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Everything is generated on the fly from a seeded RNG, so there is no dataset on
disk and every clip comes with ground-truth metadata (per-frame trajectory) that
the evaluator can check generated videos against.
"""
from __future__ import annotations
import math
from dataclasses import dataclass
import numpy as np
import torch
# ---------------------------------------------------------------- vocabulary
SHAPES = ["circle", "square", "triangle", "star", "ring", "cross"]
COLORS = {
"red": (230, 40, 40),
"green": (40, 200, 60),
"blue": (50, 90, 240),
"yellow": (245, 220, 40),
"cyan": (40, 220, 230),
"magenta": (220, 50, 220),
"white": (245, 245, 245),
"orange": (250, 140, 20),
}
SIZES = {"small": 0.11, "medium": 0.16, "big": 0.23} # radius as a fraction of frame size
BACKGROUNDS = ["black", "white", "gray", "navy", "gradient"]
# motion name -> caption words
MOTIONS = {
"left": "moves left",
"right": "moves right",
"up": "moves up",
"down": "moves down",
"up-left": "moves up left",
"up-right": "moves up right",
"down-left": "moves down left",
"down-right": "moves down right",
"bounces": "bounces",
"grows": "grows",
"shrinks": "shrinks",
"spins": "spins",
"still": "stays still",
}
DIRECTIONS = {
"left": (-1, 0), "right": (1, 0), "up": (0, -1), "down": (0, 1),
"up-left": (-1, -1), "up-right": (1, -1), "down-left": (-1, 1), "down-right": (1, 1),
}
ROTATIONALLY_SYMMETRIC = {"circle", "ring"} # spinning these is invisible, so never caption it
# Combos never rendered during training; used to test compositional generalisation.
HELDOUT_SHAPE_COLOR = {("star", "red"), ("circle", "yellow"), ("triangle", "cyan"), ("square", "magenta")}
HELDOUT_SHAPE_MOTION = {("ring", "down"), ("cross", "grows"), ("triangle", "bounces"), ("star", "left")}
SPECIALS = ["<pad>", "<unk>", "<null>"]
_WORDS = ["a", "and", "on", "background", "moves", "stays", "still", "left", "right", "up", "down",
"bounces", "grows", "shrinks", "spins", *SIZES, *COLORS, *SHAPES, *BACKGROUNDS]
VOCAB = SPECIALS + sorted(set(_WORDS))
PAD, UNK, NULL = 0, 1, 2
MAX_TOKENS = 24
class Tokenizer:
def __init__(self, max_len: int = MAX_TOKENS):
self.max_len = max_len
self.index = {w: i for i, w in enumerate(VOCAB)}
def encode(self, caption: str) -> list[int]:
ids = [self.index.get(w, UNK) for w in caption.lower().split()]
return (ids or [NULL])[: self.max_len]
def __call__(self, captions: list[str]) -> torch.Tensor:
out = torch.full((len(captions), self.max_len), PAD, dtype=torch.long)
for i, c in enumerate(captions):
ids = self.encode(c)
out[i, : len(ids)] = torch.tensor(ids)
return out
def null(self, n: int) -> torch.Tensor:
"""Token rows for the unconditional (classifier-free guidance) branch."""
out = torch.full((n, self.max_len), PAD, dtype=torch.long)
out[:, 0] = NULL
return out
# ---------------------------------------------------------------- sampling captions
@dataclass
class ClipConfig:
frames: int = 16
size: int = 48
p_two_objects: float = 0.3
p_mention_bg: float = 0.85
supersample: int = 2
# Curriculum: restrict what gets sampled (None = everything).
shapes: tuple[str, ...] | None = None
colors: tuple[str, ...] | None = None
sizes: tuple[str, ...] | None = None
motions: tuple[str, ...] | None = None
backgrounds: tuple[str, ...] | None = None
@classmethod
def simple(cls, **kw) -> "ClipConfig":
"""Stage-1 curriculum: one object, black background, 3 shapes, 4 colours, 5 motions."""
base = dict(p_two_objects=0.0, p_mention_bg=0.0, shapes=("circle", "square", "triangle"),
colors=("red", "green", "blue", "yellow"), motions=("left", "right", "up", "down", "bounces"),
backgrounds=("black",))
return cls(**{**base, **kw})
def _pick(rng: np.random.Generator, options, allowed):
opts = [o for o in options if allowed is None or o in allowed]
return opts[rng.integers(len(opts))]
def is_heldout(meta: dict) -> bool:
return any((o["shape"], o["color"]) in HELDOUT_SHAPE_COLOR or (o["shape"], o["motion"]) in HELDOUT_SHAPE_MOTION
for o in meta["objects"])
def _clashes(color: str, bg: str) -> bool:
return (color, bg) in {("white", "white"), ("blue", "navy")}
def _random_object(rng: np.random.Generator, bg: str, cfg: ClipConfig) -> dict:
while True:
shape = _pick(rng, SHAPES, cfg.shapes)
color = _pick(rng, COLORS, cfg.colors)
motion = _pick(rng, MOTIONS, cfg.motions)
size = _pick(rng, SIZES, cfg.sizes)
if not _clashes(color, bg) and not (motion == "spins" and shape in ROTATIONALLY_SYMMETRIC):
return {"shape": shape, "color": color, "size": size, "motion": motion}
def _random_meta(rng: np.random.Generator, cfg: ClipConfig, split: str) -> dict:
"""split: 'train' (no held-out combos), 'heldout' (one object, held-out combo), 'any'."""
