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Up through chain rule in SimplestNetworkExample of nn/part3
This commit is contained in:
Grant Sanderson
parent
76ea80230d
commit
ac079f182a
1 changed files with 228 additions and 20 deletions
248
nn/part3.py
248
nn/part3.py
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@ -2002,7 +2002,7 @@ class SimplestNetworkExample(PreviewLearning):
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"z_color" : GREEN,
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"cost_color" : RED,
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"desired_output_color" : YELLOW,
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"derivative_scale_vale" : 0.7,
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"derivative_scale_val" : 0.85,
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}
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def construct(self):
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self.force_skipping()
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@ -2022,6 +2022,8 @@ class SimplestNetworkExample(PreviewLearning):
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self.show_derivative_wrt_w()
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self.show_chain_of_events()
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self.show_chain_rule()
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self.name_chain_rule()
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self.indicate_everything_on_screen()
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self.compute_derivatives()
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self.fire_together_wire_together()
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self.show_derivative_wrt_b()
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@ -2301,6 +2303,7 @@ class SimplestNetworkExample(PreviewLearning):
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terms = self.weighted_sum_terms
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terms.generate_target()
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terms.target.next_to(self.formula, UP, aligned_edge = RIGHT)
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terms.target.shift(MED_LARGE_BUFF*RIGHT)
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equals = TexMobject("=")
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equals.next_to(terms.target[0][0], LEFT)
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@ -2486,6 +2489,10 @@ class SimplestNetworkExample(PreviewLearning):
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mob.number_line.next_to(mob, UP, MED_LARGE_BUFF, LEFT)
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else:
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mob.number_line.next_to(mob, RIGHT)
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if mob is C0:
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mob.number_line.x_max = 0.5
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for tick_mark in mob.number_line.tick_marks[1::2]:
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mob.number_line.tick_marks.remove(tick_mark)
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mob.dot = Dot(color = mob.get_color())
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mob.dot.move_to(
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mob.number_line.number_to_point(mob.val)
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@ -2494,7 +2501,7 @@ class SimplestNetworkExample(PreviewLearning):
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path_arc = 0
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dot_spot = mob.dot.get_bottom()
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else:
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path_arc = -0.8*np.pi
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path_arc = -0.7*np.pi
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dot_spot = mob.dot.get_top()
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if mob is C0:
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mob_spot = mob[0].get_corner(UP+RIGHT)
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@ -2555,17 +2562,27 @@ class SimplestNetworkExample(PreviewLearning):
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]
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]
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def shake_dot(run_time = 2, rate_func = there_and_back):
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self.play(
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ApplyMethod(
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wL.dot.shift, LEFT,
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rate_func = rate_func,
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run_time = run_time
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),
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*dot_update_anims
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)
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wL_line = Line(wL.dot.get_center(), wL.dot.get_center()+LEFT)
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del_wL = TexMobject("\\partial w^{(L)}")
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del_wL.scale(self.derivative_scale_vale)
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del_wL.brace = Brace(wL_line, UP)
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del_wL.scale(self.derivative_scale_val)
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del_wL.brace = Brace(wL_line, UP, buff = SMALL_BUFF)
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del_wL.highlight(wL.get_color())
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del_wL.next_to(del_wL.brace, UP, SMALL_BUFF)
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C0_line = Line(C0.dot.get_center(), C0.dot.get_center()+MED_SMALL_BUFF*RIGHT)
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del_C0 = TexMobject("\\partial C_0")
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del_C0.scale(self.derivative_scale_vale)
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del_C0.brace = Brace(C0_line, UP)
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del_C0.scale(self.derivative_scale_val)
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del_C0.brace = Brace(C0_line, UP, buff = SMALL_BUFF)
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del_C0.highlight(C0.get_color())
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del_C0.next_to(del_C0.brace, UP, SMALL_BUFF)
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@ -2574,32 +2591,189 @@ class SimplestNetworkExample(PreviewLearning):
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GrowFromCenter(sym.brace),
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Write(sym, run_time = 1)
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)
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self.play(
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ApplyMethod(
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wL.dot.shift, LEFT,
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run_time = 2,
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rate_func = there_and_back
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),
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*dot_update_anims
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)
