Upload iterative_pagerank.py with huggingface_hub
Browse files- iterative_pagerank.py +691 -0
iterative_pagerank.py
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| 1 |
+
"""
|
| 2 |
+
Non-autoregressive iterative PageRank model.
|
| 3 |
+
|
| 4 |
+
PageRank IS power iteration — the same linear operation applied repeatedly
|
| 5 |
+
until convergence. This maps perfectly to shared-weight iterative transformers.
|
| 6 |
+
|
| 7 |
+
Architecture:
|
| 8 |
+
- Input: N nodes, each gets its adjacency row (directed graph)
|
| 9 |
+
- Shared transformer body (bidirectional attention)
|
| 10 |
+
- Output: each node predicts its PageRank value (regression)
|
| 11 |
+
- Iterative refinement mirrors power iteration
|
| 12 |
+
- Train with K=16, eval with K=16..256+
|
| 13 |
+
|
| 14 |
+
Difficulty knobs:
|
| 15 |
+
- Damping factor d: higher d → more structure-dependent → harder
|
| 16 |
+
- Graph type: random (easy) → power-law/hub (hard)
|
| 17 |
+
- Edge density: affects spectral gap → convergence rate
|
| 18 |
+
|
| 19 |
+
Usage:
|
| 20 |
+
python scripts/iterative_pagerank.py --device cpu --steps 500 --batch 64 --n-nodes 16
|
| 21 |
+
python scripts/iterative_pagerank.py --device cuda --steps 50000 --batch 2048 --compile
|
| 22 |
+
"""
|
| 23 |
+
|
| 24 |
+
import argparse
|
| 25 |
+
import math
|
| 26 |
+
import time
|
| 27 |
+
from contextlib import nullcontext
|
| 28 |
+
from dataclasses import dataclass
|
| 29 |
+
|
| 30 |
+
import torch
|
| 31 |
+
import torch.nn as nn
|
| 32 |
+
import torch.nn.functional as F
|
| 33 |
+
|
| 34 |
+
|
| 35 |
+
# ---------------------------------------------------------------------------
|
| 36 |
+
# Config
|
| 37 |
+
# ---------------------------------------------------------------------------
|
| 38 |
+
|
| 39 |
+
@dataclass
|
| 40 |
+
class PageRankConfig:
|
| 41 |
+
n_nodes: int = 64
|
| 42 |
+
d_model: int = 128
|
| 43 |
+
n_heads: int = 4
|
| 44 |
+
n_layers: int = 4
|
| 45 |
+
d_ff: int = 512
|
| 46 |
+
dropout: float = 0.1
|
| 47 |
+
train_iters: int = 16
|
| 48 |
+
rope_base: float = 10.0
|
| 49 |
+
damping: float = 0.85 # PageRank damping factor
|
| 50 |
+
|
| 51 |
+
# Reverse curriculum: hard mixed graphs from start (sotaku-style)
|
| 52 |
+
# graph_type_weights: [random, preferential_attachment, hub_spoke]
|
| 53 |
+
curriculum: tuple = (
|
| 54 |
+
(0.0, 0.08, (0.2, 0.5, 0.3)),
|
| 55 |
+
(1.0, 0.08, (0.2, 0.5, 0.3)),
|
| 56 |
+
)
|
| 57 |
+
|
| 58 |
+
|
| 59 |
+
# ---------------------------------------------------------------------------
|
| 60 |
+
# RoPE
|
| 61 |
+
# ---------------------------------------------------------------------------
|
| 62 |
+
|
| 63 |
+
def build_rope_cache(seq_len, head_dim, base=10.0, device="cpu"):
|
| 64 |
+
theta = 1.0 / (base ** (torch.arange(0, head_dim, 2, device=device).float() / head_dim))
|
| 65 |
+
positions = torch.arange(seq_len, device=device).float()
|
| 66 |
+
freqs = torch.outer(positions, theta)
|
| 67 |
+
return freqs.cos(), freqs.sin()
|
| 68 |
+
|
| 69 |
+
|
| 70 |
+
def apply_rope(x, cos, sin):
|
| 71 |
+
d2 = x.shape[-1] // 2
|
| 72 |
+
x1, x2 = x[..., :d2], x[..., d2:]
|
| 73 |
+
cos, sin = cos[:x.shape[2], :], sin[:x.shape[2], :]
|
| 74 |
+
return torch.cat([x1 * cos - x2 * sin, x2 * cos + x1 * sin], dim=-1)
|
| 75 |
+
|
| 76 |
+
|
| 77 |
+
# ---------------------------------------------------------------------------
|
| 78 |
+
# Transformer layers
|
| 79 |
+
# ---------------------------------------------------------------------------
|
| 80 |
+
|
| 81 |
+
class MultiHeadAttention(nn.Module):
|
| 82 |
+
def __init__(self, d_model, n_heads, dropout=0.1):
|
| 83 |
+
super().__init__()
|
| 84 |
+
self.n_heads = n_heads
|
| 85 |
+
self.head_dim = d_model // n_heads
|
| 86 |
+
self.wq = nn.Linear(d_model, d_model, bias=False)
|
| 87 |
+
self.wk = nn.Linear(d_model, d_model, bias=False)
|
| 88 |
+
self.wv = nn.Linear(d_model, d_model, bias=False)
|
| 89 |
+
self.wo = nn.Linear(d_model, d_model, bias=False)
|
| 90 |
+
self.dropout = nn.Dropout(dropout)
|
| 91 |
+
|
| 92 |
+
def forward(self, x, cos, sin, adj_bias=None):
|
| 93 |
+
B, N, D = x.shape
|
| 94 |
+
q = self.wq(x).view(B, N, self.n_heads, self.head_dim).transpose(1, 2)
|
| 95 |
+
k = self.wk(x).view(B, N, self.n_heads, self.head_dim).transpose(1, 2)
|
| 96 |
+
v = self.wv(x).view(B, N, self.n_heads, self.head_dim).transpose(1, 2)
