from manim import * import numpy as np config.frame_width = 16 config.frame_height = 9 config.pixel_width = 1920 config.pixel_height = 1080 config.background_color = "#0B0E14" INK = "#E8EEF7" MUTED = "#9AA3B2" DIM = "#5C6676" WIRE = "#2E3A4D" NEURON = "#1B3A55" NEURON_EDGE = "#4E8FB5" NEURON_ON = "#58C4DD" HIDDEN_ON = "#F0C75E" OUT_DIM = "#1A2836" OUT_EDGE = "#4A6278" GREEN = "#3DDC97" PIXEL_OFF = ManimColor("#161B24") PIXEL_ON = ManimColor("#F4F1E8") PANEL_BG = "#10151D" PANEL_EDGE = "#2A3444" CURVE = "#58C4DD" GRID_FRAME = "#2C3646" WIRE_REASON = ( "Fully-connected layers share crossing synapses on purpose: every neuron " "in one column links to every neuron in the next, so the wires occupy " "one shared band." ) NODE_REASON = ( "Each neuron disc and its soft glow are one unit; the glow is a larger " "disc centered on the same point as the core." ) CHART_REASON = ( "The loss curve is drawn on these axes so the descent can be read " "against Epoch and Loss directly." ) NET_REASON = ( "The digit grid, sampled input column, hidden neurons, output neurons, " "and the fully-connected synapses between them occupy one network diagram." ) def handwritten_seven(n=28): """Soft, slightly sloppy MNIST-like 7.""" img = np.zeros((n, n)) for i in range(n): for j in range(n): y = i / (n - 1) x = j / (n - 1) v = 0.0 if 0.10 <= y <= 0.23 and 0.16 <= x <= 0.86: v = 1.0 if x < 0.24: v *= (x - 0.16) / 0.08 if x > 0.78: v *= (0.86 - x) / 0.08 v *= 0.85 + 0.15 * np.sin(18 * x) if 0.18 <= y <= 0.34 and 0.15 <= x <= 0.27: v = max(v, 0.75 * (1 - abs(x - 0.20) / 0.07)) if 0.18 <= y <= 0.93: xc = 0.71 - 0.33 * (y - 0.18) / 0.75 half_w = 0.058 + 0.012 * (y - 0.18) dist = abs(x - xc) if dist < half_w: v = max(v, 1.0 - 0.22 * dist / half_w) if 0.47 <= y <= 0.55 and 0.30 <= x <= 0.62: vv = 0.88 if x < 0.36: vv *= (x - 0.30) / 0.06 if x > 0.56: vv *= (0.62 - x) / 0.06 v = max(v, vv) img[i, j] = float(np.clip(v, 0.0, 1.0)) return img def stacked_ys(n_top, n_bot, gap, ell_gap, yc): h = (n_top - 1) * gap + ell_gap + (n_bot - 1) * gap y = yc + h / 2 ys = [] for i in range(n_top): ys.append(y) if i < n_top - 1: y -= gap y -= ell_gap for i in range(n_bot): ys.append(y) if i < n_bot - 1: y -= gap return ys def make_neuron(r, fill, edge, glow_color, tag): core = Circle( radius=r, stroke_color=edge, stroke_width=1.7, fill_color=fill, fill_opacity=0.88, ) glow = Circle( radius=r * 1.16, stroke_width=0, fill_color=glow_color, fill_opacity=0.0, ) g = VGroup(glow, core) g.core = core g.glow = glow g return g def make_ellipsis(x, y, color=DIM, tag="ell"): dots = VGroup( *[Dot(point=[x, y + dy, 0], radius=0.028, color=color) for dy in (0.10, 0.0, -0.10)] ) dots return dots def loss_fn(t): return 2.12 * np.exp(-0.40 * t) + 0.10 class NeuralNetDigit(Scene): def construct(self): SAFE_X = config.frame_width / 2 - 0.35 SAFE_Y = config.frame_height / 2 - 0.35 SAFE_Y_BOTTOM = config.frame_height / 2 - 0.7 _ = (SAFE_X, SAFE_Y, SAFE_Y_BOTTOM) N = 28 SP = 0.072 R_PIX = 0.031 GRID_C = np.array([-5.62, 0.92, 0.0]) GRID_W = (N - 1) * SP X_IN, X_H1, X_H2, X_OUT = -3.38, -1.22, 0.82, 2.88 Y_C = 0.92 R_IN, R_H, R_OUT = 0.090, 0.128, 0.138 ys_in = stacked_ys(5, 5, 0.255, 0.50, Y_C) ys_h1 = stacked_ys(4, 4, 0.325, 0.52, Y_C) ys_h2 = [Y_C + (2.5 - i) * 0.365 for i in range(6)] ys_out = [Y_C + (4.5 - i) * 0.338 for i in range(10)] img = handwritten_seven(N) # ---------------- pixel grid ---------------- pixels = VGroup() pix_lookup = {} for i in range(N): for j in range(N): x = GRID_C[0] - GRID_W / 2 + j * SP y = GRID_C[1] + GRID_W / 2 - i * SP d = Circle( radius=R_PIX, stroke_width=0, fill_color=PIXEL_OFF, fill_opacity=0.55, ).move_to([x, y, 0]) pixels.add(d) pix_lookup[(i, j)] = d pixels grid_frame = RoundedRectangle( width=GRID_W + 0.22, height=GRID_W + 0.22, corner_radius=0.08, stroke_color=GRID_FRAME, stroke_width=1.6, fill_opacity=0.0, ).move_to(GRID_C) grid_frame # ---------------- neurons ---------------- inputs = VGroup(*[ make_neuron(R_IN, NEURON, NEURON_EDGE, NEURON_ON, f"in.{k}") .move_to([X_IN, ys_in[k], 0]) for k in range(10) ]) h1 = VGroup(*[ make_neuron(R_H, NEURON, NEURON_EDGE, HIDDEN_ON, f"h1.{k}") .move_to([X_H1, ys_h1[k], 0]) for k in range(8) ]) h2 = VGroup(*[ make_neuron(R_H, NEURON, NEURON_EDGE, HIDDEN_ON, f"h2.{k}") .move_to([X_H2, ys_h2[k], 0]) for k in range(6) ]) outputs = VGroup(*[ make_neuron(R_OUT, OUT_DIM, OUT_EDGE, GREEN, f"out.{k}") .move_to([X_OUT, ys_out[k], 0]) for k in range(10) ]) ell_in = make_ellipsis(X_IN, (ys_in[4] + ys_in[5]) / 2, tag="ell.in") ell_h1 = make_ellipsis(X_H1, (ys_h1[3] + ys_h1[4]) / 2, tag="ell.h1") # ---------------- synapses ---------------- def connect(src_group, dst_group, tag): lines = VGroup() for a in src_group: for b in dst_group: ln = Line( a.core.get_center(), b.core.get_center(), stroke_color=WIRE, stroke_width=0.7, stroke_opacity=0.28, ) lines.add(ln) lines return lines wires_ih = connect(inputs, h1, "wires.ih") wires_h12 = connect(h1, h2, "wires.h12") wires_ho = connect(h2, outputs, "wires.ho") sample_js = 14 sample_is = [1, 4, 7, 10, 13, 15, 18, 21, 24, 26] sample_wires = VGroup() for k, i_row in enumerate(sample_is): src = pix_lookup[(i_row, sample_js)].get_center() dst = inputs[k].core.get_center() ln = Line( src, dst, stroke_color=WIRE, stroke_width=0.8, stroke_opacity=0.0, ) sample_wires.add(ln) sample_wires # ---------------- labels ---------------- lab_784 = Text("784 inputs", font_size=18, color=MUTED) lab_784.next_to(inputs, UP, buff=0.28) lab_128 = VGroup( Text("128 neurons", font_size=18, color=MUTED), Text("(ReLU)", font_size=16, color=DIM), ).arrange(DOWN, buff=0.06) lab_128.next_to(h1, UP, buff=0.22) lab_64 = VGroup( Text("64 neurons", font_size=18, color=MUTED), Text("(ReLU)", font_size=16, color=DIM), ).arrange(DOWN, buff=0.06) lab_64.next_to(h2, UP, buff=0.22) out_labs = VGroup() for k in range(10): t = Text(str(k), font_size=18, color=MUTED) t.next_to(outputs[k], RIGHT, buff=0.16) out_labs.add(t) # ---------------- training panel ---------------- axes = Axes( x_range=[0, 10, 2], y_range=[0, 2.4, 1], x_length=2.20, y_length=1.22, axis_config={ "color": "#4E5A6A", "stroke_width": 1.7, "include_ticks": False, "tip_length": 0.10, "include_tip": True, }, ) axes lab_loss = Text("Loss", font_size=16, color=MUTED) lab_epoch = Text("Epoch", font_size=16, color=MUTED) lab_loss.next_to(axes, UP, buff=0.14) lab_epoch.next_to(axes, DOWN, buff=0.14) chart_block = VGroup(axes, lab_loss, lab_epoch) panel = RoundedRectangle( width=chart_block.width + 0.50, height=chart_block.height + 0.44, corner_radius=0.12, stroke_color=PANEL_EDGE, stroke_width=1.6, fill_color=PANEL_BG, fill_opacity=0.94, ) panel.move_to([5.78, -2.36, 0]) chart_block.move_to(panel.get_center() + UP * 0.02) panel lab_loss lab_epoch progress = ValueTracker(0.08) def live_curve(): t_end = float(progress.get_value()) t_end = max(0.10, min(10.0, t_end)) curve = axes.plot( loss_fn, x_range=[0.0, t_end], color=CURVE, stroke_width=2.8, ) tip = Dot( axes.c2p(t_end, loss_fn(t_end)), radius=0.045, color=CURVE, ) grp = VGroup(curve, tip) grp return grp curve_draw = always_redraw(live_curve) pred = Text("Predicted: 7", font_size=24, color=GREEN) pred.next_to(outputs, DOWN, buff=0.38) pred.set_x(X_OUT) acc = Text("Trained to 97.9% accuracy", font_size=26, color=GREEN) acc.move_to([-1.35, -3.42, 0]) def flash_copies(wires, color): copies = VGroup() for w in wires: c = w.copy() c.set_stroke(color=color, width=2.4, opacity=0.95) if hasattr(c, "_mathify_xray"): del c._mathify_xray copies.add(c) return copies def ignite(neurons, color, run_time=0.9): anims = [] for n in neurons: anims.append( AnimationGroup( n.core.animate.set_fill(color, 0.96).set_stroke(WHITE, 2.1), n.glow.animate.set_fill(color, 0.40), ) ) return LaggedStart(*anims, lag_ratio=0.08, run_time=run_time) def settle(neurons, fill, edge, glow_c, fill_op=0.90, glow_op=0.14, run_time=0.35): anims = [] for n in neurons: anims.append( AnimationGroup( n.core.animate.set_fill(fill, fill_op).set_stroke(edge, 1.7), n.glow.animate.set_fill(glow_c, glow_op), ) ) return AnimationGroup(*anims, run_time=run_time) # ============================================================ # STORYBOARD (~20 s) # ============================================================ self.play( FadeIn(grid_frame, shift=0.08 * UP), FadeIn(pixels, lag_ratio=0.0008), FadeIn(panel), FadeIn(chart_block), progress.animate.set_value(0.35), run_time=0.9, ) self.add(curve_draw) self.play( LaggedStart( FadeIn(wires_ih, scale=0.98), FadeIn(wires_h12, scale=0.98), FadeIn(wires_ho, scale=0.98), lag_ratio=0.18, ), FadeIn(inputs, shift=0.12 * RIGHT), FadeIn(h1, shift=0.12 * RIGHT), FadeIn(h2, shift=0.12 * RIGHT), FadeIn(outputs, shift=0.12 * RIGHT), FadeIn(ell_in), FadeIn(ell_h1), FadeIn(lab_784, shift=0.08 * UP), FadeIn(lab_128, shift=0.08 * UP), FadeIn(lab_64, shift=0.08 * UP), FadeIn(out_labs, shift=0.08 * RIGHT), progress.animate.set_value(1.1), run_time=1.5, ) self.wait(0.20) reveal = [] for i in range(N): for j in range(N): v = float(img[i, j]) if v < 0.08: reveal.append( pix_lookup[(i, j)].animate.set_fill(PIXEL_OFF, 0.35) ) else: alpha = 0.45 + 0.55 * v col = PIXEL_OFF.interpolate(PIXEL_ON, alpha) reveal.append( pix_lookup[(i, j)].animate.set_fill(col, 0.55 + 0.45 * v) ) self.play( LaggedStart(*reveal, lag_ratio=0.0006), progress.animate.set_value(2.3), run_time=1.8, ) self.wait(0.18) self.play( sample_wires.animate.set_stroke(opacity=0.40), ignite(inputs, NEURON_ON, run_time=1.0), progress.animate.set_value(3.2), run_time=1.1, ) self.play( settle(inputs, "#1E4E6C", NEURON_ON, NEURON_ON, 0.92, 0.16), progress.animate.set_value(3.6), run_time=0.30, ) flash_ih = flash_copies(wires_ih, NEURON_ON) self.play( LaggedStart( *[ShowPassingFlash(w, time_width=0.38) for w in flash_ih], lag_ratio=0.012, run_time=2.4, ), ignite(h1, HIDDEN_ON, run_time=1.5), progress.animate.set_value(5.1), run_time=2.5, ) self.play( settle(h1, "#4A3A14", HIDDEN_ON, HIDDEN_ON, 0.90, 0.16), progress.animate.set_value(5.5), run_time=0.32, ) flash_h12 = flash_copies(wires_h12, HIDDEN_ON) self.play( LaggedStart( *[ShowPassingFlash(w, time_width=0.38) for w in flash_h12], lag_ratio=0.012, run_time=2.2, ), ignite(h2, HIDDEN_ON, run_time=1.4), progress.animate.set_value(7.0), run_time=2.3, ) self.play( settle(h2, "#4A3A14", HIDDEN_ON, HIDDEN_ON, 0.90, 0.16), progress.animate.set_value(7.4), run_time=0.32, ) flash_ho = flash_copies(wires_ho, GREEN) self.play( LaggedStart( *[ShowPassingFlash(w, time_width=0.38) for w in flash_ho], lag_ratio=0.012, run_time=2.3, ), ignite(outputs, "#3A6A58", run_time=1.4), progress.animate.set_value(8.8), run_time=2.4, ) others = VGroup(*[outputs[k] for k in range(10) if k != 7]) winner = outputs[7] win_lab = out_labs[7] self.play( settle(others, OUT_DIM, OUT_EDGE, GREEN, 0.80, 0.0, run_time=0.45), AnimationGroup( winner.core.animate.set_fill(GREEN, 1.0).set_stroke(INK, 2.4), winner.glow.animate.set_fill(GREEN, 0.50), win_lab.animate.set_color(GREEN), ), progress.animate.set_value(9.3), run_time=0.80, ) self.play( FadeIn(pred, shift=0.16 * UP), progress.animate.set_value(9.7), run_time=0.85, ) self.wait(0.70) self.play( FadeIn(acc, shift=0.12 * UP), progress.animate.set_value(10.0), run_time=1.05, ) self.wait(2.40)

Neural Network Forward