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shake_dot()
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self.dither()
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self.set_variables_as_attrs(
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dot_update_anims, del_wL, del_C0,
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shake_dot, del_wL, del_C0,
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)
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def show_derivative_wrt_w(self):
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pass
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del_wL = self.del_wL
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del_C0 = self.del_C0
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cost_word = self.cost_word
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cost_arrow = self.cost_arrow
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shake_dot = self.shake_dot
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wL = self.comp_graph.wL
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dC_dw = TexMobject(
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"{\\partial C_0", "\\over", "\\partial w^{(L)} }"
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)
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dC_dw[0].highlight(del_C0.get_color())
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dC_dw[2].highlight(del_wL.get_color())
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dC_dw.scale(self.derivative_scale_val)
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dC_dw.to_edge(UP, buff = MED_SMALL_BUFF)
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dC_dw.shift(3.5*LEFT)
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full_rect = SurroundingRectangle(dC_dw)
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full_rect_copy = full_rect.copy()
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words = TextMobject("What we want")
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words.next_to(full_rect, RIGHT)
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words.highlight(YELLOW)
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denom_rect = SurroundingRectangle(dC_dw[2])
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numer_rect = SurroundingRectangle(dC_dw[0])
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self.play(
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ReplacementTransform(del_C0.copy(), dC_dw[0]),
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ReplacementTransform(del_wL.copy(), dC_dw[2]),
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Write(dC_dw[1], run_time = 1)
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)
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self.play(
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FadeOut(cost_word),
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FadeOut(cost_arrow),
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ShowCreation(full_rect),
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Write(words, run_time = 1),
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)
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self.dither(2)
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self.play(
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FadeOut(words),
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ReplacementTransform(full_rect, denom_rect)
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)
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self.play(Transform(dC_dw[2].copy(), del_wL, remover = True))
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shake_dot()
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self.play(ReplacementTransform(denom_rect, numer_rect))
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self.play(Transform(dC_dw[0].copy(), del_C0, remover = True))
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shake_dot()
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self.dither()
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self.play(ReplacementTransform(numer_rect, full_rect_copy))
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self.play(FadeOut(full_rect_copy))
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self.dither()
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self.dC_dw = dC_dw
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def show_chain_of_events(self):
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pass
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comp_graph = self.comp_graph
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wL, zL, aL, C0 = [
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getattr(comp_graph, attr)
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for attr in ["wL", "zL", "aL", "C0"]
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]
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del_wL = self.del_wL
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del_C0 = self.del_C0
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zL_line = Line(ORIGIN, MED_LARGE_BUFF*LEFT)
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zL_line.shift(zL.dot.get_center())
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del_zL = TexMobject("\\partial z^{(L)}")
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del_zL.highlight(zL.get_color())
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del_zL.brace = Brace(zL_line, DOWN, buff = SMALL_BUFF)
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aL_line = Line(ORIGIN, MED_SMALL_BUFF*LEFT)
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aL_line.shift(aL.dot.get_center())
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del_aL = TexMobject("\\partial a^{(L)}")
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del_aL.highlight(aL.get_color())
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del_aL.brace = Brace(aL_line, DOWN, buff = SMALL_BUFF)
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for sym in del_zL, del_aL:
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sym.scale(self.derivative_scale_val)
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sym.brace.stretch_about_point(
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0.5, 1, sym.brace.get_top(),
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)
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sym.shift(
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sym.brace.get_bottom()+SMALL_BUFF*DOWN \
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-sym[0].get_corner(UP+RIGHT)
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)
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syms = [del_wL, del_zL, del_aL, del_C0]
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for s1, s2 in zip(syms, syms[1:]):
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self.play(
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ReplacementTransform(s1.copy(), s2),
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ReplacementTransform(s1.brace.copy(), s2.brace),
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)
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self.shake_dot(run_time = 1.5)
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self.dither(0.5)
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self.dither()
