Blame for code/pimamba/analysis.py

"""Post-hoc analysis: aggregation tables, figures, and micro->macro sensitivity.

Everything here is CPU-only and reads ``results/runs/<tag>/`` produced by
``pimamba.train``.  Used to generate the tables and figures of the report.
"""
from __future__ import annotations

import json
import os
from pathlib import Path
from typing import Dict, Iterable, List, Optional

import numpy as np
import pandas as pd

ROOT = Path(os.environ.get("PIMAMBA_ROOT")
            or Path(__file__).resolve().parents[2])
RUNS = ROOT / "results" / "runs"
FIGS = ROOT / "results" / "figures"
TABLES = ROOT / "results" / "tables"

MODEL_LABEL = {
    "mlp": "MLP", "gru": "GRU", "lstm": "LSTM", "transformer": "Transformer",
    "mamba": "Mamba (S6)", "mamba2": "Mamba-2", "pimamba": "PI-Mamba",
    "pimamba_nocouple": "PI-Mamba w/o coupling",
    "pimamba_phys": "PI-Mamba + physics loss",
    "pimamba_nogeom": "PI-Mamba w/o geometry",
    "pimamba_noflags": "PI-Mamba w/o shape flags",
    "pimamba_noensemble": "PI-Mamba w/o ensemble",
    "pimamba_noinit": "PI-Mamba w/o initial state",
    "pimamba_nonorm": "PI-Mamba w/o normalisation",
    "pimamba_phys005": "PI-Mamba + physics loss (0.05)",
    # ---- next generation (2024-2026) ----
    "llama": "LLaMA-style Transformer",
    "xlstm": "xLSTM (mLSTM)",
    "gdn": "Gated DeltaNet",
    "hymba": "Mamba+Attention hybrid",
    "koopman": "Deep Koopman",
    "node": "Neural ODE",
    "rssm": "RSSM world model",
    "flow": "Flow matching (generative)",
    "pimamba2": "PI-Mamba v2 (Taylor)",
}

PRIMARY_COLS = ["sigma_r2", "sigma_shape_r2", "macro_r2_primary",
                "rho_total_r2", "twin_r2", "xi_FCC_r2", "peak_rel_err"]


def load_summary() -> pd.DataFrame:
    df = pd.read_csv(ROOT / "results" / "summary.csv")
    return df


def agg(df: pd.DataFrame, by: str, cols: Optional[Iterable[str]] = None) -> pd.DataFrame:
    cols = list(cols or PRIMARY_COLS)
    g = df.groupby(by)
    mean = g[cols].mean()
    sd = g[cols].std()
    n = g.size().rename("n")
    out = mean.copy()
    for c in cols:
        out[c + "_sd"] = sd[c]
        out[c] = out[c].map(lambda v: round(float(v), 3))
        out[c + "_sd"] = out[c + "_sd"].map(lambda v: round(float(v), 3))
    return out.join(n).reset_index()


def markdown_table(df: pd.DataFrame, cols: List[str], rename: Dict[str, str] = None) -> str:
    rename = rename or {}
    head = "| " + " | ".join(rename.get(c, c) for c in cols) + " |"
    sep = "|" + "|".join(["---"] * len(cols)) + "|"
    lines = [head, sep]
    for _, r in df.iterrows():
        cells = []
        for c in cols:
            v = r[c]
            if isinstance(v, float):
                cells.append("nan" if not np.isfinite(v) else f"{v:.3f}")
            else:
                cells.append(str(v))
        lines.append("| " + " | ".join(cells) + " |")
    return "\n".join(lines)


def fmt_pm(mean: float, sd: float, nd: int = 3) -> str:
    if not np.isfinite(mean):
        return "n/a"
    if not np.isfinite(sd):
        return f"{mean:.{nd}f}"
    return f"{mean:.{nd}f} ± {sd:.{nd}f}"


