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Part 3: visualizations comparing an analyzed run against U.S. census data.
Single-model charts, styled to match the standardized Reformation Bias Audit
figures (Times-family type, Wong 2011 palettes, consistent legend chrome).
Cross-model / multi-panel comparison figures are not rendered here.
Figure map (paper -> here, one model at a time):
Fig 1 skin_tone_colorspace() L* vs H* cloud, colored by race
Fig 2.2 race_vs_census_scatter() All races, colored by race
Fig 3 race_vs_census_scatter() one race, colored by proxy + annotations
Table 2 compute_tvd() Total Variation Distance vs census
Fig 4 prompt_race_bar() per-prompt stacked bars vs census
Fig 8 homogeneity_gap_bars() intra-minus-inter cosine gap by race
Fig 10 homogeneity_violin() box+strip+bootstrap CI by L* bin
"""
import io
import os
import tempfile
import zlib
import numpy as np
import pandas as pd
import matplotlib
matplotlib.use("Agg") # headless: render to figures, never open a window
import matplotlib.pyplot as plt
from matplotlib.colors import hsv_to_rgb
from matplotlib.lines import Line2D
from matplotlib.patches import Patch, Rectangle
from mpl_toolkits.axes_grid1 import make_axes_locatable
try:
from adjustText import adjust_text
except ImportError: # optional; annotated scatter still draws labels
adjust_text = None
# ── GLOBAL FONT: Times-family serif, matching the paper ───────────────────
plt.rcParams["font.family"] = "serif"
plt.rcParams["font.serif"] = ["Liberation Serif", "Times New Roman", "DejaVu Serif"]
plt.rcParams.update({
"font.size": 16,
"axes.titlesize": 17,
"axes.labelsize": 17,
"xtick.labelsize": 15,
"ytick.labelsize": 15,
"legend.fontsize": 15,
"legend.title_fontsize": 16,
"figure.titlesize": 19,
"axes.linewidth": 0.9,
"grid.linewidth": 0.5,
"figure.dpi": 120,
"savefig.dpi": 200,
})
# ---- canonical races + palettes (Wong 2011 / colorblind-safe) ----------
RACES = ["White", "Black", "Asian", "Hispanic", "Other"]
PRIMARY_RACES = ["White", "Black", "Asian", "Hispanic"] # paper scatters omit Other
PLOT_ORDER = ["White", "Asian", "Black", "Hispanic", "Other"] # scatter z-order
LEGEND_RACE_ORDER = ["White", "Black", "Asian", "Hispanic", "Other"]
FIG8_RACE_ORDER = ["White", "Black", "Asian", "Hispanic", "Other"]
PROXY_ORDER = ["occupation", "surname", "geography"]
RACE_CANON = {
"White/Caucasian": "White", "White": "White",
"Black/African": "Black", "Black": "Black",
"Asian": "Asian",
"Hispanic/Latino": "Hispanic", "Hispanic": "Hispanic",
"Other": "Other", "Other/Unclear": "Other",
}
RACE_COLORS = {
"Asian": "#009E73",
"Black": "#0072B2",
"Hispanic": "#F0E442",
"Other": "#CC79A7",
"White": "#D55E00",
"Unknown": "#BBBBBB",
}
PROXY_COLORS = {
"Occupation": "#7570B3",
"Surname": "#E7298A",
"Geography": "#66A61E",
"occupation": "#7570B3",
"surname": "#E7298A",
"geography": "#66A61E",
}
L_BINS = [(0, 40), (40, 55), (55, 70), (70, 101)]
FACE_DET_MIN = 0.85
MIN_BIN_SIZE = 5
N_BOOTSTRAP = 1000
CI_LEVEL = 95
SKIN_PALETTE = plt.get_cmap("copper")(np.linspace(0.15, 0.9, 4))
# ====================================================================== style
def apply_paper_style(ax):
"""Clean, publication-ready axis styling."""
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["left"].set_color("#CCCCCC")
ax.spines["bottom"].set_color("#CCCCCC")
ax.tick_params(colors="#444444", length=3)
ax.yaxis.label.set_color("#222222")
ax.xaxis.label.set_color("#222222")
def style_legend(leg, text_colors=None):
"""White background, thin light-grey border, black text."""
if leg is None:
return leg
frame = leg.get_frame()
frame.set_facecolor("white")
frame.set_edgecolor("#CCCCCC")
frame.set_linewidth(0.8)
frame.set_alpha(0.95)
texts = leg.get_texts()
for i, t in enumerate(texts):
t.set_color(text_colors[i] if text_colors else "black")
return leg
def _legend_outside(ax, *args, **kwargs):
"""Park the legend to the right of the axes so it never covers data."""
kwargs.setdefault("loc", "center left")
kwargs.setdefault("bbox_to_anchor", (1.04, 0.5))
kwargs.setdefault("borderaxespad", 0.0)
kwargs.setdefault("frameon", True)
leg = ax.legend(*args, **kwargs)
return style_legend(leg)
def _legend_above(ax, *args, **kwargs):
"""Park the legend above the axes (good when a colorbar sits below)."""
kwargs.setdefault("loc", "lower center")
kwargs.setdefault("bbox_to_anchor", (0.5, 1.04))
kwargs.setdefault("borderaxespad", 0.0)
kwargs.setdefault("frameon", True)
kwargs.setdefault("ncol", kwargs.get("ncol", 3))
leg = ax.legend(*args, **kwargs)
return style_legend(leg)
def _repel_labels(texts, ax, xs=None, ys=None):
"""Push text labels off each other and off the data points, with leader lines."""
if not texts:
return
if adjust_text is None:
return
common = dict(
ax=ax,
arrowprops=dict(arrowstyle="-", color="#666666", lw=0.7, alpha=0.85,
shrinkA=4, shrinkB=4),
)
if xs is not None and ys is not None:
common["x"] = np.asarray(xs)
common["y"] = np.asarray(ys)
try:
adjust_text(
texts,
expand_points=(1.6, 1.6),
expand_text=(1.3, 1.3),
force_points=(0.5, 0.6),
force_text=(0.9, 1.1),
lim=800,
avoid_self=True,
**common,
)
except TypeError:
try:
adjust_text(
texts,
expand=(1.4, 1.5),
force_text=(0.8, 1.0),
force_points=(0.5, 0.7),
**common,
)
except TypeError:
adjust_text(texts, ax=ax, arrowprops=common["arrowprops"])
def fig_to_svg_html(fig):
"""Vector (SVG) markup for in-app preview. Dense scatters may be rasterized
inside the SVG so the file stays light; axes and type stay vector."""
