model. To test the forward-model hypothesis, we analyzed activities of 94 mossy fibers (inputs to the cerebellar cortex), 83 Purkinje cells (output from the cerebellar cortex to dentate nucleus), and 73 dentate nucleus cells (cerebellar output) in the cerebro-cerebellum, all recorded from a monkey performing step-tracking movements of the right wrist. We found that the firing rates of one population could be reconstructed as a weighted linear sum of those of preceding populations. We then went on to investigate if the current outputs of the cerebellum (dentate cells) could predict the future inputs of the cerebellum (mossy fibers). The firing rates of mossy fibers at time t + t1 could be well reconstructed from as a weighted sum of firing rates of dentate cells at time t, thereby proving that the dentate activities contained predictive information about the future inputs. The average goodness-of-fit (R2) decreased moderately from 0.89 to 0.86 when t1 was increased from 20 to 100 ms, hence indicating that the prediction is able to compensate the latency of sensory feedback. The linear equations derived from the firing rates resembled those of a predictor known as Kalman filter composed of prediction and filtering steps. In summary, our analysis of cerebellar activities supports the forward-model hypothesis of the cerebellum.