# ---------------------------------------------------------------------------
# figures
# ---------------------------------------------------------------------------
def _plt():
    import matplotlib
    matplotlib.use("Agg")
    import matplotlib.pyplot as plt
    plt.rcParams.update({"figure.dpi": 150, "font.size": 8,
                         "axes.spines.top": False, "axes.spines.right": False})
    return plt


def fig_model_comparison(df: pd.DataFrame, fname="fig1_model_comparison.png"):
    plt = _plt()
    sub = df[df.suite == "main"]
    order = ["mlp", "gru", "lstm", "transformer", "mamba", "mamba2", "pimamba"]
    metrics = [("sigma_r2", "Stress $R^2$"), ("sigma_shape_r2", "Curve-shape $R^2$"),
               ("rho_total_r2", "Dislocation $R^2$"),
               ("peak_rel_err", "Peak-stress rel. err. (lower better)")]
    fig, axes = plt.subplots(1, 4, figsize=(10, 2.6), sharey=False)
    for ax, (col, title) in zip(axes, metrics):
        m = [sub[sub.model == k][col].mean() for k in order]
        s = [sub[sub.model == k][col].std() for k in order]
        colr = ["#b0b0b0"] * 6 + ["#c0392b"]
        ax.bar(range(len(order)), m, yerr=s, color=colr, capsize=2,
               error_kw={"lw": 0.8})
        ax.set_xticks(range(len(order)))
        ax.set_xticklabels([MODEL_LABEL[k].replace(" ", "\n") for k in order],
                           rotation=90, fontsize=6)
        ax.set_title(title, fontsize=8)
        ax.axhline(0, color="k", lw=0.5)
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname


def fig_curves(tag: str, fname=None, max_samples=6):
    """Predicted vs reference stress-strain and microstructural evolution."""
    plt = _plt()
    d = np.load(RUNS / tag / "predictions.npz", allow_pickle=True)
    pred, true, mask, sids = d["pred"], d["true"], d["mask"], d["sids"]
    m = json.loads((RUNS / tag / "metrics.json").read_text())
    from .data import TARGET_KEYS
    js = TARGET_KEYS.index("sigma")
    n = min(max_samples, len(sids))
    sel = np.argsort([-np.nanmax(np.abs(true[i, :, js])) for i in range(len(sids))])[:n]
    fig, axes = plt.subplots(1, 3, figsize=(9, 2.6))
    eps = np.linspace(0, 0.2, true.shape[1])
    for i in sel:
        mm = mask[i, :, js] > 0
        axes[0].plot(eps[mm], true[i, mm, js], color="k", lw=0.8, alpha=0.55)
        axes[0].plot(eps[mm], pred[i, mm, js], color="#c0392b", lw=0.8,
                     ls="--", alpha=0.75)
    axes[0].set_xlabel("true strain"); axes[0].set_ylabel("stress (GPa)")
    axes[0].set_title("stress-strain", fontsize=7)
    from matplotlib.lines import Line2D
    axes[0].legend(handles=[Line2D([], [], color="k", lw=0.9, label="MD reference"),
                            Line2D([], [], color="#c0392b", lw=0.9, ls="--",
                                   label="PI-Mamba")], fontsize=6, frameon=False)
    for j, lab, col in ((TARGET_KEYS.index("rho_total"), "dislocation density", "#2c7fb8"),
                        (TARGET_KEYS.index("twin"), "twin density", "#31a354")):
        for i in sel:
            mm = mask[i, :, j] > 0
            if mm.sum() < 2:
                continue
            axes[1 if j == TARGET_KEYS.index("rho_total") else 2].plot(
                eps[mm], true[i, mm, j], color="k", lw=0.7, alpha=0.45)
            axes[1 if j == TARGET_KEYS.index("rho_total") else 2].plot(
                eps[mm], pred[i, mm, j], color=col, lw=0.7, ls="--", alpha=0.8)
    axes[1].set_xlabel("true strain"); axes[1].set_ylabel(r"$\rho$ ($10^{19}$ m$^{-2}$)")
    axes[1].set_title("total dislocation density", fontsize=7)
    axes[2].set_xlabel("true strain"); axes[2].set_ylabel(r"$\rho_{twin}$ (nm$^{-1}$)")
    axes[2].set_title("twin density", fontsize=7)
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fname = fname or f"fig_curves_{tag}.png"
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname# ---------------------------------------------------------------------------
# micro -> macro coupling analysis (step 2, question 2)
# ---------------------------------------------------------------------------
def _load_model(tag: str, device="cpu"):
    """Rebuild a trained model from ``results/runs/<tag>``."""
    import torch
    from .data import TARGETS
    from .models import build_model