buf = io.BytesIO()
fig.savefig(buf, format="svg", bbox_inches="tight", dpi=200)
svg = buf.getvalue().decode("utf-8")
if svg.lstrip().startswith("<?xml"):
svg = svg.split("?>", 1)[-1]
stripped = svg.lstrip()
if stripped[:9].upper() == "<!DOCTYPE":
svg = stripped[stripped.find(">") + 1:]
if "preserveAspectRatio" not in svg:
svg = svg.replace("<svg ", '<svg preserveAspectRatio="xMidYMid meet" ', 1)
return f'<div class="chart-svg">{svg}</div>'
def fig_to_pdf_path(fig, stem):
"""Write a vector PDF and return its path (for per-chart download)."""
path = os.path.join(tempfile.gettempdir(), f"{stem}.pdf")
fig.savefig(path, format="pdf", bbox_inches="tight", dpi=200)
return path
def _empty_fig(msg):
fig, ax = plt.subplots(figsize=(8, 5))
ax.text(0.5, 0.5, msg, ha="center", va="center", wrap=True, fontsize=16, color="#444444")
ax.axis("off")
return fig
def _canon_race_series(df):
col = None
for name in ("race_classification", "Race", "race"):
if name in df.columns:
col = name
break
if col is None:
return pd.Series(np.nan, index=df.index)
return df[col].map(RACE_CANON)
def model_name(df):
vals = df["model"].dropna().unique()
return vals[0] if len(vals) else "model"
def _proxy_label(cat):
return str(cat).strip().title()
def _proxy_color(cat):
return PROXY_COLORS.get(cat, PROXY_COLORS.get(_proxy_label(cat), "#888888"))
def _display_prompt_name(category, name):
"""Surname census names are stored ALL CAPS; title-case just those."""
if name is None or (isinstance(name, float) and np.isnan(name)):
return ""
name = str(name)
if str(category).lower() == "surname":
return name.title()
return name
def _underscores_to_words(text):
"""Old runs stored prompts as a_person_from_Hawaii — show them as plain English."""
if text is None or (isinstance(text, float) and np.isnan(text)):
return ""
return " ".join(str(text).replace("_", " ").split())
def prompt_sentence(category, prompt_id, census=None, fallback=None):
"""Human-readable prompt, one per (category, prompt_id).
Surname's three phrasing variants collapse to the same sentence
(e.g. "A person with the last name Smith").
"""
name = None
if census is not None and prompt_id is not None:
try:
crow = census.set_index(["category", "prompt_id"]).loc[
(str(category).lower(), int(prompt_id))
]
if "prompt_name" in crow.index and pd.notna(crow["prompt_name"]):
name = str(crow["prompt_name"])
except (KeyError, TypeError, ValueError):
name = None
cat = str(category).lower()
if name:
if cat == "geography":
return f"A person from {name}"
if cat == "surname":
return f"A person with the last name {name.title()}"
if cat == "occupation":
return f"A person that works as {name}"
return name
plain = _underscores_to_words(fallback)
return plain or f"{_proxy_label(category)} {prompt_id}"
def _l_bin_label(lo, hi):
if lo == 0:
return f"L* < {hi}"
if hi >= 101:
return f"L* \u2265 {lo}"
return f"L* {lo}\u2013{hi}"
def _model_race_distribution(sub):
"""Fractions of classified images by canonical race for one prompt group."""
r = _canon_race_series(sub).dropna()
total = len(r)
if total == 0:
return None
counts = r.value_counts()
return {race: counts.get(race, 0) / total for race in RACES}
def hue_to_rgb_reference(hue):
return hsv_to_rgb([hue / 360.0, 1.0, 1.0])
def add_hue_colorbar(ax, x_min, x_max, xlabel="H* (Hue Angle, degrees)"):
"""Reference color bar beneath an L*/H* scatter — no ticks, x-axis label only."""
divider = make_axes_locatable(ax)
cax = divider.append_axes("bottom", size="5%", pad=0.35)
gradient = np.linspace(x_min, x_max, 2000)
gradient_colors = np.array([hue_to_rgb_reference(h) for h in gradient])
cax.imshow(gradient_colors.reshape(1, -1, 3), extent=[x_min, x_max, 0, 1], aspect="auto")
cax.set_xlim(x_min, x_max)
cax.set_ylim(0, 1)
cax.set_yticks([])
cax.set_xticks([])
cax.set_xlabel(xlabel, fontweight="bold")
def plot_with_uniform_layering(ax, data_dict, x_col, y_col, s=20, rasterized=True, alpha=0.6):
"""Scatter in a fixed race layering order (PLOT_ORDER). Extra groups
(e.g. Unknown) are drawn underneath so they don't hide classified points."""
ax.set_facecolor("white")
handles_labels = []
extra = [k for k in data_dict if k not in PLOT_ORDER]
order = extra + list(PLOT_ORDER)
for idx, race in enumerate(order):
if race not in data_dict or len(data_dict[race]) == 0:
continue
race_data = data_dict[race]
handle = ax.scatter(
race_data[x_col], race_data[y_col],
alpha=alpha, s=s, color=RACE_COLORS.get(race, "#BBBBBB"),
edgecolors="white", linewidths=0.4, zorder=2 + idx,
rasterized=rasterized,
)
handles_labels.append((handle, race, len(race_data)))
return handles_labels
# ====================================================================== TVD
TVD_SUMMARY_COLS = ["group", "mean", "ci_low", "ci_high", "std", "n"]
def _bootstrap_mean_ci(values, n_boot=N_BOOTSTRAP, ci=CI_LEVEL, seed=0):
"""Percentile bootstrap CI for the mean of a 1-d sample. Returns (lo, hi)."""
