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InterpretGradientComponents in nn/part3
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Grant Sanderson
parent
c5891ce25e
commit
1db52f7e6d
1 changed files with 285 additions and 2 deletions
287
nn/part3.py
287
nn/part3.py
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@ -47,13 +47,296 @@ class TODOInsertDefinitionOfCostFunction(TODOStub):
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"message" : "Insert Definition of cost function"
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}
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class TODOInsertGradientNudging(TODOStub):
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CONFIG = {
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"message" : "Insert GradientNudging"
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}
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class InterpretGradientComponents(GradientNudging):
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CONFIG = {
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"network_mob_config" : {
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"layer_to_layer_buff" : 3,
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},
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"stroke_width_exp" : 2,
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"n_decimals" : 6,
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"n_steps" : 3,
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"start_cost" : 3.48,
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"delta_cost" : -0.21,
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}
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def construct(self):
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self.setup_network()
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self.add_cost()
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self.add_gradient()
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self.change_weights_repeatedly()
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self.ask_about_high_dimensions()
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self.circle_magnitudes()
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self.isolate_particular_weights()
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self.shift_cost_expression()
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self.tweak_individual_weights()
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def setup_network(self):
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self.network_mob.scale(0.55)
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self.network_mob.to_corner(UP+RIGHT)
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self.color_network_edges()
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def add_cost(self):
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rect = SurroundingRectangle(self.network_mob)
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rect.highlight(RED)
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arrow = Vector(DOWN, color = RED)
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arrow.shift(rect.get_bottom())
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cost = DecimalNumber(self.start_cost)
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cost.highlight(RED)
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cost.next_to(arrow, DOWN)
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cost_expression = TexMobject(
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"C(", "w_0, w_1, \\dots, w_{13{,}001}", ")", "="
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)
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for tex in "()":
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cost_expression.highlight_by_tex(tex, RED)
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cost_expression.next_to(cost, DOWN)
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cost_group = VGroup(cost_expression, cost)
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cost_group.arrange_submobjects(RIGHT)
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cost_group.next_to(arrow, DOWN)
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self.add(rect, arrow, cost_group)
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self.set_variables_as_attrs(
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cost, cost_expression, cost_group,
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network_rect = rect
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)
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def change_weights_repeatedly(self):
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decimals = self.grad_vect.decimals
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grad_terms = self.grad_vect.contents
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edges = VGroup(*reversed(list(
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it.chain(*self.network_mob.edge_groups)
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)))
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cost = self.cost
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for x in range(self.n_steps):
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self.move_grad_terms_into_position(grad_terms.copy())
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self.play(*self.get_weight_adjustment_anims(edges, cost))
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self.play(*self.get_decimal_change_anims(decimals))
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def ask_about_high_dimensions(self):
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grad_vect = self.grad_vect
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words = TextMobject(
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"Direction in \\\\ ${13{,}002}$ dimensions?!?")
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words.highlight(YELLOW)
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words.move_to(grad_vect).to_edge(DOWN)
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arrow = Arrow(
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words.get_top(),
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grad_vect.get_bottom(),
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buff = SMALL_BUFF
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)
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randy = Randolph()
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randy.scale(0.6)
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randy.next_to(words, LEFT)
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randy.shift_onto_screen()
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self.play(
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Write(words, run_time = 2),
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GrowArrow(arrow),
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)
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self.play(FadeIn(randy))
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self.play(randy.change, "confused", words)
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self.play(Blink(randy))
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self.dither()
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self.play(*map(FadeOut, [randy, words, arrow]))
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def circle_magnitudes(self):
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rects = VGroup()
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for decimal in self.grad_vect.decimals:
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rects.add(SurroundingRectangle(VGroup(*decimal[-4:])))
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rects.highlight(WHITE)
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self.play(LaggedStart(ShowCreation, rects))
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self.play(FadeOut(rects))
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def isolate_particular_weights(self):
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vect_contents = self.grad_vect.contents
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w_terms = self.cost_expression[1]
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edges = self.network_mob.edge_groups
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edge1 = self.network_mob.layers[1].neurons[3].edges_in[0].copy()
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edge2 = self.network_mob.layers[1].neurons[9].edges_in[15].copy()
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VGroup(edge1, edge2).set_stroke(width = 4)
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d1 = DecimalNumber(3.2)
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d2 = DecimalNumber(0.1)
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VGroup(edge1, d1).highlight(YELLOW)
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VGroup(edge2, d2).highlight(MAROON_B)
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new_vect_contents = VGroup(
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TexMobject("\\vdots"),
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d1, TexMobject("\\vdots"),
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d2, TexMobject("\\vdots"),
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)
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new_vect_contents.arrange_submobjects(DOWN)
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new_vect_contents.move_to(vect_contents)
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new_w_terms = TexMobject(
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"\\dots", "w_n", "\\dots", "w_k", "\\dots"
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)
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new_w_terms.move_to(w_terms, DOWN)
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new_w_terms[1].highlight(d1.get_color())
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new_w_terms[3].highlight(d2.get_color())
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for d, edge in (d1, edge1), (d2, edge2):
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d.arrow = Arrow(
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d.get_right(), edge.get_center(),
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color = d.get_color()
