"""Generate Plotly HTML figures (CDN, self-contained data) for the logbook.""" import json, math, sys import plotly.graph_objects as go def fig_noise(): d = json.load(open("noise_audit_results.json")) r = d["rows"] B = [x["B"] for x in r] fig = go.Figure() fig.add_scatter(x=B, y=[x["N3_median"] for x in r], mode="lines+markers", name="measured N₃ (median)") fig.add_scatter(x=B, y=[x["pred_Eq1"] for x in r], mode="lines+markers", name="(B/d_model)·√(d_k log m) [Eq.1, up to const]", line=dict(dash="dash")) fig.add_scatter(x=B, y=[x["signal"] for x in r], mode="lines+markers", name="true-edge signal (≈ d_k, block-independent)", line=dict(dash="dot")) fig.add_hline(y=d["d_k"] / 2, line=dict(color="red", dash="dot"), annotation_text="τ = d_k/2 (separation fails above)") fig.update_layout(title=f"Claim 3 — superposition noise N₃(B) grows linearly in block size B " f"(m={d['m']}, d_model={d['d_model']}, d_k={d['d_k']})", xaxis_title="block size B (= targets served by a head)", yaxis_title="score", xaxis_type="log", yaxis_type="log", template="plotly_white", legend=dict(y=0.02, x=0.02)) fig.write_html("fig_claim3.html", include_plotlyjs="cdn") # raw csv with open("fig_claim3.csv", "w") as f: f.write("B,signal,N3_median,N3_max,pred_Eq1\n") for x in r: f.write(f"{x['B']},{x['signal']:.2f},{x['N3_median']:.2f},{x['N3_max']:.2f},{x['pred_Eq1']:.2f}\n") print("wrote fig_claim3.html / .csv") def fig_claim4(): d = json.load(open("results_base.json")) S = [r for r in d["summary"] if "D_K_star" in r] x = [r["x"] for r in S]; y = [r["D_K_star"] for r in S] slope = d.get("fit", {}).get("slope"); r2 = d.get("fit", {}).get("r2") fig = go.Figure() fig.add_scatter(x=x, y=y, mode="markers+text", text=[f"({r['m']},{r['d_model']})" for r in S], textposition="top center", name="D_K* (measured)", marker=dict(size=10, color=["red" if r["d_model"] == 16 and r["m"] > 64 else "royalblue" for r in S])) xs = [0, max(x) * 1.05] if slope: fig.add_scatter(x=xs, y=[slope * v for v in xs], mode="lines", name=f"fit: D_K*={slope:.2f}·x (R²={r2:.3f})", line=dict(dash="dash")) fig.update_layout(title="Claim 4 — empirical capacity law D_K* vs m·log(m)/d_model " "(red = d_model=16, m>64 outliers)", xaxis_title="x = m·log m / d_model", yaxis_title="D_K* (min key dim for 0.99 F1)", template="plotly_white") fig.write_html("fig_claim4.html", include_plotlyjs="cdn") with open("fig_claim4.csv", "w") as f: f.write("m,d_model,x,D_K_star,h_star,d_k_star\n") for r in S: f.write(f"{r['m']},{r['d_model']},{r['x']:.2f},{r['D_K_star']},{r.get('h_star')},{r.get('d_k_star')}\n") print(f"wrote fig_claim4.html / .csv (n={len(S)})") def fig_claim5(): d = json.load(open("results_gpt2.json")) agg = {} for r in d["records"]: agg.setdefault((r["D_K"], r["h"]), []).append(r["test_acc"]) DKs = sorted({k[0] for k in agg}); hs = sorted({k[1] for k in agg}) fig = go.Figure() for h in hs: xs = [dk for dk in DKs if (dk, h) in agg] ys = [sum(agg[(dk, h)]) / len(agg[(dk, h)]) for dk in xs] fig.add_scatter(x=xs, y=ys, mode="lines+markers", name=f"h={h}") fig.update_layout(title="Claim 5 — GPT-2 block: test accuracy vs D_K by head count " f"(m={d['config']['m']}, d_model=768, ℓ={d['config']['ell']})", xaxis_title="D_K (total key dim)", yaxis_title="test accuracy", template="plotly_white") fig.write_html("fig_claim5.html", include_plotlyjs="cdn") with open("fig_claim5.csv", "w") as f: f.write("D_K,h,mean_test_acc,n\n") for (dk, h), v in sorted(agg.items()): f.write(f"{dk},{h},{sum(v)/len(v):.4f},{len(v)}\n") print("wrote fig_claim5.html / .csv") def fig_claim6(): d = json.load(open("results_claim6.json")) fig = go.Figure() for (m, dm) in sorted({(r["m"], r["d_model"]) for r in d}): rows = [r for r in d if r["m"] == m and r["d_model"] == dm] rows.sort(key=lambda r: r["D_K"]) xs = [r["D_K"] for r in rows] for tag, name in [("t16e16", "train16/eval16"), ("t32e32", "train32/eval32"), ("t16e32", "train16/eval32")]: fig.add_scatter(x=xs, y=[r[tag] for r in rows], mode="lines+markers", name=f"({m},{dm}) {name}") fig.update_layout(title="Claim 6 — capacity threshold vs context length ℓ∈{16,32} and length generalization", xaxis_title="D_K", yaxis_title="test micro-F1", template="plotly_white") fig.write_html("fig_claim6.html", include_plotlyjs="cdn") print("wrote fig_claim6.html") if __name__ == "__main__": which = sys.argv[1] if len(sys.argv) > 1 else "all" fns = {"noise": fig_noise, "claim4": fig_claim4, "claim5": fig_claim5, "claim6": fig_claim6} if which == "all": for f in fns.values(): try: f() except Exception as e: print("skip", f.__name__, e) else: fns[which]()