vals = np.asarray(values, dtype=float)
vals = vals[np.isfinite(vals)]
if len(vals) == 0:
return float("nan"), float("nan")
rng = np.random.default_rng(seed)
n = len(vals)
draws = rng.choice(vals, size=(n_boot, n), replace=True)
boot_means = draws.mean(axis=1)
lo_pct = (100 - ci) / 2
lo, hi = np.percentile(boot_means, [lo_pct, 100 - lo_pct])
return float(lo), float(hi)
def _tvd_summary_row(group, values):
values = np.asarray(values, dtype=float)
seed = zlib.adler32(f"tvd|{group}".encode()) & 0xFFFFFFFF
lo, hi = _bootstrap_mean_ci(values, seed=seed)
return {
"group": group,
"mean": float(np.mean(values)),
"ci_low": lo,
"ci_high": hi,
"std": float(np.std(values, ddof=1)) if len(values) > 1 else 0.0,
"n": int(len(values)),
}
def compute_tvd(df, census):
"""Per-prompt TVD (0.5 * sum|model - census| over races), then summarized.
Returns (per_prompt_df, summary_df). TVD is computed for each prompt that
has at least one classified image, matching the paper's per-prompt
definition. Summary is mean + 95% bootstrap CI (over prompts) per proxy
category, plus an Overall row.
"""
census_idx = census.set_index(["category", "prompt_id"])
rows = []
for (cat, pid), sub in df.groupby(["category", "prompt_id"]):
cat = str(cat).lower()
try:
pid = int(pid)
except (TypeError, ValueError):
continue
dist = _model_race_distribution(sub)
if dist is None or (cat, pid) not in census_idx.index:
continue
crow = census_idx.loc[(cat, pid)]
tvd = 0.5 * sum(abs(dist[r] - float(crow[r])) for r in RACES)
rows.append({"category": cat, "prompt_id": pid, "tvd": tvd})
per_prompt = pd.DataFrame(rows)
if per_prompt.empty:
return per_prompt, pd.DataFrame(columns=TVD_SUMMARY_COLS)
summary = []
seen = set()
for cat in PROXY_ORDER:
g = per_prompt[per_prompt["category"] == cat]
if g.empty:
continue
summary.append(_tvd_summary_row(cat, g["tvd"].to_numpy()))
seen.add(cat)
for cat, g in per_prompt.groupby("category"):
if cat in seen:
continue
summary.append(_tvd_summary_row(str(cat), g["tvd"].to_numpy()))
summary.append(_tvd_summary_row("Overall", per_prompt["tvd"].to_numpy()))
summary_df = pd.DataFrame(summary, columns=TVD_SUMMARY_COLS)
for col in ("mean", "ci_low", "ci_high", "std"):
summary_df[col] = summary_df[col].round(3)
summary_df["n"] = summary_df["n"].astype(int)
return per_prompt, summary_df
def _agg_points(df, census):
"""One row per (prompt, race): census % vs model output %."""
census_idx = census.set_index(["category", "prompt_id"])
recs = []
for (cat, pid), sub in df.groupby(["category", "prompt_id"]):
cat = str(cat).lower()
try:
pid = int(pid)
except (TypeError, ValueError):
continue
dist = _model_race_distribution(sub)
if dist is None or (cat, pid) not in census_idx.index:
continue
crow = census_idx.loc[(cat, pid)]
prompt_name = crow["prompt_name"] if "prompt_name" in crow.index else f"{cat} {pid}"
for race in RACES:
recs.append({
"category": cat, "prompt_id": pid, "race": race,
"prompt_name": prompt_name,
"census_pct": float(crow[race]) * 100.0,
"model_pct": dist[race] * 100.0,
})
return pd.DataFrame(recs)
# ====================================================================== Fig 2.2 / Fig 3
def race_vs_census_scatter(df, census, race_filter=None):
"""Census % (x) vs model output % (y), one point per (prompt, race).
race_filter=None/'All' -> all primary races, colored by race (Fig 2.2).
race_filter='Black' (etc.) -> that race only, colored by proxy, with the
furthest/closest points labeled (Fig 3).
"""
pts = _agg_points(df, census)
if pts.empty:
return _empty_fig("No race-classification data to plot.\nRun Part 2 with 'Race classification' enabled.")
if race_filter and race_filter != "All":
return _annotated_race_scatter(pts, race_filter)
fig, ax = plt.subplots(figsize=(10.5, 7.5))
ax.set_facecolor("white")
model_data = pts[pts["race"].isin(PRIMARY_RACES)]
for race in PRIMARY_RACES:
race_data = model_data[model_data["race"] == race]
ax.scatter(
race_data["census_pct"], race_data["model_pct"],
alpha=0.6, s=55, c=RACE_COLORS[race], marker="o",
label=race, edgecolors="white", linewidth=0.5, zorder=2,
rasterized=True,
)
ax.plot([0, 100], [0, 100], "k--", linewidth=2, alpha=0.7, zorder=1)
ax.grid(True, alpha=0.3, linewidth=0.5)
ax.set_xlim(0, 100)
ax.set_ylim(0, 100)
ax.set_aspect("equal", adjustable="box")
ax.set_xlabel("Census Demographic %", fontweight="bold")
ax.set_ylabel("Model Output %", fontweight="bold")
_legend_outside(ax)
return fig
def _spaced_annotation_rows(df, n, min_dist=8.0):
"""Take up to n rows, skipping any whose (x, y) sits on top of one already kept."""
picked = []
pts = []
for _, row in df.iterrows():
xy = np.array([row["census_pct"], row["model_pct"]], dtype=float)
if pts and np.min(np.linalg.norm(np.vstack(pts) - xy, axis=1)) < min_dist:
continue
picked.append(row)
pts.append(xy)
if len(picked) >= n:
break
return picked
def _annotated_race_scatter(pts, race, annotate_top_n=10):
"""Fig 3: one race, colored by proxy, furthest/closest points labeled."""
model_data = pts[pts["race"] == race].copy()
if model_data.empty:
return _empty_fig(f"No {race} classification data to plot.")
