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Two 1D signals are shown side by side. Each signal's x-axis is divided
into 9 equal segments. Independently for each segment, the right signal
may or may not have a short smooth perturbation applied at the segment's
centre (raised-cosine blend, endpoints anchored so the splice is
seamless). Task: count how many of the 9 segments are identical between
left and right. Answer is an integer 0..9.
"""
from __future__ import annotations
import argparse
import json
import random
from pathlib import Path
from typing import Any, Dict, List, Tuple
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import numpy as np
from tqdm import tqdm
# ---------------------------------------------------------------------------
# Constants
# ---------------------------------------------------------------------------
N_SAMPLES = 2000
X_RANGE = (0.0, 2000.0)
GRID_N = 9 # segments along x
assert N_SAMPLES % GRID_N == 0 or True # integer cell boundaries handled numerically
# Each perturbation is a contiguous span of this many samples, centred in
# its segment. Must be well below the segment length so the transition
# band never straddles a segment boundary.
SEGMENT_WIDTH = N_SAMPLES // GRID_N # ≈ 222 samples per segment
PERTURB_WIDTH = 110 # ~half of one segment
assert PERTURB_WIDTH < SEGMENT_WIDTH - 2 * 15
# Raised-cosine splice blend at each edge of the perturbation.
TRANSITION_BAND = 15
RESYNTH_PAD = 40
MIN_DEVIATION_MULT = 0.4
INTRA_SEGMENT_NOISE_SIGMA = 0.04
PANEL_W = 1500
PANEL_H = 440
BG_COLOR = "#ffffff"
LINE_COLOR = "#1f4e79"
GRID_COLOR = "#c0c6d0" # segment-boundary grid (visible)
GRID_WIDTH = 1.2
BORDER_COLOR = "#888888"
BORDER_WIDTH = 1.5
LABEL_COLOR = "#333333"
HIGHLIGHT_COLOR = "#dc1e1e"
MARGIN_PX = 70
GAP_PX = 110
LABEL_HEIGHT = 44
def _build_question() -> str:
n = GRID_N
return (
f"Two 1D signals are shown side by side. Each signal's x-axis is "
f"divided into {n} equal segments by thin vertical gridlines, and "
f"each segment is numbered 1 through {n} above the gridlines (the "
f"two signals share the same numbering). Compare the left (Signal A) "
f"and right (Signal B) signals segment by segment. List the numbers "
f"of all segments that DIFFER between Signal A and Signal B, in "
f"ascending order, separated by commas (for example: \"2, 5, {n}\"). "
f"If no segments differ, write \"none\". "
f"Provide your final answer enclosed in <answer>...</answer> tags."
)
QUESTION = (
"Two 1D signals are shown side by side. Each signal's x-axis is "
"divided into 9 equal segments by thin vertical gridlines. Compare "
"the left and right signals segment by segment. Count how many of "
"the 9 segments are DIFFERENT between the two signals. Report the "
"count as an integer between 0 and 9. "
"Provide your final answer enclosed in <answer>...</answer> tags."
)
# ---------------------------------------------------------------------------
# Signal generator
# ---------------------------------------------------------------------------
def _gaussian_kernel(sigma: float) -> np.ndarray:
radius = max(1, int(sigma * 4))
k = np.arange(-radius, radius + 1, dtype=np.float64)
w = np.exp(-(k * k) / (2.0 * sigma * sigma))
return w / w.sum()
def _smoothed_noise(rng: random.Random, sigma: float) -> np.ndarray:
raw = np.array([rng.gauss(0.0, 1.0) for _ in range(N_SAMPLES)], dtype=np.float64)
kernel = _gaussian_kernel(sigma)
return np.convolve(raw, kernel, mode="same")
def generate_signal(rng: random.Random) -> np.ndarray:
coarse = _smoothed_noise(rng, sigma=rng.uniform(60.0, 110.0))
medium = _smoothed_noise(rng, sigma=rng.uniform(18.0, 35.0))
fine = _smoothed_noise(rng, sigma=rng.uniform(4.0, 8.0))
micro = _smoothed_noise(rng, sigma=rng.uniform(1.5, 2.5))
def _norm(a: np.ndarray) -> np.ndarray:
s = float(np.std(a)) or 1.0
return a / s
y = (
1.8 * _norm(coarse)
+ 0.75 * _norm(medium)
+ 0.40 * _norm(fine)
+ 0.20 * _norm(micro)
)
y = y + np.random.normal(0.0, INTRA_SEGMENT_NOISE_SIGMA, size=y.shape)
return y
# ---------------------------------------------------------------------------
# Segment geometry and perturbation selection
# ---------------------------------------------------------------------------
def _segment_bounds(idx: int) -> Tuple[int, int]:
"""Return (start, end) sample-index bounds of segment idx (end exclusive)."""
