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CS 182Sections 101 & 102slides created by Leon Barrettwith thanks toEva Mok and Joe MakinFeb. 1, 2008Annoucements• a1 is due at 5pm on Tuesday• Remember to submit it electronically• a2 out on TuesdayWhere we stand• Last Week–Neural development–Connectionist modeling• Coming up–Psycholinguistics–Brain imaging–Neural nets and Backpropa1 questions?Flexor-Crossed ExtensorReflex(Sheridan 1900)Painful StimulusReflex CircuitsWith Inter-neuronsNeural 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 guideNeural 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• VisionNeural Tube formationNeural 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 learnNeural 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 understandingNeuron 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 thresholdThe McCullough-Pitts Neuronyj: output from unit jWij: weight on connection from j to ixi: weighted sum of input to unit ixifyjwijyixi = ∑j wij yjyi = f(xi)ti : targetLet’s try an example: the AND function•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?111001010000y0i2i1x0fi1w01y0i2b=1w02w0bMany answers would worky = f (w01i1 + w02i2 + w0bb)recall the threshold functionthe separation happens when w01i1 + w02i2 + w0bb = 0move things around and you geti2 = - (w01/w02)i1 - (w0bb/w02)i2i1Neuron 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 thingsNeuron models• How does a Sigma-Pi neuron differ from a McCullough-Pitts neuron?–It multiplies sets of inputsSigma-Pi unitsSigma-Pi


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Berkeley COMPSCI 182 - Section Notes

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