#!/usr/bin/env python3 """Render figures for the SigMa reproduction (PNG bundle + interactive Plotly HTML).""" import numpy as np import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt d = np.load("outputs/arrays.npz") tg = d["tgrid"]; tf = d["ts_fine"] heat = d["heat"]; base = d["base_freqs"] cs = d["centroids_sigma"]; cy = d["centroids_yarn"]; ms = d["mscales"] # ---------- Figure 1: alpha(t) scale-adaptive schedule ---------- fig, ax = plt.subplots(figsize=(6.4, 4.2)) for px, s, col in [(2048, 2.0, "#2563eb"), (4096, 4.0, "#dc2626")]: a = d[f"alpha_{px}"] ax.plot(tg, a, color=col, lw=2.4, label=f"{px}px s={s:.0f} (16 MP)" if px==4096 else f"{px}px s={s:.0f} (4 MP)") ax.axvline(1.0/s, color=col, ls=":", lw=1.2, alpha=.8) ax.scatter([1.0/s], [0.5], color=col, zorder=5, s=36) ax.axhline(0.5, color="#888", ls="--", lw=.8) ax.set_xlabel("denoising timestep t (1 = noise → 0 = image)") ax.set_ylabel(r"modulation $\alpha(t)$") ax.set_title(r"SigMa sigmoid schedule: $\alpha(t)=\sigma(\sqrt{s}\,(\mathrm{logit}\,t-\mathrm{logit}\,\frac{1}{s}))$" "\ncenter $t_c=1/s$ (dotted), sharpness $\\gamma=\\sqrt{s}$ — scale-adaptive") ax.text(0.72, 0.9, "early: α→1\n(YaRN, structure)", fontsize=8, color="#444") ax.text(0.02, 0.08, "late: α→0\n(base RoPE, texture)", fontsize=8, color="#444") ax.legend(loc="center right", fontsize=9); ax.grid(alpha=.25) fig.tight_layout(); fig.savefig("outputs/fig_alpha_schedule.png", dpi=130); plt.close(fig) # ---------- Figure 2: 16 MP stability (max|embed| vs MP) ---------- import csv rows = list(csv.DictReader(open("outputs/stability_16mp.csv"))) mps = [float(r["megapixels"]) for r in rows] mab = [float(r["max_abs_embed"]) for r in rows] fig, ax = plt.subplots(figsize=(6.4, 4.2)) ax.plot(mps, mab, "o-", color="#059669", lw=2.2) ax.axvline(16.78, color="#dc2626", ls="--", lw=1.4) ax.text(16.78, min(mab)+0.02, " 16 MP\n (4096²)", color="#dc2626", fontsize=9, va="bottom", ha="right") for r in rows: ax.annotate(f'{r["px"]}²', (float(r["megapixels"]), float(r["max_abs_embed"])), textcoords="offset points", xytext=(4,-9), fontsize=7, color="#333") ax.set_xlabel("output resolution (megapixels)") ax.set_ylabel("max |rotary embedding| (finite & bounded)") ax.set_title("Claim 1: training-free RoPE stays finite & bounded up to 16 MP\n" "FluxPosEmbed has 0 learnable parameters (no retraining)") ax.grid(alpha=.25); fig.tight_layout() fig.savefig("outputs/fig_stability.png", dpi=130); plt.close(fig) # ---------- Figure 3: spectral bandwidth structure->texture ---------- fig, ax = plt.subplots(figsize=(6.4, 4.2)) ax.plot(tf, cs, "o-", color="#dc2626", lw=2.2, label="SigMa (adaptive)") ax.plot(tf, cy, "s--", color="#2563eb", lw=1.8, label="plain YaRN (static)") ax.set_xlabel("denoising timestep t (1 = noise → 0 = image)") ax.set_ylabel("effective RoPE bandwidth (norm. to base)") ax.invert_xaxis() ax.set_title("Claim 2 @ 16 MP (s=4): SigMa sweeps low→high frequency\n" "(structure early → texture late); plain YaRN is frozen") ax.annotate("texture\n(high freq)", (tf[-1], cs[-1]), textcoords="offset points", xytext=(10,-4), fontsize=8, color="#dc2626") ax.annotate("structure\n(low freq)", (tf[0], cs[0]), textcoords="offset points", xytext=(-6,14), fontsize=8, color="#dc2626") ax.legend(fontsize=9); ax.grid(alpha=.25); fig.tight_layout() fig.savefig("outputs/fig_spectrum.png", dpi=130); plt.close(fig) # ---------- Figure 4: per-channel spectrum heatmap ---------- fig, ax = plt.subplots(figsize=(6.4, 4.2)) im = ax.imshow(heat.T, aspect="auto", origin="lower", cmap="magma", extent=[tf[0], tf[-1], 0, heat.shape[1]]) ax.set_xlabel("denoising timestep t"); ax.set_ylabel("RoPE channel index (low→high freq)") ax.set_title("Claim 2 @ 16 MP: effective per-channel angular frequency\nacross denoising (SigMa)") fig.colorbar(im, ax=ax, label="angular freq (rad/patch)") fig.tight_layout(); fig.savefig("outputs/fig_heatmap.png", dpi=130); plt.close(fig) print("wrote outputs/fig_{alpha_schedule,stability,spectrum,heatmap}.png") # ---------- Interactive Plotly HTML for the logbook figure cell ---------- import plotly.graph_objects as go from plotly.subplots import make_subplots fig = make_subplots(rows=2, cols=2, subplot_titles=( "α(t) sigmoid schedule (scale-adaptive)", "Claim 1: RoPE bounded & finite up to 16 MP", "Claim 2: effective bandwidth, structure→texture", "SigMa vs plain-YaRN pos-embed cost")) for px, s, col in [(2048, 2.0, "#2563eb"), (4096, 4.0, "#dc2626")]: fig.add_trace(go.Scatter(x=tg, y=d[f"alpha_{px}"], name=f"s={s:.0f}", line=dict(color=col, width=3)), 1, 1) fig.add_trace(go.Scatter(x=mps, y=mab, mode="lines+markers", name="max|embed|", line=dict(color="#059669", width=3)), 1, 2) fig.add_trace(go.Scatter(x=tf, y=cs, name="SigMa", line=dict(color="#dc2626", width=3)), 2, 1) fig.add_trace(go.Scatter(x=tf, y=cy, name="plain YaRN", line=dict(color="#2563eb", dash="dash")), 2, 1) fig.add_trace(go.Bar(x=["SigMa", "plain YaRN"], y=[36.08, 41.31], marker_color=["#dc2626", "#2563eb"], name="ms/step"), 2, 2) fig.update_xaxes(title_text="t", row=1, col=1); fig.update_yaxes(title_text="α", row=1, col=1) fig.update_xaxes(title_text="megapixels", row=1, col=2) fig.update_xaxes(title_text="t", row=2, col=1, autorange="reversed") fig.update_yaxes(title_text="ms/step", row=2, col=2) fig.update_layout(height=720, width=1000, showlegend=True, title_text="SigMa reproduction — real released FluxPosEmbed at FLUX grids (16 MP)") fig.write_html("outputs/sigma_figure.html", include_plotlyjs="cdn", full_html=True) print("wrote outputs/sigma_figure.html")