|
| 97 |
+
q, k = apply_rope(q, cos, sin), apply_rope(k, cos, sin)
|
| 98 |
+
attn = F.scaled_dot_product_attention(
|
| 99 |
+
q, k, v, attn_mask=adj_bias,
|
| 100 |
+
dropout_p=self.dropout.p if self.training else 0.0,
|
| 101 |
+
)
|
| 102 |
+
return self.wo(attn.transpose(1, 2).contiguous().view(B, N, D))
|
| 103 |
+
|
| 104 |
+
|
| 105 |
+
class TransformerBlock(nn.Module):
|
| 106 |
+
def __init__(self, d_model, n_heads, d_ff, dropout=0.1):
|
| 107 |
+
super().__init__()
|
| 108 |
+
self.norm1 = nn.RMSNorm(d_model)
|
| 109 |
+
self.attn = MultiHeadAttention(d_model, n_heads, dropout)
|
| 110 |
+
self.norm2 = nn.RMSNorm(d_model)
|
| 111 |
+
self.ff = nn.Sequential(
|
| 112 |
+
nn.Linear(d_model, d_ff, bias=False),
|
| 113 |
+
nn.ReLU(),
|
| 114 |
+
nn.Linear(d_ff, d_model, bias=False),
|
| 115 |
+
nn.Dropout(dropout),
|
| 116 |
+
)
|
| 117 |
+
|
| 118 |
+
def forward(self, x, cos, sin, adj_bias=None):
|
| 119 |
+
x = x + self.attn(self.norm1(x), cos, sin, adj_bias)
|
| 120 |
+
x = x + self.ff(self.norm2(x))
|
| 121 |
+
return x
|
| 122 |
+
|
| 123 |
+
|
| 124 |
+
# ---------------------------------------------------------------------------
|
| 125 |
+
# PageRank Model
|
| 126 |
+
# ---------------------------------------------------------------------------
|
| 127 |
+
|
| 128 |
+
class IterativePageRankModel(nn.Module):
|
| 129 |
+
def __init__(self, config: PageRankConfig):
|
| 130 |
+
super().__init__()
|
| 131 |
+
self.config = config
|
| 132 |
+
d = config.d_model
|
| 133 |
+
N = config.n_nodes
|
| 134 |
+
|
| 135 |
+
# Input: adjacency row (N) → d_model
|
| 136 |
+
self.input_proj = nn.Linear(N, d, bias=False)
|
| 137 |
+
|
| 138 |
+
# Prediction feedback: previous PR estimate (1 scalar per node) → d_model
|
| 139 |
+
self.pred_proj = nn.Linear(1, d, bias=False)
|
| 140 |
+
|
| 141 |
+
# Shared transformer
|
| 142 |
+
self.layers = nn.ModuleList([
|
| 143 |
+
TransformerBlock(d, config.n_heads, config.d_ff, config.dropout)
|
| 144 |
+
for _ in range(config.n_layers)
|
| 145 |
+
])
|
| 146 |
+
self.final_norm = nn.RMSNorm(d)
|
| 147 |
+
|
| 148 |
+
# Output: d_model → 1 (PageRank logit per node)
|
| 149 |
+
self.output_head = nn.Linear(d, 1, bias=False)
|
| 150 |
+
|
| 151 |
+
cos, sin = build_rope_cache(N, d // config.n_heads, config.rope_base)
|
| 152 |
+
self.register_buffer("rope_cos", cos)
|
| 153 |
+
self.register_buffer("rope_sin", sin)
|
| 154 |
+
|
| 155 |
+
def _transformer_step(self, h_input, cos, sin, adj_bias):
|
| 156 |
+
x = h_input
|
| 157 |
+
for layer in self.layers:
|
| 158 |
+
x = layer(x, cos, sin, adj_bias)
|
| 159 |
+
x = self.final_norm(x)
|
| 160 |
+
return self.output_head(x)
|
| 161 |
+
|
| 162 |
+
def forward(self, adj, n_iters=None):
|
| 163 |
+
"""
|
| 164 |
+
adj: (B, N, N) directed adjacency matrix
|
| 165 |
+
Returns: list of PR predictions (B, N), one per iteration
|
| 166 |
+
"""
|
| 167 |
+
if n_iters is None:
|
| 168 |
+
n_iters = self.config.train_iters
|
| 169 |
+
|
| 170 |
+
B, N, _ = adj.shape
|
| 171 |
+
device = adj.device
|
| 172 |
+
|
| 173 |
+
# Adjacency bias for attention: edges get a boost
|
| 174 |
+
adj_bias = adj * 2.0
|
| 175 |
+
adj_bias = adj_bias.unsqueeze(1) # (B, 1, N, N)
|
| 176 |
+
|
| 177 |
+
# Encode graph structure
|
| 178 |
+
h = self.input_proj(adj) # (B, N, d)
|
| 179 |
+
|
| 180 |
+
all_prs = []
|
| 181 |
+
# Initial PR estimate: uniform
|
| 182 |
+
pr_pred = torch.full((B, N, 1), 1.0 / N, device=device)
|
| 183 |
+
|
| 184 |
+
for _ in range(n_iters):
|
| 185 |
+
h_input = h + self.pred_proj(pr_pred)
|
| 186 |
+
logits = self._transformer_step(h_input, self.rope_cos, self.rope_sin, adj_bias)
|
| 187 |
+
# logits: (B, N, 1) → softmax across nodes to get PR distribution
|
| 188 |
+
pr = F.softmax(logits.squeeze(-1), dim=-1) # (B, N)
|
| 189 |
+
all_prs.append(pr)
|
| 190 |
+
pr_pred = pr.unsqueeze(-1).detach()
|
| 191 |
+
|
| 192 |
+
return all_prs
|
| 193 |
+
|
| 194 |
+
|
| 195 |
+
# ---------------------------------------------------------------------------
|
| 196 |
+
# Ground truth PageRank (power iteration)
|
| 197 |
+
# ---------------------------------------------------------------------------
|
| 198 |
+
|
| 199 |
+
def compute_pagerank(adj: torch.Tensor, damping: float = 0.85, n_iters: int = 30, tol: float = 1e-8):
|
| 200 |
+
"""Compute PageRank via power iteration.
