5 White noise stimulusWhite noise is used to as a stimulus to measure the spike triggered average response as in the electric fish experiment.
6 Fourier transformIn practice, only approximate white noise signals can be generated with a flat spectrum up to a cut-off frequency.
7 H1 neuron in visual system of blowfly A: Stimulus is velocity profile;B: response of H1 neuron of the fly visual system;C: rest(t) using the linear kernel D(t) (solid line) and actual neural rate r(t) agree when rates vary slowly.D(t) is constructed using white noise
10 Early visual system: Retina 5 types of cells:Rods and cones: photo-transduction into electrical signalLateral interaction of Bipolar cells through Horizontal cells. No action potentials for local computationAction potentials in retinal ganglion cells coupled by Amacrine cells. NoteG_1 off responseG_2 on responseA: Anatomy of retina of dog (Cajal 1911)B: Recording in mud puppy (amphibian). Stimulus is flash of light (1 sec)
11 Pathway from retina via LGN to V1 Lateral geniculate nucleus (LGN) cells receive input from Retinal ganglion cells from both eyes.Both LGNs represent both eyes but different parts of the worldNeurons in retina, LGN and visual cortex have receptive fields:Neurons fire only in response to higher/lower illumination within receptive fieldNeural response depends (indirectly) on illumination outside receptive field
12 Simple and complex cells Cells in retina, LGN, V1 are simple or complexSimple cells:Model as linear filterComplex cellsShow invariance to spatial position within the receptive fieldPoorly described by linear model
13 Retinotopic mapNeighboring image points are mapped onto neighboring neurons in V1Visual world is centered on fixation point.The left/right visual world maps to the right/left V1Distance on the display (eccentricity) is measured in degrees by dividing by distance to the eyeDistances on the display screen (eccentricity) are measured in degrees by dividing by distance to the eye
14 Retinotopic mapA: The pattern on the cortex was produced by imaging a radioactive analogue of glucose that was taken up by active neurons while a monkey viewed a visual image consisting of concentric circles and radial lines$\lambda=12 mm,\epsilon_0=1^0$
22 Temporal receptive fields Space-time evolution of V1 cat receptive fieldON/OFF boundary changes to OFF/ON boundary over time.Extrema locations do not change with time: separable kernel D(x,y,t)=Ds(x,y)Dt(t)Cat V1
34 Stochastic neural networks The top two layers form an associative memory whose energy landscape models the low dimensional manifolds of the digits.The energy valleys have names2000 top-level neurons10 label neurons500 neuronsThe model learns to generate combinations of labels and images.To perform recognition we start with a neutral state of the label units and do an up-pass from the image followed by a few iterations of the top-level associative memory.500 neurons28 x 28 pixel imageHinton
35 Samples generated by letting the associative memory run with one label clamped using Gibbs sampling Hinton
36 Examples of correctly recognized handwritten digits that the neural network had never seen before Hinton
37 How well does it discriminate on MNIST test set with no extra information about geometric distortions?Generative model based on RBM’s %Support Vector Machine (Decoste et. al.) %Backprop with 1000 hiddens (Platt) ~1.6%Backprop with >300 hiddens ~1.6%K-Nearest Neighbor ~ 3.3%See Le Cun et. al for more resultsIts better than backprop and much more neurally plausible because the neurons only need to send one kind of signal, and the teacher can be another sensory input.Hinton
38 Summary Linear filters Visual system (retina, LGN, V1) Visual stimuli White noise stimulus for optimal estimationVisual system (retina, LGN, V1)Visual stimuliV1Spatial receptive fieldsTemporal receptive fieldsSpace-time receptive fieldsNon-separable receptive fields, Direction selectivityLGN and RetinaNon-separable ON center OFF surround cellsV1 direction selective simple cells as sum of LGN simple cells
39 Exercise 2.3 Is based on Kara, Reinagel, Reid (Neuron, 2000). Simultaneous single unit recordings of retinal ganglion cells, LGN relay cells and simple cells from primary visual cortexSpike count variability (Fano) less than Poisson, doubling from RGC to LGN and from LGN to cortex.Data explained by Poisson with refractory periodFig. 1,2,3