start = round(idx * N_SAMPLES / GRID_N)
end = round((idx + 1) * N_SAMPLES / GRID_N)
return int(start), int(end)
def _perturb_window(segment_idx: int) -> Tuple[int, int]:
"""Return (start, end) sample indices of the perturbation window,
centred within segment ``segment_idx``."""
s, e = _segment_bounds(segment_idx)
mid = (s + e) // 2
half = PERTURB_WIDTH // 2
p_start = mid - half
p_end = p_start + PERTURB_WIDTH
return p_start, p_end
MIN_PERTURBED = 0
MAX_PERTURBED = GRID_N
def _sample_perturbed_segments(rng: random.Random) -> List[int]:
"""Uniform num_perturbed ∈ {MIN_PERTURBED..MAX_PERTURBED}, then that many
segments chosen at random."""
num_perturbed = rng.randint(MIN_PERTURBED, MAX_PERTURBED)
all_idx = list(range(GRID_N))
rng.shuffle(all_idx)
return sorted(all_idx[:num_perturbed])
# ---------------------------------------------------------------------------
# Perturbation (segment-resynthesis with edge-anchored raised-cosine splice)
# ---------------------------------------------------------------------------
def _resynthesise_segment(
rng: random.Random,
left: np.ndarray,
start: int,
end: int,
sig_std: float,
max_tries: int = 30,
) -> np.ndarray:
n = end - start
orig = left[start:end]
a = float(left[start])
b = float(left[end - 1])
min_dev = MIN_DEVIATION_MULT * sig_std
for _ in range(max_tries):
cand_full = generate_signal(rng)
if len(cand_full) <= n + 2 * RESYNTH_PAD:
continue
cs = rng.randint(RESYNTH_PAD, len(cand_full) - n - RESYNTH_PAD)
cand = cand_full[cs:cs + n].copy()
ca, cb = float(cand[0]), float(cand[-1])
t = np.linspace(0.0, 1.0, n)
cand = cand - ((1.0 - t) * (ca - a) + t * (cb - b))
margin = min(TRANSITION_BAND, max(5, n // 10))
interior_dev = float(np.max(np.abs(cand[margin:n - margin] - orig[margin:n - margin])))
if interior_dev < min_dev:
continue
return cand
raise RuntimeError("Could not synthesise a sufficiently different segment.")
