CS 182 Sections Leon Barrett

Transcription

1 CS 182 Sections Leon Barrett bad puns alert! (

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3 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).

4 Where we stand Last Week Learning backprop color This Week cognitive linguistics

5 Back-Propagation Algorithm yj wij xi f yi ti:target xi = j wij yj yi = f(xi) Sigmoid: y i = f ( xi ) = e xi We define the error term for a single node to be ti - yi

6 Gradient Descent i2 i1 global mimimum: this is your goal it should be 4-D (3 weights) but you get the idea

7 Equations 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 term

8 The output layer learning rate wjk wij yi ti: target Wij Wij α Wij = α k j i E Wij E E yi xi = = ( ti yi ) f ' ( xi ) y j Wij yi xi Wij E = Error = ½ i (ti yi)2 The derivative of the sigmoid is just y i (1 y i ) Wij = α ( ti yi ) yi (1 yi ) y j Wij = α y j δ i E Wij δ i = ( t i yi ) y i (1 yi )

9 The hidden layer wjk wij yi ti: target W jk = α E W jk E E y j x j = W jk y j x j W jk k j i E = Error = ½ i (ti yi)2 E E yi xi = = (ti yi ) f ' ( xi ) Wij y j i yi xi y j i E = (ti yi ) f ' ( xi ) Wij f ' ( x j ) yk W jk i W jk = α (ti yi ) yi (1 yi ) Wij y j (1 y j ) yk i W jk = α yk δ j δ j = (ti yi ) yi (1 yi ) Wij y j (1 y j ) i δ j = Wij δ i y j (1 y j ) i

10 Let s just do an example 0 i1 0 i2 b=1 w w w0b x00.5 1/(1+e^-0.5) f y i1 i2 y E = Error = ½ i (ti yi)2 E = ½ (t0 y0) E = ½ ( )2 = δ i = ( t i yi ) y i (1 yi ) Wij = α y j δ i W01 = α y1 δ 0 0 δ 0 = ( t 0 y 0 ) y 0 (1 y 0 ) 0 δ 0 = ( ) ( ) = α i1 δ 0 W02 = α y2 δ 0 = α i2 δ 0 W0b = α yb δ 0 = α b δ 0 = α learning rate δ 0 = suppose α = 0.5 W0b = =

11 Biological learning 1. 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

12 LTP and Hebb s Rule Hebb s Rule: neurons that fire together wire together strengthen weaken Long Term Potentiation (LTP) is the biological basis of Hebb s Rule Calcium channels are the key mechanism

13 Why is Hebb s rule incomplete? here s a contrived example: tastebud tastes rotten eats food drinks water should you punish all the connections? gets sick

14 During normal low-frequency trans-mission, glutamate interacts with NMDA and nonnmda (AMPA) and metabotropic receptors. With highfrequency stimulation, Calcium comes in

15 Recruitment learning What is recruitment learning? Why do we need it in our story? How does it relate to triangle nodes?

16 Models of Learning Hebbian ~ coincidence Recruitment ~ one trial Supervised ~ correction (backprop) Reinforcement ~ delayed reward Unsupervised ~ similarity

17 Questions! 1. How do humans detect color biologically? 2. Are color names arbitrary? What are the findings surrounding this?

18 Questions! How do humans detect color biologically? Are color names arbitrary? What are the findings surrounding this?

19 A Tour of the Visual System two regions of interest: retina LGN

20 Rods and Cones in the Retina

21 The Microscopic View

22 What Rods and Cones Detect Notice how they aren t distributed evenly, and the rod is more sensitive to shorter wavelengths

23 Center / Surround Strong activation in center, inhibition on surround The effect you get using these center / surround cells is enhanced edges top: the stimuli itself middle: brightness of the stimuli bottom: response of the retina You ll see this idea get used in Regier s model

24 How 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 slowly

25 Color Opponent Cells Mean Spikes / Sec +R-G +Y-B These cells are found in the LGN Four color channels: Red, Green, Blue, Yellow R/G, B/Y pairs 50 much like center/surround cells +G-R B-Y 400 (Monkey brain) Wavelength (mμ) 700 We can use these to determine the visual system s fundamental hue responses

26 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 terms

27 Results of Kay s Color Study Stage I II IIIa / IIIb IV V VI VII W or R or Y W W W W W W Bk or G or Bu R or Y R or Y R R R R Bk or G or Bu G or Bu Y Y Y Y Bk G or Bu G G G Bk Bu Bu Bu Bk Bk Bk Y+Bk (Brown) Y+Bk (Brown) W R Y R+W (Pink) Bk or G or Bu R + Bu (Purple) R+Y (Orange) B+W (Grey) If you group languages into the number of basic color terms they have, as the number of color terms increases, additional terms specify focal colors