    d = RUNS / tag
    ck = torch.load(d / "model.pt", map_location=device, weights_only=False)
    cfg = ck["cfg"]
    m = build_model(cfg["model"], n_static=int(np.sum(ck["keep_mask"])),
                    n_out=len(TARGETS), d_model=cfg["d_model"],
                    n_layers=cfg["n_layers"], d_state=cfg["d_state"],
                    dropout=cfg["dropout"], coupling=cfg["coupling"]).to(device)
    m.load_state_dict(ck["state"])
    m.eval()
    meta = json.loads((d / "metrics.json").read_text())
    return m, cfg, meta, ck


def coupling_sensitivity(tag: str, channel: str = "rho_total", delta: float = 0.05,
                         device="cpu") -> Dict[str, float]:
    """Finite-difference counterfactual on the micro -> macro coupling path.

    The stress head sees ``[h, W * micro]``; we perturb one micro channel by
    ``delta`` (in its normalised units) and measure the relative change of the
    predicted flow stress, averaged over all evaluated trajectories and strains.
    """
    import torch
    from .data import PROC
    m, cfg, meta, ck = _load_model(tag, device)
    if m.micro_proj is None:
        return {"error": "model has no coupling path"}

    # micro vector layout = [4 phase fractions, 7 dislocation types, twin]
    # i.e. the full 13-dim output minus the leading stress channel
    from .data import TARGETS as _TG
    idx = {t.key: i - 1 for i, t in enumerate(_TG) if i > 0}
    ch = idx[channel]

    rec = []
    def pre_hook(module, args):
        x = args[0].clone()
        x[..., ch] = x[..., ch] + delta
        rec.append(1)
        return (x,)

    d = np.load(RUNS / tag / "predictions.npz", allow_pickle=True)
    # re-run the model on the same test samples
    from .data import PackedDataset, Normalizer, build_static_frame, collate
    mtab = pd.read_csv(PROC / "samples_meta.csv")
    traj = pd.read_csv(PROC / "trajectories.csv")
    Xraw, names, kinds = build_static_frame(mtab)
    km = np.asarray(ck["keep_mask"], dtype=bool)
    keep = [n for n, k in zip(names, km) if k]
    norm = Normalizer.from_json(meta["normalizer"])
    test_ids = [int(s) for s in meta["test_ids"]]
    ds = PackedDataset(test_ids, mtab, traj, norm, names, kinds, km)
    dl = torch.utils.data.DataLoader(ds, batch_size=8, shuffle=False, collate_fn=collate)

    base, pert = [], []
    with torch.no_grad():
        for st, x, Y, M, _ in dl:
            base.append(m(st, x)["pred"][..., 0].numpy())
            h = m.micro_proj.register_forward_pre_hook(pre_hook)
            pert.append(m(st, x)["pred"][..., 0].numpy())
            h.remove()
    b = np.concatenate(base, 0)
    p = np.concatenate(pert, 0)
    # stress is z-scored (no asinh), so the inverse is a plain affine map
    rb = b * norm.tgt_sd[0] + norm.tgt_mu[0]
    rp = p * norm.tgt_sd[0] + norm.tgt_mu[0]
    rel = (rp - rb) / np.maximum(np.abs(rb), 1e-6)
    return {
        "tag": tag, "channel": channel, "delta_norm": delta,
        "mean_rel_change": float(np.mean(rel)),
        "median_abs_rel_change": float(np.median(np.abs(rel))),
        "p95_abs_rel_change": float(np.percentile(np.abs(rel), 95)),
        "sign_consistency": float(np.mean(np.sign(rel) == np.sign(np.mean(rel)))),
    }


def autograd_sensitivity(tag: str, device="cpu") -> pd.DataFrame:
    """d sigma / d (normalised micro channel) via autograd, per strain point."""
    import torch
    from .data import PROC, PackedDataset, Normalizer, build_static_frame, collate

