""" Score Matching Animation: score field ∇log p(x) + Langevin dynamics @fminxyz Series 2, Post 2 — 5 марта 2026 1080x1080 px, 2 fps, 25 сек (50 frames) """ import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation from matplotlib.colors import LinearSegmentedColormap OUTPUT = "/root/Strategy/content/drafts/score_matching_animation.mp4" FPS = 2 N_FRAMES = 50 # ── Gaussian mixture params ────────────────────────────────────────────────── MU1 = np.array([-1.8, 0.0]) MU2 = np.array([1.8, 0.0]) SIGMA = 0.75 W1, W2 = 0.5, 0.5 rng = np.random.default_rng(42) def gauss(x, y, mu, sigma): return np.exp(-((x - mu[0])**2 + (y - mu[1])**2) / (2 * sigma**2)) def mixture(x, y): return W1 * gauss(x, y, MU1, SIGMA) + W2 * gauss(x, y, MU2, SIGMA) def score(x, y): """∇ log p(x) = ∇p(x) / p(x) (analytically for Gaussian mixture)""" eps = 1e-12 g1 = gauss(x, y, MU1, SIGMA) g2 = gauss(x, y, MU2, SIGMA) p = W1 * g1 + W2 * g2 dpx = W1 * g1 * (-(x - MU1[0]) / SIGMA**2) + W2 * g2 * (-(x - MU2[0]) / SIGMA**2) dpy = W1 * g1 * (-(y - MU1[1]) / SIGMA**2) + W2 * g2 * (-(y - MU2[1]) / SIGMA**2) return dpx / (p + eps), dpy / (p + eps) # ── Grids ──────────────────────────────────────────────────────────────────── x_fine = np.linspace(-4, 4, 200) y_fine = np.linspace(-3, 3, 150) Xf, Yf = np.meshgrid(x_fine, y_fine) P = mixture(Xf, Yf) x_q = np.linspace(-3.5, 3.5, 18) y_q = np.linspace(-2.5, 2.5, 14) Xq, Yq = np.meshgrid(x_q, y_q) Sx, Sy = score(Xq, Yq) S_mag = np.sqrt(Sx**2 + Sy**2 + 1e-12) # Clip and normalize for display S_cap = np.clip(S_mag, 0, 6) Sx_n = Sx / S_mag * S_cap / 6 Sy_n = Sy / S_mag * S_cap / 6 # ── Langevin dynamics simulation ───────────────────────────────────────────── N_PART = 18 # Start particles spread randomly pts = rng.uniform(-3.5, 3.5, (N_PART, 2)) pts[:, 1] = rng.uniform(-2.5, 2.5, N_PART) ALPHA = 0.5 # step size NOISE_STD = 0.15 trajectories = [pts.copy()] for _ in range(N_FRAMES - 30): sx_p, sy_p = score(pts[:, 0], pts[:, 1]) pts[:, 0] = pts[:, 0] + ALPHA * sx_p + rng.normal(0, NOISE_STD, N_PART) pts[:, 1] = pts[:, 1] + ALPHA * sy_p + rng.normal(0, NOISE_STD, N_PART) pts[:, 0] = np.clip(pts[:, 0], -4, 4) pts[:, 1] = np.clip(pts[:, 1], -3, 3) trajectories.append(pts.copy()) # ── Color maps ─────────────────────────────────────────────────────────────── bg_color = '#0d0d1a' cmap_dist = LinearSegmentedColormap.from_list( 'dist', ['#0d0d1a', '#1a1a4e', '#2244aa', '#4488ff', '#88ccff'], N=256 ) # ── Figure setup ───────────────────────────────────────────────────────────── DPI = 108 # 108 * 10 = 1080 fig, ax = plt.subplots(figsize=(10, 10), dpi=DPI, facecolor=bg_color) ax.set_facecolor(bg_color) def draw_frame(i): ax.clear() ax.set_facecolor(bg_color) ax.set_xlim(-4, 4) ax.set_ylim(-3, 3) ax.set_aspect('equal') ax.axis('off') # ── Phase logic ────────────────────────────────────────────────────────── # Phase 1: frames 0-14 → show distribution # Phase 2: frames 15-29 → reveal score field # Phase 3: frames 30-49 → Langevin dynamics # Always: distribution background dist_alpha = min(1.0, (i + 1) / 8) levels = np.linspace(0.005, P.max() * 0.98, 15) ax.contourf(Xf, Yf, P, levels=levels, cmap=cmap_dist, alpha=dist_alpha) ax.contour(Xf, Yf, P, levels=levels[::3], colors='#4488ff', alpha=0.25, linewidths=0.6) if i < 15: # Phase 1: distribution only fade = min(1.0, (i + 1) / 6) ax.text(0, -2.6, 'p(x) — смесь двух гауссиан', ha='center', fontsize=15, color='#8899cc', fontfamily='monospace', alpha=fade) ax.text(0, 2.65, 'Score Matching: ∇log p(x)', ha='center', fontsize=17, fontweight='bold', color='white', fontfamily='monospace', alpha=fade) elif i < 30: # Phase 2: score field appears t = (i - 15) / 14 q_alpha = min(t * 1.5, 0.9) ax.quiver(Xq, Yq, Sx_n, Sy_n, color='#00e57a', alpha=q_alpha, scale=16, headwidth=4, headlength=5, width=0.004, zorder=5) ax.text(0, -2.6, '∇log p(x) — каждая стрелка ведёт к моде', ha='center', fontsize=14, color='#00e57a', fontfamily='monospace', alpha=q_alpha) ax.text(0, 2.65, 'Score: ∇log p(x)', ha='center', fontsize=17, fontweight='bold', color='white', fontfamily='monospace') else: # Phase 3: Langevin dynamics j = i - 30 # frame index in trajectory j = min(j, len(trajectories) - 1) ax.quiver(Xq, Yq, Sx_n, Sy_n, color='#00e57a', alpha=0.25, scale=16, headwidth=4, headlength=5, width=0.003, zorder=4) # Draw trajectory tails tail_len = min(j + 1, 8) for p_idx in range(N_PART): if j > 0: t_start = max(0, j - tail_len + 1) traj = np.array([trajectories[k][p_idx] for k in range(t_start, j + 1)]) ax.plot(traj[:, 0], traj[:, 1], '-', color='#ff7700', alpha=0.35, linewidth=1.0, zorder=5) pos = trajectories[j][p_idx] ax.plot(pos[0], pos[1], 'o', color='#ff9933', markersize=8, alpha=0.92, zorder=6, markeredgecolor='white', markeredgewidth=0.5) ax.text(0, -2.6, 'Ланжевен: xₜ₊₁ = xₜ + α·∇log p(xₜ) + √(2α)·ξ', ha='center', fontsize=12, color='#ff9933', fontfamily='monospace') ax.text(0, 2.65, 'Langevin Dynamics → Sampling', ha='center', fontsize=17, fontweight='bold', color='white', fontfamily='monospace') # Step counter ax.text(3.8, -2.8, f't={i:02d}', ha='right', fontsize=11, color='#445566', fontfamily='monospace') anim = animation.FuncAnimation(fig, draw_frame, frames=N_FRAMES, interval=1000 // FPS) anim.save(OUTPUT, writer='ffmpeg', fps=FPS, dpi=DPI, extra_args=['-vcodec', 'libx264', '-pix_fmt', 'yuv420p', '-crf', '22', '-preset', 'fast']) plt.close() print(f"Saved: {OUTPUT}")