Modeling How Bats Capture Targets

1
Modeling How Bats Capture Targets

• Harry R. Erwin, PhD
• Hybrid Intelligent Systems Group
• School of Computing and Technology
• University of Sunderland

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Well, How Do Bats Capture Targets?

• Figure from Webster and Brazier, Experimental
  Studies on Target Detection, Evaluation and
  Interception by Echo-locating Bats, 1965.
• A bat (Myotis lucifugus) capturing a moth in
  foliage.
• 100 millisecond intervals.
• The bat had first detected the tree about 500
  milliseconds before the first image.
• Data available to the bata few biosonar
  snapshots in the dark.

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Evidence for Predictive Target Capture in Bats

• Definition non-predictiveuses the current
  state estimate or last known target localization
  to control the capture. E.g., simple homing, lead
  pursuit, lag pursuit.
• Antonym predictiveuses models of the targets
  motion and of the bats self-motion to select a
  capture strategy to optimize the capture
  probability.
• For the evidence, see Campbell, K.A. and R.A.
  Suthers, Predictive tracking of horizontally
  moving targets by the fishing bat, Noctilio
  leporinus, in Animal Sonar Processes and
  Performance, P.E. Nachtigall and P.W. Moore,
  Editors. 1988, Plenum Press. p. 501-506.

4
Modeling trajectory prediction using neural
microcircuits

• Based on
• H. Jaeger and H. Haas, "Harnessing nonlinearity
  predicting chaotic systems and saving energy in
  wireless telecommunication," Science, vol. 304,
  pp. 78-80, 2004.
• W. Maass, T. Natschläger, and H. Markram,
  "Real-time computing without stable states a new
  framework for neural computation based on
  perturbations," Neural Computation, vol. 14, pp.
  2531-2560, 2002, and
• N. Bertschinger and T. Natschläger, "Real-time
  computation at the edge of chaos in recurrent
  neural networks," Neural Computation, vol. 16,
  pp. 1413-1436, 2004.

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Background

• Natschläger, et al. (2002), suggest that the
  stereotypical neural microcircuits of the cortex
  may be the computational units of the brain.
• These microcircuits appear well-adapted to
  handling continuous streams of information, but
  sensorimotor integration in actively echolocating
  bats requires a computational unit that can
  generate a continuous output stream representing
  the location of a target from asynchronously
  received discrete echo returns.
• Hence this research.

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A Simple Task Performed by Bats

• Model nonstationary target acceleration,
  velocity, and position accurately enough to be
  able to approach the target within 5-10
  centimeters.
• Handle asynchronous echo return timing (with
  inter-cry intervals ranging over 2-3 orders of
  magnitude).
• Predict forward over a variable time interval
  ranging up to a second. (This can be estimated as
  the distance to the target divided by the closing
  rate.)

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Modeling Approach

• Used an Echo State Machine (Jaeger and Haas,
  2004). All cells were standard perceptrons with a
  sigmoidal output.
• Target trajectory was represented by a pair of
  arrays of place cells organized in general
  Cartesian coordinates.
• Sensory afference structured similarly, but with
  the input place cells signaling only when a
  return was received. A flag indicated that a
  return was received during an interval.
• Echo reservoir with 100-1000 cells.
• Output place cells continuously reflected input
  from the echo reservoir cells, input place cells,
  previous output place cell values, the flag
  variable, and constant bias.

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Initial Parameterization

• Based on behavioural data.
• 100 place cells in each of X and Y dimensions
  over a 1 meter interval.
• Radius of target motion 25-35 cm, uniformly
  distributed (UD).
• Center of motion UD over a 30x30 cm square.
• 5-7 radians/sec in either direction, UD.
• 20 msec interval.
• Initial phase UD between 0 and 2?.
• Cry rate 12-15.6 cries/sec UD.

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Model Structure
Input Array
OutputArray
Echo State Reservoir
Circle indicates internal feedback
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Programming the Echo State Machine

• Initialized with random synaptic weight values
  (other than those onto the output cells).
• Took the internal synaptic weight values for the
  echo state reservoir and computed the spectral
  radius (treating the synaptic weights as defining
  a linear transformation). Scaled the weights of
  the reservoir to make the spectral radius to
  0.98. (This value defines how quickly the
  internal state fades.)

