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plot_coupling_bounds.py
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plot_coupling_bounds.py
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import numpy as np
import argparse
import pandas as pd
import torch
import matplotlib
from matplotlib import pyplot as plt
def sanitize_filename(text):
sanitized = text.replace(" ", "_").replace("?", "")
return sanitized
def parse_arguments():
parser = argparse.ArgumentParser(
description="Compare coupling methods for model distributions and plot results including bounds.")
parser.add_argument("--model_large", type=str, required=True, help="Name of the large model")
parser.add_argument("--model_small", type=str, required=True, help="Name of the small model")
parser.add_argument("--input_text", type=str, required=True,
help="Input text used for generating the token distributions")
parser.add_argument("--num_tokens", type=int, default=32, help="Number of tokens to generate")
parser.add_argument("--num_retries", type=int, default=20000, help="Number of retries for statistical tests")
return parser.parse_args()
def d_tv(p, q):
return 1 - torch.sum(torch.min(p, q))
def gumbel_simulation(p, q, seed=42):
torch.manual_seed(seed)
num_elements = len(p)
h = torch.rand(num_elements).to('cuda')
choice_p = torch.argmin(-torch.log(h) / p)
choice_q = torch.argmin(-torch.log(h) / q)
return choice_p == choice_q
def wmh_simulation(p, q, seed=42):
torch.manual_seed(seed)
max_vals = torch.max(p, q)
sum_max_vals = torch.sum(max_vals).item()
i = j = None
while i is None or j is None:
dart = torch.rand(1).item() * sum_max_vals
cumulative_sum = torch.cumsum(max_vals, dim=0)
hit_index = torch.searchsorted(cumulative_sum, torch.tensor(dart, device='cuda')).item()
hit_point = (dart - (cumulative_sum[hit_index] - max_vals[hit_index]).item())
if i is None and hit_point <= p[hit_index]:
i = hit_index
if j is None and hit_point <= q[hit_index]:
j = hit_index
return i == j
def calculate_coupling_bounds(args):
df_large = pd.read_csv(f"./data/{sanitize_filename(args.input_text)}/{args.model_large}_probs.csv")
df_small = pd.read_csv(f"./data/{sanitize_filename(args.input_text)}/{args.model_small}_probs.csv")
results = []
for i in range(args.num_tokens):
p = torch.tensor(df_large.loc[i].to_numpy(), dtype=torch.float64).to('cuda')
q = torch.tensor(df_small.loc[i].to_numpy(), dtype=torch.float64).to('cuda')
res_gumbel = sum(gumbel_simulation(p, q, seed=args.num_retries * i + ret) for ret in
range(args.num_retries)) / args.num_retries
res_wmh = sum([wmh_simulation(p, q, seed=args.num_retries * i + ret) for ret in
range(args.num_retries)]) / args.num_retries
dtv = d_tv(p, q)
sum_max = torch.sum(torch.max(p, q))
min_pq = torch.min(p, q)
max_pq = torch.max(p, q)
tlw = torch.sum(min_pq / (min_pq + sum_max - max_pq))
results.append({
'Token': i + 1,
'DTV': dtv.item(),
'Gumbel': res_gumbel,
'WMH': res_wmh,
'Tight Lower Bound': tlw.item(),
'Upper Bound': 1 - dtv.item(),
'Lower Bound': (1 - dtv.item()) / (1 + dtv.item())
})
results_df = pd.DataFrame(results)
return results_df
def plot_coupling_bounds(args, results_df):
matplotlib.rc('font', **{'family': 'serif', 'serif': ['Helvetica']})
matplotlib.rc('text', usetex=True)
matplotlib.rc('text', usetex=True)
matplotlib.rcParams['text.latex.preamble'] = r"\usepackage{amsmath}"
matplotlib.rc('font', family='serif', size=50)
x = np.linspace(0, 1, 1000)
y1 = 1 - x
y2 = (1 - x) / (1 + x)
plt.figure(figsize=(18, 14))
line1, = plt.plot(x, y1,
label=r'$1-D_{\mathrm{TV}}(\mathcal{P},\mathcal{Q})$ \fontfamily{cmr}\selectfont{(Optimal)}',
color="#1f77b4", linewidth=7)
line2, = plt.plot(x, y2,
label=r'$\frac{1-D_{\mathrm{TV}}(\mathcal{P},\mathcal{Q})}{1+D_{\mathrm{TV}}(\mathcal{P},\mathcal{Q})}$ \fontfamily{cmr}\selectfont{(Thm. 3 Bound)}',
color="#d62728", linewidth=7)
first_legend = plt.legend(handles=[line1, line2], loc='best', fontsize=52)
plt.gca().add_artist(first_legend)
scatter1 = plt.scatter(results_df['DTV'], results_df['Gumbel'], color="#8B008B", edgecolors='none',
label=r'\fontfamily{cmr}\selectfont{Gumbel Sampling}', alpha=1, marker='o', s=500)
scatter2 = plt.scatter(results_df['DTV'], results_df['WMH'], color="#556B2F", edgecolors='none',
label=r'\fontfamily{cmr}\selectfont{Weighted MinHash}', alpha=1, marker='D', s=350)
plt.legend(handles=[scatter1, scatter2], loc='lower left', fontsize=52)
plt.xlabel(r'$D_{\mathrm{TV}}(\mathcal{P},\mathcal{Q})$', fontsize=52)
plt.ylabel(r'$\Pr[a = b]$', fontsize=52)
plt.title(r"\fontfamily{cmr}\selectfont{" + f"{args.input_text}" + "}", fontsize=52)
plt.grid(True)
plt.savefig(f"{sanitize_filename(args.input_text)}.png", format="pdf", bbox_inches="tight")
plt.show()
if __name__ == "__main__":
args = parse_arguments()
results_df = calculate_coupling_bounds(args)
plot_coupling_bounds(args, results_df)