File size: 18,263 Bytes
262b9d5 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 | """
Condensate Layer 1: The Graph Builder
Takes access logs from the Membrane (Layer 0) and builds a weighted
graph of memory access patterns. Discovers:
- Temporal edges: A accessed near B β weighted edge
- Causal chains: A always before B β directed edge with timing
- Clusters: groups of regions always accessed together (proto-hyperedges)
- Hot/cold classification: access frequency distribution
This is the substrate's raw material. Layer 2 (predictor) will use
this graph to predict future accesses.
Usage:
from membrane import Membrane
from graph_builder import GraphBuilder
# ... run workload with Membrane wrapping ...
log = Membrane.get_log()
graph = GraphBuilder()
graph.build(log)
graph.print_analysis()
graph.save("access_graph.json")
"""
import numpy as np
from collections import defaultdict
import json
class AccessNode:
"""A memory region tracked in the graph."""
__slots__ = ['path', 'access_count', 'read_count', 'write_count',
'total_bytes', 'first_access_ns', 'last_access_ns',
'access_times_ns', '_temp_class']
def __init__(self, path):
self.path = path
self.access_count = 0
self.read_count = 0
self.write_count = 0
self.total_bytes = 0
self.first_access_ns = float('inf')
self.last_access_ns = 0
self.access_times_ns = []
self._temp_class = "WARM" # default
def record(self, ts_ns, event_type, size_bytes):
self.access_count += 1
if event_type == "READ":
self.read_count += 1
else:
self.write_count += 1
self.total_bytes += size_bytes
self.first_access_ns = min(self.first_access_ns, ts_ns)
self.last_access_ns = max(self.last_access_ns, ts_ns)
self.access_times_ns.append(ts_ns)
@property
def temperature(self):
"""Normalized access frequency. Higher = hotter."""
return self.access_count
def to_dict(self):
return {
"path": self.path,
"access_count": self.access_count,
"reads": self.read_count,
"writes": self.write_count,
"total_bytes": self.total_bytes,
}
class CausalEdge:
"""A directed edge: source is accessed BEFORE target."""
__slots__ = ['source', 'target', 'count', 'timing_deltas_ns',
'mean_delta_ns', 'std_delta_ns', 'weight']
def __init__(self, source, target):
self.source = source
self.target = target
self.count = 0
self.timing_deltas_ns = []
self.mean_delta_ns = 0.0
self.std_delta_ns = 0.0
self.weight = 0.0 # computed after all edges built
def add_observation(self, delta_ns):
self.count += 1
self.timing_deltas_ns.append(delta_ns)
def finalize(self):
"""Compute statistics after all observations."""
if self.timing_deltas_ns:
arr = np.array(self.timing_deltas_ns, dtype=np.float64)
self.mean_delta_ns = float(np.mean(arr))
self.std_delta_ns = float(np.std(arr))
# Weight: frequency Γ timing consistency
# High count + low variance = strong causal edge
consistency = 1.0 / (1.0 + self.std_delta_ns / max(self.mean_delta_ns, 1.0))
self.weight = self.count * consistency
def to_dict(self):
return {
"source": self.source,
"target": self.target,
"count": self.count,
"mean_delta_ms": round(self.mean_delta_ns / 1_000_000, 3),
"std_delta_ms": round(self.std_delta_ns / 1_000_000, 3),
"weight": round(self.weight, 2),
}
class Cluster:
"""A group of paths always accessed together β proto-hyperedge."""
def __init__(self, cluster_id, members):
self.cluster_id = cluster_id
self.members = set(members)
self.total_coaccesses = 0
def to_dict(self):
return {
"id": self.cluster_id,
"members": sorted(self.members),
"size": len(self.members),
"total_coaccesses": self.total_coaccesses,
}
class GraphBuilder:
"""Builds a weighted access pattern graph from Membrane logs.
The graph has:
- Nodes: memory regions (paths) with access statistics
- Causal edges: directed, weighted, with timing information
- Clusters: groups of paths that always co-access (proto-hyperedges)
"""
def __init__(self, causal_window_ns=5_000_000, cluster_threshold=0.7):
"""
Args:
causal_window_ns: Max time gap (ns) to consider causal.
Default 5ms β wide enough for Python overhead.
cluster_threshold: Co-access ratio to form a cluster.
0.7 = paths must co-access 70%+ of the time.
"""
self.causal_window_ns = causal_window_ns
self.cluster_threshold = cluster_threshold
self.nodes = {} # path β AccessNode
self.edges = {} # (source, target) β CausalEdge
self.clusters = [] # list of Cluster
self._built = False
def build(self, log_entries):
"""Build the graph from Membrane log entries.
Args:
log_entries: list of (timestamp_ns, event_type, path, size_bytes)
"""
if not log_entries:
print(" Warning: empty log, nothing to build")
return
# Phase 1: Build nodes
for ts, event_type, path, size_bytes in log_entries:
if path not in self.nodes:
self.nodes[path] = AccessNode(path)
self.nodes[path].record(ts, event_type, size_bytes)
# Phase 2: Build causal edges
# Sort by timestamp for sequential scanning
sorted_log = sorted(log_entries, key=lambda e: e[0])
for i, (ts_i, _, path_i, _) in enumerate(sorted_log):
# Look forward within the causal window
for j in range(i + 1, len(sorted_log)):
ts_j, _, path_j, _ = sorted_log[j]
delta = ts_j - ts_i
if delta > self.causal_window_ns:
break # past the window
if path_i == path_j:
continue # self-loop, skip
# Directed edge: i happened before j
key = (path_i, path_j)
if key not in self.edges:
self.edges[key] = CausalEdge(path_i, path_j)
self.edges[key].add_observation(delta)
# Finalize edge statistics
for edge in self.edges.values():
edge.finalize()
# Phase 3: Discover clusters (proto-hyperedges)
self._discover_clusters()
# Phase 4: Classify temperature
self._classify_temperature()
self._built = True
def _discover_clusters(self):
"""Find groups of paths that are consistently co-accessed.