def _splice_with_blend(
signal: np.ndarray,
start: int,
end: int,
replacement: np.ndarray,
) -> None:
n = end - start
band = min(TRANSITION_BAND, n // 2)
w = np.ones(n)
if band > 0:
edge = 0.5 * (1.0 - np.cos(np.linspace(0.0, np.pi, band + 2)[1:-1]))
w[:band] = edge
w[-band:] = edge[::-1]
signal[start:end] = (1.0 - w) * signal[start:end] + w * replacement
def build_sample(
rng: random.Random,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray, List[Dict[str, Any]]]:
x = np.linspace(X_RANGE[0], X_RANGE[1], N_SAMPLES)
left = generate_signal(rng)
right = left.copy()
sig_std = float(np.std(left)) or 1.0
perturbed = set(_sample_perturbed_segments(rng))
segment_records: List[Dict[str, Any]] = []
for idx in range(GRID_N):
seg_start, seg_end = _segment_bounds(idx)
is_perturbed = idx in perturbed
record: Dict[str, Any] = {
"segment": idx,
"seg_start_index": seg_start,
"seg_end_index": seg_end,
"seg_x_start": float(x[seg_start]),
"seg_x_end": float(x[min(seg_end, N_SAMPLES) - 1]),
"perturbed": is_perturbed,
}
if is_perturbed:
p_start, p_end = _perturb_window(idx)
replacement = _resynthesise_segment(rng, left, p_start, p_end, sig_std)
_splice_with_blend(right, p_start, p_end, replacement)
record.update({
"perturb_start_index": int(p_start),
"perturb_end_index": int(p_end),
"perturb_x_start": float(x[p_start]),
"perturb_x_end": float(x[p_end - 1]),
})
segment_records.append(record)
return x, left, right, segment_records
# ---------------------------------------------------------------------------
# Rendering
# ---------------------------------------------------------------------------
LEGEND_W_SCALE = 0.40 # legend width = 40% of a signal panel
LEGEND_H = 80 # legend bar height (px) — independent of signal panel height
def _legend_dims() -> Tuple[int, int]:
return int(round(PANEL_W * LEGEND_W_SCALE)), int(LEGEND_H)
def _panel_origins() -> Tuple[Tuple[float, float],
Tuple[float, float],
Tuple[float, float]]:
"""(ox, oy) for legend (small bar, vertically centered), Signal A,
Signal B. Layout: [legend] [GAP] [Signal A] [GAP] [Signal B]."""
oy_signal = MARGIN_PX + LABEL_HEIGHT
leg_w, leg_h = _legend_dims()
ox_legend = MARGIN_PX
oy_legend = oy_signal + (PANEL_H - leg_h) / 2
ox_left = ox_legend + leg_w + GAP_PX
ox_right = ox_left + PANEL_W + GAP_PX
return (ox_legend, oy_legend), (ox_left, oy_signal), (ox_right, oy_signal)
def _canvas_size() -> Tuple[int, int]:
leg_w, _ = _legend_dims()
w = MARGIN_PX + leg_w + GAP_PX + PANEL_W + GAP_PX + PANEL_W + MARGIN_PX
h = MARGIN_PX + LABEL_HEIGHT + PANEL_H + MARGIN_PX
return int(w), int(h)
def _draw_legend(ax: plt.Axes, ox: float, oy: float) -> None:
"""Small horizontal index bar: N cells partitioned by vertical
gridlines, each labeled with its 1-based segment number."""
leg_w, leg_h = _legend_dims()
cell_w = leg_w / GRID_N
legend_bg = mpatches.Rectangle(
(ox, oy), leg_w, leg_h,
facecolor="#e8e6e0", edgecolor=BORDER_COLOR,
linewidth=BORDER_WIDTH, zorder=2,
)
ax.add_patch(legend_bg)
for i in range(1, GRID_N):
gx = ox + i * cell_w
ax.plot([gx, gx], [oy, oy + leg_h],
color="#888", linewidth=GRID_WIDTH, zorder=3)
fontsize = max(10, int(min(cell_w, leg_h) * 0.40))
for i in range(GRID_N):
cx = ox + i * cell_w + cell_w / 2
cy = oy + leg_h / 2
ax.text(cx, cy, str(i + 1),
ha="center", va="center",
fontsize=fontsize, fontweight="bold",
color="#222", zorder=4)
def _draw_panel(
ax: plt.Axes,
x: np.ndarray,
y: np.ndarray,
ox: float,
oy: float,
y_lo: float,
y_hi: float,
) -> None:
sx = PANEL_W / (X_RANGE[1] - X_RANGE[0])
sy = PANEL_H / (y_hi - y_lo) if y_hi > y_lo else 1.0
px = ox + (x - X_RANGE[0]) * sx
py = oy + PANEL_H - (y - y_lo) * sy
ax.plot(px, py, color=LINE_COLOR, linewidth=1.8, zorder=3, antialiased=True)
def _draw_segment_grid(ax: plt.Axes, ox: float, oy: float) -> None:
"""Draw GRID_N-1 internal vertical dividers, partitioning the panel
x-axis into ``GRID_N`` equal segments."""
