Download Modelling Cerebellar Function in Saccadic Adaptation

Multi-scale Models of the Cerebellum: Role
of the Adaptive Filter Model
Paul Dean, Christian Rössert & John Porrill
University of Sheffield
REALNET
Adaptive Filter Models of the
Cerebellum
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First proposed by Fujita in 1982, based on the original Marr-Albus
framework
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We have argued that many models of the cerebellar role in motor
control (especially eye or arm movement) are based in the adaptive
filter
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Such popularity would suggest that the adaptive-filter model probably
has a role to play in multi-scale modelling of the cerebellum
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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.
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Slide No 2
Fixed Filter
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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))
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Adjustable Filters
• Again familiar from audio
• Knobs (A) to alter gain (volume) and frequency response (B)
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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
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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
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Analysis-Synthesis Filter
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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.
Slide No 7
How are Weights Adjusted?
Adjuster Signal
• This is where the adjuster signal comes in
• Each weight receives the same adjuster signal (more usually
referred to as ‘error’ or ‘teaching’ signal)
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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
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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”
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The Forward Model
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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.
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Role of Adaptive Filter
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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.
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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.
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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
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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
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Seems to fit climbing fibre properties
Herculano-Houzel, S. (2010). Frontiers in Neuroanatomy, 4, Article 12.
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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.
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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
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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”
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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)
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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?
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Examples
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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?
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Examples
• Conductance-based integrate and fire neurons
• Used for eyeblink conditioning and OKR
• Talked about this morning
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Examples
• Integrate and fire neurons using EDLUT simulator
• Used to investigate possible roles of granular-layer plasticity
• Will be talked about shortly
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Question
• Candidates for bridging the gap between abstract (adaptivefilter) and detailed (compartmental) models
• How can they be used to increase understanding of the
connection between features at the cellular level, and
algorithmic competence?
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Slide No 23