Population coding in the cerebellum: a machine learning perspective

Abstract

The cerebellum resembles a feedforward, three-layer network of neurons in which the "hidden layer" consists of Purkinje cells (P-cells), and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared to the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus, complex spikes can not only act as a teaching signal for a P-cell, but through complex spike synchrony a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

Adaptive control of movement deceleration during saccades

“…Despite the simplicity of the model, however, it has been difficult to identify behavioral correlates of the putative fast and slow states. Neural correlates of the fast and slow processes have been found in the synaptic plasticity mechanisms of single neurons or groups of neurons in the cerebellum [3,18,[18][19][20][21][22][23]. Correlates of the fast and slow processes have also been noted in distinct regions of the cerebral cortex and the cerebellum [24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

“…It seems likely that changes in the deceleration period commands are at least partly due to an adaptive response from the cerebellum. Cerebellar Purkinje cells (P-cells) may be organized into groups based on their preference for direction of visual error [ 21 , 56 ]. This preference for error is expressed via tuning of complex spike probability with respect to the direction of the visual error [ 21 , 56 , 57 ].…”

“…Cerebellar Purkinje cells (P-cells) may be organized into groups based on their preference for direction of visual error [ 21 , 56 ]. This preference for error is expressed via tuning of complex spike probability with respect to the direction of the visual error [ 21 , 56 , 57 ]. When a saccade concludes and there is a visual error, the result is an increase in the probability of complex spikes for some P-cells, and a decrease in complex spike probability for other P-cells.…”

“…Thus, experience of a single error may be followed by differing amounts of learning among various P-cells. This hints that the multiple timescales of adaptation, as expressed in behavior, may be at least partly due to the diverse responses of various P-cell populations to a single error [ 21 ].…”

Widespread inhibitory projections from the cerebellar interposed nucleus

“…Dichotomous roles for different cell types have been most clearly hypothesized in delay eyelid conditioning models, where glutamatergic neurons are proposed to produce the conditioned response while inhibitory neurons regulate the learning 'setpoint' via projections to the IO, the source of climbing fibers (Bengtsson et al, 2007;Garcia & Mauk, 1998;Kim et al, 1998;Kim et al, 2020;McCormick & Thompson, 1984;Medina et al, 2001;Medina et al, 2002;Ten Brinke et al, 2017;Thompson & Steinmetz, 2009). These studies assume that premotor and nucleo-olivary neurons respond in roughly equivalent ways during behavior (Shadmehr, 2020). Differences in the intrinsic and synaptic properties of these neurons, however, raise the likelihood that this prediction may not be realized Najac & Raman, 2017;Özcan et al, 2020;Uusisaari & Knöpfel, 2008;Uusisaari et al, 2007;Uusisaari & Knöpfel, 2011).…”