code/figures.py

"""Build the Plotly figures (HTML + raw CSV) for each claim page from summary.json."""

import csv
import json
import os

import numpy as np
import plotly.graph_objects as go

HERE = os.path.dirname(os.path.abspath(__file__))
RES = os.path.join(HERE, "results")
FIG = os.path.join(HERE, "figs")
os.makedirs(FIG, exist_ok=True)

S = json.load(open(os.path.join(RES, "summary.json")))

LAYOUT = dict(
    template="plotly_white", width=760, height=460,
    margin=dict(l=70, r=30, t=60, b=60),
    font=dict(family="Inter, system-ui, sans-serif", size=13),
    legend=dict(bgcolor="rgba(255,255,255,0.75)", bordercolor="#d0d0d0",
                borderwidth=1),
)
PAL = ["#3B6FE0", "#E07B39", "#2E9E6B", "#B5446E", "#7A5AC6", "#8A8F98"]


# Poster cards need rasters, not interactive HTML. Export at 3x so a ~760px
# figure lands ~2280px wide -- above posterly's 1.5x asset floor for a print card.
PNG = os.environ.get("CL_FIG_PNG", "") == "1"


def save(fig, name, rows, header):
    fig.update_layout(**LAYOUT)
    fig.write_html(os.path.join(FIG, name + ".html"), include_plotlyjs="cdn")
    if PNG:
        fig.write_image(os.path.join(FIG, name + ".png"), scale=3)
    with open(os.path.join(FIG, name + ".csv"), "w", newline="") as f:
        w = csv.writer(f)
        w.writerow(header)
        w.writerows(rows)
    print("wrote", name)


def ref(x, y0, slope, x0=None):
    """power-law reference line through (x0, y0)."""
    x = np.asarray(x, float)
    x0 = x0 if x0 is not None else x[0]
    return y0 * (x / x0) ** slope


# ---------------------------------------------------------------- Claim 1
if "claim1" in S:
    c = S["claim1"]

    # F1: finite-width remainder vs m
    r = c["remainder_vs_m"]
    m = np.array(r["m"], float)
    fig = go.Figure()
    fig.add_scatter(x=m, y=r["remainder"], mode="markers+lines", name="|measured − first-order|",
                    line=dict(color=PAL[0], width=2), marker=dict(size=9))
    fig.add_scatter(x=m, y=ref(m, r["remainder"][0], -0.5),
                    mode="lines", name="m<sup>−1/2</sup> reference (Thm 1, 3rd term)",
                    line=dict(color=PAL[0], width=1.5, dash="dash"))
    fig.add_scatter(x=m, y=r["remainder_M"], mode="markers+lines",
                    name="residual after using empirical (1/m)WᵀW",
                    line=dict(color=PAL[2], width=2), marker=dict(size=9, symbol="square"))
    fig.add_scatter(x=m, y=r["first_order"], mode="lines",
                    name="first-order (kernel) term — m-independent",
                    line=dict(color=PAL[5], width=1.5, dash="dot"))
    fig.update_xaxes(type="log", title="hidden width m")
    fig.update_yaxes(type="log", title="|train-time forgetting| contribution")
    fig.update_layout(title=f"Finite-width remainder decays as m<sup>{r['slope']:.2f}</sup> "
                            f"(Thm 1 predicts −0.5)")
    save(fig, "c1_remainder_vs_m",
         list(zip(r["m"], r["remainder"], r["remainder_M"], r["first_order"])),
         ["m", "abs_remainder", "abs_remainder_empiricalM", "abs_first_order"])

