405 lines
17 KiB
Python
405 lines
17 KiB
Python
"""AstrAI promo: Transformer GQA attention animation.
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Shows the Grouped-Query Attention (GQA) mechanism with orthogonal data-flow lines:
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Input → Q/K/V Projections → Repeat KV → SDPA → O Projection → Output
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"""
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from manim import *
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import numpy as np
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class Transformer(Scene):
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"""Animates the GQA attention mechanism with orthogonal connection lines."""
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def construct(self):
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title = Text("Grouped-Query Attention (GQA)", font_size=42, color=BLUE)
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title.to_edge(UP, buff=0.35)
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self.play(Write(title))
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# ── Helper: box ──
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def mk(name, color, w=2.6, h=0.72, fs=10):
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box = Rectangle(
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width=w, height=h, color=color, fill_opacity=0.12, stroke_width=1.5
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)
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lbl = Text(name, font_size=fs, color=color)
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return VGroup(box, lbl)
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# ── Layout ──
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inp = Text("x (hidden states)", font_size=15, color=GRAY)
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inp.move_to(UP * 2.8)
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y1 = 1.5
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q_grp = mk("Q Projection\n1536 → 24×64", YELLOW)
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k_grp = mk("K Projection\n1536 → 4×64", YELLOW)
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v_grp = mk("V Projection\n1536 → 4×64", YELLOW)
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q_grp.move_to(LEFT * 3.0 + UP * y1)
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k_grp.move_to(UP * y1)
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v_grp.move_to(RIGHT * 3.0 + UP * y1)
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y2 = 0.0
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repeat_grp = mk("Repeat KV\n4 heads → 24 heads", GREEN, 2.4, 0.68, 10)
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repeat_grp.move_to(UP * y2)
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y3 = -1.6
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sdpa_grp = mk(
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"Scaled Dot-Product\nAttention Q·Kᵀ/√d", BLUE, 2.8, 0.74, 10
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)
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sdpa_grp.move_to(UP * y3)
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y4 = -3.0
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o_grp = mk("O Projection\n1536 → 1536", PURPLE, 2.2, 0.68, 10)
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o_grp.move_to(UP * y4)
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out = Text("x' (hidden states)", font_size=15, color=GRAY)
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out.next_to(o_grp, DOWN, buff=0.4)
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# ── Animate boxes ──
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self.play(Write(inp))
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all_boxes = [q_grp, k_grp, v_grp, repeat_grp, sdpa_grp, o_grp]
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for g in all_boxes:
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self.play(FadeIn(g, shift=UP * 0.1), run_time=0.2)
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# ── Input trunk → branch → Q/K/V (enter from directly above) ──
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trunk_bottom = np.array([0, q_grp.get_top()[1] + 0.35, 0])
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trunk = Line(inp.get_bottom(), trunk_bottom, color=GRAY, stroke_width=1.5)
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self.play(Create(trunk), run_time=0.15)
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branch_left = Line(
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np.array([q_grp.get_top()[0], trunk_bottom[1], 0]),
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np.array([k_grp.get_top()[0], trunk_bottom[1], 0]),
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color=GRAY, stroke_width=1.5,
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)
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branch_right = Line(
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np.array([k_grp.get_top()[0], trunk_bottom[1], 0]),
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np.array([v_grp.get_top()[0], trunk_bottom[1], 0]),
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color=GRAY, stroke_width=1.5,
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)
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self.play(Create(branch_left), Create(branch_right), run_time=0.2)
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drop_q = Line(
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np.array([q_grp.get_top()[0], trunk_bottom[1], 0]),
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q_grp.get_top(),
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color=GRAY, stroke_width=1.5,
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)
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drop_k = Line(
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np.array([k_grp.get_top()[0], trunk_bottom[1], 0]),
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k_grp.get_top(),
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color=GRAY, stroke_width=1.5,
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)
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drop_v = Line(
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np.array([v_grp.get_top()[0], trunk_bottom[1], 0]),
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v_grp.get_top(),
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color=GRAY, stroke_width=1.5,
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)
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for ln in [drop_q, drop_k, drop_v]:
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self.play(Create(ln), run_time=0.12)
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input_lines = VGroup(trunk, branch_left, branch_right, drop_q, drop_k, drop_v)
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# ── K/V → Repeat KV (trunk-branch, enter from above) ──
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kv_junc_y = repeat_grp.get_top()[1] + 0.3
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drop_k2 = Line(
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k_grp.get_bottom(),
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np.array([k_grp.get_bottom()[0], kv_junc_y, 0]),
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color=GRAY, stroke_width=1.5,
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)
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drop_v2 = Line(
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v_grp.get_bottom(),
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np.array([v_grp.get_bottom()[0], kv_junc_y, 0]),
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color=GRAY, stroke_width=1.5,
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)
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kv_branch = Line(
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np.array([v_grp.get_bottom()[0], kv_junc_y, 0]),
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np.array([k_grp.get_bottom()[0], kv_junc_y, 0]),
