Vision and the statistics of the visual environment

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Vision and the statistics of the visual
environment

• Eero P Simoncelli
• Current Opinion in Neurobiology 2003, 13 144-149
• Presented by Yuguo Yu
• CNBC CNS Meeting 2003

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1. Background!2. What this Paper tell
us?3. Still questions?
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How do visual neurons encode natural signals in
the real world?
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For an incoming signal, what happens in each
level from retinal to visual cortex?
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As a result of natural selection, visual systems
are believed to be optimized for the visual
properties of the natural world. What the
optimization means here?

• Represent the input signals
• Maximize information
• minimum redundancy?
• minimum error and highest fidelity?
• Cost minimum energy?

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Before hypothesis, look at the property of the
natural signal

• Spatial signals Power spectra 1/f2

Temporal signals 1/f
D.L.Ruderman and W. Bialek (1994). Statistics of
Natural Images Scaling in the Woods Phys. Rev.
Lett.
Voss and Clarke (1975) 1/f noise in music and
speech, Science.
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Statistical properties (1D signals)

• Signal energy distribution decrease with increase
  of frequency.
• Long term correlation.

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Idea of efficient coding

• Attneave (1954) Suggested that the goal of
  visual perception is to produce an efficient
  representation of the incoming signal.
• Barlow (1961) hypothesized that the role of
  early sensory neurons is to decorrelate (or
  remove statistical redundancy in ) the sensory
  input.
• This means that the neurons will decompose the
  input signal into statistically independent
  responses with less correlation. It is a maximal
  information representation with a decorrelation
  or whiten process.

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• Understanding efficient coding principle
• Efficient coding in single neuron
• Neuron should fully utilize its output
  capacity (firing rate? Spiking timing?) in
  encoding information efficiently.
• Efficient coding in a group neurons
• Each neuron carries independent information,
• the responses of different neurons should be
  statistically independent from each other.

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Questions

• Whether the hypothesis of efficient coding is
  true in the real case?
• How to prove that?
• What factors or mechanisms inside neurons can
  support efficient coding in single neuron and in
  neuron network?

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• Simonconcelli in this paper reviewed recent 2
  years discoveries which try to answer the first
  two questions
• 1. Criticisms to this hypothesis, and related
  experiments.
• 2. Supported experiments.
• 3. Derive a analytical model for the efficient
  coding of the natural signals and then compare it
  with physiological data.

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1. Criticisms to this hypothesis, and related
experiments.

• The purpose of vision is not to reconstruct
  completely the visual world. (Maybe true maybe
  not).
• Information theory may be irrelevant.
• (who can give a relevant one, if not
  information)
• Correlated firing activities are popular in
  various brain areas. (not use natural signals??)
• The number neurons devoted to processing sensory
  information seems to expand from sensory to
  cortex, suggesting that the brain increase
  redundancy. (well, they maybe use different
  coding schemes.)
• Sometime redundancy is needed to against
  noise---a robust code. (well, may not constitute
  a fatal flaw)

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• Simonconcelli in this paper reviewed recent 2
  years discoveries which try to answer the first
  two questions in 3 classes
• 1. Criticisms to this hypothesis, and related
  experiments.
• (the responses to these criticisms may not
  right, but we still dont know the truth)
• 2. Supported experiments.
• 3. Derive a analytical model for the efficient
  coding of the natural signals and then compare it
  with physiological data.

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2. Supported experiments.

• (1). Single neuron case fully utilize neurons
  response means maximize information or encoding
  efficiency in the presence of noise.
• A. If the constraint is maximal firing rate, the
  optimal distribution is uniform

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Laughlin (1981) responses of the large monopolar
cell in the fly visual system satisfy informax.
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2. Supported experiments.

• (1). Single neuron case fully utilize neurons
  response means maximize information or encoding
  efficiency in the presence of noise.
• A. If the constraint is maximal firing rate, the
  optimal distribution is uniform
• B. If the mean firing rate are invariant, the
  optimal distribution is exponential

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Experiments by Baddeley, V1, IT Neurons,
naturalistic conditions. Treves and De Polavieja
considered noise effect, Also invariant mean
firing rate is not a true condition.
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2. Supported experiments.

• (2) Network case
• Nirenberg showed that RGN neurons act as
  independent encoder. (not really)
• Reich found V1 neurons responses are
  nearly independent under white noise
  stimulation.
• Vinje and Gallant reported that V1
  neurons may perform sparse coding for natural
  images.

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Nirenberg showed that RGN neurons act as
independent encoder. (not really, nearby neurons
are tuned to similar stimuli, showing large
correlation)
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Vinje and Gallant showed that stimulation of
non-classical receptive field of V1 neuron
increases response sparseness.
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2. Supported experiments.

