multi-scale models of the cerebellum: role of the adaptive filter model paul dean, christian...

Multi-scale Models of the Cerebellum: Role of the Adaptive Filter Model

Paul Dean, Christian Rössert & John Porrill

University of Sheffield

REALNET

Slide No 2Sardinia 2013

Adaptive Filter Models of the Cerebellum

• First proposed by Fujita in 1982, based on the original Marr-Albus framework

• We have argued that many models of the cerebellar role in motor control (especially eye or arm movement) are based in the adaptive filter

• Such popularity would suggest that the adaptive-filter model probably has a role to play in multi-scale modelling of the cerebellum

• What role? What is the basis for the popularity?

Dean, P., Porrill, J., Ekerot, C. F., & Jorntell, H. (2010). The cerebellar microcircuit as an adaptive filter: experimental and computational evidence. Nature Reviews Neuroscience, 11(1), 30-43.


Fixed Filter

• Fixed filters are familiar from audio• Example here (B, C) a low-pass filter that selectively attenuates high frequencies• (Can also be equivalently described in terms of its impulse response (A))


Adjustable Filters

• Again familiar from audio• Knobs (A) to alter gain (volume) and frequency response (B)


Adjustable Filters

• Can be quite fancy, e.g. a graphic equalizer

• Gain of individual frequency channels adjustable for the ultimate listening experience

• BUT – still has to be adjusted by hand


Adaptive Filters

• What we want is an adjustable filter where the adjustments are made automatically

• Therefore need some sort of ‘adjuster signal’, to tell the filter what to do

• Demonstrated by the Analysis-Synthesis filter


Analysis-Synthesis Filter

• Input ‘analysed’ into component signals using a bank of fixed filters (here leaky integrators).

• Components are then weighted and recombined (synthesised) to produce the output

• Weight values can be adjusted; allows shape of output to be altered. Output is in effect ‘sculpted’ from components.


How are Weights Adjusted?

• This is where the adjuster signal comes in• Each weight receives the same adjuster signal (more usually

referred to as ‘error’ or ‘teaching’ signal)

Adjuster Signal


Learning Rule

• The adaptive filter changes its weights according to the correlation between input component and teaching signal, i.e.

– if positive correlation, reduce weight

– if negative correlation, increase weight

• Learning stops when there is no correlation between component and teaching signals

• In effect, the analysis-synthesis filter implements a decorrelation algorithm


Adaptive Filters Work

• Adaptive filters are very widely used in signal processing – e.g. communications, radar, sonar, navigation, seismology, biomedical engineering, and financial engineering

• As already mentioned, widely used to model the cerebellum in the control of eye, eyelid and arm movements

• More recently, shown to be a good candidate for the adaptive element in “Internal Models”


The Forward Model

• Example of in internal model – the ‘forward model’• Suggested in relation to cerebellum by e.g. Miall, Wolpert• Use to predict sensory effects of movement• Useful for e.g. distinguishing external sensory signals from those produced by one’s

own movement

Miall, R. C., & Wolpert, D. M. (1996). Forward models for physiological motor control. Neural Networks, 9(8), 1265-1279.


Role of Adaptive Filter

• Can show that the adaptive filter is capable of learning forward models• Expands cerebellar role from motor control to sensory prediction (and possibly

‘cognitive’ prediction?)

Porrill, J., Dean, P., & Anderson, S. R. (2013). Adaptive filters and internal models: Multilevel description of cerebellar function. Neural Networks, in press.


How Realistic is the Adaptive Filter Model?

1. Analysis: granular layer produces components of input (mossy fibre) signals

2. Components weighted by parallel-fibre Purkinje cell synapses

3. Weights adjusted by climbing fibre signal

4. Purkinje cell combines weighted components to produce output.


Explains Two Striking Features

1. A very large number of fixed filters are required at the analysis stage to ensure adequate coverage of all contingencies – in biology, the precise nature of the required response cannot be known in advance• Granule cells constitute ~80% of neurons in the human brain

(Herculano-Houzel 2010)

2. The adjuster signal must not interfere with system output, but must be able to affect all weights• Seems to fit climbing fibre properties

Herculano-Houzel, S. (2010). Frontiers in Neuroanatomy, 4, Article 12.

Broad-Brush Realism?

• “The structure of the granular layer network and its mossy fibre inputs is well suited for spreading diverse sets of information (referred to here as ‘diversity spreading’).” (p.625)

• The huge diversity of parallel fibre codings, which are widely distributed over the molecular layer, has the advantage that guiding signals (provided by climbing fibres) can select and sculpt those codings that are needed to improve behaviour as required in a particular spatiotemporal context.” (p.630).

• Consistent with analysis-synthesis adaptive filter


Gao, Z. Y., van Beugen, B. J., & De Zeeuw, C. I. (2012). Distributed synergistic plasticity and cerebellar learning. Nature Reviews Neuroscience, 13(9), 619-635.


What’s the Problem?

• Although there may be a broad sense in which adaptive filter models are ‘realistic’, the details are clearly not realistic

– Synapses can be either positive or negative– Firing rates not spikes– Neither single neurons nor populations represented explicitly

• However, this can’t be simply be solved by switching to current very detailed compartmental models - it can be difficult to determine just what these can do functionally

• Problem:– Abstract models can be used for control but lack detail– Detailed models have not been shown to be capable of control


Bridging the Gap

• Natural question: is there a suitable intermediate level of modelling?• Sydney Brenner: “There is a theory called the ‘cell theory’ that is about

150 years old. So I think studying the cell gives the proper perspective. You can then look downwards onto the molecule and upwards to the organism. So it is neither top down nor bottom up, rather it is middle out, and I think that is going to be the correct approach”


Bridging the Gap

• Criterion #1: neurons and synapses represented explicitly but in as simplified a form as possible

• Criterion #2: network’s signal processing characteristics can be specified (and shown to be capable – or not – of adaptive filter functionality)


Possible Benefits

• May be possible to assess computational impact of specific additional detailed features

• Are there features related to e.g. homeostasis rather than computational power?

• Are there features that enable the circuit to do computations that adaptive filters cannot do?


Examples

• Update of a model started in 1991• Integrate and fire neurons• Used for classical conditioning of eyeblink• As yet no analysis of its computational properties?


Examples

• Conductance-based integrate and fire neurons• Used for eyeblink conditioning and OKR• Talked about this morning


Examples

• Integrate and fire neurons using EDLUT simulator• Used to investigate possible roles of granular-layer plasticity• Will be talked about shortly

Question

• Candidates for bridging the gap between abstract (adaptive-filter) and detailed (compartmental) models

• How can they be used to increase understanding of the connection between features at the cellular level, and algorithmic competence?


multi-scale models of the cerebellum: role of the adaptive filter model paul dean, christian...

Documents

hand slide

adaptivefilter model

adaptive filter models

adaptive filters

decorrelation algorithm

frequency response b

fixed filter fixed filters

adjustable filters