    # F2: sampling vs population part of the first-order term, vs n
    r = c["vs_n"]
    n = np.array(r["n"], float)
    fig = go.Figure()
    fig.add_scatter(x=n, y=r["fo_fluct"], mode="markers+lines",
                    name="sampling part → ηT√(K−k)/(d√n)",
                    line=dict(color=PAL[0], width=2), marker=dict(size=9))
    fig.add_scatter(x=n, y=ref(n, r["fo_fluct"][0], -0.5), mode="lines",
                    name="n<sup>−1/2</sup> reference",
                    line=dict(color=PAL[0], width=1.5, dash="dash"))
    fig.add_scatter(x=n, y=r["fo_mean"], mode="markers+lines",
                    name="population part → ηT√(K−k)/(d²·polylog d)  [n-independent floor]",
                    line=dict(color=PAL[1], width=2), marker=dict(size=9, symbol="square"))
    fig.add_scatter(x=n, y=r["measured"], mode="markers",
                    name="total measured forgetting",
                    marker=dict(size=7, color=PAL[5], symbol="x"))
    fig.update_xaxes(type="log", title="samples per task n")
    fig.update_yaxes(type="log", title="|contribution to F<sup>tr</sup>|")
    fig.update_layout(title=f"Sampling term ∝ n<sup>{r['slope_fluct']:.2f}</sup>; "
                            f"population term flat (slope {r['slope_mean']:+.2f})")
    save(fig, "c1_terms_vs_n",
         list(zip(r["n"], r["fo_fluct"], r["fo_mean"], r["measured"])),
         ["n", "abs_sampling_term", "abs_population_term", "abs_measured"])

    # F3: sqrt(K-k)
    r = c["vs_Kk"]
    x = np.array(r["Kk"], float)
    fig = go.Figure()
    fig.add_scatter(x=x, y=r["forget"], error_y=dict(type="data", array=r["sem"]),
                    mode="markers+lines", name="measured |F<sup>tr</sup><sub>k,K</sub>|",
                    line=dict(color=PAL[0], width=2), marker=dict(size=10))
    fig.add_scatter(x=x, y=ref(x, r["forget"][0], 0.5), mode="lines",
                    name="√(K−k) reference", line=dict(color=PAL[1], width=2, dash="dash"))
    fig.update_xaxes(type="log", title="number of subsequent tasks K − k")
    fig.update_yaxes(type="log", title="|train-time forgetting|")
    fig.update_layout(title=f"Forgetting ∝ (K−k)<sup>{r['slope']:.2f}</sup> "
                            f"(Thm 1 predicts 0.50)")
    save(fig, "c1_vs_Kk", list(zip(r["Kk"], r["forget"], r["sem"])),
         ["K_minus_k", "abs_forget", "sem"])

    # F4: orthogonality control
    r = c["overlap_control"]
    fig = go.Figure()
    fig.add_scatter(x=r["overlap"], y=r["forget"],
                    error_y=dict(type="data", array=r["sem"]),
                    mode="markers+lines", line=dict(color=PAL[3], width=2),
                    marker=dict(size=10), name="|F<sup>tr</sup><sub>1,K</sub>|")
    fig.update_xaxes(title="cosine overlap between task-1 and later-task means")
    fig.update_yaxes(type="log", title="|train-time forgetting|")
    fig.update_layout(title="Control: relaxing the orthogonality assumption of Thm 1",
                      showlegend=False)
    save(fig, "c1_overlap_control", list(zip(r["overlap"], r["forget"], r["sem"])),
         ["mean_overlap", "abs_forget", "sem"])

# ---------------------------------------------------------------- Claim 1 (GD)
if "claim1_gd" in S:
    c = S["claim1_gd"]
    fig = go.Figure()
    names = {"n": "vs n (samples)", "m": "vs m (width)",
             "etaT": "vs T (horizon, η fixed)", "eta": "vs η (T fixed)"}
    rows = []
    for i, (tag, lab) in enumerate(names.items()):
        if tag not in c:
            continue
        d = c[tag]
        x = np.array(d["x"], float)
        y = np.array(d["train_forget"], float)
        fig.add_scatter(x=x / x[0], y=y, error_y=dict(type="data", array=d["sem"]),
                        mode="markers+lines", name=f"{lab}  (slope {d['slope']:+.2f})",
                        line=dict(color=PAL[i], width=2), marker=dict(size=9))
        rows += [[tag, a, b, s] for a, b, s in zip(d["x"], d["train_forget"], d["sem"])]
    fig.update_xaxes(type="log", title="parameter, relative to smallest value in sweep")
    fig.update_yaxes(type="log", title="|train-time forgetting| of task 1")
    fig.update_layout(title="Full GD (no linearization): forgetting vs each Thm-1 parameter")
    save(fig, "c1_gd_sweeps", rows, ["sweep", "x", "abs_forget", "sem"])

