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Reading population codes: a neural implementation of ideal observers

Reading population codes: a neural implementation of ideal observers. Sophie Deneve, Peter Latham, and Alexandre Pouget. encode. Stimulus (s). neurons. Response (r). decode. Tuning curves. sensory and motor info often encoded in “tuning curves”

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Reading population codes: a neural implementation of ideal observers

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  1. Reading population codes: a neural implementation of ideal observers Sophie Deneve, Peter Latham, and Alexandre Pouget

  2. encode Stimulus (s) neurons Response (r) decode

  3. Tuning curves • sensory and motor info often encoded in “tuning curves” • neurons give a characteristic “bell shaped” response

  4. Difficulty of decoding • noisy neurons create variable responses to same stimuli • brain must estimate encoded variables from the “noisy hill” of a population response

  5. Population vector estimator • assign each neuron a vector • vector length is proportional to activity • vector direction corresponds to preferred direction Sum vectors

  6. Population vector estimator • Vector summation is equivalent to fitting a cosine function • peak of cosine is estimate of direction

  7. How good is an estimator? • need to compare variance of estimator after repeated presentations to a lower bound • the maximum likelihood estimate gives the lower variance bound for a given amount of independent noise VS

  8. encode Stimulus (s) neurons Response (r) decode

  9. Maximum Likelihood Decoding Maximum likelihood estimator Decoding Encoding

  10. Goal: biological ML estimator • recurrent neural network with broadly tuned units • can achieve ML estimate with noise independent of firing rate • can approximate ML estimate with activity-dependent noise

  11. General Architecture Pλ Preferred Frequency • units are fully connected and are arranged in frequency columns and orientation rows • weights implement a 2-D Gaussian filter: 20 Preferred orientation PΘ 20

  12. Input tuning curves • circular normal functions with some spontaneous activity: • Gaussian noise is added to inputs:

  13. Unit updates & normalization • units are convolved with filter (local excitation) • responses are normalized divisively (global inhibition)

  14. Results • Rapidly converges • strongly dependent on contrast

  15. Results • sigmoidal response curve after 3 iterations, becomes a step after 20 • actual neuron

  16. Noise Effects Flat Noise • Width of input tuning curve held constant • width of output tuning curve varied by adjusting spatial extent of the weights Proportional Noise

  17. Analysis Flat Noise Q1: Why does the optimal width depend on noise? Q2: Why does the network perform better for flat noise? Proportional Noise

  18. Analysis Smallest achievable variance: = inverse of the covariance matrix of the noise Θ = vector of the derivative of the input tuning curve with respect to For Gaussian noise: Trace term is 0 when R is independent of Θ (flat noise)

  19. Summary • network gives a good approximation of the optimal tuning curve determined by ML • type of noise (flat vs proportional) affected variance and optimal tuning width

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