model_data["residual"] = (model_data["model_pct"] - model_data["census_pct"]).abs()
fig, ax = plt.subplots(figsize=(13, 8.5))
ax.set_facecolor("white")
for proxy in PROXY_ORDER:
proxy_data = model_data[model_data["category"].astype(str).str.lower() == proxy]
if proxy_data.empty:
continue
ax.scatter(
proxy_data["census_pct"], proxy_data["model_pct"],
alpha=0.6, s=150, c=_proxy_color(proxy), marker="s",
label=_proxy_label(proxy), edgecolors="white", linewidth=1, zorder=2,
rasterized=True,
)
furthest = _spaced_annotation_rows(
model_data.sort_values("residual", ascending=False), annotate_top_n, min_dist=12.0,
)
closest = []
ax.set_xlim(-12, 112)
ax.set_ylim(-12, 112)
texts = []
for row, face in [(r, "white") for r in furthest] + [(r, "#ccffcc") for r in closest]:
x, y = float(row["census_pct"]), float(row["model_pct"])
lx, ly = x, y
if y < 8:
ly = 14
elif y > 92:
ly = 86
texts.append(ax.annotate(
_display_prompt_name(row["category"], row["prompt_name"]),
xy=(x, y), xytext=(lx, ly),
xycoords="data", textcoords="data",
fontsize=11, color=_proxy_color(row["category"]), ha="center", va="center",
bbox=dict(boxstyle="round,pad=0.3", fc=face,
ec=_proxy_color(row["category"]), alpha=0.92, linewidth=1.1),
zorder=6,
))
ax.plot([0, 100], [0, 100], "k--", linewidth=2, alpha=0.7, zorder=1)
_repel_labels(texts, ax)
ax.set_xlabel("Census Demographic %", fontweight="bold")
ax.set_ylabel("Model Output %", fontweight="bold")
_legend_outside(ax)
ax.grid(True, alpha=0.3)
ax.set_aspect("equal", adjustable="box")
return fig
# ====================================================================== Fig 4
def prompt_tvd(df, census, category, prompt_id):
"""TVD of one prompt vs its census row. None if there is nothing to compare."""
cat = str(category).lower()
sub = df[
(df["category"].astype(str).str.lower() == cat)
& (df["prompt_id"] == int(prompt_id))
]
dist = _model_race_distribution(sub)
if dist is None:
return None
try:
crow = census.set_index(["category", "prompt_id"]).loc[(cat, int(prompt_id))]
except KeyError:
return None
return 0.5 * sum(abs(dist[r] - float(crow[r])) for r in RACES)
def prompt_race_bar(df, census, category, prompt_id, count_labels=False):
"""Stacked race breakdown for one prompt: census row under the model's row.
All phrasing variants that share a prompt_id (surname has three) are pooled.
count_labels: also print n/N on the model bar (playground, small n).
"""
cat = str(category).lower()
sub = df[
(df["category"].astype(str).str.lower() == cat)
& (df["prompt_id"] == int(prompt_id))
]
dist = _model_race_distribution(sub)
if dist is None:
return _empty_fig("No classified images for this prompt.")
crow = census.set_index(["category", "prompt_id"]).loc[(cat, int(prompt_id))]
race_order = ["White", "Black", "Asian", "Hispanic", "Other"]
races = _canon_race_series(sub).dropna()
n_total = len(races)
counts = races.value_counts()
model_vals = [dist[r] * 100 for r in race_order]
census_vals = [float(crow[r]) * 100 for r in race_order]
# Census at the bottom (y=0), model above — same stacking as the paper Fig 4.
row_labels = ["Census", str(model_name(df))]
data = np.array([census_vals, model_vals])
fig, ax = plt.subplots(figsize=(11, 3.6))
y_pos = np.arange(len(row_labels))
left = np.zeros(len(row_labels))
for i, race in enumerate(race_order):
values = data[:, i]
bars = ax.barh(
y_pos, values, left=left, color=RACE_COLORS[race],
edgecolor="white", linewidth=1.2, label=race, height=0.75,
)
n_race = int(counts.get(race, 0))
for row_i, (bar, val, start) in enumerate(zip(bars, values, left)):
if val <= 6:
continue
weight = "bold" if val >= 10 else "normal"
if count_labels and row_i == 1 and n_total:
label = f"{n_race}/{n_total}"
else:
label = f"{val:.0f}%"
ax.text(
start + val / 2, bar.get_y() + bar.get_height() / 2,
label, ha="center", va="center", fontsize=13,
fontweight=weight, color="#2d2d2d", clip_on=True,
)
left += values
ax.set_yticks(y_pos)
ax.set_yticklabels(row_labels)
ax.set_xlim(0, 100)
ax.set_xlabel("Percentage (%)", labelpad=8)
fallback = None
if "prompt_text" in sub.columns and len(sub):
texts = sub["prompt_text"].dropna().astype(str)
if len(texts):
fallback = max(texts, key=lambda t: len(_underscores_to_words(t)))
title = prompt_sentence(category, prompt_id, census, fallback=fallback)
ax.set_title(f'"{title}"', fontweight="bold", pad=12)
ax.tick_params(axis="y", length=0, pad=8)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["left"].set_visible(False)
ax.spines["bottom"].set_color("#666666")
ax.set_axisbelow(True)
ax.grid(axis="x", alpha=0.2, linestyle="--", linewidth=0.5, color="#999999")
handles = [
Rectangle((0, 0), 1, 1, facecolor=RACE_COLORS[r], edgecolor="white", linewidth=1.2)
for r in race_order
]
# Below the bars so it cannot collide with the prompt title.
leg = fig.legend(
handles, race_order, loc="upper center", ncol=5, bbox_to_anchor=(0.5, -0.12),
columnspacing=1.5, handletextpad=0.5, handlelength=1.5,
)
style_legend(leg)
fig.subplots_adjust(bottom=0.28)
return fig
# ====================================================================== Fig 1
def _ensure_h_star(df):
"""Fill missing H* from a*/b*. Does not drop or quality-filter any rows."""