# ---------------------------------------------------------------- Claim 2
if "claim2" in S:
    c = S["claim2"]
    lab = {"prescribed": "Thm 1 regime: n=Θ(d²K), ηT=Θ(d²), m large",
           "fixed_n": "control: n held constant (violates n=Θ̃(d²K))",
           "long_train": "control: ηT ∝ d³ (violates ηT=Θ(d²))",
           "small_m": "control: m = 300 (violates the width condition)"}
    fig = go.Figure()
    rows = []
    for i, (k, v) in enumerate(c.items()):
        fig.add_scatter(x=v["d"], y=v["forget"], error_y=dict(type="data", array=v["sem"]),
                        mode="markers+lines", name=f"{lab.get(k,k)}  (slope {v['slope']:+.2f})",
                        line=dict(color=PAL[i], width=2), marker=dict(size=10))
        rows += [[k, a, b, s] for a, b, s in zip(v["d"], v["forget"], v["sem"])]
    fig.update_xaxes(type="log", title="dimension d")
    fig.update_yaxes(type="log", title="|train-time forgetting| of task 1")
    fig.update_layout(title="Claim 2: forgetting → 0 with d only inside the prescribed regime")
    save(fig, "c2_regime", rows, ["variant", "d", "abs_forget", "sem"])

# ---------------------------------------------------------------- Claim 3
if "claim3" in S:
    c = S["claim3"]
    # The error is identically 0 at every configuration, so a bar chart of it
    # carries no information.  What separates the configurations is the *loss*
    # half of Theorem 2, which only becomes small at the prescribed horizon.
    fig = go.Figure()
    rows = []
    for i, etaT in enumerate(sorted({rec["etaT"] for rec in c})):
        g = [rec for rec in c if rec["etaT"] == etaT]
        d2 = g[0]["etaT_over_d2"]
        fig.add_bar(x=[f"n={r['n']}<br>m={r['m']}" for r in g],
                    y=[r["train_loss_end_max"] for r in g],
                    name=f"ηT={etaT:.0f} = {d2:.2f}·d²",
                    marker_color=PAL[i % len(PAL)])
    for rec in c:
        rows.append([rec["eta"], rec["etaT"], rec["n"], rec["m"],
                     rec["train_err_end_max"], rec["test_err_end_max"],
                     rec["train_loss_end_max"], rec["test_loss_end_max"]])
    fig.add_hline(y=0.0, line=dict(color=PAL[5], width=1))
    fig.update_yaxes(title="max over K tasks of train loss at w<sub>K</sub>")
    fig.update_layout(
        title=("Claim 3: misclassification error is 0 everywhere (all 32 runs);<br>"
               "the <i>loss</i> half of Thm 2 is what needs ηT = Θ(d²)"),
        barmode="group")
    save(fig, "c3_loss_vs_horizon", rows,
         ["eta", "etaT", "n", "m", "max_train_err", "max_test_err",
          "max_train_loss", "max_test_loss"])

