Fig 1.
Cerebellar-collicular circuitry for calibration of unimodal sensory maps.
a) Simplified diagram of cerebellar cortical microcircuit, in which mossy-fibre inputs u are recoded in the granular layer to produce parallel-fibre signals pj. These signals influence the simple spike firing z of Purkinje cells via the synapses w. Purkinje cells also a receive a climbing-fibre input e. b) Interpretation of the microcircuit as an adaptive filter. In the adaptive filter model, each microzone has two inputs (climbing fibre, mossy fibre) and a single Purkinje cell output. Processing in the granular layer is represented by a set of fixed filters G1 … GN whose outputs p1 … pN are weighted by w1 … wN where the weights correspond to the efficacies of the synapses between parallel fibres and Purkinje cells. Purkinje cells linearly sum the weighted parallel-fibre signals to produce their simple-spike output z = Σwipi. The climbing-fibre input e acts as a teaching or error signal that alters the weights w1 … wN using the covariance learning rule 𝛅wi = -β<epi>. c) Compact schematic used to illustrate the parallel fibre (PF), Purkinje cell (PC), and climbing fibre part of the circuit in subsequent diagrams. d) Schematic diagram of the proposed recalibration architecture for a distorted unimodal collicular map. Unimodal sensory signals, corresponding to target locations (xd, yd), are written into the map, which because of the distortion provides an inaccurate estimate of target location (xg, yg) that is used to generate a correspondingly inaccurate orienting response. The map output is also sent to the cerebellum, where it is converted into a coarse-coded, normalised set of parallel-fibre (PF) signals. These are sent to two cerebellar microzones, each represented in the diagram by a single Purkinje cell, that receive climbing fibre inputs that initially signal errors (xd-xg, yd-yg) in the orienting response. These errors are used to alter PF-PC synapses, generating cerebellar output that shifts the map so that the orienting response is now made to the new location (xa, ya). This process is repeated until the error (xd−xa, yd-ya) becomes zero. Further details in text.
Fig 2.
Recalibration of a single target map with curvilinear distortion.
a) The left hand panel shows an initially accurate map (green line) in the superior colliculus (SC), with artificially induced curvilinear distortion (red line) (details in Methods). The shifts in the map to correct for the distortion are dependent on the location in the map, and are indicated by black arrows. The learnt cerebellar recalibration of the distorted grid (teal line) is shown in the middle panel. The right hand panel shows the combined learnt weights in the x- and y-directions corresponding to each coarse coded parallel fibre signal (weights initially zero). b) Time course of recalibration, showing how RMS errors in orienting responses change with number of target presentations. c) Example of learnt dynamic cerebellar recalibration. The left-hand panel shows the shift in the map (red arrow) required to produce an accurate orienting response to the inaccurate target location provided by the distorted map. The centre panel shows the coarse-coded, normalised parallel fibre signals produced by the inaccurate target location. The right hand panel shows that after learning the parallel fibre signals now shift the map by just the required amount to produce an accurate response.
Fig 3.
Calibration of combined unimodal maps.
a) Individual sensors are assumed to write into 2D unimodal topographic maps, each of which provides a probabilistic representation of target position as shown in Fig 1. The outputs of these unimodal maps are then combined to produce an overall multimodal map, and the position of peak activity on this map drives the orienting response. The problem is how errors in the orienting response can be used to calibrate both unimodal and multimodal maps. b) Combining information from multiple sensors using probabilistic maps can produce a more accurate estimate of location. c) Information between two sensors combines to give a more focused estimate of location. The top plots show individual sensor maps and the bottom the combined map.
Fig 4.
Schematic of architecture for calibrating multiple topographic maps.
a) The overall topographic map combines information from unimodal maps that are each obtained from a unimodal sensory input. The combined map is used to drive the orienting response, which if incorrect generates an error signal. Parallel fibre signals are a combination of all coarse coded individual sensory maps. Separate Purkinje cells are used to calibrate each unimodal map individually. Gating is introduced to solve credit assignment issues that arise due to the same error signal training all individual sensors. b) Map response to target at centre when sensor is not gated (∑ = [0.0225 0; 0 0.0225]). c) Map response to target at centre when sensor is gated (∑ = [4.5 0; 0 4.5]). The spread of possible target locations is increased when gating is included.
Fig 5.
Calibrating multiple unimodal maps: Role of gating.
a) Demonstration of the credit attribution problem for multiple sensors. Sensors are miscalibrated in such a way that their errors cancel. If all sensor modules are trained by the same overall error signal the individual sensors will not learn even though they are inaccurate. b) One sensor has zero error, but the overall error is non-zero. When all sensor modules are trained by the same error signal any behavioural error is necessarily attributed to all sensors and so the individual sensors are forced to learn even if they are accurate. c) When errors are gated (details in text) both maps are calibrated even though their errors originally cancelled (panel a). d) Gating also prevents an accurate map from being altered (panel b). In both cases the credit attribution problem is solved.
Fig 6.
Sensor cross-talk is eliminated when independent sensor noise is present.
a) Cross talk weights (given as RMS values) over iterations. When independent sensor noise is present, the cross-talk weights are driven toward zero. b) Individual sensor calibration with and without independent sensor noise. Independent sensor noise eliminates errors in individual sensor calibrations that arise due to cross-talk. The calibrated results are plotted for the case when the input from the other sensor is set to zero. c) Overall RMS errors when both sensors are on and stable for the case when independent sensory noise is included.
Fig 7.
Predictive calibration of a single target map with curvilinear distortion.
a) Schematic diagram of the proposed recalibration architecture for predictive recalibration. The desired target position is delayed and distorted before writing into a topographic map. Parallel fibre (PF) signals are the filtered outputs (here a bank of 3 leaky integrator filters are used) of a coarse coded, normalised topographic map. b) Representation of target trajectory before distortion with 5 sample delay. Examples of the differences between the desired (represented by a red +) and delayed (represented by blue x) targets are indicated by an arrow. The velocities of the example target trajectory ranged from (-1.61,-1.82) units/sec to (1.74, 1.72) units/sec. c) RMS errors over iterations when learning to track a target using delayed and distorted sensory information. d) Cerebellar learning to predictively recalibrate delayed, distorted signals and estimate the target location. Over iterations, the estimated target trajectory learns to track the desired target trajectory.
Fig 8.
Receptive fields shift in response to a moving target.
a) Sound waves generated by movements of a mouse are received by the owl’s left and right ears (adapted from [36]). For horizontal positions stimulus location is indicated by interaural time difference (ITD), and stimulus movement by changes in ITD. b, c, d) Learnt shifts when tracking a moving target with different velocities using the adaptive filter model. Weights were learnt by tracking a moving target over a single sweep when there was a delay of 100 samples (dt = 5ms) between the estimated and ideal target location (but no sensor distortion). b) Shift of receptive field of target when target is moving with a velocity of 1ms-1. c) Shift of receptive filed when target is moving with a velocity of -1ms-1. d) Shift for different positive velocities of 0.125, 0.5, 1, 2 ms-1(thicker lines correspond to faster speeds). The results are comparable to predictive shifts presented in [23].