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485127c | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 | import torch
from torch import nn
from tqdm import tqdm
from BSpline import BSpline
def optimal_beta(a: torch.Tensor, B: torch.Tensor, c: torch.Tensor = None) -> torch.Tensor:
REGULARIZATION = 0.01
# Solve B u = a
alpha = REGULARIZATION * torch.eye(B.shape[0], device=B.device, dtype=B.dtype) # Regularization term
u = torch.linalg.solve(B+alpha, a)
if c is None:
w = u
else:
# Solve B v = c
v = torch.linalg.solve(B+alpha, c)
mu = torch.dot(c, u) / torch.dot(c, v)
w = u - mu * v
# Normalize to satisfy w^T B w = 1
norm = torch.sqrt(torch.dot(w, B @ w))
return w / norm
def get_bias_vector_mc(token_list, model, bspline: BSpline, args, compute_cov: bool = False, sample_size: int = 5000):
"""
Monte Carol based method
sample_size: sampling size
"""
model.eval()
device = args.device
n_bases = bspline.n_bases
if bspline.add_intercept:
n_bases += 1
bias_list = []
cov_list = []
for tokens in tqdm(token_list):
input_ids = tokens.input_ids[0]
with torch.no_grad():
logits = model(**tokens).logits[0, :-1] # (seq_len, vocab_size)
seq_len, vocab_size = logits.shape
probs = torch.softmax(logits, dim=-1) # (seq_len, vocab)
logp = torch.log_softmax(logits, dim=-1) # (seq_len, vocab)
labels = input_ids[1:] # (seq_len,)
log_ll = logp[torch.arange(seq_len), labels] # (seq_len,)
w_j = bspline.predict(log_ll.clamp_min(bspline.start).reshape(-1)).to(device)
w_j = w_j.reshape(seq_len, n_bases)
sampled_indices = torch.multinomial(probs, num_samples=sample_size, replacement=True)
sampled_logp = logp.gather(1, sampled_indices)
flat_sampled_logp = sampled_logp.clamp_min(bspline.start).reshape(-1)
flat_basis_samples = bspline.predict(flat_sampled_logp).to(device)
basis_samples = flat_basis_samples.reshape(seq_len, sample_size, n_bases)
mean_ref = basis_samples.mean(dim=1) # (seq_len, n_bases)
bias_sample = (w_j - mean_ref).sum(dim=0) # (n_bases,)
bias_list.append(bias_sample)
if compute_cov:
cov_sample = torch.zeros(n_bases, n_bases, device=device)
for t in range(seq_len):
phi_samples = basis_samples[t]
sample_mean = phi_samples.mean(dim=0)
centered_samples = phi_samples - sample_mean
cov_t = (centered_samples.t() @ centered_samples) / (sample_size - 1)
if bspline.add_intercept:
cov_t[0, :] = 0.0
cov_t[:, 0] = 0.0
cov_sample += cov_t
cov_list.append(cov_sample)
bias_vector = torch.stack(bias_list, dim=0).mean(dim=0) # (n_bases,)
if compute_cov:
cov_matrix = torch.stack(cov_list, dim=0).mean(dim=0) # (n_bases, n_bases)
return bias_vector, cov_matrix
return bias_vector
def get_bias_vector(token_list, model, bspline: BSpline, args, compute_cov: bool = False, speedup_rate = 1):
"""
For each text in text_list, compute the bias vector
(mean difference between sampled basis and expected basis)
and, if requested, the covariance matrix of basis differences.
Returns bias (n_bases,) and optionally cov (n_bases, n_bases).
