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Up to derivatives in self.revert_to_original_skipping_status()
This commit is contained in:
Grant Sanderson
parent
589fd5e028
commit
34b4ea089c
1 changed files with 283 additions and 21 deletions
304
nn/part3.py
304
nn/part3.py
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@ -2002,6 +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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}
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def construct(self):
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self.force_skipping()
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@ -2101,10 +2102,10 @@ class SimplestNetworkExample(PreviewLearning):
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self.dither()
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def label_neurons(self):
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neurons = [
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neurons = VGroup(*[
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self.network_mob.layers[i].neurons[0]
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for i in -1, -2
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]
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])
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decimals = VGroup()
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a_labels = VGroup()
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a_label_arrows = VGroup()
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@ -2167,7 +2168,8 @@ class SimplestNetworkExample(PreviewLearning):
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self.play(*map(FadeOut, [not_exponents, superscript_rects]))
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self.set_variables_as_attrs(
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a_labels, a_label_arrows, decimals
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a_labels, a_label_arrows, decimals,
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last_neurons = neurons
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)
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def show_desired_output(self):
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@ -2290,41 +2292,301 @@ class SimplestNetworkExample(PreviewLearning):
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self.play(sigma_group.restore)
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self.dither()
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weighted_sum_terms = VGroup(wL, aLm1, bL)
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weighted_sum_terms = VGroup(wL, aLm1, plus, bL)
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self.set_variables_as_attrs(
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formula, weighted_sum_terms
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)
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def introduce_z(self):
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terms = self.weighted_sum_terms
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brace = Brace(terms, UP, buff = SMALL_BUFF)
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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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equals = TexMobject("=")
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equals.next_to(terms.target[0][0], LEFT)
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z_label = TexMobject("z^{(L)}")
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z_label.next_to(brace, UP, buff = SMALL_BUFF)
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z_label.next_to(equals, LEFT)
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z_label.align_to(terms.target, DOWN)
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z_label.highlight(self.z_color)
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rect = SurroundingRectangle(terms)
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rect.highlight(GREEN)
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z_label2 = z_label.copy()
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aL_start = VGroup(*self.formula[:4])
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aL_start.generate_target()
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aL_start.target.align_to(z_label, LEFT)
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z_label2.next_to(aL_start.target, RIGHT, SMALL_BUFF)
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z_label2.align_to(aL_start.target[0], DOWN)
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rp = self.formula[-1]
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rp.generate_target()
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rp.target.next_to(z_label2, RIGHT, SMALL_BUFF)
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rp.target.align_to(aL_start.target, DOWN)
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self.play(MoveToTarget(terms))
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self.play(Write(z_label), Write(equals))
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self.play(
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ReplacementTransform(z_label.copy(), z_label2),
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MoveToTarget(aL_start),
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MoveToTarget(rp),
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)
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self.dither()
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zL_formula = VGroup(z_label, equals, terms)
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aL_formula = VGroup(aL_start, z_label2, rp)
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self.set_variables_as_attrs(z_label, zL_formula, aL_formula)
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def break_into_computational_graph(self):
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network_early_layers = VGroup(*it.chain(
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self.network_mob.layers[:2],
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self.network_mob.edge_groups[:2]
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))
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wL, aL, plus, bL = self.weighted_sum_terms
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top_terms = VGroup(wL, aL, bL).copy()
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zL = self.z_label.copy()
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aL = self.formula[0].copy()
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y = self.y_label.copy()
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C0 = self.cost_equation[0].copy()
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targets = VGroup()
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for mob in top_terms, zL, aL, C0:
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mob.generate_target()
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targets.add(mob.target)
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y.generate_target()
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top_terms.target.arrange_submobjects(RIGHT, buff = MED_LARGE_BUFF)
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targets.arrange_submobjects(DOWN, buff = LARGE_BUFF)
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targets.center().to_corner(DOWN+LEFT)
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y.target.next_to(aL.target, LEFT, LARGE_BUFF, DOWN)
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top_lines = VGroup(*[
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Line(
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term.get_bottom(),
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zL.target.get_top(),
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buff = SMALL_BUFF
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)
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for term in top_terms.target
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])
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z_to_a_line, a_to_c_line, y_to_c_line = all_lines = [
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Line(
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m1.target.get_bottom(),
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m2.target.get_top(),
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buff = SMALL_BUFF
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)
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for m1, m2 in [
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(zL, aL),
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(aL, C0),
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(y, C0)
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]
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]
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for mob in [top_lines] + all_lines:
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yellow_copy = mob.copy().highlight(YELLOW)
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mob.flash = ShowCreationThenDestruction(yellow_copy)
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self.play(MoveToTarget(top_terms))
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self.dither()
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self.play(MoveToTarget(zL))
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self.play(
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ShowCreation(top_lines, submobject_mode = "all_at_once"),
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top_lines.flash
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)
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self.dither()
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self.play(MoveToTarget(aL))
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self.play(
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FadeOut(network_early_layers),
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ShowCreation(z_to_a_line),
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z_to_a_line.flash
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)
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self.dither()
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self.play(MoveToTarget(y))
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self.play(MoveToTarget(C0))
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self.play(*it.chain(*[
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[ShowCreation(line), line.flash]
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for line in a_to_c_line, y_to_c_line
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]))
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self.dither(2)
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comp_graph = VGroup()
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comp_graph.wL, comp_graph.aLm1, comp_graph.bL = top_terms
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comp_graph.top_lines = top_lines
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comp_graph.zL = zL
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comp_graph.z_to_a_line = z_to_a_line
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comp_graph.aL = aL
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comp_graph.y = y