sub = df.copy()
if "h_star" not in sub.columns:
sub["h_star"] = np.nan
a_col = "a" if "a" in sub.columns else ("A" if "A" in sub.columns else None)
b_col = "b" if "b" in sub.columns else ("B" if "B" in sub.columns else None)
if a_col and b_col:
missing = sub["h_star"].isna()
if missing.any():
h = np.degrees(np.arctan2(sub.loc[missing, b_col], sub.loc[missing, a_col])) % 360
sub.loc[missing, "h_star"] = h
return sub
def normalize_viz_df(df):
"""Map older/HF column names onto the schema the charts expect."""
if df is None:
return df
out = df.copy()
aliases = {
"race_classification": ("Race", "race"),
"category": ("proxy_cat", "proxy"),
"prompt_id": ("promptID", "promptId"),
"prompt_text": ("prompt",),
"a": ("A",),
"b": ("B",),
"h_star": ("H", "h", "H_star"),
"L": ("l", "L_star"),
}
for dest, srcs in aliases.items():
if dest in out.columns:
continue
for src in srcs:
if src in out.columns:
out[dest] = out[src]
break
if "category" in out.columns:
out["category"] = out["category"].astype(str).str.lower()
if "prompt_id" in out.columns:
out["prompt_id"] = pd.to_numeric(out["prompt_id"], errors="coerce")
return _ensure_h_star(out)
def skin_tone_colorspace(df, marker_size=20, rasterized=True):
"""L* vs H* skin-tone cloud, colored by race, with a hue reference bar.
Every image with a CIELAB reading is plotted — no face-detection /
embedding-quality filter (those apply only to homogeneity charts).
Unclassified race is kept as Unknown.
"""
if df is None or "L" not in df.columns:
return _empty_fig("No skin-tone data to plot.\nRun Part 2 with 'Skin tone' enabled.")
sub = _ensure_h_star(df)
# Include all images that have lightness + hue. Do not filter on
# face_det_score, n_faces_detected, or embed_status.
sub = sub[sub["L"].notna() & sub["h_star"].notna()].copy()
if sub.empty:
return _empty_fig("No skin-tone data to plot.\nRun Part 2 with 'Skin tone' enabled.")
if "race_classification" in sub.columns:
sub["race"] = _canon_race_series(sub).fillna("Unknown")
else:
sub["race"] = "Unknown"
h = sub["h_star"].to_numpy()
h_2nd, h_98th = np.percentile(h, [2, 98])
h_range = max(h_98th - h_2nd, 5.0)
x_margin = h_range * 0.08
x_min = np.floor(max(0, h_2nd - x_margin) / 5) * 5
x_max = np.ceil(min(360.0, h_98th + x_margin) / 5) * 5
if x_max <= x_min:
x_max = x_min + 25
fig, ax = plt.subplots(figsize=(9, 7.5))
data_by_race = {race: sub[sub["race"] == race] for race in RACE_COLORS}
handles_labels = plot_with_uniform_layering(
ax, data_by_race, x_col="h_star", y_col="L",
s=marker_size, rasterized=rasterized,
alpha=0.85 if marker_size >= 50 else 0.6,
)
ax.set_ylabel("L* (Lightness)", fontweight="bold")
hl_by_race = {race: (hnd, n) for hnd, race, n in handles_labels}
legend_order = LEGEND_RACE_ORDER + [r for r in hl_by_race if r not in LEGEND_RACE_ORDER]
ordered = [(race, hl_by_race[race]) for race in legend_order if race in hl_by_race]
handles = [hnd for _, (hnd, n) in ordered]
labels = [f"{race} (n={n})" for race, (hnd, n) in ordered]
if handles:
_legend_above(ax, handles, labels, ncol=min(len(labels), 3))
ax.grid(True, alpha=0.25, linewidth=0.5, zorder=1)
ax.set_xlim(x_min, x_max)
ax.set_ylim(0, 100)
for spine in ax.spines.values():
spine.set_edgecolor("black")
spine.set_linewidth(1)
add_hue_colorbar(ax, x_min, x_max)
ax.set_xlabel("")
return fig
def skin_tone_strip(df):
"""Playground-scale skin-tone chart: each face as a point on the L* axis."""
from .skin_tone import lab_to_hex
if df is None or "L" not in df.columns:
return _empty_fig("No skin-tone data to plot.")
sub = df[df["L"].notna()].copy()
if sub.empty:
return _empty_fig("No face detected for skin-tone measurement.")
n_missing = len(df) - len(sub)
lo = float(sub["L"].min())
hi = float(sub["L"].max())
fig, ax = plt.subplots(figsize=(9.5, 2.8))
ax.set_xlim(0, 100)
ax.set_ylim(-0.7, 0.7)
ax.axhline(0, color="#B0B0B0", lw=1.3, zorder=1)
ax.plot([lo, hi], [0, 0], color="#555555", lw=2.2, solid_capstyle="round", zorder=2)
for _, row in sub.iterrows():
try:
hex_color = lab_to_hex(row["L"], row["a"], row["b"])
except Exception:
hex_color = "#CCCCCC"
ax.scatter(
float(row["L"]), 0, s=280, c=hex_color,
edgecolors="#222222", linewidths=0.8, zorder=3,
)
ax.set_yticks([])
ax.set_xlabel("L* (0 = black, 100 = white)", fontweight="bold")
ax.set_xticks([0, 25, 50, 75, 100])
apply_paper_style(ax)
ax.spines["left"].set_visible(False)
ax.tick_params(axis="y", length=0)
spread = hi - lo
ax.text(
50, -0.55,
f"Lightness span {lo:.0f}–{hi:.0f} (spread {spread:.0f})"
+ (f" · {n_missing} with no face" if n_missing else ""),
ha="center", va="top", fontsize=13, color="#444444",
)
return fig
# ====================================================================== embeddings
def _stack_embeddings(df, emb_col, dim, require_face=False):
"""Return (matrix (n,dim), sub_df) for rows with a valid embedding.
require_face matches the paper's homogeneity subset: detection score
>= 0.85 and a single face (n_faces_detected == 1 when that column exists).