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color=GRAY, stroke_width=1.5,
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)
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kv_trunk = Line(
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np.array([k_grp.get_bottom()[0], kv_junc_y, 0]),
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repeat_grp.get_top(),
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color=GRAY, stroke_width=1.5,
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)
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kv_lines = VGroup(drop_k2, drop_v2, kv_branch, kv_trunk)
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self.play(Create(kv_lines), run_time=0.3)
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# ── Q → SDPA (bypasses Repeat KV, from above) ──
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qs_junc_y = sdpa_grp.get_top()[1] + 0.3
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line_qs = VMobject(color=GRAY, stroke_width=1.5)
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line_qs.set_points_as_corners([
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q_grp.get_bottom(),
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np.array([q_grp.get_bottom()[0], qs_junc_y, 0]),
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np.array([sdpa_grp.get_top()[0], qs_junc_y, 0]),
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sdpa_grp.get_top(),
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])
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self.play(Create(line_qs), run_time=0.15)
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line_rs = orth_line(repeat_grp.get_bottom(), sdpa_grp.get_top(), GRAY)
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self.play(Create(line_rs), run_time=0.15)
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line_so = orth_line(sdpa_grp.get_bottom(), o_grp.get_top(), GRAY)
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self.play(Create(line_so), run_time=0.15)
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line_oo = orth_line(o_grp.get_bottom(), out.get_top(), GRAY)
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self.play(Create(line_oo), run_time=0.15)
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self.play(Write(out))
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self.wait(0.4)
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all_lines = VGroup(
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input_lines, kv_lines, line_qs,
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line_rs, line_so, line_oo,
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)
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# ── RoPE highlight ──
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rope_q = SurroundingRectangle(q_grp, color=TEAL, buff=0.12)
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rope_k = SurroundingRectangle(k_grp, color=TEAL, buff=0.12)
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rope_t = Text(
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"RoPE: rotary position encoding\napplied to Q and K",
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font_size=13, color=TEAL,
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)
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rope_t.next_to(VGroup(rope_q, rope_k), UP, buff=0.25)
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self.play(Create(rope_q), Create(rope_k), Write(rope_t))
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self.wait(1.5)
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self.play(FadeOut(rope_q), FadeOut(rope_k), FadeOut(rope_t))
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# ── GQA ratio highlight ──
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gqa_h = SurroundingRectangle(
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VGroup(q_grp, k_grp, v_grp), color=YELLOW, buff=0.2
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)
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gqa_t = Text(
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"GQA 6:1 — 24 Q-heads → 4 KV-heads\nKV cache reduced by 83%",
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font_size=13, color=YELLOW,
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)
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gqa_t.next_to(gqa_h, RIGHT, buff=0.5)
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self.play(Create(gqa_h), Write(gqa_t))
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self.wait(1.8)
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# ── Repeat KV highlight ──
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kv_h = SurroundingRectangle(
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VGroup(k_grp, v_grp), color=GREEN, buff=0.12
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)
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kv_t = Text(
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"repeat_kv(): broadcast\n4 heads → 24 heads",
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font_size=12, color=GREEN,
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)
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kv_t.next_to(kv_h, RIGHT, buff=0.5)
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self.play(Create(kv_h), Write(kv_t))
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self.wait(1.5)
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# ── Fade all ──
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self.play(
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*[FadeOut(g) for g in all_boxes],
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FadeOut(all_lines),
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FadeOut(kv_h), FadeOut(kv_t),
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FadeOut(gqa_h), FadeOut(gqa_t),
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FadeOut(inp), FadeOut(out), FadeOut(title),
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)
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# ── Specs card ──
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st = Text("Model Specifications", font_size=36, color=BLUE)
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st.to_edge(UP, buff=0.5)
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rows_data = [
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("Parameters", "~1.0B"),
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("Layers", "24 × DecoderBlock"),
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("Hidden Dim", "1536"),
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("Q Heads / KV Heads", "24 / 4 (GQA, 6:1)"),
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("Head Dim", "64"),
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("FFN Dim", "4608 (SwiGLU)"),
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("Max Length", "2048"),
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("Precision", "bfloat16"),
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]
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table = VGroup()
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for label, value in rows_data:
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row = VGroup(
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Text(label + ":", font_size=15, color=GRAY),
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Text(value, font_size=15, color=WHITE),
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).arrange(RIGHT, buff=0.4, aligned_edge=LEFT)
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table.add(row)
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table.arrange(DOWN, buff=0.1, aligned_edge=LEFT)
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table.next_to(st, DOWN, buff=0.4)
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self.play(Write(st), Write(table))
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self.wait(2)
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self.play(FadeOut(st), FadeOut(table))
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# ═══════════════════════════════════════════════════
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# 12. Q / K / V — what do they mean?
