| |
| """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"] |
|
|
| |
| 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) |
|
|
| |
| 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) |
|
|
| |
| 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) |
|
|
| |
| 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") |
|
|
| |
| 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") |
|
|