• (3) evidence from Auditory system
• Chechik (NIPS2001) found that steps along a
  ascending sensory pathway, the number of neurons
  increase, their firing rate decrease, and neurons
  become tuned to more complex and independent
  features, redundancy reduced.
• -----this may be true for other sensory
  pathway.

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2. Supported experiments

• (4) Neural systems exhibits improved performance
  under natural conditions.
• a. Lewen, H1 neurons can respond over a broader
  range of velocities outdoor than indoors scenes.

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G.D.Lewen, (2001,NetworkComput.Neural
Syst.12,317) Neural coding of naturalistic
motion stimuli.
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2. Supported experiments

• (4) Neural systems exhibits improved performance
  under natural conditions.
• a. Lewen, H1 neurons can respond over a broader
  range of velocities outdoor than indoors scenes.
• b. Ringach showed that receptive field revealed
  by Natural signals is better than by white noise
  method.

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Ringach, J.Vis 2002,212
Natural signals
White noise approach
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• These experiments implied that neurons may
  perform a optimal coding in the natural
  conditions, and this optimal coding may be
  efficient coding.

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• Simonconcelli in this paper reviewed recent 2
  years discoveries which try to answer the first
  two questions
• 1. Criticisms to this hypothesis, and related
  experiments.
• 2. Supported experiments.
• 3. Derive a analytical model for the efficient
  coding of the natural signals and then compare it
  with physiological data.

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Optimal models

• Performing efficient coding principle, is
  decomposing natural signals into
  multiple-channels independent components by a set
  of filters. These filters are found spatially
  localized, oriented and bandpass, similar to
  visual neurons spatial receptive field and
  auditory neurons filters.
• ICA results suggest that neurons may be designed
  to perform efficient coding.

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Olshausen and Field, Emergence of simple-cell
receptive field properties by learning a sparse
code for natural images, Nature 381, 607-609,
1996.
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M.S. Lewicki, Nature Neuroscience (2002) found
that Auditory nerve filters best match those ICA
filters derived from environmental sounds and
speech.
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Optimal models

• Performing efficient coding principle, is
  decomposing natural signals into
  multiple-channels independent components by a set
  of filters. These filters are found spatially
  localized, oriented and bandpass, similar to
  visual neurons spatial receptive field and
  auditory neurons filters.
• ICA results suggest that neurons may be designed
  to perform efficient coding.

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Other principles?

• 1. Neural coding with a minimal metabolic cost
• ----Levy WB,
• Optimal compromise is

supported by experiments by Balasubramanian
(2002). Maximize the efficiency given the mean
firing frequency
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2.Timescale over which environmental statistics
influence a sensory system

• Range from millenia (evolution), to months
  (neural development), to minutes or seconds
  (short-term adaptation).
• a. long term effect may be involved to adjust the
  structure of the neural systems to be of best
  performance.
• b. short term adaptation may acts to reduce
  dependences between neurons (Barlow 1989).

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Conclusion

• Efficient coding may be a possible principle used
  in neural systems and can help us to understand
  sensory system design.

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Open questions

• 1 . What factors or mechanisms inside neurons can
  support efficient coding in single neuron and in
  neuron network? Especially, from retina to V1.
• 2. Correlate synchronized activities are found
  ubiquitous in various sensory and cortex areas.
  If from retina to cortex, neural responses become
  more and more decorrelated and whitened, what are
  the origin reasons for these synchrony rhythms?
  What the roles of them?
• 3. What is the relationship between synchrony
  and sparseness?

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For the first open question
Using a cortex neuronal model producing the
following results, so it seems efficient coding
may have its popular basis in model
Autocorr. Of models responses
Autocorr. Of three Input signals
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For the second open question

• Dan (1998,Nature.Neurosci.V1.501) found that
  precise temporal correlation may be used to
  encode additional information (20 of total) in
  areas from thalamus to visual cortex.
• Salinas (2001, Nature. V2.539) reviewed that
  correlated activities may be important for
  attention, and control the information flow in
  brain. Correlated activities may increase coding
  efficiency. (2003).
• Mehta (2002, Nature V417,741)  indicated that the
  firing activities among group of neurons become
  more correlated in the learning process in cortex
  neurons. These correlated oscillation activities
  play an important role in inducing postsynaptic
  neurons generate highly precisely spiking
  patterns, leading the neural code from rate code
  to temporal code.

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For the third open question

• What is the relationship between synchrony and
  sparseness?
• Based on efficient coding principle, if a
  group neurons efficiently encode a image, the
  responses of these neurons should be
  uncorrelated.

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M.Diesmann (1999,Nature,402) indicated that
uncorrelated activities are easy to be destroyed
in the propagation among networks, while
correlated precisely activities can be stably
transmitted. Experiments supported by A.D.Reyes
(2003 Nature Neurosci.)
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• THANKS!