"""
model.eval()
device = args.device
n_bases = bspline.n_bases
if bspline.add_intercept:
n_bases += 1
bias_list = []
cov_list = []
for tokens in tqdm(token_list):
input_ids = tokens.input_ids[0]
with torch.no_grad():
logits = model(**tokens).logits[0, :-1] # (seq_len, vocab_size)
seq_len, vocab_size = logits.shape
probs = torch.softmax(logits, dim=-1) # (seq_len, vocab)
vocab_size = int(vocab_size / speedup_rate)
probs, _ = torch.topk(probs, k=vocab_size, dim=-1)
probs = probs / probs.sum(dim=-1, keepdim=True)
logp = torch.log_softmax(logits, dim=-1) # (seq_len, vocab)
# Basis at the actual next-token labels
labels = input_ids[1:] # (seq_len,)
# Index basis per position
log_ll = logp[torch.arange(seq_len), labels] # (seq_len, n_bases)
w_j = bspline.predict(log_ll.clamp_min(bspline.start).reshape(-1)).to(device)
w_j = w_j.reshape(seq_len, n_bases)
# Expected basis at the next-token
logp, _ = torch.topk(logp, k=vocab_size, dim=-1)
# Compute basis for all log-probabilities
flat_logp = logp.clamp_min(bspline.start).reshape(-1)
flat_basis = bspline.predict(flat_logp).to(device) # (seq_len*vocab, n_bases)
basis = flat_basis.reshape(seq_len, vocab_size, n_bases) # (seq_len, vocab, n_bases)
# Expected basis per position: E[basis] = sum_k p_{ik} * basis_{ik}
mean_ref = (probs.unsqueeze(-1) * basis).sum(dim=1) # (seq_len, n_bases)
# Bias: average difference over positions
bias_sample = (mean_ref - w_j).sum(dim=0) # (n_bases,)
bias_list.append(bias_sample)
if compute_cov:
###### Naive version ######
cov_sample = torch.zeros(n_bases, n_bases, device=device)
for t in range(seq_len):
p_t = probs[t] # (vocab,)
phi_t = basis[t] # (vocab, n_bases)
# E_b[phi_t]: (n_bases,)
Ex_t = (p_t.unsqueeze(1) * phi_t).sum(dim=0)
# E_b[phi_t phi_t^T]: (n_bases, n_bases)
ExxT_t = phi_t.t() @ (p_t.unsqueeze(1) * phi_t)
cov_t = ExxT_t - Ex_t.unsqueeze(1) @ Ex_t.unsqueeze(0)
cov_sample += cov_t
###### Faster version ######
# wb = probs.unsqueeze(-1) * basis # (T, V, K)
# # 2) compute E[φ φᵀ] summed over t,b:
# # for each t: basis[t].T @ wb[t] → (K, K)
# # sum over t with a single bmm + sum:
# ExxT = torch.sum(torch.bmm(basis.transpose(1,2), wb), dim=0) # (K, K)
# Ex_t = wb.sum(dim=1) # (T, K)
# sum_outer = torch.einsum('tk,tl->kl', Ex_t, Ex_t) # (K, K)
# cov_sample = ExxT - sum_outer
cov_list.append(cov_sample)
bias_vector = torch.stack(bias_list, dim=0).mean(dim=0) # (n_bases,)
if compute_cov:
cov_matrix = torch.stack(cov_list, dim=0).mean(dim=0) # (n_bases, n_bases)
return bias_vector, cov_matrix
return bias_vector
class BSplineTheory(nn.Module):
def __init__(self, bspline_args, machine_text: bool = False):
super().__init__()
self.bspline = BSpline(**bspline_args)
self.machine_text = machine_text
self.beta_hat = None
def fit(self, human_token_list, machine_token_list, model, args):
device = args.device
print("Learning w function...")
print("Fetching bias and covariance for human texts...")
bias_a, cov_B = get_bias_vector(human_token_list, model, self.bspline, args, compute_cov=True)
print("Computing beta_hat...")
# print("bias_a:", torch.round(bias_a, decimals=2))
# print("cov_B:", torch.round(cov_B, decimals=2))
if self.machine_text:
print("Fetching bias for machine-generated texts...")
bias_c = get_bias_vector(machine_token_list, model, self.bspline, args, compute_cov=False)
# print("bias_c:", torch.round(bias_c, decimals=2))
else:
bias_c = None
self.beta_hat = optimal_beta(
bias_a.to(device), cov_B.to(device),
bias_c.to(device) if bias_c is not None else None
)
print("beta_hat:", torch.round(self.beta_hat, decimals=3))
def forward(self, x: torch.Tensor) -> torch.Tensor:
device = x.device
flat = x.clamp_min(self.bspline.start).reshape(-1)
basis = self.bspline.predict(flat).to(device) # (flat_len, n_bases)
w_flat = basis @ self.beta_hat.to(device) # (flat_len,)
return w_flat.reshape(x.shape)
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