slides created by Leon Barrett CS 182 Sections 101 & 102 slides created by Leon Barrett with thanks to Eva Mok and Joe Makin Feb. 1, 2008

Annoucements a1 is due at 5pm on Tuesday Remember to submit it electronically a2 out on Tuesday

Where we stand Last Week Neural development Connectionist modeling Coming up Psycholinguistics Brain imaging Neural nets and Backprop

a1 questions?

Flexor- Crossed Extensor Reflex (Sheridan 1900) Reflex Circuits With Inter-neurons Painful Stimulus

Neural development How do neurons develop? Pre-neuron cells split into neurons Neurons migrate Neuron axons follow chemical clues to destinations Pruning of synapses What is a chemical gradient? How does a neuron use one? changing concentration; neuron uses this as a guide

Neural development What is the neural plate? the neural tube? The neural plate is a layer of cells that will become neurons In early development, the embryo curls up laterally, so the neural plate is curled into a tube What is a critical period? Can you name one? A period outside of which certain learning cannot occur There are critical periods at least for: Language Vision

Neural Tube formation

Neural development When you consume alcohol, thousands of neurons die. How does your brain deal with this? Duplicated, inhibited connections New neurons don't (usually) grow, but new connections can grow Humans come pre-wired for learning Some plasticity Activity dependent fine tuning Long term memory Pre-wiring biases the way we learn

Neural modeling Why model neurons? to understand them and the brain to try to accomplish what they do Why model them in different ways? to do those different things science: modeling at different levels allows different types of understanding

Neuron models What is a McCullough-Pitts neuron? Calculate “activation” by weighted sum of inputs Use a function to map activation to output What sorts of output functions does it use? Linear – why is this bad? Threshold Sigmoid – smoothed threshold

The McCullough-Pitts Neuron xi f yj wij yi xi = ∑j wij yj yi = f(xi) ti : target yj: output from unit j Wij: weight on connection from j to i xi: weighted sum of input to unit i

Let’s try an example: the AND function w01 y0 i2 b=1 w02 w0b 1 y0 i2 i1 Assume you have a threshold function centered at the origin What should you set w01, w02 and w0b to be so that you can get the right answers for y0?

Many answers would work y = f (w01i1 + w02i2 + w0bb) recall the threshold function the separation happens when w01i1 + w02i2 + w0bb = 0 move things around and you get i2 = - (w01/w02)i1 - (w0bb/w02) i2 i1

Neuron models If neurons spike, what biological feature do non-integer values correspond to? Firing rate What is unbiological about the McCullough-Pitts model? Time is ignored Weights are unlimited Hugely simplifies computations Some people propose that real neurons do complicated quantum-mechanical things

Neuron models How does a Sigma-Pi neuron differ from a McCullough-Pitts neuron? It multiplies sets of inputs

Sigma-Pi units

Sigma-Pi Unit