"""
sub = df[df[emb_col].notna()].copy()
if require_face:
if "embed_status" in sub.columns:
sub = sub[sub["embed_status"].isin(["ok"])]
if "face_det_score" in sub.columns:
sub = sub[sub["face_det_score"].fillna(0) >= FACE_DET_MIN]
if "n_faces_detected" in sub.columns:
sub = sub[sub["n_faces_detected"] == 1]
if sub.empty:
return np.empty((0, dim)), sub
vecs = []
keep = []
for idx, v in sub[emb_col].items():
arr = np.asarray(v, dtype=np.float32)
if arr.shape == (dim,) and not np.all(np.isnan(arr)):
vecs.append(arr)
keep.append(idx)
if not vecs:
return np.empty((0, dim)), sub.loc[[]]
mat = np.vstack(vecs)
mat = mat / (np.linalg.norm(mat, axis=1, keepdims=True) + 1e-9)
return mat, sub.loc[keep]
EMB_DIMS = {"face_emb": 512, "clip_emb": 1024}
def _pairwise_sims(mat):
"""Upper-triangle pairwise cosine similarities (rows assumed unit-norm)."""
n = len(mat)
return (mat @ mat.T)[np.triu_indices(n, k=1)]
def _bootstrap_ci_mean(embeddings, n_boot=N_BOOTSTRAP, ci=CI_LEVEL, rng=None):
"""Bootstrap CI for the mean pairwise cosine similarity within a set."""
if rng is None:
rng = np.random.default_rng(0)
n = len(embeddings)
boot_means = np.empty(n_boot)
for b in range(n_boot):
idx = rng.choice(n, n, replace=True)
boot_means[b] = _pairwise_sims(embeddings[idx]).mean()
lo_pct = (100 - ci) / 2
hi_pct = 100 - lo_pct
return np.percentile(boot_means, [lo_pct, hi_pct]), float(boot_means.mean())
def homogeneity_violin(df, emb_col="face_emb"):
"""Fig 10: box + strip + bootstrap CI of pairwise cosine sim by L* bin.
Equal-n within the model: each plotted bin is randomly subsampled to the
size of the smallest eligible bin (n >= MIN_BIN_SIZE), so bin comparisons
aren't confounded by uneven sample sizes.
"""
dim = EMB_DIMS.get(emb_col, 512)
mat, sub = _stack_embeddings(df, emb_col, dim, require_face=True)
if len(sub) == 0 or "L" not in sub.columns or sub["L"].notna().sum() == 0:
return _empty_fig(
f"No usable {emb_col} + skin-tone data.\n"
f"(CLIP embeddings aren't present yet.)" if emb_col == "clip_emb"
else f"No usable {emb_col} + skin-tone data to plot."
)
L = sub["L"].to_numpy()
bin_indices = []
for (lo, hi), color in zip(L_BINS, SKIN_PALETTE):
idx = np.where((L >= lo) & (L < hi))[0]
bin_indices.append((idx, _l_bin_label(lo, hi), color))
eligible = [len(idx) for idx, _, _ in bin_indices if len(idx) >= MIN_BIN_SIZE]
if not eligible:
return _empty_fig(
f"Not enough images per skin-tone bin for a homogeneity plot.\n"
f"Need >={MIN_BIN_SIZE} images in a bin."
)
equal_n = min(eligible)
if equal_n < 2:
return _empty_fig(
f"Not enough images per skin-tone bin for a homogeneity plot.\n"
f"Need >={MIN_BIN_SIZE} images in a bin."
)
rng = np.random.default_rng(42)
strip_rng = np.random.default_rng(1)
plot_data, plot_means, valid_labels, valid_colors = [], [], [], []
ci_los, ci_his = [], []
for idx, lab, color in bin_indices:
if len(idx) < equal_n:
continue
chosen = rng.choice(idx, equal_n, replace=False)
block = mat[chosen]
sims = _pairwise_sims(block)
boot_seed = zlib.adler32(f"{emb_col}|{lab}|{equal_n}".encode()) & 0xFFFFFFFF
boot_rng = np.random.default_rng(boot_seed)
(ci_lo, ci_hi), _ = _bootstrap_ci_mean(block, rng=boot_rng)
plot_data.append(sims)
plot_means.append(float(sims.mean()))
valid_labels.append(lab)
valid_colors.append(color)
ci_los.append(ci_lo)
ci_his.append(ci_hi)
if not plot_data:
return _empty_fig(
f"Not enough images per skin-tone bin for a homogeneity plot.\n"
f"Need >={MIN_BIN_SIZE} images in a bin."
)
all_sims = np.concatenate(plot_data)
y_lo = min(float(all_sims.min()), float(min(ci_los)))
y_hi = max(float(all_sims.max()), float(max(ci_his)))
y_pad = (y_hi - y_lo) * 0.10 or 0.02
y_lim = (y_lo - y_pad, y_hi + y_pad)
fig, ax = plt.subplots(figsize=(8.5, 7.5))
fig.patch.set_facecolor("white")
ax.set_facecolor("white")
positions = list(range(len(plot_data)))
for i, sims_arr in enumerate(plot_data):
jitter = strip_rng.uniform(-0.10, 0.10, size=len(sims_arr))
ax.scatter(
np.full(len(sims_arr), positions[i]) + jitter,
sims_arr,
color=valid_colors[i], alpha=0.12, s=8,
linewidths=0, zorder=2, rasterized=True,
)
bp = ax.boxplot(
plot_data, positions=positions, widths=0.45,
patch_artist=True, showfliers=False, zorder=4,
medianprops=dict(color="#111111", linewidth=1.8),
boxprops=dict(edgecolor="#111111", linewidth=1.0),
whiskerprops=dict(color="#111111", linewidth=1.0),
capprops=dict(color="#111111", linewidth=1.0),
)
for patch, color in zip(bp["boxes"], valid_colors):
patch.set_facecolor(color)
patch.set_alpha(0.55)
ci_offset = [p + 0.32 for p in positions]
err_lower = [max(0.0, m - lo) for m, lo in zip(plot_means, ci_los)]
err_upper = [max(0.0, hi - m) for m, hi in zip(plot_means, ci_his)]
ax.errorbar(
ci_offset, plot_means,
yerr=[err_lower, err_upper],
fmt="D", color="#111111",
ecolor="#111111", elinewidth=1.8,
capsize=5, capthick=1.8,
markersize=8, markerfacecolor="white", markeredgewidth=1.6,
zorder=7,
)
ax.set_ylim(y_lim)
ax.set_xlim(-0.6, len(positions) - 1 + 0.6)
ax.set_xticks(positions)
ax.set_xticklabels(valid_labels, rotation=15, ha="right", fontweight="bold")
ax.set_xlabel("\u2190 Darker Lighter \u2192", fontweight="bold")
ax.set_ylabel("Cosine Similarity", fontweight="bold")
for tick_label in ax.get_yticklabels():
tick_label.set_fontweight("bold")
legend_elems = [
Line2D([0], [0], marker="D", color="none", markerfacecolor="white",
markeredgecolor="#111111", markersize=9,
label=f"Mean \u00b1 {CI_LEVEL}% bootstrap CI"),
]
_legend_above(ax, handles=legend_elems, ncol=1)
apply_paper_style(ax)
ax.grid(axis="y", color="#DDDDDD", linewidth=0.7)
ax.set_axisbelow(True)
return fig
def _equal_n_race_gaps(mat, races, emb_col="face_emb"):
"""Intra−inter cosine gap per race, with equal-n sampling within the model.