    m, cfg, meta, ck = _load_model(tag, device)
    if m.micro_proj is None:
        return pd.DataFrame()
    mtab = pd.read_csv(PROC / "samples_meta.csv")
    traj = pd.read_csv(PROC / "trajectories.csv")
    Xraw, names, kinds = build_static_frame(mtab)
    km = np.asarray(ck["keep_mask"], dtype=bool)
    norm = Normalizer.from_json(meta["normalizer"])
    test_ids = [int(s) for s in meta["test_ids"]]
    ds = PackedDataset(test_ids, mtab, traj, norm, names, kinds, km)
    dl = torch.utils.data.DataLoader(ds, batch_size=1, shuffle=False, collate_fn=collate)

    labels = ["xi_BCC", "xi_FCC", "xi_HCP", "xi_other"] + \
             [f"rho_{i}" for i in range(7)] + ["twin"]
    rows = []
    for st, x, Y, M, sid in dl:
        m.zero_grad(set_to_none=True)
        # capture the micro vector by hooking micro_proj input
        cache = {}
        def pre(module, args):
            a = args[0].clone().requires_grad_(True)
            cache["micro"] = a
            return (a,)
        h = m.micro_proj.register_forward_pre_hook(pre)
        out = m(st, x)
        h.remove()
        sig = out["pred"][..., 0]
        g = torch.autograd.grad(sig.sum(), cache["micro"])[0][0]  # (T, n_micro)
        arr = g.detach().numpy()
        eps = np.linspace(0, 0.2, arr.shape[0])
        for k, lab in enumerate(labels):
            rows.append(pd.DataFrame({"strain": eps, "channel": lab,
                                      "grad": arr[:, k], "sid": int(sid[0])}))
    return pd.concat(rows, ignore_index=True)


def fig_sensitivity(df: pd.DataFrame, fname="fig_coupling_sensitivity.png"):
    plt = _plt()
    chans = ["xi_BCC", "xi_FCC", "xi_HCP", "rho_total", "twin"]
    fig, ax = plt.subplots(figsize=(4.2, 2.6))
    for c in chans:
        if c not in set(df.channel):
            continue
        g = df[df.channel == c].groupby("strain").grad
        mu, sd = g.mean(), g.std()
        ax.plot(mu.index, mu.values, lw=1.0, label=c)
        ax.fill_between(mu.index, mu - sd, mu + sd, alpha=0.15, lw=0)
    ax.set_xlabel("true strain"); ax.set_ylabel(r"$\partial \sigma/\partial z_{micro}$")
    ax.set_title("micro -> macro coupling sensitivity", fontsize=8)
    ax.legend(fontsize=6, frameon=False)
    ax.axhline(0, color="k", lw=0.4)
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname


def fig_ablation(df: pd.DataFrame, fname="fig4_ablation.png"):
    plt = _plt()
    sub = df[df.suite == "ablation"]
    names = [n for n in sub.variant.unique()]
    names.sort(key=lambda n: -sub[sub.variant == n].sigma_r2.mean())
    fig, ax = plt.subplots(figsize=(5.2, 2.4))
    m = [sub[sub.variant == n]["sigma_r2"].mean() for n in names]
    s = [sub[sub.variant == n]["sigma_r2"].std() for n in names]
    s = [0.0 if not np.isfinite(v) else v for v in s]
    ax.bar(range(len(names)), m, yerr=s, color="#2c7fb8", capsize=2,
           error_kw={"lw": 0.8})
    ax.set_xticks(range(len(names)))
    ax.set_xticklabels([MODEL_LABEL.get(n, n) for n in names], rotation=30,
                       ha="right", fontsize=6)
    ax.set_ylabel("stress $R^2$")
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname


def fig_dataeff(df: pd.DataFrame, fname="fig5_data_efficiency.png"):
    plt = _plt()
    sub = df[df.suite == "dataeff"].copy()
    if not len(sub):
        return None
    sub["frac"] = sub.variant.str.split("@").str[-1].astype(float)
    fig, ax = plt.subplots(figsize=(3.4, 2.4))
    for mdl, g in sub.groupby("model"):
        a = g.groupby("frac").sigma_r2
        ax.errorbar(a.mean().index, a.mean().values, yerr=a.std().values,
                    marker="o", ms=3, lw=1, capsize=2,
                    label=MODEL_LABEL.get(mdl, mdl))
    ax.set_xlabel("fraction of training set"); ax.set_ylabel("stress $R^2$")
    ax.legend(fontsize=6, frameon=False)
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname


def fig_selectivity(tag: str, fname="fig6_selectivity.png", device="cpu"):
    """Visualise the input-dependent step size Delta_t of the S6 blocks.

