Spatial and Temporal processing in Auditory Networks

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Spatial and Temporal processing in Auditory
Networks

• Vidit Jain
• Computer Science Department
• University of Massachusetts Amherst

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Motivation

• Why we are studying this?

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Mammalian Ear
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Cochlea
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Organ of Corti
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Cochlea
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Auditory Network
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Auditory Cortex
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Overview

• Composition of the frequency spectrum of acoustic
  stimulus
• Spectral Estimation
• Spectral Analysis

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Single Neuron Model

• Definitions
• Spike train, qj(t)
• Impulse response, hij(t)
• Linear time-invariant transformation

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Single Neuron Model

• Definitions (contd.)
• Intracellular potential
• Instantaneous firing rate

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Single Neuron Model

• Choice of hij(t)
• Depends on the objectives of modeling and
  computational costs involved

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Single Neuron Model
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Single Neuron Model
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Neural Networks for Spectral Estimation

• The Mean Rate Hypothesis
• The Periodicity Hypothesis
• Lateral Inhibitory Networks

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The Mean rate Hypothesis

• Spatial Processing
• Mean firing rate of the auditory nerve fibers
• Average activity of a fiber population at CF
  along tonotopic axis
• Amplitude as basilar membrane vibrations
• Ignores phase

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The Mean rate Hypothesis(Implementation)

• No interconnections
• Tonotopically organized array of neurons
• Each neuron integrates the activity

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The Mean rate Hypothesis(Issues)

• Dynamic range issue
• Range 30-40 dB
• Require 70-80 dB
• Experimental recordings (Sachs and Young, 1979)

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The Periodicity Hypothesis

• Temporal Processing
• Firing patterns of nerve fibers can phase-lock to
  the temporal waveform
• Use of frequency analysis, (explicitly through
  Fourier transform)
• Requires time delay mechanisms

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The Periodicity Hypothesis(Implementation)

• Cosinusoidal Comb Filter (Young and Sachs(1979)
• Measure degree of phase-locking to a bank of
  band-pass filters

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The Periodicity Hypothesis(Implementation)

• ADD FIGURE fig 11.3

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The Periodicity Hypothesis(Implementation)

• Exact delay critical
• Intracellular potential given by

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The Periodicity Hypothesis(Implementation)

• Taking Fourier Transform
• The output Power Spectrum

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The Periodicity Hypothesis(Implementation)

• The first term emphasizes the fc and its
  harmonics relative to other frequencies (COMB
  FILTER)
• The second term is the low pass filter
• The final output will reflect the input fiber
  responses in the neighborhood of fc

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The Periodicity Hypothesis(Issues)

• Regular and exact series of time delays
• Changes in axonal lengths
• Changes in membrane time constants
• Anatomical evidences only in the medial superior
  olivary (MSO) nucleus

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Lateral Inhibitory Networks

• Spatiotemporal Processing
• Two properties of traveling waves
• Amplitude amplitude decay
• Phase lag accumulation
• These cause edges / sharp discontinuities
• Recurrent and Non-recurrent

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Lateral Inhibitory Networks

• ADD FIGURE 11.4

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Non-recurrent Lateral Inhibitory Networks

• Simplifying by rewriting input weights

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Non-recurrent Lateral Inhibitory Networks

• Generating continuous system equation
• Taking Fourier Transforms

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Non-recurrent Lateral Inhibitory Networks

• The first term is purely spatial
• Second term purely temporal, low pass filter

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Recurrent Lateral Inhibitory Networks

• Around a steady-state potential and input
• y and e are small signal fluctuations around
  steady-state

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Recurrent Lateral Inhibitory Networks

• Generating continuous system equation
• Taking Fourier Transforms

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Comparison

• For identical inhibitory connectivities, wij
  vij
• For small W(O), recurrent version is approximated
  by the non-recurrent version
• In the recursive LIN, inhibition derived from the
  outputs of neighbors, whereas in non-recursive
  LIN it is derived from the inputs to the
  neighbors
• Difference between the stability properties
• Coupling of the temporal and spatial components

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Spatial Processing with LIN

• ADD FIGURE 11.5

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Spatial Processing with LIN

• Edge Detection
• High spatial frequency at edges
• Transfer function has high-pass transfer
  characteristics
• w(x) profile determines the effectiveness of LIN
  in sharpening the input profiles

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Spatial Processing with LIN

• Peak Selection
• Each neuron in the network inhibits equally all
  other neurons, but not itself
• Stronger inhibition suppress the inputs in the
  valley of input patterns
• At the strongest inhibition, only the largest
  peak of the input survives
• Slight modification for local maxima

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Temporal Processing with LIN

• For higher spatial frequencies, time constant
  increases and output is attenuated at lower
  temporal frequencies.
• Intuition based on time required for feedback
• Sharpening not effective for high temporal
  frequencies
• f 1-2 kHz, t 0.1-0.2 msec
• Oscillations can be simulated (?)

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Summary of LIN

• Edge detection and peak selection can be done
• Difference from purely temporal analysis
• Indirect role in encoding the spectrum, thus
  dont require specific neural structure e.g.
  organized time delays

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Biological Feasibility

• Feasible!!!
• Recurrent LIN first found in the compound eye of
  horseshoe crab, Limulus (Hartline 1974)
• Possibility of evidence of non-recurrent LIN in
  the olfactory bulb (Rall 1970)

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Cortical Model

• Auditory spectrum repeatedly represented in AI at
  various degrees of resolution
• Repeated layers of tonotopically ordered neurons
  with the receptive field widths gradually
  changing along the isofrequency axis
• Cortical cells analyze input spectral profiles in
  a linear manner (superposition principle)

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Biological Plausibility of a Neural Network Model

• Countless candidates for the network model
• Only intuitive guidelines
• Mostly guided by the work in vision processing

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MP3 Encoding !!!

• Absolute hearing threshold
• 2kHz-20kHz
• Processing in critical bands
• Masking
• One component making another inaudible
• Compression ratio 121, without affection
  perception

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References

• Spatial and Temporal Processing in Central
  Auditory Networks, Shabib Shamma
• Young, Sachs 1979
• http//www.benbest.com/science/anatmind/anatmd6.ht
  ml