while True:
bg = _pick(rng, BACKGROUNDS, cfg.backgrounds)
if split == "heldout":
obj = _random_object(rng, bg, cfg)
if rng.random() < 0.5:
obj["shape"], obj["color"] = sorted(HELDOUT_SHAPE_COLOR)[rng.integers(len(HELDOUT_SHAPE_COLOR))]
else:
obj["shape"], obj["motion"] = sorted(HELDOUT_SHAPE_MOTION)[rng.integers(len(HELDOUT_SHAPE_MOTION))]
objects = [obj]
else:
n = 2 if rng.random() < cfg.p_two_objects else 1
objects = [_random_object(rng, bg, cfg) for _ in range(n)]
meta = {"objects": objects, "bg": bg, "mention_bg": bool(rng.random() < cfg.p_mention_bg)}
if any(_clashes(o["color"], bg) for o in objects):
continue
if split == "train" and is_heldout(meta):
continue
return meta
def caption_of(meta: dict) -> str:
parts = []
for o in meta["objects"]:
size = "" if o["size"] == "medium" else o["size"] + " "
parts.append(f"a {size}{o['color']} {o['shape']} {MOTIONS[o['motion']]}")
cap = " and ".join(parts)
if meta.get("mention_bg", True):
cap += f" on a {meta['bg']} background"
return cap
def parse_caption(caption: str) -> dict:
"""Inverse of caption_of (without trajectories). Unmentioned size -> 'medium', bg -> None."""
words = caption.lower().split()
bg = None
if "on" in words:
i = words.index("on")
bg = words[i + 2] if i + 2 < len(words) else None
words = words[:i]
phrases, cur = [], []
for w in words:
if w == "and":
phrases.append(cur)
cur = []
else:
cur.append(w)
phrases.append(cur)
motion_by_words = {v: k for k, v in MOTIONS.items()}
objects = []
for p in phrases:
p = [w for w in p if w != "a"]
size = next((w for w in p if w in SIZES), "medium")
color = next((w for w in p if w in COLORS), None)
shape = next((w for w in p if w in SHAPES), None)
rest = " ".join(p[p.index(shape) + 1:]) if shape in p else ""
objects.append({"shape": shape, "color": color, "size": size, "motion": motion_by_words.get(rest)})
return {"objects": objects, "bg": bg, "mention_bg": bg is not None}
def sample_prompts(n: int, split: str = "train", seed: int = 0, cfg: ClipConfig | None = None) -> list[tuple[str, dict]]:
rng = np.random.default_rng(seed)
cfg = cfg or ClipConfig()
out = []
for _ in range(n):
meta = _random_meta(rng, cfg, split)
out.append((caption_of(meta), meta))
return out
# ---------------------------------------------------------------- rendering
def _background(bg: str, S: int) -> np.ndarray:
img = np.empty((S, S, 3), np.float32)
if bg == "gradient":
ramp = np.linspace(20, 120, S, dtype=np.float32)[:, None, None]
img[:] = ramp * np.array([0.6, 0.8, 1.0], np.float32)
else:
img[:] = {"black": (0, 0, 0), "white": (250, 250, 250), "gray": (128, 128, 128), "navy": (15, 20, 80)}[bg]
return img
def _polygon_mask(px, py, verts) -> np.ndarray:
"""Even-odd point-in-polygon test, vectorised over pixels."""
inside = np.zeros(px.shape, bool)
n = len(verts)
for i in range(n):
x1, y1 = verts[i]
x2, y2 = verts[(i + 1) % n]
crosses = (y1 > py) != (y2 > py)
xint = (x2 - x1) * (py - y1) / (y2 - y1 + 1e-12) + x1
inside ^= crosses & (px < xint)
return inside
def _regular(n: int, r: float, angle: float, cx: float, cy: float, inner: float | None = None):
pts = []
k = 2 * n if inner else n
for i in range(k):
a = angle - math.pi / 2 + 2 * math.pi * i / k
rr = (inner if i % 2 else r) if inner else r
pts.append((cx + rr * math.cos(a), cy + rr * math.sin(a)))
return pts
def _shape_mask(shape: str, px, py, cx, cy, r, angle) -> np.ndarray:
dx, dy = px - cx, py - cy
if shape == "circle":
return dx * dx + dy * dy <= r * r
if shape == "ring":
d2 = dx * dx + dy * dy
return (d2 <= r * r) & (d2 >= (0.55 * r) ** 2)
if shape == "square":
return _polygon_mask(px, py, _regular(4, r * 1.15, angle + math.pi / 4, cx, cy))
if shape == "triangle":
return _polygon_mask(px, py, _regular(3, r * 1.2, angle, cx, cy))
if shape == "star":
return _polygon_mask(px, py, _regular(5, r * 1.25, angle, cx, cy, inner=r * 0.5))
if shape == "cross":
c, s = math.cos(angle), math.sin(angle)
u, v = c * dx + s * dy, -s * dx + c * dy
arm = 0.33 * r
return ((np.abs(u) <= r) & (np.abs(v) <= arm)) | ((np.abs(v) <= r) & (np.abs(u) <= arm))
raise ValueError(shape)
def _trajectory(rng: np.random.Generator, obj: dict, T: int) -> list[tuple[float, float, float, float]]:
"""Per-frame (cx, cy, r, angle) in normalised [0,1] frame coordinates."""