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# ═══════════════════════════════════════════════════
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qkv_title = Text("Scaled Dot-Product Attention", font_size=34, color=BLUE)
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qkv_title.to_edge(UP, buff=0.35)
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self.play(Write(qkv_title))
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self.wait(0.2)
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q_txt = Text("Q = Query", font_size=24, color=YELLOW)
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k_txt = Text("K = Key", font_size=24, color=ORANGE)
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v_txt = Text("V = Value", font_size=24, color=GREEN)
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qkv_labels = VGroup(q_txt, k_txt, v_txt).arrange(RIGHT, buff=1.5)
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qkv_labels.next_to(qkv_title, DOWN, buff=0.6)
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self.play(Write(qkv_labels))
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q_desc = Text("\"what am I looking for?\"", font_size=12, color=YELLOW) \
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.next_to(q_txt, DOWN, buff=0.12)
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k_desc = Text("\"what do I have?\"", font_size=12, color=ORANGE) \
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.next_to(k_txt, DOWN, buff=0.12)
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v_desc = Text("\"what do I contribute?\"", font_size=12, color=GREEN) \
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.next_to(v_txt, DOWN, buff=0.12)
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self.play(Write(q_desc), Write(k_desc), Write(v_desc))
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self.wait(2.0)
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self.play(FadeOut(qkv_labels), FadeOut(q_desc), FadeOut(k_desc), FadeOut(v_desc))
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# ── Full formula ──
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full_eq = MathTex(
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r"\operatorname{Attention}(Q,K,V)=\operatorname{softmax}\!\left(\frac{QK^\top}{\sqrt{d_k}}\right)\!V",
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font_size=36, color=WHITE,
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)
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full_eq.next_to(qkv_title, DOWN, buff=0.6)
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self.play(Write(full_eq))
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self.wait(1.2)
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# ── Step-by-step decomposition ──
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steps = [
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(MathTex(r"\text{(1) } S = QK^\top", font_size=28, color=YELLOW),
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Text("score matrix — pairwise token similarity", font_size=13, color=GRAY)),
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(MathTex(r"\text{(2) } S / \sqrt{d_k}", font_size=28, color=ORANGE),
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Text("scale — prevents gradient explosion", font_size=13, color=GRAY)),
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(MathTex(r"\text{(3) } \operatorname{softmax}(\cdots)", font_size=28, color=GREEN),
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Text("normalize — each row sums to 1 (probability)", font_size=13, color=GRAY)),
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(MathTex(r"\text{(4) } \cdots \cdot V", font_size=28, color=BLUE),
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Text("weighted sum — aggregate values by attention", font_size=13, color=GRAY)),
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]
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step_group = VGroup()
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step_descs = VGroup()
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for eq, desc in steps:
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sg = VGroup(eq, desc).arrange(DOWN, buff=0.08)
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step_group.add(sg)
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step_descs.add(desc)
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step_group.arrange(DOWN, buff=0.25, aligned_edge=LEFT)
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step_group.next_to(full_eq, DOWN, buff=0.7)
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self.play(FadeOut(full_eq))
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for sg in step_group:
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self.play(Write(sg), run_time=0.3)
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self.wait(2.0)
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self.play(FadeOut(step_group))
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# ═══════════════════════════════════════════════════
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# 13. Attention score heatmap — concrete example
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# ═══════════════════════════════════════════════════
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hm_title = Text("Attention Score Heatmap", font_size=34, color=BLUE)
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hm_title.to_edge(UP, buff=0.35)
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hm_sub = Text("\"The cat sat on the mat\" — causal, per-token attention weights",
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font_size=14, color=GRAY).next_to(hm_title, DOWN, buff=0.12)
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self.play(FadeOut(qkv_title), Write(hm_title), Write(hm_sub))
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tokens = ["<s>", "The", "cat", "sat", "on", "the", "mat"]
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n = len(tokens)
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cell_size = 0.52
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gap = 0.04
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grid_high = n * cell_size + (n - 1) * gap
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grid_left = -grid_high / 2
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grid_top = 1.4
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# attention weights (after softmax + causal mask)
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weights = [
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[1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],
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[0.05, 0.95, 0.00, 0.00, 0.00, 0.00, 0.00],
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[0.02, 0.20, 0.78, 0.00, 0.00, 0.00, 0.00],
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[0.01, 0.05, 0.40, 0.54, 0.00, 0.00, 0.00],
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[0.00, 0.02, 0.07, 0.35, 0.56, 0.00, 0.00],
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[0.00, 0.01, 0.03, 0.10, 0.30, 0.56, 0.00],
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[0.00, 0.00, 0.01, 0.05, 0.12, 0.35, 0.47],