# ------------------------------------------- Claim 3 control: cluster noise
if "claim3_noise" in S:
    c = S["claim3_noise"]
    rws = c["rows"]
    sc = [r["sigma_c"] for r in rws]
    fig = go.Figure()
    for j, (key, lab, sym) in enumerate([
            ("train_err_max", "max train error at w<sub>K</sub>", "circle"),
            ("test_err_max", "max test error at w<sub>K</sub>", "square"),
            ("train_err_own_max", "max error on own task at w<sub>k</sub>", "diamond")]):
        fig.add_scatter(x=sc, y=[r[key] for r in rws], mode="markers+lines",
                        name=lab, line=dict(color=PAL[j], width=2),
                        marker=dict(size=9, symbol=sym))
    fig.add_hline(y=0.5, line=dict(color=PAL[5], width=1, dash="dot"),
                  annotation_text="chance", annotation_position="top left")
    fig.add_vline(x=0.1, line=dict(color=PAL[4], width=1.5, dash="dash"),
                  annotation_text="σ_c prescribed by Thm 1/2",
                  annotation_position="top right")
    fig.update_xaxes(title="cluster noise coefficient σ_c   (σ = σ_c/√d)", type="log")
    fig.update_yaxes(title="misclassification error", range=[-0.03, 0.58])
    fig.update_layout(
        title=(f"Claim 3 control: relaxing Theorem 2's noise condition "
               f"(d={c['d']}, m={c['m']}, n={c['n']}, K={c['K']}, ηT={c['eta']*c['T']:.0f})"))
    save(fig, "c3_noise_control",
         [[r["sigma_c"], r["seeds"], r["train_err_max"], r["test_err_max"],
           r["train_err_own_max"], r["train_loss_max"]] for r in rws],
         ["sigma_c", "seeds", "max_train_err", "max_test_err",
          "max_own_task_err", "max_train_loss"])

# ---------------------------------------------------------------- Claims 4/5
if "claim45" in S:
    c = S["claim45"]
    if "n" in c:
        d = c["n"]
        x = np.array(d["x"], float)
        g = np.abs(np.array(d["gap"]))
        fig = go.Figure()
        fig.add_scatter(x=x, y=g, error_y=dict(type="data", array=d["sem"]),
                        mode="markers+lines", name="measured 𝔼[F<sub>k</sub>(w<sub>K</sub>) − F̂<sub>k</sub>(w<sub>K</sub>)]",
                        line=dict(color=PAL[0], width=2), marker=dict(size=10))
        fig.add_scatter(x=x, y=ref(x, g[0], -1.0), mode="lines",
                        name="1/n reference (Thm 3)",
                        line=dict(color=PAL[1], width=2, dash="dash"))
        fig.update_xaxes(type="log", title="samples per task n")
        fig.update_yaxes(type="log", title="delayed generalization gap")
        fig.update_layout(title=f"Claim 4: gap ∝ n<sup>{d['slope_gap']:.2f}</sup> "
                                f"(Thm 3 predicts −1)")
        save(fig, "c4_gap_vs_n", list(zip(d["x"], d["gap"], d["sem"], d["rhs_thm3"])),
             ["n", "gen_gap", "sem", "rhs_thm3_unscaled"])

    if "T" in c:
        d = c["T"]
        x = np.array(d["x"], float)
        g = np.abs(np.array(d["gap"]))
        b3 = np.array(d["rhs_thm3"]) * d["c3"]
        b4 = np.array(d["rhs_thm4"]) * d["c4"]
        fig = go.Figure()
        fig.add_scatter(x=x, y=g, error_y=dict(type="data", array=d["sem"]),
                        mode="markers+lines", name="measured gap",
                        line=dict(color=PAL[0], width=2.5), marker=dict(size=10))
        fig.add_scatter(x=x, y=b3, mode="markers+lines",
                        name=f"Thm 3 bound ∝ ηT (fitted slope {d['slope_thm3']:+.2f})",
                        line=dict(color=PAL[1], width=2, dash="dash"), marker=dict(size=8))
        fig.add_scatter(x=x, y=b4, mode="markers+lines",
                        name=f"Thm 4 bound ∝ Σ<sub>t</sub>F̂<sub>k</sub> (fitted slope {d['slope_thm4']:+.2f})",
                        line=dict(color=PAL[2], width=2, dash="dot"), marker=dict(size=8))
        fig.update_xaxes(type="log", title="iterations per task T")
        fig.update_yaxes(type="log", title="delayed generalization gap / bound")
        fig.update_layout(title="Claim 5: Thm 4's bound grows far slower in T than Thm 3's")
        save(fig, "c5_bounds_vs_T",
             list(zip(d["x"], d["gap"], d["rhs_thm3"], d["rhs_thm4"], d["cum_train_loss"])),
             ["T", "gen_gap", "rhs_thm3_unscaled", "rhs_thm4_unscaled",
              "cum_train_loss_task1"])