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comp_graph.a_to_c_line = a_to_c_line
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comp_graph.y_to_c_line = y_to_c_line
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comp_graph.C0 = C0
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comp_graph.digest_mobject_attrs()
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self.comp_graph = comp_graph
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def show_preceding_layer_in_computational_graph(self):
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shift_vect = DOWN
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comp_graph = self.comp_graph
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comp_graph.save_state()
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comp_graph.generate_target()
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comp_graph.target.shift(shift_vect)
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rect = SurroundingRectangle(comp_graph.aLm1)
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attrs = ["wL", "aLm1", "bL", "zL"]
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new_terms = VGroup()
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for attr in attrs:
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term = getattr(comp_graph, attr)
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tex = term.get_tex_string()
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if "L-1" in tex:
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tex = tex.replace("L-1", "L-2")
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else:
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tex = tex.replace("L", "L-1")
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new_term = TexMobject(tex)
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new_term.highlight(term.get_color())
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new_term.move_to(term)
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new_terms.add(new_term)
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new_edges = VGroup(
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comp_graph.top_lines.copy(),
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comp_graph.z_to_a_line.copy(),
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)
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new_subgraph = VGroup(new_terms, new_edges)
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self.play(ShowCreation(rect))
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self.play(
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GrowFromCenter(brace),
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Write(z_label),
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new_subgraph.next_to, comp_graph.target, UP, SMALL_BUFF,
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UpdateFromAlphaFunc(
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new_terms,
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lambda m, a : m.set_fill(opacity = a)
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),
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MoveToTarget(comp_graph),
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rect.shift, shift_vect
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)
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self.play(FadeOut(rect))
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self.dither(2)
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self.play(
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FadeOut(new_subgraph),
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comp_graph.restore,
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rect.shift, -shift_vect,
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rect.set_stroke, BLACK, 0
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)
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self.remove(rect)
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self.dither()
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self.set_variables_as_attrs(z_label, z_brace = brace)
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def break_into_computational_graph(self):
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pass
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def show_preceding_layer_in_computational_graph(self):
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pass
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def show_number_lines(self):
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pass
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comp_graph = self.comp_graph
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wL, aLm1, bL, zL, aL, C0 = [
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getattr(comp_graph, attr)
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for attr in ["wL", "aLm1", "bL", "zL", "aL", "C0"]
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]
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wL.val = self.network.weights[-1][0][0]
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aL.val = self.decimals[0].number
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zL.val = sigmoid_inverse(aL.val)
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C0.val = (aL.val - 1)**2
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number_line = UnitInterval(
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unit_size = 2,
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stroke_width = 2,
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tick_size = 0.075,
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color = LIGHT_GREY,
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)
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for mob in wL, zL, aL, C0:
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mob.number_line = number_line.deepcopy()
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if mob is wL:
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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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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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)
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if mob is wL:
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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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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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tip_length = 0.15
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else:
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mob_spot = mob.get_corner(UP+RIGHT)
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tip_length = 0.2
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mob.arrow = Arrow(
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mob_spot, dot_spot,
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use_rectangular_stem = False,
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path_arc = path_arc,
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tip_length = tip_length,
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buff = SMALL_BUFF,
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)
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mob.arrow.highlight(mob.get_color())
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mob.arrow.set_stroke(width = 5)
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self.play(ShowCreation(
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mob.number_line,
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submobject_mode = "lagged_start"
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))
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self.play(
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ShowCreation(mob.arrow),
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ReplacementTransform(
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mob.copy(), mob.dot,
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path_arc = path_arc
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)
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)
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self.dither()
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def ask_about_w_sensitivity(self):
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pass
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wL, aLm1, bL, zL, aL, C0 = [
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getattr(self.comp_graph, attr)
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for attr in ["wL", "aLm1", "bL", "zL", "aL", "C0"]
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]
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aLm1_val = self.last_neurons[1].get_fill_opacity()
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bL_val = self.network.biases[-1][0]
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get_wL_val = lambda : wL.number_line.point_to_number(
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wL.dot.get_center()
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)
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get_zL_val = lambda : get_wL_val()*aLm1_val+bL_val
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get_aL_val = lambda : sigmoid(get_zL_val())
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get_C0_val = lambda : (get_aL_val() - 1)**2
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def generate_dot_update(term, val_func):
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def update_dot(dot):
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dot.move_to(term.number_line.number_to_point(val_func()))
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return dot
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return update_dot
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dot_update_anims = [
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UpdateFromFunc(term.dot, generate_dot_update(term, val_func))
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for term, val_func in [
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(zL, get_zL_val),
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(aL, get_aL_val),
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(C0, get_C0_val),
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]
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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.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.highlight(C0.get_color())
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del_C0.next_to(del_C0.brace, UP, SMALL_BUFF)
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for sym in del_wL, del_C0:
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self.play(
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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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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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)
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def show_derivative_wrt_w(self):
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pass
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