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]
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cells = VGroup()
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for i in range(n):
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for j in range(n):
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w = weights[i][j]
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if j > i:
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color = DARK_GRAY
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fill_op = 0.15
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elif w < 0.001:
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color = DARKER_GRAY
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fill_op = 0.2
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else:
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color = interpolate_color(BLUE, RED, w)
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fill_op = 0.75
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sq = Square(
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side_length=cell_size, fill_color=color,
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fill_opacity=fill_op, stroke_width=0.5,
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stroke_color=GRAY,
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)
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x = grid_left + j * (cell_size + gap) + cell_size / 2
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y = grid_top - i * (cell_size + gap) - cell_size / 2
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sq.move_to([x, y, 0])
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cells.add(sq)
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self.play(FadeIn(sq, scale=0.6), run_time=0.015)
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# row labels (query) on the left
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row_lbls = VGroup()
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for i, tok in enumerate(tokens):
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lbl = Text(tok, font_size=12, color=GRAY)
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y = grid_top - i * (cell_size + gap) - cell_size / 2
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lbl.next_to([grid_left - 0.15, y, 0], LEFT, buff=0.08)
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row_lbls.add(lbl)
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q_label = Text("Q", font_size=11, color=WHITE, weight=BOLD)
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q_label.move_to(row_lbls[0].get_left() + LEFT * 0.3).shift(UP * 0.15)
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self.play(*[Write(l) for l in row_lbls], Write(q_label))
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# column labels (key) on top
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col_lbls = VGroup()
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for j, tok in enumerate(tokens):
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lbl = Text(tok, font_size=9, color=GRAY).rotate(PI / 6)
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x = grid_left + j * (cell_size + gap) + cell_size / 2
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lbl.next_to([x, grid_top + 0.06, 0], UP, buff=0.04)
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col_lbls.add(lbl)
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k_label = Text("K", font_size=11, color=WHITE, weight=BOLD)
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k_label.next_to(col_lbls[0], UP, buff=0.06)
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self.play(*[Write(l) for l in col_lbls], Write(k_label))
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self.wait(1.0)
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# causal mask — per-cell red overlay aligned to grid
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mask_overlays = VGroup()
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for i in range(n):
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for j in range(n):
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if j > i:
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x = grid_left + j * (cell_size + gap) + cell_size / 2
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y = grid_top - i * (cell_size + gap) - cell_size / 2
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sq = Square(
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side_length=cell_size, fill_color=RED,
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fill_opacity=0.10, stroke_width=0.5,
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stroke_color=RED, stroke_opacity=0.3,
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)
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sq.move_to([x, y, 0])
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mask_overlays.add(sq)
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causal_txt = Text("causal mask\n(future tokens hidden)", font_size=11, color=RED) \
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.next_to(cells[6], UP, buff=0.25).align_to(cells[6], RIGHT)
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self.play(FadeIn(mask_overlays), Write(causal_txt))
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self.wait(1.5)
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self.play(FadeOut(mask_overlays), FadeOut(causal_txt))
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# highlight key patterns
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h1 = SurroundingRectangle(cells[2 * n + 1], color=ORANGE, stroke_width=2, buff=0.04)
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h2 = SurroundingRectangle(cells[3 * n + 2], color=ORANGE, stroke_width=2, buff=0.04)
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h3 = SurroundingRectangle(cells[4 * n + 3], color=ORANGE, stroke_width=2, buff=0.04)
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h4 = SurroundingRectangle(cells[5 * n + 4], color=ORANGE, stroke_width=2, buff=0.04)
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h5 = SurroundingRectangle(cells[6 * n + 5], color=ORANGE, stroke_width=2, buff=0.04)
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hl_text = Text("previous token attends to next\n(causal sequence learning)", font_size=11, color=ORANGE) \
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.next_to(cells[(n - 1) * n + (n - 1)], RIGHT, buff=0.8)
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self.play(Create(h1), Create(h2), Create(h3), Create(h4), Create(h5), Write(hl_text))
|
||
self.wait(2.0)
|
||
self.play(FadeOut(h1), FadeOut(h2), FadeOut(h3), FadeOut(h4), FadeOut(h5), FadeOut(hl_text))
|
||
|
||
# fade all heatmap
|
||
self.play(
|
||
FadeOut(hm_title), FadeOut(hm_sub),
|
||
FadeOut(cells), FadeOut(row_lbls), FadeOut(col_lbls),
|
||
FadeOut(q_label), FadeOut(k_label),
|
||
)
|
||
|
||
|
||
def orth_line(start, end, color=GRAY):
|
||
"""Create an L-shaped orthogonal line from start to end."""
|
||
mid = np.array([start[0], end[1], 0])
|
||
path = VMobject(color=color, stroke_width=1.5)
|
||
path.set_points_as_corners([start, mid, end])
|
||
return path
|