Sparse Coding as a Generative Model

Transcription

1 Sparse Coding as a Generative Model image vector neural activity (sparse) feature vector other stuff

2 Find activations by descending E

3 Coefficients via gradient descent Driving input (excitation) Lateral inhibition Self Inhibition

4 Network dynamics for descending E Internal state (membrane potential): Broadcasted activity: The membrane potential follows the energy gradient: membrane leak term

5 Leaky integrator model.

6 Determining the Thresholding Function L1 Sparseness Penalty Other transfer functions can also be used! As long as the thresholding function is monotonically increasing.

7 Neuron output is thresholded membrane potential A network of neurons following these dynamics will always lower E, or else leave it unchanged, as long as is a monotonically increasing function of.

8 CJ Rozell et al. Sparse Coding via Thresholding and Local Competition in Neural Circuits Neural Computation Network implementation of LCA dynamics T T T T T

9 M Zhu, CJ Rozell. Modeling Inhibitory Interneurons in Efficient Sensory Coding Models. PLoS Comp Bio Adding Inhibitory Interneurons G matrix captures all of the recurrent influence G can be decomposed by matrix factorization Inhibitory > Excitatory Connections Interneuron Gains (diagonal) Excitatory > Inhibitory Connections Simple solution does not provide biologically realistic results

10 M Zhu, CJ Rozell. Modeling Inhibitory Interneurons in Efficient Sensory Coding Models. PLoS Comp Bio Alternate Solution Decompose G matrix into low rank + sparse matrices Decompose low rank matrix to separate excitatory and inhibitory connections Two subpopulations of inhibitory interneurons, one from L and one from S

11 Inhibitory Interneurons M Zhu, CJ Rozell. Modeling Inhibitory Interneurons in Efficient Sensory Coding Models. PLoS Comp Bio. 2015

12 M Zhu, CJ Rozell. Modeling Inhibitory Interneurons in Efficient Sensory Coding Models. PLoS Comp Bio Subpopulations match experimental data Low rank population Sparse population

13 M Zhu, CJ Rozell. Modeling Inhibitory Interneurons in Efficient Sensory Coding Models. PLoS Comp Bio Inhibitory Interneurons Solves original sparse coding problem Respects Dale s law Matches measured E/I cell ratios Matches diversity of orientation tuning found in mammal study

14 Neuroscience connections: predictions & explanations

15 Training set images from van Hateren natural scenes database

16 Diversity of simple-cell RFs in macaque V1 (Ringach 2002, Rehn & Sommer 2007)

17 V1 is highly overcomplete LGN afferents IVb layer 4 cortex Barlow (1981) 0 1mm C I b and IV

18 1.25x 2.5x 5x 10x

19 Full 10x dictionary

20

21 Explaining away Active inference provides a more descriptive representation Feedforward response (bi) Sparsified response (ai)! +! +! +! +! + Population nonlinearity

22 Sparsification prediction Outputs of sparse coding network (a i ) Pixel values Image I(x,y)

23 Active decorrelation Linear non-linear Sparse coding Physiology - cat M Zhu, CJ Rozell

24 M Zhu, CJ Rozell. Visual Nonclassical Receptive Field Effects Emerge from Sparse Coding in a Dynamical System, PLoS Comp Bio Non-Classical Receptive Field Effects End-Stopping Cat V1 Simple Cell LCA Model Neuron

25 M Zhu, CJ Rozell. Visual Nonclassical Receptive Field Effects Emerge from Sparse Coding in a Dynamical System, PLoS Comp Bio Non-Classical Receptive Field Effects Cross Orientation Suppression Cat V1 Simple Cell LCA Model Neuron

26 M Zhu, CJ Rozell. Visual Nonclassical Receptive Field Effects Emerge from Sparse Coding in a Dynamical System, PLoS Comp Bio Non-Classical Receptive Field Effects Other effects compared in this paper: End-stopping Surround suppression/facilitation RF expansion contrast invariant orientation tuning cross-orientation suppression

27 Evidence for sparse coding Mushroom body, locust (Laurent) HVC, zebra finch (Fee) Auditory cortex, mouse (DeWeese & Zador) Hippocampus, rat/primate (Thompson & Best; Skaggs) Motor cortex, rabbit (Swadlow) Barrel cortex, rat (Brecht) Visual cortex, monkey/cat (Vinje & Gallant) Visual cortex, cat (Gray; McCormick) Inferotemporal cortex, human (Fried & Koch) Olshausen BA, Field DJ (2004) Sparse coding of sensory inputs. Current Opinion in Neurobiology, 14,