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import numpy as np
options = [str(i) for i in range(10)] + ["Text"]
# (1) A one-hot moving from token 0 to token 10 (“Text”)
dirac = [
{
"name": f"Dirac: all mass on token {options[i]}",
"values": [1.0 if j == i else 0.0 for j in range(11)],
"ground_truth": "4",
"explanation": "A Dirac distribution: all probability on a single token.",
}
for i in range(11)
]
# (2) A Gaussian with peak_mass=0.6 at center, remaining mass=0.4 spread by a Gaussian ---
def make_gauss_values(center, n=11, sigma=1.5, peak_mass=0.6):
xs = np.arange(n)
# unnormalized Gaussian
kernel = np.exp(-0.5 * ((xs - center) / sigma) ** 2)
# zero out the center, re-normalize the *other* weights to sum to 1
others = kernel.copy()
others[center] = 0.0
others /= others.sum()
# allocate 0.6 to the center, 0.4 to the rest
vals = others * (1.0 - peak_mass)
vals[center] = peak_mass
return vals.tolist()
gauss = [
{
"name": f"Gaussian: center at token {options[c]}",
"values": make_gauss_values(c),
"ground_truth": "4",
"explanation": "Gaussian-style: 0.6 mass at the highlighted token, 0.4 spread smoothly to its neighbors.",
}
for c in range(11)
]
def make_bimodal_scenarios(gt_token: str, options: list[str]) -> list[dict]:
"""
Build a list of { name, values, explanation } dicts, where
each scenario splits 50/50 between tokens (gt±offset),
wrapping around via Python’s % operator.
"""
n = len(options)
gt_idx = options.index(gt_token)
scenarios = []
for offset in range(n):
left = (gt_idx - offset) % n
right = (gt_idx + offset) % n
# build the 50/50 (or 1.0 at gt when offset=0) vector
vals = [0.0] * n
if left == right:
vals[left] = 1.0
else:
vals[left] = 0.5
vals[right] = 0.5
label = f"({options[left]}, {options[right]})"
scenarios.append(
{
"name": label,
"values": vals,
"explanation": "50/50 mass at these two tokens (wrapping).",
}
)
return scenarios
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