|
| 201 |
+
|
| 202 |
+
adj: (B, N, N) directed adjacency (adj[i,j]=1 means edge from i to j)
|
| 203 |
+
Returns: (B, N) PageRank values summing to 1
|
| 204 |
+
"""
|
| 205 |
+
B, N, _ = adj.shape
|
| 206 |
+
device = adj.device
|
| 207 |
+
|
| 208 |
+
# Out-degree per node
|
| 209 |
+
out_deg = adj.sum(dim=-1, keepdim=True).clamp(min=1) # (B, N, 1)
|
| 210 |
+
|
| 211 |
+
# Transition matrix: M[j,i] = adj[i,j] / out_deg[i]
|
| 212 |
+
# (probability of going from i to j)
|
| 213 |
+
M = (adj / out_deg).transpose(1, 2) # (B, N, N)
|
| 214 |
+
|
| 215 |
+
# Power iteration
|
| 216 |
+
pr = torch.full((B, N), 1.0 / N, device=device)
|
| 217 |
+
teleport = (1 - damping) / N
|
| 218 |
+
|
| 219 |
+
for _ in range(n_iters):
|
| 220 |
+
pr_new = teleport + damping * (M @ pr.unsqueeze(-1)).squeeze(-1)
|
| 221 |
+
# Handle dangling nodes (no outgoing edges): redistribute their mass
|
| 222 |
+
dangling_mass = pr * (adj.sum(dim=-1) == 0).float()
|
| 223 |
+
pr_new = pr_new + damping * dangling_mass.sum(dim=-1, keepdim=True) / N
|
| 224 |
+
# Normalize
|
| 225 |
+
pr_new = pr_new / pr_new.sum(dim=-1, keepdim=True)
|
| 226 |
+
|
| 227 |
+
if (pr_new - pr).abs().max() < tol:
|
| 228 |
+
break
|
| 229 |
+
pr = pr_new
|
| 230 |
+
|
| 231 |
+
return pr
|
| 232 |
+
|
| 233 |
+
|
| 234 |
+
# ---------------------------------------------------------------------------
|
| 235 |
+
# Graph generation
|
| 236 |
+
# ---------------------------------------------------------------------------
|
| 237 |
+
|
| 238 |
+
def generate_random_graph(batch_size, n_nodes, edge_prob, device):
|
| 239 |
+
"""Erdos-Renyi directed random graph."""
|
| 240 |
+
adj = (torch.rand(batch_size, n_nodes, n_nodes, device=device) < edge_prob).float()
|
| 241 |
+
adj[:, range(n_nodes), range(n_nodes)] = 0 # no self-loops
|
| 242 |
+
return adj
|
| 243 |
+
|
| 244 |
+
|
| 245 |
+
def generate_preferential_attachment(batch_size, n_nodes, n_edges_per_node, device):
|
| 246 |
+
"""Barabasi-Albert: sequential node addition with degree-proportional attachment.
|
| 247 |
+
Creates true power-law degree distribution. Uses CPU for generation, moves to device.
|
| 248 |
+
"""
|
| 249 |
+
adj = torch.zeros(batch_size, n_nodes, n_nodes)
|
| 250 |
+
m = max(1, n_edges_per_node)
|
| 251 |
+
|
| 252 |
+
# Start with a small clique
|
| 253 |
+
for i in range(min(m + 1, n_nodes)):
|
| 254 |
+
for j in range(i + 1, min(m + 1, n_nodes)):
|
| 255 |
+
adj[:, i, j] = 1
|
| 256 |
+
|
| 257 |
+
for new_node in range(m + 1, n_nodes):
|
| 258 |
+
deg = adj[:, :new_node, :new_node].sum(dim=-1) + adj[:, :new_node, :new_node].sum(dim=-2)
|
| 259 |
+
deg = deg + 1
|
| 260 |
+
probs = deg / deg.sum(dim=-1, keepdim=True)
|
| 261 |
+
|
| 262 |
+
for _ in range(m):
|
| 263 |
+
targets = torch.multinomial(probs, 1).squeeze(-1)
|
| 264 |
+
adj[torch.arange(batch_size), new_node, targets] = 1
|
| 265 |
+
reverse = torch.rand(batch_size) < 0.5
|
| 266 |
+
adj[torch.arange(batch_size)[reverse], targets[reverse], new_node] = 1
|
| 267 |
+
|
| 268 |
+
return adj.to(device)
|
| 269 |
+
|
| 270 |
+
|
| 271 |
+
def generate_hub_spoke(batch_size, n_nodes, n_hubs, device):
|
| 272 |
+
"""Hub-spoke graphs: few hub nodes connected to many spokes.