    Delta_t is what makes the SSM *selective*: small Delta -> long memory (elastic
    regime), large Delta -> fast forgetting (yielding / dislocation multiplication).
    """
    import torch
    import torch.nn.functional as F
    from .data import PROC, PackedDataset, Normalizer, build_static_frame, collate

    plt = _plt()
    m, cfg, meta, ck = _load_model(tag, device)
    mtab = pd.read_csv(PROC / "samples_meta.csv")
    traj = pd.read_csv(PROC / "trajectories.csv")
    Xraw, names, kinds = build_static_frame(mtab)
    km = np.asarray(ck["keep_mask"], dtype=bool)
    norm = Normalizer.from_json(meta["normalizer"])
    test_ids = [int(s) for s in meta["test_ids"]]
    ds = PackedDataset(test_ids, mtab, traj, norm, names, kinds, km)
    dl = torch.utils.data.DataLoader(ds, batch_size=1, shuffle=False, collate_fn=collate)

    blocks = list(getattr(m, "blocks", []))
    if not blocks:
        return None
    caps: Dict[int, List[np.ndarray]] = {i: [] for i in range(len(blocks))}
    handles = []
    for i, blk in enumerate(blocks):
        def mk(i):
            def hook(module, inp, out):
                caps[i].append(F.softplus(out).detach().mean(-1)[0].numpy())
            return hook
        handles.append(blk.dt_proj.register_forward_hook(mk(i)))

    sig, eps = [], []
    with torch.no_grad():
        for st, x, Y, M, sid in dl:
            m(st, x)
            sig.append(Y[0, :, 0].numpy())
            eps.append(x[0, :, 0].numpy() * 0.2)
    for h in handles:
        h.remove()

    fig, axes = plt.subplots(1, 2, figsize=(6.4, 2.3))
    ax = axes[0]
    for i in range(len(blocks)):
        d = np.stack(caps[i])  # (N, T)
        ax.plot(eps[0], d.mean(0), lw=1.0, label=f"layer {i+1}")
        ax.fill_between(eps[0], d.mean(0) - d.std(0), d.mean(0) + d.std(0),
                        alpha=0.15, lw=0)
    ax.set_xlabel("true strain"); ax.set_ylabel(r"$\bar\Delta_t$ (softplus)")
    ax.set_title(r"learned step size $\Delta_t$", fontsize=8)
    ax.legend(fontsize=6, frameon=False)

    ax = axes[1]
    D = np.stack(caps[0])              # (N, T) first-layer Delta_t
    S_ = np.stack(sig)                 # (N, T) reference stress
    d0 = D.mean(0)
    s = S_.mean(0)
    dsde = np.abs(np.gradient(s, eps[0]))
    ax.scatter(dsde, d0, s=3, alpha=0.4)
    ax.set_xlabel(r"$|d\sigma/d\varepsilon|$ (GPa)"); ax.set_ylabel(r"$\bar\Delta_t$")
    ax.set_title("selectivity vs. hardening rate", fontsize=8)
    r = float(np.corrcoef(dsde, d0)[0, 1])
    # per-sample detrending removes the shared strain trend, which would
    # otherwise create a spurious correlation between two decaying curves
    dw, sw = [], []
    for i in range(D.shape[0]):
        di = np.gradient(S_[i], eps[0])
        dw.append(D[i] - D[i].mean())
        sw.append(np.abs(di) - np.abs(di).mean())
    r_detr = float(np.corrcoef(np.concatenate(dw), np.concatenate(sw))[0, 1])
    ax.text(0.05, 0.88, f"r={r:.2f}  (within-sample r={r_detr:.2f})",
            transform=ax.transAxes, fontsize=6)
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname, {"r_pooled": float(r), "r_detrended": r_detr}