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Training the Echo State Machine

• Ran the system to generate a large number of cell
  activation sequences with desired input values
  and with the output cells clamped to their
  corresponding correct values. (Note this assumed
  that state was an attractor!) Sampled only after
  the initialization transient for each sequence.
• Used least squares estimation to determine the
  weights at the output cells needed to produce the
  clamped values. As long as the resulting system
  was robust, it was expected to converge to the
  desired behavior.

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Initial Results

• The echo state machine failed to interpolate
  between updates, and the reservoir did not
  maintain a continuous representation of a track,
  probably due to the magnitude of the time delays
  in the network.
• In addition, as the place cells were almost
  always inactive, setting all cells inactive was a
  solution that produced a low error and so tended
  to be found by the training algorithm, suggesting
  that the assumption that the desired output state
  was a robust attractor was false.

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Discussion

• The failure to interpolate between state updates
  suggests persistent neural activity is necessary
  and should probably be neuron-local rather than
  generated by the network to produce changes on
  the right time scales.
• The zero (or spontaneous activity) state acting
  as an attractor suggests that selective feedback
  strength is too weak in the system (based on
  Brunel, 2003). This is a problem with the
  training algorithm used (least squares fit).

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Required Characteristics of Model Neurons

• Persistent activity is necessary, probably at the
  neural (rather than network) level.
• See Fellous, J.-M. and Sejnowski, T. J. (2003)
  Cerebral Cortex, 13, 1232-1241, where they
  discuss evidence for this based on in vitro
  experiments involving cortical slice
  preparations. Note, their results have been
  challenged.
• In addition, there has to be some way of
  integrating forward velocity and acceleration to
  calculate a forward displacement, so simple
  persistent activity is insufficient.

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Displacement or Local Representations?

• It would be useful if the predicted displacement
  could be computed globally as a vector and then
  added to the latest known location of the target.
• This would involve output place cells receiving
  two inputsthe last known location and the
  displacement representation.

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Simplified Network Topology
Displacement Signals
D
E
Input Place Cells
B
A
X
Y
Output Place Cells
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Analysis

• Displacement signal D should fail to activate
  cell Y if cell A is active and should succeed if
  cell B is active.
• Displacement signal E should activate cell Y if
  cell A is active, and should fail if B is active.
• So what happens?
• Pay attention to cell Y, where the action is.
• Hint Minsky and Papert (1969)

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Equations

• First consider cell A acting on cell Y
• DwDY AwAY lt T (subthreshold)
• EwEY AwAY gt T (suprathreshold)
• Hence EwEY gt DwDY
• Now consider cell B acting on the same cell
• DwDY BwBY gt T (suprathreshold)
• EwEY BwBY lt T (subthreshold)
• Hence DwDY gt EwEY, a contradiction

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Discussion

• It is hard (but not impossible) to use neural
  networks to do vector arithmetic.
• Hence trajectories are likely to be represented
  locallye.g., by a linked list of neural elements
  (to use computing terminology). Each element
  would retain a full local state.
• See Priebe, Churchland, and Lisberger,
  Reconstruction of Target Speed for the Guidance
  of Pursuit Eye Movements. Journal of
  Neuroscience, 2001. 21(9) p. 31963206, for
  related issues.
• Whether these neural elements are distributed is
  an interesting question.

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Further Discussion

• Note that a vector representation can be
  constructed by hand, but it requires a hidden
  layer where each neuron associates a specific
  displacement with a specific input location.
• An output place cell is then triggered if the
  displacement plus input location equals the
  corresponding output location.
• This layer would be 6-dimensional, requiring
  1,000,000 neurons for a 10x10x10 subdivision of
  space, and 1,000,000,000,000 for a 100x100x100
  subdivision.

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Where Do We Go Now?

• More realistic network architectures including
• Some form of short term memory
• Local representations
• Bistable networks
• A sensible model of forward integration
• Echo state networks (and liquid state networks)
  are too generalized, although something of the
  sort with more realistic models of neocortical
  neurons may be suitable.

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Acknowledgements

• Cynthia F. Moss, Ph.D., Department of Psychology,
  Program in Neuroscience and Cognitive Science,
  University of Maryland.
• Steven Womble, Ph.D., John Murray, and the other
  members of the Hybrid Intelligent Systems Group,
  School of Computing and Technology, University of
  Sunderland.