# ---------------------------------------------------------------- Claim 6
if "claim6" in S:
    c = S["claim6"]
    z = np.array(c["train_forget"])
    fig = go.Figure(go.Heatmap(
        z=np.log10(np.maximum(z, 1e-12)),
        x=[str(m) for m in c["m"]], y=[str(n) for n in c["n"]],
        colorscale="Viridis_r",
        colorbar=dict(title="log₁₀|F<sup>tr</sup>|"),
        text=[[f"{v:.2e}" for v in row] for row in z],
        texttemplate="%{text}", textfont=dict(size=10)))
    fig.update_xaxes(title="hidden width m")
    fig.update_yaxes(title="samples per task n")
    fig.update_layout(title="Claim 6: train-time forgetting over the joint (n, m) grid")
    rows = [[c["n"][i], c["m"][j], c["train_forget"][i][j], c["test_forget"][i][j],
             c["gen_gap"][i][j]] for i in range(len(c["n"])) for j in range(len(c["m"]))]
    save(fig, "c6_joint_grid", rows, ["n", "m", "abs_train_forget",
                                      "abs_test_forget", "gen_gap"])

    # The claim is about the grid's *shape*, which the marginal slopes read off
    # directly: a flat slope along one axis is the plateau an additive bound
    # predicts when that axis' term is not the dominant one.
    if "marginal_slopes" in c:
        mg = c["marginal_slopes"]
        fig = go.Figure()
        fig.add_scatter(
            x=[r["m"] for r in mg["vs_n"]], y=[r["slope"] for r in mg["vs_n"]],
            error_y=dict(type="data", array=[r["slope_err"] for r in mg["vs_n"]]),
            mode="markers+lines", name="d log|F<sup>tr</sup>| / d log n  (at fixed m)",
            line=dict(color=PAL[0], width=2), marker=dict(size=10))
        fig.add_scatter(
            x=[r["n"] for r in mg["vs_m"]], y=[r["slope"] for r in mg["vs_m"]],
            error_y=dict(type="data", array=[r["slope_err"] for r in mg["vs_m"]]),
            mode="markers+lines", name="d log|F<sup>tr</sup>| / d log m  (at fixed n)",
            line=dict(color=PAL[1], width=2), marker=dict(size=10, symbol="square"))
        fig.add_hline(y=0.0, line=dict(color="#444", width=1),
                      annotation_text="flat = this axis alone does nothing")
        fig.add_hline(y=-0.5, line=dict(color=PAL[5], width=1, dash="dash"),
                      annotation_text="−1/2 (Thm 1 n-term)",
                      annotation_position="bottom right")
        fig.update_xaxes(title="the other axis' value (m for the n-slopes, n for the m-slopes)",
                         type="log")
        fig.update_yaxes(title="marginal log-log slope")
        fig.update_layout(title=("Claim 6: n reduces forgetting at every width; "
                                 "m alone does not move it"))
        save(fig, "c6_marginal_slopes",
             [["vs_n", r["m"], r["slope"], r["slope_err"]] for r in mg["vs_n"]]
             + [["vs_m", r["n"], r["slope"], r["slope_err"]] for r in mg["vs_m"]],
             ["direction", "other_axis_value", "slope", "slope_err"])

