CS 182Sections 101 - 102Leon Barrett(http://www2.hi.net/s4/strangebreed.htm)bad puns alert!Announcements• a3 part 1 is due tomorrow night (submit as a3-1)• The second tester file is up, so please start part 2.• If you don't like your solution to Part 1, you can get our solution on Sunday morning.• The quiz is graded (get it after class).Where we stand• Last Week–Learning–backprop–color• This Week–cognitive linguisticsBack-Propagation AlgorithmWe define the error term for a single node to be ti - yixifyjwijyixi = ∑j wij yjyi = f(xi)ti:targetixiiexfy−+==11)(Sigmoid:Gradient Descenti2i1global mimimum: this is your goalit should be 4-D (3 weights) but you get the ideaEquations of Backprop• Weight update shown on following slides; important equations highlighted in green•Note momentum equation:– dW(t) = change in weight at time t–dW(t-1) = change in weight at time t-1–so using momentum:–dW(t) = -learning_rate * -input * delta(i) + momentum * dW(t-1)– the first part of that comes from last slides below– the second part is the momentum termk j iwjkwijE = Error = ½ ∑i (ti – yi)2yiti: targetijijijWEWW∂∂⋅−←αijijWEW∂∂⋅−=∆α( )jiiiijiiiiijyxfytWxxyyEWE⋅⋅−−=∂∂⋅∂∂⋅∂∂=∂∂)('The derivative of the sigmoid is just ( )iiyy−1( ) ( )jiiiiijyyyytW⋅−⋅−−⋅−=∆1αijijyWδα⋅−⋅−=∆( ) ( )iiiiiyyyt −⋅−= 1δThe output layerlearning ratek j iwjkwijE = Error = ½ ∑i (ti – yi)2yiti: targetThe hidden layerjkjkWEW∂∂⋅−=∆αjkjjjjjkWxxyyEWE∂∂⋅∂∂⋅∂∂=∂∂∑∑⋅⋅−−=∂∂⋅∂∂⋅∂∂=∂∂iijiiiijiiiijWxfytyxxyyEyE)(')(kjiijiiijkyxfWxfytWE⋅⋅⋅⋅−−=∂∂∑)(')(')(( )( )kjjiijiiiijkyyyWyyytW ⋅−⋅⋅−⋅−−⋅−=∆∑11)(αjkjkyWδα⋅−⋅−=∆( )( )jjiijiiiijyyWyyyt−⋅⋅−⋅−=∑11)(δ( )jjiiijjyyW−⋅⋅=∑1δδLet’s just do an exampleE = Error = ½ ∑i (ti – yi)2x0fi1w01y0i2b=1w02w0b E = ½ (t0 – y0)2111101110000y0i2i10.80.60.5000.62240.51/(1+e^-0.5) E = ½ (0 – 0.6224)2 = 0.1937ijijyWδα⋅−⋅−=∆( ) ( )iiiiiyyyt −⋅−= 1δ01δα⋅−⋅−=i00( ) ( )000001 yyyt −⋅−=δ( ) ( )6224.016224.06224.000−⋅−=δ1463.00−=δ1463.0−⋅=α0101δα⋅−⋅−=∆yW0202δα⋅−⋅−=∆yW00δα⋅−⋅−=∆bbyW02δα⋅−⋅−=i0δα⋅−⋅−=blearning ratesuppose α = 0.50731.01463.05.00−=−⋅=∆bW0.4268Biological learning1. What is Hebbian learning?2. Where has it been observed?3. What is wrong with Hebbian learning as a story of how animals learn?–hint – it's the opposite of what's wrong with backprop• Hebb’s Rule: neurons that fire together wire together• Long Term Potentiation (LTP) is the biological basis of Hebb’s Rule• Calcium channels are the key mechanismLTP and Hebb’s RulestrengthenweakenWhy is Hebb’s rule incomplete?• here’s a contrived example:• should you “punish” all the connections?tastebud tastes rotten eats food gets sickdrinks waterWith high-frequency stimulation, Calcium comes inDuring normal low-frequency trans-mission, glutamate interacts with NMDA and non-NMDA (AMPA) and metabotropic receptors.Recruitment learning•What is recruitment learning?•Why do we need it in our story?•How does it relate to triangle nodes?Models of Learning• Hebbian ~ coincidence• Recruitment ~ one trial• Supervised ~ correction (backprop)• Reinforcement ~ delayed reward• Unsupervised ~ similarityQuestions!1. How do humans detect color biologically?2. Are color names arbitrary? What are the findings surrounding this?Questions!•How do humans detect color biologically?•Are color names arbitrary? What are the findings surrounding this?A Tour of the Visual System•two regions of interest:– retina– LGNhttp://www.iit.edu/~npr/DrJennifer/visual/retina.htmlRods and Cones in the RetinaThe Microscopic ViewWhat Rods and Cones DetectNotice how they aren’t distributed evenly, and the rod is more sensitive to shorter wavelengthsCenter / Surround• Strong activation in center, inhibition on surround• The effect you get using these center / surround cells is enhanced edgestop: the stimuli itselfmiddle: brightness of the stimulibottom: response of the retina• You’ll see this idea get used in Regier’s modelhttp://www-psych.stanford.edu/~lera/psych115s/notes/lecture3/figures1.htmlHow They Fire• No stimuli: – both fire at base rate• Stimuli in center: – ON-center-OFF-surround fires rapidly– OFF-center-ON-surround doesn’t fire• Stimuli in surround: –OFF-center-ON-surround fires rapidly– ON-center-OFF-surround doesn’t fire• Stimuli in both regions:–both fire slowlyColor Opponent Cells•These cells are found in the LGN• Four color channels: Red, Green, Blue, Yellow• R/G , B/Y pairs•much like center/surround cells• We can use these to determine the visual system’s fundamental hue responsesMean Spikes / SecWavelength (mμ)25400 700+R-G5025400 700+G-R5025400 700+Y-B25400 700+B-Y(Monkey brain)The WCS Color Chips•Basic color terms:– Single word (not blue-green)–Frequently used (not mauve)– Refers primarily to colors (not lime)– Applies to any object (not blonde)FYI:English has 11 basic color termsResults of Kay’s Color StudyIf you group languages into the number of basic color terms they have, as the number of color terms increases, additional terms specify focal colorsB+W (Grey)R+Y (Orange)R + Bu (Purple)Bk or G or BuR+W (Pink)YY+Bk (Brown)Y+Bk (Brown)RBkBkBkWBuBuBuBkGGGG or BuBkYYYYG or BuBk or G or BuRRRRR or YR or YBk or G or BuWWWWWWW or R or YVIIVIVIVIIIa / IIIbIIStage
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