# ---------------------------------------------------------------------------
# CLI: python -m pimamba.analysis --coupling <tag> [--autograd <tag>] [--selectivity <tag>]
# ---------------------------------------------------------------------------
def main(argv=None):
    import argparse
    ap = argparse.ArgumentParser("pimamba.analysis")
    ap.add_argument("--coupling", metavar="TAG",
                    help="counterfactual sensitivity on the micro->macro path")
    ap.add_argument("--autograd", metavar="TAG",
                    help="d sigma / d z_micro per strain point (dumps sens.csv)")
    ap.add_argument("--selectivity", metavar="TAG",
                    help="figure of the input-dependent step size Delta_t")
    ap.add_argument("--device", default="cpu")
    args = ap.parse_args(argv)

    if args.coupling:
        rows = []
        for ch in ["rho_total", "twin", "xi_FCC", "xi_BCC", "xi_HCP"]:
            for dv in [0.05, 0.1, 0.2]:
                r = coupling_sensitivity(args.coupling, ch, dv, device=args.device)
                rows.append(r)
                print(r)
        df = pd.DataFrame(rows)
        TABLES.mkdir(parents=True, exist_ok=True)
        df.to_csv(TABLES / "coupling_elasticity.csv", index=False)
        print("wrote", TABLES / "coupling_elasticity.csv")

    if args.autograd:
        df = autograd_sensitivity(args.autograd, device=args.device)
        if len(df):
            TABLES.mkdir(parents=True, exist_ok=True)
            df.to_csv(TABLES / "sens.csv", index=False)
            print("wrote", TABLES / "sens.csv", "->", fig_sensitivity(df))

    if args.selectivity:
        print("wrote", fig_selectivity(args.selectivity, device=args.device))


if __name__ == "__main__":
    main()

def fig_next(df: pd.DataFrame, fname: str = "fig_next_comparison.png"):
    """Next-generation backbones vs the best of the first wave."""
    plt = _plt()
    order = ["pimamba", "mamba", "transformer", "llama", "xlstm", "gdn",
             "hymba", "koopman", "node", "rssm", "flow", "pimamba2"]
    sub = df[df.suite.isin(["main", "next", "v2"])].copy()
    rows = []
    for m in order:
        suite = "main" if m in ("pimamba", "mamba", "mamba2", "transformer") else None
        g = sub[(sub.model == m) & ((sub.suite == suite) if suite else True)]
        if m == "pimamba2" and "variant" in g:
            # the v2 suite shares the "pimamba2" backbone between three variants
            # (plain / peak-loss / no-coupling) -- plot only the plain one.
            g = g[g.variant == "pimamba2"]
        if not len(g):
            continue
        rows.append({"model": m, "mu": g.sigma_r2.mean(), "sd": g.sigma_r2.std(),
                     "shape": g.sigma_shape_r2.mean(),
                     "params": g.n_params.mean()})
    if not rows:
        return None
    t = pd.DataFrame(rows).sort_values("mu")
    fig, ax = plt.subplots(figsize=(4.6, 3.4))
    colors = ["C1" if m in ("pimamba", "pimamba2") else
              ("C2" if m in ("mamba", "mamba2", "transformer") else "C0")
              for m in t.model]
    ax.barh(np.arange(len(t)), t.mu, xerr=t.sd, color=colors, alpha=0.85,
            error_kw=dict(lw=0.8, capsize=2))
    ax.scatter(t["shape"], np.arange(len(t)), marker="|", color="k", s=40,
               label="shape $R^2$")
    ax.set_yticks(np.arange(len(t)))
    ax.set_yticklabels([MODEL_LABEL.get(m, m) for m in t.model], fontsize=7)
    ax.axvline(0, color="k", lw=0.6)
    ax.set_xlabel(r"stress $R^2$ (mean over runs)")
    ax.legend(fontsize=6, frameon=False, loc="lower right")
    ax.set_title("next-generation backbones", fontsize=8)
    fig.tight_layout()
    FIGS.mkdir(parents=True, exist_ok=True)
    fig.savefig(FIGS / fname, bbox_inches="tight")
    plt.close(fig)
    return FIGS / fname