# ------------------------------------------------- Claim 2 (eta*T consistency)
if "claim2_etaT" in S and S["claim2_etaT"].get("points"):
    c = S["claim2_etaT"]
    pts = c["points"]
    ds = sorted({p["d"] for p in pts})
    fig = go.Figure()
    for i, dd in enumerate(ds):
        sel = sorted([p for p in pts if p["d"] == dd], key=lambda p: p["m"])
        fig.add_scatter(x=[p["m"] for p in sel], y=[p["etaT_needed"] for p in sel],
                        mode="markers+lines", name=f"d = {dd}",
                        line=dict(color=PAL[i % len(PAL)], width=2),
                        marker=dict(size=9))
    # what the naive "effective horizon eta*T/sqrt(m)" argument would predict
    sel = sorted([p for p in pts if p["d"] == ds[0]], key=lambda p: p["m"])
    mref = np.array([p["m"] for p in sel], float)
    fig.add_scatter(x=mref, y=ref(mref, sel[0]["etaT_needed"], 0.5), mode="lines",
                    name="m<sup>1/2</sup> reference (would break the regime)",
                    line=dict(color=PAL[5], width=1.5, dash="dash"))
    fig.update_xaxes(type="log", title="hidden width m")
    fig.update_yaxes(type="log", title="smallest ηT that fits one task")
    beta = c.get("beta_m")
    sub = (f"fitted ηT<sub>needed</sub> ∝ d<sup>{c['alpha_d']:.2f}</sup>"
           f" m<sup>{beta:+.2f}</sup>") if beta is not None else ""
    fig.update_layout(title="Claim 2 consistency: does the required ηT grow with width? "
                            + sub)
    save(fig, "c2_etaT_needed",
         [[p["d"], p["m"], p["etaT_needed"], p["seeds"]] for p in pts],
         ["d", "m", "etaT_needed", "seeds"])

# ------------------------------- Claims 4/5: the non-vacuous corner (exp8)
if "claim45_nonvacuous" in S:
    c = S["claim45_nonvacuous"]
    rows = c["rows"]
    ms = sorted({r["m"] for r in rows})
    ns = sorted({r["n"] for r in rows})
    fig = go.Figure()
    # measured gap: one trace per (m, n); bounds: one trace per (m, n) too, dashed
    i = 0
    for mm in ms:
        for nn in ns:
            sel = sorted([r for r in rows if r["m"] == mm and r["n"] == nn],
                         key=lambda r: r["T"])
            if not sel:
                continue
            col = PAL[i % len(PAL)]
            i += 1
            fig.add_scatter(x=[r["T"] for r in sel], y=[r["gap"] for r in sel],
                            mode="markers+lines", name=f"measured, m={mm}, n={nn}",
                            legendgroup=f"{mm}-{nn}",
                            line=dict(color=col, width=2), marker=dict(size=8))
            fig.add_scatter(x=[r["T"] for r in sel], y=[r["rhs_thm4"] for r in sel],
                            mode="lines", name=f"Thm 4 bound, m={mm}, n={nn}",
                            legendgroup=f"{mm}-{nn}",
                            line=dict(color=col, width=1.5, dash="dash"))
    fig.update_xaxes(type="log", title="steps per task T")
    fig.update_yaxes(type="log", title="delayed generalization gap / bound")
    fig.update_layout(
        title=f"Claims 4–5: at η={c['eta']:g} the bounds are finite — "
              f"tightest slack {c['tightest']['slack4']:.1f} decades "
              f"(m={c['tightest']['m']}, n={c['tightest']['n']}, T={c['tightest']['T']})")
    save(fig, "c45_nonvacuous",
         [[r["T"], r["m"], r["n"], r["gap"], r["sem"], r["exponent_thm3"],
           r["exponent_thm4"], r["rhs_thm3"], r["rhs_thm4"], r["slack3"],
           r["slack4"]] for r in rows],
         ["T", "m", "n", "gap", "sem", "exponent_thm3", "exponent_thm4",
          "rhs_thm3", "rhs_thm4", "slack3_decades", "slack4_decades"])

print("\nall figures ->", FIG)