Each eligible race (n >= MIN_BIN_SIZE) is subsampled to the size of the
smallest eligible race so gap comparisons aren't confounded by uneven N.
Returns (gaps_dict, equal_n) where gaps_dict maps race -> gap float.
"""
race_indices = {}
for race in RACES:
idx = np.where(races == race)[0]
if len(idx) >= MIN_BIN_SIZE:
race_indices[race] = idx
if len(race_indices) < 2:
return {}, 0
equal_n = min(len(idx) for idx in race_indices.values())
if equal_n < 2:
return {}, 0
sampled = {}
for race, idx in race_indices.items():
seed = zlib.adler32(f"{emb_col}|gap|{race}|{equal_n}".encode()) & 0xFFFFFFFF
race_rng = np.random.default_rng(seed)
sampled[race] = race_rng.choice(idx, equal_n, replace=False)
gaps = {}
for race, idx in sampled.items():
others = np.concatenate([sampled[r] for r in sampled if r != race])
if len(others) < 1:
continue
iu = np.triu_indices(equal_n, k=1)
block = mat[idx]
intra = float((block @ block.T)[iu].mean())
inter = float((mat[idx] @ mat[others].T).mean())
gaps[race] = intra - inter
return gaps, equal_n
def homogeneity_gap_bars(df, emb_col="face_emb"):
"""Fig 8 (single model): intra-minus-inter mean cosine similarity, per race.
Positive gap = that race's images are more self-similar than they are
similar to other races (a signal of less-diverse / more stereotyped output).
Uses equal-n sampling: every plotted race is randomly subsampled to the
size of the smallest eligible race (n >= MIN_BIN_SIZE).
"""
dim = EMB_DIMS.get(emb_col, 512)
mat, sub = _stack_embeddings(df, emb_col, dim, require_face=True)
if len(sub) == 0:
return _empty_fig(
f"No usable {emb_col} data.\n"
"(CLIP embeddings aren't present yet.)" if emb_col == "clip_emb"
else f"No usable {emb_col} data to plot."
)
races = _canon_race_series(sub).to_numpy()
gaps_dict, equal_n = _equal_n_race_gaps(mat, races, emb_col=emb_col)
if not gaps_dict:
return _empty_fig(
f"Not enough images per race for a homogeneity gap.\n"
f"Need >={MIN_BIN_SIZE} images in at least two race groups."
)
plot_races = [r for r in FIG8_RACE_ORDER if r in gaps_dict]
gap_data = [gaps_dict[r] for r in plot_races]
x = np.arange(len(plot_races))
bar_width = 0.55
fig, ax = plt.subplots(figsize=(9, 7))
ax.set_facecolor("white")
for i, race in enumerate(plot_races):
ax.bar(
x[i], gap_data[i], width=bar_width, color=RACE_COLORS[race],
label=race, edgecolor="white", linewidth=0.5, zorder=3,
)
y_min_data, y_max_data = min(gap_data), max(gap_data)
y_range = (y_max_data - y_min_data) or 0.05
ax.set_ylim(y_min_data - y_range * 0.1, y_max_data + y_range * 0.12)
ax.set_xticks(x)
ax.set_xticklabels(plot_races, fontweight="bold")
ax.set_ylabel("Homogeneity Gap (intra \u2212 inter)")
ax.axhline(0, color="#AAAAAA", linewidth=0.8, linestyle="--")
handles = [Patch(facecolor=RACE_COLORS[r], label=r) for r in plot_races]
_legend_above(ax, handles=handles, title="Race", ncol=len(plot_races))
apply_paper_style(ax)
ax.grid(axis="y", color="#EEEEEE", linewidth=0.8)
ax.set_axisbelow(True)
return fig
# ====================================================== cross-model comparison
# Kept for callers that pool several models; the Gradio UI does not use these.
def _models_in(df):
return sorted(df["model"].dropna().unique())
def race_vs_census_grid(df, census):
"""Census-vs-model scatter, one panel per model (not shown in the UI)."""
models = _models_in(df)
if not models:
return _empty_fig("No race-classification data to compare.")
