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import numpy as np
# (1) A one-hot moving from token 0 to token 10 (“Text”)
dirac = [
{
"name": f"Dirac: all mass on token {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 {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)
]
# (3) Bimodal: two spikes of 0.5 mass each, symmetrically offset from the GT=4 ---
def make_bimodal_values(offset, n=11, gt=4):
# clamp to [0,n-1]
left = max(0, gt - offset)
right = min(n - 1, gt + offset)
vals = [0.0] * n
vals[left] = 0.5
vals[right] = 0.5
return vals
bimodal = [
{
"name": f"Bimodal: peaks at tokens {max(0, 4 - d)} & {min(10, 4 + d)}",
"values": make_bimodal_values(d),
"ground_truth": "4",
"explanation": "Two-point (bimodal) distribution: equal 0.5 mass on each peak, which move ±offset from the ground truth.",
}
for d in range(11)
]
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