|
| 273 |
+
Uses CPU for generation, moves to device.
|
| 274 |
+
"""
|
| 275 |
+
adj = torch.zeros(batch_size, n_nodes, n_nodes)
|
| 276 |
+
|
| 277 |
+
hub_indices = torch.randint(0, n_nodes, (batch_size, n_hubs))
|
| 278 |
+
|
| 279 |
+
for i in range(n_nodes):
|
| 280 |
+
for h in range(n_hubs):
|
| 281 |
+
connect = torch.rand(batch_size) < 0.6
|
| 282 |
+
hub = hub_indices[:, h]
|
| 283 |
+
adj[connect, i, hub[connect]] = 1
|
| 284 |
+
back = connect & (torch.rand(batch_size) < 0.3)
|
| 285 |
+
adj[back, hub[back], i] = 1
|
| 286 |
+
|
| 287 |
+
for h1 in range(n_hubs):
|
| 288 |
+
for h2 in range(h1 + 1, n_hubs):
|
| 289 |
+
connect = torch.rand(batch_size) < 0.8
|
| 290 |
+
adj[connect, hub_indices[connect, h1], hub_indices[connect, h2]] = 1
|
| 291 |
+
adj[connect, hub_indices[connect, h2], hub_indices[connect, h1]] = 1
|
| 292 |
+
|
| 293 |
+
noise = (torch.rand(batch_size, n_nodes, n_nodes) < 0.02).float()
|
| 294 |
+
adj = (adj + noise).clamp(max=1)
|
| 295 |
+
adj[:, range(n_nodes), range(n_nodes)] = 0
|
| 296 |
+
|
| 297 |
+
return adj.to(device)
|
| 298 |
+
|
| 299 |
+
|
| 300 |
+
def generate_batch(batch_size, config, edge_prob, graph_weights, device):
|
| 301 |
+
"""Generate mixed batch of graph types."""
|
| 302 |
+
N = config.n_nodes
|
| 303 |
+
w_random, w_pref, w_hub = graph_weights
|
| 304 |
+
|
| 305 |
+
# Determine count per type
|
| 306 |
+
n_random = int(batch_size * w_random)
|
| 307 |
+
n_pref = int(batch_size * w_pref)
|
| 308 |
+
n_hub = batch_size - n_random - n_pref
|
| 309 |
+
|
| 310 |
+
adjs = []
|
| 311 |
+
if n_random > 0:
|
| 312 |
+
adjs.append(generate_random_graph(n_random, N, edge_prob, device))
|
| 313 |
+
if n_pref > 0:
|
| 314 |
+
n_edges = max(1, int(edge_prob * N * 0.5))
|
| 315 |
+
adjs.append(generate_preferential_attachment(n_pref, N, n_edges, device))
|
| 316 |
+
if n_hub > 0:
|
| 317 |
+
n_hubs = max(2, N // 16)
|
| 318 |
+
adjs.append(generate_hub_spoke(n_hub, N, n_hubs, device))
|
| 319 |
+
|
| 320 |
+
adj = torch.cat(adjs, dim=0) if len(adjs) > 1 else adjs[0]
|
| 321 |
+
|
| 322 |
+
# Shuffle
|
| 323 |
+
perm = torch.randperm(batch_size, device=device)
|
| 324 |
+
adj = adj[perm]
|
| 325 |
+
|
| 326 |
+
# Compute ground truth PageRank
|
| 327 |
+
targets = compute_pagerank(adj, damping=config.damping)
|
| 328 |
+
|
| 329 |
+
# Stats
|
| 330 |
+
with torch.no_grad():
|
| 331 |
+
entropy = -(targets * (targets + 1e-10).log()).sum(dim=-1).mean().item()
|
| 332 |
+
max_pr = targets.max(dim=-1).values.mean().item()
|
| 333 |
+
gini = _gini(targets)
|
| 334 |
+
|
| 335 |
+
metadata = {
|
| 336 |
+
"edge_prob": edge_prob,
|
| 337 |
+
"entropy": entropy,
|
| 338 |
+
"max_pr": max_pr,
|
| 339 |
+
"gini": gini,
|
| 340 |
+
}
|
| 341 |
+
|
| 342 |
+
return adj, targets, metadata
|
| 343 |
+
|
| 344 |
+
|
| 345 |
+
def _gini(pr):
|
| 346 |
+
"""Gini coefficient of PageRank distribution. 0=uniform, 1=concentrated."""
|
| 347 |
+
sorted_pr, _ = pr.sort(dim=-1)
|
| 348 |
+
N = pr.shape[-1]
|
| 349 |
+
index = torch.arange(1, N + 1, device=pr.device).float()
|
| 350 |
+
return (2 * (index * sorted_pr).sum(dim=-1) / (N * sorted_pr.sum(dim=-1)) - (N + 1) / N).mean().item()
|
| 351 |
+
|
| 352 |
+
|
| 353 |
+
def get_curriculum_params(step, total_steps, curriculum):
|
| 354 |
+
"""Get current edge_prob and graph_weights from curriculum."""