census_idx = census.set_index(["category", "prompt_id"])
fig, axes = plt.subplots(1, len(models), figsize=(7.0 * len(models), 7.5), squeeze=False)
for ax, model in zip(axes[0], models):
sub = df[df["model"] == model]
pts = {r: ([], []) for r in PRIMARY_RACES}
for (cat, pid), g in sub.groupby(["category", "prompt_id"]):
dist = _model_race_distribution(g)
if dist is None or (cat, pid) not in census_idx.index:
continue
crow = census_idx.loc[(cat, pid)]
for r in PRIMARY_RACES:
pts[r][0].append(float(crow[r]) * 100)
pts[r][1].append(dist[r] * 100)
ax.plot([0, 100], [0, 100], "k--", linewidth=2, alpha=0.7, zorder=1)
for r in PRIMARY_RACES:
ax.scatter(
pts[r][0], pts[r][1], s=55, alpha=0.6, color=RACE_COLORS[r],
marker="o", edgecolors="white", linewidth=0.5, zorder=2,
)
ax.set_xlim(0, 100)
ax.set_ylim(0, 100)
ax.set_aspect("equal", adjustable="box")
ax.set_title(str(model), fontweight="bold", pad=12)
ax.set_xlabel("Census Demographic %", fontweight="bold")
ax.grid(True, alpha=0.3, linewidth=0.5)
axes[0][0].set_ylabel("Model Output %", fontweight="bold")
handles = [
Line2D([0], [0], marker="o", color="w", markerfacecolor=RACE_COLORS[r],
markeredgecolor="white", markersize=10, label=r)
for r in PRIMARY_RACES
]
leg = fig.legend(handles=handles, loc="upper center", ncol=4, bbox_to_anchor=(0.5, 1.02))
style_legend(leg)
fig.tight_layout()
return fig
def tvd_comparison_bars(df, census):
"""Mean TVD per model, by proxy (not shown in the UI)."""
models = _models_in(df)
if not models:
return _empty_fig("No race-classification data to compare.")
groups = ["geography", "occupation", "surname", "Overall"]
per_model = {}
for m in models:
_, summary = compute_tvd(df[df["model"] == m], census)
per_model[m] = {row["group"]: row["mean"] for _, row in summary.iterrows()}
x = np.arange(len(groups))
w = 0.8 / len(models)
fig, ax = plt.subplots(figsize=(9, 6))
ax.set_facecolor("white")
for i, m in enumerate(models):
vals = [per_model[m].get(g, np.nan) for g in groups]
ax.bar(x + i * w, vals, w, label=m, edgecolor="white", linewidth=0.5)
ax.set_xticks(x + w * (len(models) - 1) / 2)
ax.set_xticklabels([g.capitalize() for g in groups], fontweight="bold")
ax.set_ylabel("Mean TVD vs census (lower = closer)")
leg = ax.legend(loc="upper right")
style_legend(leg)
apply_paper_style(ax)
ax.grid(axis="y", color="#EEEEEE", linewidth=0.8)
ax.set_axisbelow(True)
fig.tight_layout()
return fig
def skin_tone_grid(df):
"""L* vs H* skin-tone, one panel per model (not shown in the UI)."""
models = _models_in(df)
sub_all = df[df["L"].notna() & df["h_star"].notna()]
if sub_all.empty or not models:
return _empty_fig("No skin-tone data to compare.")
h = sub_all["h_star"].to_numpy()
h_2nd, h_98th = np.percentile(h, [2, 98])
h_range = h_98th - h_2nd
x_margin = h_range * 0.05
x_min = np.floor(max(0, h_2nd - x_margin) / 5) * 5
x_max = 70
fig, axes = plt.subplots(1, len(models), figsize=(7.0 * len(models), 7.5), squeeze=False)
for ax, model in zip(axes[0], models):
sub = sub_all[sub_all["model"] == model].copy()
sub["race"] = _canon_race_series(sub)
data_by_race = {race: sub[sub["race"] == race] for race in RACE_COLORS}
plot_with_uniform_layering(ax, data_by_race, x_col="h_star", y_col="L")
ax.set_xlim(x_min, x_max)
ax.set_ylim(0, 100)
ax.set_title(str(model), fontweight="bold", pad=10)
ax.set_ylabel("L* (Lightness)", fontweight="bold")
ax.grid(True, alpha=0.25, linewidth=0.5, zorder=1)
for spine in ax.spines.values():
spine.set_edgecolor("black")
spine.set_linewidth(1)
add_hue_colorbar(ax, x_min, x_max)
fig.tight_layout()
return fig
def homogeneity_gap_grouped(df, emb_col="face_emb"):
"""Homogeneity gap per race, grouped bars by model (not shown in the UI)."""
models = _models_in(df)
dim = EMB_DIMS.get(emb_col, 512)
gaps = {}
equal_ns = {}
for m in models:
mat, sub = _stack_embeddings(df[df["model"] == m], emb_col, dim, require_face=True)
if len(sub) == 0:
continue
races = _canon_race_series(sub).to_numpy()
d, equal_n = _equal_n_race_gaps(mat, races, emb_col=f"{emb_col}|{m}")
if d:
gaps[m] = d
equal_ns[m] = equal_n
if not gaps:
kind_note = "(CLIP embeddings aren't present yet.)" if emb_col == "clip_emb" else ""
return _empty_fig(f"No usable {emb_col} data to compare across models.\n{kind_note}")
races_present = [r for r in FIG8_RACE_ORDER if any(r in gaps[m] for m in gaps)]
models_present = [m for m in models if m in gaps]
x = np.arange(len(models_present))
n_races = len(races_present)
bar_width = 0.15
fig, ax = plt.subplots(figsize=(11, 7.5))
ax.set_facecolor("white")
for i, race in enumerate(races_present):
gap_data = [gaps[m].get(race, 0) for m in models_present]
offset = (i - n_races / 2 + 0.5) * (bar_width + 0.01)
ax.bar(
x + offset, gap_data, width=bar_width, color=RACE_COLORS[race],
label=race, edgecolor="white", linewidth=0.5, zorder=3,
)
ax.set_xticks(x)
ax.set_xticklabels([str(m) for m in models_present], fontweight="bold")
ax.set_ylabel("Homogeneity Gap (intra \u2212 inter)")
ax.axhline(0, color="#AAAAAA", linewidth=0.8, linestyle="--")
handles = [Patch(facecolor=RACE_COLORS[r], label=r) for r in races_present]
leg = ax.legend(
handles=handles, title="Race", loc="upper center",
ncol=len(races_present), bbox_to_anchor=(0.5, 1.0),
)
style_legend(leg)
apply_paper_style(ax)
ax.grid(axis="y", color="#EEEEEE", linewidth=0.8)
ax.set_axisbelow(True)
fig.tight_layout()
return fig
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