r0 = SIZES[obj["size"]] * rng.uniform(0.9, 1.1)
angle0 = rng.uniform(0, 2 * math.pi)
m = obj["motion"]
ts = np.linspace(0, 1, T)
if m in DIRECTIONS:
dx, dy = DIRECTIONS[m]
dist = rng.uniform(0.35, 0.6) / (math.sqrt(2) if dx and dy else 1)
margin = r0 + 0.02
def start(d):
if d > 0:
return rng.uniform(margin, max(margin, 1 - margin - dist))
if d < 0:
return rng.uniform(min(1 - margin, margin + dist), 1 - margin)
return rng.uniform(margin, 1 - margin)
x0, y0 = start(dx), start(dy)
return [(x0 + dx * dist * t, y0 + dy * dist * t, r0, angle0) for t in ts]
if m == "bounces":
theta = rng.uniform(0, 2 * math.pi)
speed = rng.uniform(1.4, 2.2)
lo, hi = r0, 1 - r0
x, y = rng.uniform(lo, hi, size=2)
vx, vy = speed * math.cos(theta), speed * math.sin(theta)
out, dt = [], 1 / (T - 1)
for _ in range(T):
out.append((x, y, r0, angle0))
x, y = x + vx * dt, y + vy * dt
if x < lo or x > hi:
vx, x = -vx, float(np.clip(2 * np.clip(x, lo, hi) - x, lo, hi))
if y < lo or y > hi:
vy, y = -vy, float(np.clip(2 * np.clip(y, lo, hi) - y, lo, hi))
return out
margin = r0 * (1.6 if m in ("grows", "shrinks") else 1.0) + 0.02
cx, cy = rng.uniform(margin, 1 - margin, size=2)
if m == "grows":
return [(cx, cy, r0 * (0.5 + 1.1 * t), angle0) for t in ts]
if m == "shrinks":
return [(cx, cy, r0 * (1.6 - 1.1 * t), angle0) for t in ts]
if m == "spins":
spin = rng.choice([-1, 1]) * rng.uniform(0.6, 1.0) * math.pi
return [(cx, cy, r0, angle0 + spin * t) for t in ts]
return [(cx, cy, r0, angle0) for _ in ts] # still
def render(meta: dict, rng: np.random.Generator, cfg: ClipConfig) -> np.ndarray:
"""Render meta (adds meta['objects'][i]['traj']) to uint8 [T, H, W, 3]."""
T, S, ss = cfg.frames, cfg.size, cfg.supersample
big = S * ss
coords = (np.arange(big, dtype=np.float32) + 0.5) / big
px, py = np.meshgrid(coords, coords)
bg = _background(meta["bg"], big)
for o in meta["objects"]:
o["traj"] = _trajectory(rng, o, T)
frames = np.empty((T, S, S, 3), np.uint8)
for f in range(T):
img = bg.copy()
for o in meta["objects"]:
cx, cy, r, ang = o["traj"][f]
mask = _shape_mask(o["shape"], px, py, cx, cy, r, ang)
img[mask] = COLORS[o["color"]]
img = img.reshape(S, ss, S, ss, 3).mean(axis=(1, 3))
frames[f] = np.clip(img + 0.5, 0, 255).astype(np.uint8)
return frames
def make_clip(rng: np.random.Generator, cfg: ClipConfig | None = None, split: str = "train"):
cfg = cfg or ClipConfig()
meta = _random_meta(rng, cfg, split)
video = render(meta, rng, cfg)
return video, caption_of(meta), meta
# ---------------------------------------------------------------- torch dataset
def to_tensor(video: np.ndarray) -> torch.Tensor:
"""uint8 [T,H,W,3] -> float [3,T,H,W] in [-1,1]."""
return torch.from_numpy(video).permute(3, 0, 1, 2).float().div(127.5).sub(1)
class SynthVideoDataset(torch.utils.data.IterableDataset):
"""Infinite stream of (video float [3,T,H,W] in [-1,1], caption)."""
def __init__(self, cfg: ClipConfig | None = None, seed: int = 0, include_heldout: bool = False):
self.cfg = cfg or ClipConfig()
self.seed = seed
self.split = "any" if include_heldout else "train"
def __iter__(self):
info = torch.utils.data.get_worker_info()
wid = info.id if info else 0
rng = np.random.default_rng([self.seed, wid])
while True:
video, caption, _ = make_clip(rng, self.cfg, self.split)
yield to_tensor(video), caption
def collate(batch):
videos, captions = zip(*batch)
return torch.stack(videos), list(captions)
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