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)
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self.play(
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FadeOut(vect_contents),
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FadeIn(new_vect_contents),
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FadeOut(w_terms),
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FadeIn(new_w_terms),
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edges.set_stroke, LIGHT_GREY, 0.35,
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)
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self.play(GrowArrow(d1.arrow))
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self.play(ShowCreation(edge1))
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self.dither()
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self.play(GrowArrow(d2.arrow))
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self.play(ShowCreation(edge2))
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self.dither(2)
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self.cost_expression.remove(w_terms)
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self.cost_expression.add(new_w_terms)
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self.set_variables_as_attrs(
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edge1, edge2, new_w_terms,
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new_decimals = VGroup(d1, d2)
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)
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def shift_cost_expression(self):
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self.play(self.cost_group.shift, DOWN+0.5*LEFT)
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def tweak_individual_weights(self):
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cost = self.cost
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cost_num = cost.number
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edges = VGroup(self.edge1, self.edge2)
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decimals = self.new_decimals
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changes = (1.0, 1./32)
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wn = self.new_w_terms[1]
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wk = self.new_w_terms[3]
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number_line_template = NumberLine(
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x_min = -1,
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x_max = 1,
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tick_frequency = 0.25,
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numbers_with_elongated_ticks = [],
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color = WHITE
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)
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for term in wn, wk, cost:
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term.number_line = number_line_template.copy()
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term.brace = Brace(term.number_line, DOWN, buff = SMALL_BUFF)
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group = VGroup(term.number_line, term.brace)
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group.next_to(term, UP)
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term.dot = Dot()
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term.dot.highlight(term.get_color())
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term.dot.move_to(term.number_line.get_center())
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term.dot.save_state()
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term.dot.move_to(term)
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term.dot.set_fill(opacity = 0)
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groups = [
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VGroup(d, d.arrow, edge, w)
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for d, edge, w in zip(decimals, edges, [wn, wk])
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]
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for group in groups:
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group.save_state()
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for i in range(2):
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group1, group2 = groups[i], groups[1-i]
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change = changes[i]
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edge = edges[i]
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w = group1[-1]
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added_anims = []
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if i == 0:
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added_anims = [
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GrowFromCenter(cost.brace),
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ShowCreation(cost.number_line),
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cost.dot.restore
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]
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self.play(
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group1.restore,
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group2.fade, 0.7,
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GrowFromCenter(w.brace),
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ShowCreation(w.number_line),
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w.dot.restore,
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*added_anims
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)
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for x in range(2):
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func = lambda a : interpolate(
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cost_num, cost_num-change, a
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)
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self.play(
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ChangingDecimal(cost, func),
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cost.dot.shift, change*RIGHT,
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w.dot.shift, 0.25*RIGHT,
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edge.set_stroke, None, 8,
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rate_func = lambda t : wiggle(t, 4),
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run_time = 2,
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)
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self.dither()
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self.play(*map(FadeOut, [w.dot, w.brace, w.number_line]))
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######
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def move_grad_terms_into_position(self, grad_terms):
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cost_expression = self.cost_expression
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w_terms = self.cost_expression[1]
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points = VGroup(*[
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VectorizedPoint()
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for term in grad_terms
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])
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points.arrange_submobjects(RIGHT)
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points.replace(w_terms, dim_to_match = 0)
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grad_terms.generate_target()
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grad_terms.target[len(grad_terms)/2].rotate(np.pi/2)
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grad_terms.target.arrange_submobjects(RIGHT)
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grad_terms.target.scale_to_fit_width(cost_expression.get_width())
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grad_terms.target.next_to(cost_expression, DOWN)
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words = TextMobject("Nudge weights")
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words.scale(0.8)
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words.next_to(grad_terms.target, DOWN)
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self.play(
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MoveToTarget(grad_terms),
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FadeIn(words)
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)
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self.play(
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Transform(
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grad_terms, points,
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remover = True,
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submobject_mode = "lagged_start",
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run_time = 1
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),
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FadeOut(words)
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)
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def get_weight_adjustment_anims(self, edges, cost):
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start_cost = cost.number
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target_cost = start_cost + self.delta_cost
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w_terms = self.cost_expression[1]
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return [
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self.get_edge_change_anim(edges),
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LaggedStart(
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Indicate, w_terms,
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rate_func = there_and_back,
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run_time = 1.5,
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),
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ChangingDecimal(
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cost,
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lambda a : interpolate(start_cost, target_cost, a),
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run_time = 1.5
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)
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]
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