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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) | |
| ] | |