for i in range(1, GRID_N):
gx = ox + PANEL_W * i / GRID_N
ax.plot(
[gx, gx], [oy, oy + PANEL_H],
color=GRID_COLOR, linewidth=GRID_WIDTH, zorder=1,
)
def _render(
out_path: Path,
x: np.ndarray,
left: np.ndarray,
right: np.ndarray,
segment_records: List[Dict[str, Any]] | None = None,
) -> None:
w, h = _canvas_size()
dpi = 100
fig, ax = plt.subplots(1, 1, figsize=(w / dpi, h / dpi), dpi=dpi)
ax.set_xlim(0, w)
ax.set_ylim(h, 0)
ax.set_aspect("auto")
ax.axis("off")
fig.patch.set_facecolor(BG_COLOR)
ax.set_facecolor(BG_COLOR)
(ox_legend, oy_legend), (ox_left, oy), (ox_right, _) = _panel_origins()
_draw_legend(ax, ox_legend, oy_legend)
leg_w, _ = _legend_dims()
ax.text(
ox_legend + leg_w / 2, oy_legend - 12,
"Index", ha="center", va="bottom",
fontsize=13, fontweight="bold", color=LABEL_COLOR,
)
y_all = np.concatenate([left, right])
y_lo = float(y_all.min())
y_hi = float(y_all.max())
pad = (y_hi - y_lo) * 0.08 if y_hi > y_lo else 1.0
y_lo -= pad
y_hi += pad
for ox in (ox_left, ox_right):
border = mpatches.Rectangle(
(ox, oy), PANEL_W, PANEL_H,
facecolor="none", edgecolor=BORDER_COLOR,
linewidth=BORDER_WIDTH, zorder=2,
)
ax.add_patch(border)
_draw_segment_grid(ax, ox, oy)
_draw_panel(ax, x, left, ox_left, oy, y_lo, y_hi)
_draw_panel(ax, x, right, ox_right, oy, y_lo, y_hi)
ax.text(
ox_left + PANEL_W / 2, MARGIN_PX + LABEL_HEIGHT * 0.3,
"Signal A", ha="center", va="center",
fontsize=15, fontweight="bold", color=LABEL_COLOR,
)
ax.text(
ox_right + PANEL_W / 2, MARGIN_PX + LABEL_HEIGHT * 0.3,
"Signal B", ha="center", va="center",
fontsize=15, fontweight="bold", color=LABEL_COLOR,
)
if segment_records:
sx = PANEL_W / (X_RANGE[1] - X_RANGE[0])
for rec in segment_records:
if not rec.get("perturbed"):
continue
px_start = (rec["perturb_x_start"] - X_RANGE[0]) * sx
px_end = (rec["perturb_x_end"] - X_RANGE[0]) * sx
for ox in (ox_left, ox_right):
ax.add_patch(mpatches.Rectangle(
(ox + px_start, oy),
px_end - px_start, PANEL_H,
facecolor=HIGHLIGHT_COLOR, edgecolor="none", alpha=0.18, zorder=4,
))
fig.savefig(out_path, facecolor=BG_COLOR)
plt.close(fig)
def render_pair(
out_path: Path,
x: np.ndarray,
left: np.ndarray,
right: np.ndarray,
) -> None:
_render(out_path, x, left, right)
def render_answer(
out_path: Path,
x: np.ndarray,
left: np.ndarray,
right: np.ndarray,
segment_records: List[Dict[str, Any]],
) -> None:
_render(out_path, x, left, right, segment_records)
# ---------------------------------------------------------------------------
# Annotation
# ---------------------------------------------------------------------------
def build_annotation(
image_name: str,
segment_records: List[Dict[str, Any]],
) -> Dict[str, Any]:
num_identical = sum(1 for r in segment_records if not r["perturbed"])
num_different = GRID_N - num_identical
diff_indices = sorted(
r["segment"] + 1 for r in segment_records if r.get("perturbed")
)
answer = ", ".join(str(i) for i in diff_indices) if diff_indices else "none"
return {
"image": image_name,
"num_segments": GRID_N,
"num_identical": num_identical,
"num_different": num_different,
"diff_indices": diff_indices,
"segments": segment_records,
"question": _build_question(),
"answer": answer,
}