|
| 355 |
+
frac = step / max(1, total_steps)
|
| 356 |
+
for i in range(len(curriculum) - 1):
|
| 357 |
+
f0, p0, w0 = curriculum[i]
|
| 358 |
+
f1, p1, w1 = curriculum[i + 1]
|
| 359 |
+
if f0 <= frac <= f1:
|
| 360 |
+
if f1 == f0:
|
| 361 |
+
return p0, w0
|
| 362 |
+
t = (frac - f0) / (f1 - f0)
|
| 363 |
+
p = p0 + t * (p1 - p0)
|
| 364 |
+
w = tuple(a + t * (b - a) for a, b in zip(w0, w1))
|
| 365 |
+
return p, w
|
| 366 |
+
return curriculum[-1][1], curriculum[-1][2]
|
| 367 |
+
|
| 368 |
+
|
| 369 |
+
# ---------------------------------------------------------------------------
|
| 370 |
+
# Training
|
| 371 |
+
# ---------------------------------------------------------------------------
|
| 372 |
+
|
| 373 |
+
def train(config, args):
|
| 374 |
+
device = args.device
|
| 375 |
+
|
| 376 |
+
if device == "cuda":
|
| 377 |
+
torch.set_float32_matmul_precision('high')
|
| 378 |
+
torch.backends.cuda.matmul.allow_tf32 = True
|
| 379 |
+
torch.backends.cudnn.allow_tf32 = True
|
| 380 |
+
|
| 381 |
+
model = IterativePageRankModel(config).to(device)
|
| 382 |
+
n_params = sum(p.numel() for p in model.parameters())
|
| 383 |
+
print(f"Model params: {n_params:,} ({n_params/1e6:.2f}M)")
|
| 384 |
+
print(f"Config: {config.n_layers}L, d={config.d_model}, h={config.n_heads}, "
|
| 385 |
+
f"ff={config.d_ff}, iters={config.train_iters}, N={config.n_nodes}")
|
| 386 |
+
print(f"Damping: {config.damping}")
|
| 387 |
+
print(f"Device: {device}")
|
| 388 |
+
print()
|
| 389 |
+
|
| 390 |
+
optimizer = torch.optim.AdamW(model.parameters(), lr=args.lr, betas=(0.9, 0.95), weight_decay=0.01)
|
| 391 |
+
|
| 392 |
+
def lr_schedule(step):
|
| 393 |
+
if step < args.warmup:
|
| 394 |
+
return step / args.warmup
|
| 395 |
+
progress = (step - args.warmup) / max(1, args.steps - args.warmup)
|
| 396 |
+
return 0.01 + 0.99 * 0.5 * (1 + math.cos(math.pi * progress))
|
| 397 |
+
|
| 398 |
+
scheduler = torch.optim.lr_scheduler.LambdaLR(optimizer, lr_schedule)
|
| 399 |
+
|
| 400 |
+
if args.compile and device == "cuda":
|
| 401 |
+
print("Compiling transformer step...")
|
| 402 |
+
model._transformer_step = torch.compile(model._transformer_step)
|
| 403 |
+
print("Compile done.")
|
| 404 |
+
|
| 405 |
+
use_amp = device == "cuda"
|
| 406 |
+
scaler = torch.amp.GradScaler('cuda', enabled=use_amp)
|
| 407 |
+
autocast_ctx = torch.amp.autocast('cuda', dtype=torch.bfloat16) if use_amp else nullcontext()
|
| 408 |
+
|
| 409 |
+
# Pre-generate graph pool for fast sampling during training
|
| 410 |
+
pool_size = min(args.steps * args.batch, 100_000) # cap at 100K graphs
|
| 411 |
+
print(f"Pre-generating {pool_size:,} graphs...")
|
| 412 |
+
edge_prob, graph_weights = get_curriculum_params(0, args.steps, config.curriculum)
|
| 413 |
+
pool_adj, pool_targets, pool_meta = generate_batch(pool_size, config, edge_prob, graph_weights, device)
|
| 414 |
+
print(f"Pool ready. Gini={pool_meta['gini']:.2f}, max_pr={pool_meta['max_pr']:.4f}")
|
| 415 |
+
|
| 416 |
+
t0 = time.time()
|
| 417 |
+
|
| 418 |
+
for step in range(args.steps + 1):
|
| 419 |
+
model.train()
|
| 420 |
+
|
| 421 |
+
# Sample batch from pre-generated pool
|
| 422 |
+
idx = torch.randint(0, pool_size, (args.batch,), device=device)
|
| 423 |
+
adj = pool_adj[idx]
|
| 424 |
+
targets = pool_targets[idx]
|
| 425 |
+
meta = pool_meta
|
| 426 |
+
|
| 427 |
+
with autocast_ctx:
|
| 428 |
+
all_prs = model(adj)
|
| 429 |
+
|
| 430 |