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self.set_variables_as_attrs(del_zL, del_aL)
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def show_chain_rule(self):
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pass
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dC_dw = self.dC_dw
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dz_dw = TexMobject(
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"{\\partial z^{(L)}", "\\over", "\\partial w^{(L)}}"
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)
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da_dz = TexMobject(
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"{\\partial a^{(L)}", "\\over", "\\partial z^{(L)}}"
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)
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dC_da = TexMobject(
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"{\\partial C0}", "\\over", "\\partial a^{(L)}}"
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)
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dz_dw[2].highlight(self.del_wL.get_color())
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VGroup(dz_dw[0], da_dz[2]).highlight(self.z_color)
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dC_da[0].highlight(self.cost_color)
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equals = TexMobject("=")
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group = VGroup(equals, dz_dw, da_dz, dC_da)
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group.arrange_submobjects(RIGHT, SMALL_BUFF)
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group.scale(self.derivative_scale_val)
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group.next_to(dC_dw, RIGHT)
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for mob in group[1:]:
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target_y = equals.get_center()[1]
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y = mob[1].get_center()[1]
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mob.shift((target_y - y)*UP)
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last_sym = dC_dw[2]
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self.play(Write(equals, run_time = 1))
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for fraction in group[1:]:
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self.play(LaggedStart(
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FadeIn, VGroup(*fraction[:2]),
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lag_ratio = 0.75,
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run_time = 1
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))
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self.play(ReplacementTransform(
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last_sym.copy(), fraction[2]
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))
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self.dither()
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last_sym = fraction[0]
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self.shake_dot()
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self.dither()
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self.chain_rule_equation = VGroup(dC_dw, *group)
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def name_chain_rule(self):
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graph_parts = self.get_all_comp_graph_parts()
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equation = self.chain_rule_equation
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rect = SurroundingRectangle(equation)
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group = VGroup(equation, rect)
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group.generate_target()
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group.target.to_corner(UP+LEFT)
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words = TextMobject("Chain rule")
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words.highlight(YELLOW)
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words.next_to(group.target, DOWN)
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self.play(ShowCreation(rect))
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self.play(
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MoveToTarget(group),
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Write(words, run_time = 1),
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graph_parts.scale, 0.7, graph_parts.get_bottom()
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)
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self.dither(2)
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self.play(*map(FadeOut, [rect, words]))
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def indicate_everything_on_screen(self):
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everything = VGroup(*self.get_top_level_mobjects())
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everything = VGroup(*filter(
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lambda m : not m.is_subpath,
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everything.family_members_with_points()
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))
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self.play(LaggedStart(
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Indicate, everything,
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rate_func = wiggle,
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lag_ratio = 0.2,
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run_time = 5
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))
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self.dither()
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def compute_derivatives(self):
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pass
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self.play(FadeOut(self.all_comp_graph_parts))
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def fire_together_wire_together(self):
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pass
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@ -2623,6 +2797,40 @@ class SimplestNetworkExample(PreviewLearning):
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decimal.set_fill(BLACK)
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decimal.move_to(neuron)
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return decimal
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def get_all_comp_graph_parts(self):
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comp_graph = self.comp_graph
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result = VGroup(comp_graph)
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for attr in "wL", "zL", "aL", "C0":
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sym = getattr(comp_graph, attr)
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comp_graph.add(
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sym.arrow, sym.number_line, sym.dot
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)
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del_sym = getattr(self, "del_" + attr)
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comp_graph.add(del_sym, del_sym.brace)
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self.all_comp_graph_parts = result
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return result
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