# ---------------------------------------------------------------------------
# Dataset generation
# ---------------------------------------------------------------------------
def generate_dataset(
rng: random.Random,
count: int,
output_dir: Path,
) -> None:
images_dir = output_dir / "images"
answers_dir = output_dir / "answers"
images_dir.mkdir(parents=True, exist_ok=True)
answers_dir.mkdir(parents=True, exist_ok=True)
annotations: List[Dict[str, Any]] = []
data_items: List[Dict[str, Any]] = []
np.random.seed(rng.randint(0, 2**31 - 1))
for idx in tqdm(range(count), desc="Generating signal diff pairs"):
for _ in range(20):
try:
x, left, right, segment_records = build_sample(rng)
break
except RuntimeError:
continue
else:
raise RuntimeError(f"Failed to build sample {idx}")
image_name = f"signal_diff_{idx:05d}.png"
img_path = images_dir / image_name
ans_path = answers_dir / image_name
render_pair(img_path, x, left, right)
render_answer(ans_path, x, left, right, segment_records)
rel_image = f"images/{image_name}"
diff_indices = sorted(
r["segment"] + 1 for r in segment_records if r.get("perturbed")
)
answer = ", ".join(str(i) for i in diff_indices) if diff_indices else "none"
annotations.append(build_annotation(rel_image, segment_records))
data_items.append({
"image": rel_image,
"question": _build_question(),
"answer": answer,
})
with (output_dir / "annotations.jsonl").open("w", encoding="utf-8") as fh:
for rec in annotations:
fh.write(json.dumps(rec) + "\n")
data_json = {
"task": "spot_the_signal_diff",
"category": "visual_attribute_transfer",
"count": len(data_items),
"items": data_items,
}
with (output_dir / "data.json").open("w", encoding="utf-8") as fh:
json.dump(data_json, fh, indent=2)
fh.write("\n")
# ---------------------------------------------------------------------------
# CLI
# ---------------------------------------------------------------------------
def parse_args() -> argparse.Namespace:
p = argparse.ArgumentParser(
description="Generate 'Spot the Signal Diff' visual benchmark dataset."
)
p.add_argument("--output-root", type=Path, default=".")
p.add_argument("--count", type=int, default=20)
p.add_argument("--seed", type=int, default=42)
p.add_argument("--difficulty", type=int, default=5,
help="Integer difficulty >=0; scales perturbed segments and perturbation amplitude.")
return p.parse_args()
def main() -> None:
import math
args = parse_args()
rng = random.Random(args.seed)
d = max(0, int(args.difficulty))
global GRID_N, SEGMENT_WIDTH, PERTURB_WIDTH
global MIN_PERTURBED, MAX_PERTURBED, MIN_DEVIATION_MULT
global INTRA_SEGMENT_NOISE_SIGMA, PANEL_W
GRID_N = 5 + d
SEGMENT_WIDTH = N_SAMPLES // GRID_N
PERTURB_WIDTH = min(110, max(30, SEGMENT_WIDTH - 2 * TRANSITION_BAND - 10))
MIN_PERTURBED = 1
MAX_PERTURBED = GRID_N
scale = 0.5 / (1.0 + 0.1 * d)
MIN_DEVIATION_MULT = MIN_DEVIATION_MULT * scale
INTRA_SEGMENT_NOISE_SIGMA = 0.03 + 0.01 * d
# Canvas scaling (X-axis only): panel width scales with sqrt((5+d)/5).
s = math.sqrt(max(1.0, (5 + d) / 5))
PANEL_W = int(round(PANEL_W * s))
generate_dataset(rng, args.count, args.output_root)
print(f"Saved {args.count} signal diff pairs to {args.output_root}")
if __name__ == "__main__":
main()
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