+
# Loss: KL divergence at every iteration (intermediate supervision)
|
| 431 |
+
# targets is the true PR distribution, all_prs[i] is predicted distribution
|
| 432 |
+
loss = 0.0
|
| 433 |
+
for pr_pred in all_prs:
|
| 434 |
+
# KL(target || pred) = sum(target * log(target/pred))
|
| 435 |
+
loss += F.kl_div(
|
| 436 |
+
(pr_pred + 1e-10).log(),
|
| 437 |
+
targets,
|
| 438 |
+
reduction='batchmean',
|
| 439 |
+
)
|
| 440 |
+
loss /= len(all_prs)
|
| 441 |
+
|
| 442 |
+
optimizer.zero_grad()
|
| 443 |
+
scaler.scale(loss).backward()
|
| 444 |
+
scaler.unscale_(optimizer)
|
| 445 |
+
torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)
|
| 446 |
+
scaler.step(optimizer)
|
| 447 |
+
scaler.update()
|
| 448 |
+
scheduler.step()
|
| 449 |
+
|
| 450 |
+
if step % args.log_interval == 0:
|
| 451 |
+
elapsed = time.time() - t0
|
| 452 |
+
with torch.no_grad():
|
| 453 |
+
final_pr = all_prs[-1]
|
| 454 |
+
mse = ((final_pr - targets) ** 2).mean().item()
|
| 455 |
+
# Ranking accuracy: Kendall tau correlation
|
| 456 |
+
rank_acc = _ranking_accuracy(final_pr, targets)
|
| 457 |
+
# Top-5 accuracy
|
| 458 |
+
top5_acc = _topk_accuracy(final_pr, targets, k=5)
|
| 459 |
+
|
| 460 |
+
print(f"Step {step:5d} | KL: {loss.item():.4f} | MSE: {mse:.6f} | "
|
| 461 |
+
f"Rank: {rank_acc:.1%} | Top5: {top5_acc:.1%} | "
|
| 462 |
+
f"Gini: {meta['gini']:.2f} | {elapsed:.1f}s")
|
| 463 |
+
|
| 464 |
+
if step > 0 and step % args.eval_interval == 0:
|
| 465 |
+
evaluate(model, config, device, args.eval_batch)
|
| 466 |
+
|
| 467 |
+
print("\n" + "=" * 70)
|
| 468 |
+
print("FINAL EVALUATION")
|
| 469 |
+
print("=" * 70)
|
| 470 |
+
evaluate(model, config, device, args.eval_batch, verbose=True)
|
| 471 |
+
|
| 472 |
+
if args.save_path:
|
| 473 |
+
save_checkpoint(model, config, args)
|
| 474 |
+
|
| 475 |
+
return model
|
| 476 |
+
|
| 477 |
+
|
| 478 |
+
def _ranking_accuracy(pred_pr, true_pr):
|
| 479 |
+
"""Fraction of pairwise orderings that match."""
|
| 480 |
+
pred_rank = pred_pr.argsort(dim=-1, descending=True).argsort(dim=-1)
|
| 481 |
+
true_rank = true_pr.argsort(dim=-1, descending=True).argsort(dim=-1)
|
| 482 |
+
# Pairwise concordance (simplified Kendall tau)
|
| 483 |
+
B, N = pred_pr.shape
|
| 484 |
+
correct = 0
|
| 485 |
+
total = 0
|
| 486 |
+
# Sample pairs for efficiency
|
| 487 |
+
n_pairs = min(100, N * (N - 1) // 2)
|
| 488 |
+
for _ in range(n_pairs):
|
| 489 |
+
i, j = torch.randint(0, N, (2,))
|
| 490 |
+
if i == j:
|
| 491 |
+
continue
|
| 492 |
+
pred_order = pred_pr[:, i] > pred_pr[:, j]
|
| 493 |
+
true_order = true_pr[:, i] > true_pr[:, j]
|
| 494 |
+
correct += (pred_order == true_order).float().sum().item()
|
| 495 |
+
total += B
|
| 496 |
+
return correct / max(1, total)
|
| 497 |
+
|
| 498 |
+
|
| 499 |
+
def _topk_accuracy(pred_pr, true_pr, k=5):
|
| 500 |
+
"""Fraction of true top-k nodes that appear in predicted top-k."""
|
| 501 |
+
pred_topk = pred_pr.topk(k, dim=-1).indices # (B, k)
|
| 502 |
+
true_topk = true_pr.topk(k, dim=-1).indices # (B, k)
|
| 503 |
+
# Check overlap
|
| 504 |
+
hits = 0
|
| 505 |
+
for i in range(k):
|
| 506 |
+
hits += (pred_topk == true_topk[:, i:i+1]).any(dim=-1).float().sum().item()
|
| 507 |
+
return hits / (pred_pr.shape[0] * k)
|
| 508 |
+
|
| 509 |
+
|
| 510 |
+
def evaluate(model, config, device, eval_batch=1024, verbose=False):
|
| 511 |
+
"""Evaluate across graph types and iteration counts."""
|
| 512 |
+
model.eval()
|
| 513 |
+
|
| 514 |
+
graph_configs = [
|
| 515 |
+
("Random p=0.15", 0.15, (1.0, 0.0, 0.0)),
|
| 516 |
+
("Preferential", 0.10, (0.0, 1.0, 0.0)),
|
| 517 |
+
("Hub-spoke", 0.10, (0.0, 0.0, 1.0)),
|
| 518 |
+
("Mixed (hard)", 0.08, (0.2, 0.5, 0.3)),
|
| 519 |
+
]
|
| 520 |
+
iter_counts = [config.train_iters, 32, 64, 128, 256]
|
| 521 |
+
|
| 522 |
+
for name, ep, gw in graph_configs:
|
| 523 |
+
adj, targets, meta = generate_batch(eval_batch, config, ep, gw, device)
|
| 524 |
+
|
| 525 |
+
print(f"\n {name} (gini={meta['gini']:.2f}, max_pr={meta['max_pr']:.4f})")
|
| 526 |
+
print(f" {'Iters':>6s} | {'KL':>8s} | {'MSE':>10s} | {'Rank':>6s} | {'Top5':>6s}")
|
| 527 |
+
print(f" {'-'*6} | {'-'*8} | {'-'*10} | {'-'*6} | {'-'*6}")
|
| 528 |
+
|
| 529 |
+
for n_iters in iter_counts:
|
| 530 |
+
with torch.no_grad():
|
| 531 |
+
all_prs = model(adj, n_iters=n_iters)
|
| 532 |
+
final_pr = all_prs[-1]
|
| 533 |
+
kl = F.kl_div((final_pr + 1e-10).log(), targets, reduction='batchmean').item()
|
| 534 |
+
mse = ((final_pr - targets) ** 2).mean().item()
|
| 535 |
+
rank_acc = _ranking_accuracy(final_pr, targets)
|
| 536 |
+
top5_acc = _topk_accuracy(final_pr, targets, k=5)
|
| 537 |
+
|
| 538 |
+
print(f" {n_iters:6d} | {kl:8.4f} | {mse:10.6f} | {rank_acc:5.1%} | {top5_acc:5.1%}")
|
| 539 |
+
|
| 540 |
+
if verbose:
|
| 541 |
+
# Show examples from hub-spoke (most non-uniform PR)
|
| 542 |
+
adj, targets, _ = generate_batch(4, config, 0.10, (0.0, 0.0, 1.0), device)
|
| 543 |
+
with torch.no_grad():
|
| 544 |
+
all_prs = model(adj, n_iters=256)
|
| 545 |
+
final_pr = all_prs[-1]
|
| 546 |
+
|
| 547 |
+
print(f"\n Sample predictions (hub-spoke, 256 iters):")
|
| 548 |
+
for i in range(min(4, len(adj))):
|
| 549 |
+
true_topk = targets[i].topk(5)
|
| 550 |
+
pred_topk = final_pr[i].topk(5)
|
| 551 |
+
true_str = ", ".join(f"n{idx}={val:.3f}" for val, idx in zip(true_topk.values, true_topk.indices))
|
| 552 |
+
pred_str = ", ".join(f"n{idx}={val:.3f}" for val, idx in zip(pred_topk.values, pred_topk.indices))
|
| 553 |
+
mse_i = ((final_pr[i] - targets[i]) ** 2).mean().item()
|
| 554 |
+
print(f" MSE={mse_i:.6f}")
|
| 555 |
+
print(f" True top5: {true_str}")
|
| 556 |
+
print(f" Pred top5: {pred_str}")
|
| 557 |
+
|
| 558 |
+
|
| 559 |
+
def save_checkpoint(model, config, args):
|
| 560 |
+
import json, os, tempfile
|
| 561 |
+
|
| 562 |
+
raw_model = model._orig_mod if hasattr(model, '_orig_mod') else model
|
| 563 |
+
checkpoint = {
|
| 564 |
+
"model_state_dict": raw_model.state_dict(),
|
| 565 |
+
"config": {
|
| 566 |
+
"n_nodes": config.n_nodes,
|
| 567 |
+
"d_model": config.d_model,
|
| 568 |
+
"n_heads": config.n_heads,
|
| 569 |
+
"n_layers": config.n_layers,
|
| 570 |
+
"d_ff": config.d_ff,
|
| 571 |
+
"dropout": config.dropout,
|
| 572 |
+
"train_iters": config.train_iters,
|
| 573 |
+
"rope_base": config.rope_base,
|
| 574 |
+
"damping": config.damping,
|
| 575 |
+
},
|
| 576 |
+
}
|
| 577 |
+
torch.save(checkpoint, args.save_path)
|
| 578 |
+
print(f"\nCheckpoint saved to {args.save_path}")
|
| 579 |
+
|
| 580 |
+
if args.upload_hf:
|
| 581 |
+
from huggingface_hub import HfApi
|
| 582 |
+
api = HfApi()
|
| 583 |
+
try:
|
| 584 |
+
api.create_repo(args.upload_hf, exist_ok=True)
|
| 585 |
+
except Exception as e:
|
| 586 |
+
print(f"Warning: {e}")
|
| 587 |
+
|
| 588 |
+
api.upload_file(path_or_fileobj=args.save_path, path_in_repo="model.pt", repo_id=args.upload_hf)
|
| 589 |
+
api.upload_file(path_or_fileobj=os.path.abspath(__file__), path_in_repo="iterative_pagerank.py", repo_id=args.upload_hf)
|
| 590 |
+
|
| 591 |
+
config_json = json.dumps(checkpoint["config"], indent=2)
|
| 592 |
+
with tempfile.NamedTemporaryFile(mode='w', suffix='.json', delete=False) as f:
|
| 593 |
+
f.write(config_json)
|
| 594 |
+
cfg_path = f.name
|
| 595 |
+
api.upload_file(path_or_fileobj=cfg_path, path_in_repo="config.json", repo_id=args.upload_hf)
|
| 596 |
+
os.unlink(cfg_path)
|
| 597 |
+
|
| 598 |
+
n_params = sum(p.numel() for p in raw_model.parameters())
|
| 599 |
+
card = f"""# Iterative PageRank Model
|
| 600 |
+
|
| 601 |
+
Non-autoregressive iterative transformer that learns PageRank via shared-weight refinement.
|
| 602 |
+
|
| 603 |
+
## Architecture
|
| 604 |
+
- **Params:** {n_params:,}
|
| 605 |
+
- **Layers:** {config.n_layers} (shared across {config.train_iters} iterations)
|
| 606 |
+
- **Width:** {config.d_model}, **Heads:** {config.n_heads}
|
| 607 |
+
- **Graph size:** {config.n_nodes} nodes (directed)
|
| 608 |
+
- **Damping:** {config.damping}
|
| 609 |
+
|
| 610 |
+
## Task
|
| 611 |
+
Given a directed graph's adjacency matrix, predict each node's PageRank value.
|
| 612 |
+
The model learns power iteration implicitly through iterative refinement.
|
| 613 |
+
|
| 614 |
+
## Metrics
|
| 615 |
+
- **KL divergence:** between predicted and true PR distribution
|
| 616 |
+
- **Ranking accuracy:** pairwise ordering correctness
|
| 617 |
+
- **Top-k accuracy:** overlap of predicted vs true top-k important nodes
|
| 618 |
+
|
| 619 |
+
## Usage
|
| 620 |
+
```python
|
| 621 |
+
import torch
|
| 622 |
+
from iterative_pagerank import IterativePageRankModel, PageRankConfig, generate_batch
|
| 623 |
+
|
| 624 |
+
ckpt = torch.load("model.pt", weights_only=True)
|
| 625 |
+
config = PageRankConfig(**ckpt["config"])
|
| 626 |
+
model = IterativePageRankModel(config)
|
| 627 |
+
model.load_state_dict(ckpt["model_state_dict"])
|
| 628 |
+
model.eval()
|
| 629 |
+
|
| 630 |
+
adj, targets, meta = generate_batch(1, config, edge_prob=0.1,
|
| 631 |
+
graph_weights=(0.0, 0.0, 1.0), device="cpu")
|
| 632 |
+
with torch.no_grad():
|
| 633 |
+
all_prs = model(adj, n_iters=64)
|
| 634 |
+
print(f"Predicted: {{all_prs[-1][0].topk(5)}}")
|
| 635 |
+
print(f"True: {{targets[0].topk(5)}}")
|
| 636 |
+
```
|
| 637 |
+
"""
|
| 638 |
+
with tempfile.NamedTemporaryFile(mode='w', suffix='.md', delete=False) as f:
|
| 639 |
+
f.write(card)
|
| 640 |
+
card_path = f.name
|
| 641 |
+
api.upload_file(path_or_fileobj=card_path, path_in_repo="README.md", repo_id=args.upload_hf)
|
| 642 |
+
os.unlink(card_path)
|
| 643 |
+
|
| 644 |
+
print(f"Uploaded to https://huggingface.co/{args.upload_hf}")
|
| 645 |
+
|
| 646 |
+
|
| 647 |
+
# ---------------------------------------------------------------------------
|
| 648 |
+
# Entry point
|
| 649 |
+
# ---------------------------------------------------------------------------
|
| 650 |
+
|
| 651 |
+
def main():
|
| 652 |
+
parser = argparse.ArgumentParser(description="Iterative PageRank model")
|
| 653 |
+
parser.add_argument("--device", default="cuda" if torch.cuda.is_available() else "cpu")
|
| 654 |
+
parser.add_argument("--steps", type=int, default=50000)
|
| 655 |
+
parser.add_argument("--batch", type=int, default=2048)
|
| 656 |
+
parser.add_argument("--eval-batch", type=int, default=1024)
|
| 657 |
+
parser.add_argument("--lr", type=float, default=2e-3)
|
| 658 |
+
parser.add_argument("--warmup", type=int, default=1400)
|
| 659 |
+
parser.add_argument("--log-interval", type=int, default=100)
|
| 660 |
+
parser.add_argument("--eval-interval", type=int, default=5000)
|
| 661 |
+
parser.add_argument("--compile", action="store_true")
|
| 662 |
+
parser.add_argument("--save-path", type=str, default=None)
|
| 663 |
+
parser.add_argument("--upload-hf", type=str, default=None)
|
| 664 |
+
|
| 665 |
+
parser.add_argument("--d-model", type=int, default=128)
|
| 666 |
+
parser.add_argument("--n-layers", type=int, default=4)
|
| 667 |
+
parser.add_argument("--n-heads", type=int, default=4)
|
| 668 |
+
parser.add_argument("--d-ff", type=int, default=512)
|
| 669 |
+
parser.add_argument("--train-iters", type=int, default=16)
|
| 670 |
+
parser.add_argument("--n-nodes", type=int, default=64)
|
| 671 |
+
parser.add_argument("--damping", type=float, default=0.85)
|
| 672 |
+
parser.add_argument("--dropout", type=float, default=0.1)
|
| 673 |
+
|
| 674 |
+
args = parser.parse_args()
|
| 675 |
+
|
| 676 |
+
config = PageRankConfig(
|
| 677 |
+
n_nodes=args.n_nodes,
|
| 678 |
+
d_model=args.d_model,
|
| 679 |
+
n_heads=args.n_heads,
|
| 680 |
+
n_layers=args.n_layers,
|
| 681 |
+
d_ff=args.d_ff,
|
| 682 |
+
dropout=args.dropout,
|
| 683 |
+
train_iters=args.train_iters,
|
| 684 |
+
damping=args.damping,
|
| 685 |
+
)
|
| 686 |
+
|
| 687 |
+
train(config, args)
|
| 688 |
+
|
| 689 |
+
|
| 690 |
+
if __name__ == "__main__":
|
| 691 |
+
main()
|