Uses a simple greedy approach:
1. For each pair of paths, compute co-access ratio
2. Build adjacency from pairs above threshold
3. Connected components = clusters
"""
if len(self.nodes) < 2:
return
paths = list(self.nodes.keys())
n = len(paths)
# Build co-access matrix
# co_access[i][j] = times i and j were accessed within window / min(count_i, count_j)
path_to_idx = {p: i for i, p in enumerate(paths)}
cocount = np.zeros((n, n), dtype=np.int32)
for (src, tgt), edge in self.edges.items():
i, j = path_to_idx.get(src), path_to_idx.get(tgt)
if i is not None and j is not None:
cocount[i][j] += edge.count
cocount[j][i] += edge.count
# Normalize to co-access ratio
counts = np.array([self.nodes[p].access_count for p in paths], dtype=np.float64)
min_counts = np.minimum.outer(counts, counts)
min_counts = np.maximum(min_counts, 1.0) # avoid div by zero
coratio = cocount / min_counts
# Build adjacency and find connected components
adjacency = defaultdict(set)
for i in range(n):
for j in range(i + 1, n):
if coratio[i][j] >= self.cluster_threshold:
adjacency[i].add(j)
adjacency[j].add(i)
# BFS to find connected components
visited = set()
cluster_id = 0
for start in range(n):
if start in visited:
continue
if start not in adjacency:
continue
# BFS
component = set()
queue = [start]
while queue:
node = queue.pop(0)
if node in visited:
continue
visited.add(node)
component.add(node)
for neighbor in adjacency.get(node, []):
if neighbor not in visited:
queue.append(neighbor)
if len(component) >= 2:
members = [paths[i] for i in component]
cluster = Cluster(cluster_id, members)
# Sum co-access counts within cluster
for i in component:
for j in component:
if i != j:
cluster.total_coaccesses += cocount[i][j]
self.clusters.append(cluster)
cluster_id += 1
def _classify_temperature(self):
"""Tag nodes as hot/warm/cold based on access distribution."""
if not self.nodes:
return
counts = [n.access_count for n in self.nodes.values()]
if not counts:
return
# Use percentiles for classification
p75 = np.percentile(counts, 75)
p25 = np.percentile(counts, 25)
for node in self.nodes.values():
if node.access_count >= p75:
node._temp_class = "HOT"
elif node.access_count >= p25:
node._temp_class = "WARM"
else:
node._temp_class = "COLD"
def get_causal_chains(self, min_weight=2.0, max_depth=10):
"""Extract causal chains β sequences of AβBβC with strong edges.
Returns list of chains, each chain is [(path, mean_delta_ms), ...]
"""
if not self._built:
return []
# Build adjacency list of strong edges, sorted by weight
successors = defaultdict(list)
for (src, tgt), edge in self.edges.items():
if edge.weight >= min_weight:
successors[src].append((tgt, edge))
# Sort successors by weight descending
for src in successors:
successors[src].sort(key=lambda x: -x[1].weight)
# Find chains starting from each node
chains = []
visited_starts = set()
# Start from nodes that have strong outgoing but weak incoming
incoming_weight = defaultdict(float)
outgoing_weight = defaultdict(float)
for (src, tgt), edge in self.edges.items():
if edge.weight >= min_weight:
outgoing_weight[src] += edge.weight
incoming_weight[tgt] += edge.weight
# Good chain starts: strong outgoing, weaker incoming
candidates = []
for path in successors:
out_w = outgoing_weight.get(path, 0)
in_w = incoming_weight.get(path, 0)
if out_w > 0:
candidates.append((path, out_w - in_w))
candidates.sort(key=lambda x: -x[1])
for start, _ in candidates:
if start in visited_starts:
continue
# Follow the strongest chain
chain = [(start, 0.0)]
current = start
seen = {start}
for _ in range(max_depth):
if current not in successors:
break
# Take the strongest unvisited successor
found = False
for next_path, edge in successors[current]:
if next_path not in seen:
chain.append((next_path, edge.mean_delta_ns / 1_000_000))
seen.add(next_path)
current = next_path
found = True
break
if not found:
break
if len(chain) >= 2:
chains.append(chain)
visited_starts.update(p for p, _ in chain)
return chains
def print_analysis(self):
"""Print a comprehensive analysis of the access graph."""
if not self._built:
print(" Graph not built yet. Call build() first.")
return
print(f"\n{'='*60}")
print(f" CONDENSATE β Layer 1 Graph Analysis")
print(f"{'='*60}")
# Node summary
hot = [n for n in self.nodes.values() if getattr(n, '_temp_class', '') == 'HOT']
warm = [n for n in self.nodes.values() if getattr(n, '_temp_class', '') == 'WARM']
cold = [n for n in self.nodes.values() if getattr(n, '_temp_class', '') == 'COLD']
print(f"\n Nodes: {len(self.nodes)} total")
print(f" HOT: {len(hot)} (top 25% access frequency)")
print(f" WARM: {len(warm)} (middle 50%)")
print(f" COLD: {len(cold)} (bottom 25%)")
if hot:
print(f"\n Hottest nodes:")
for node in sorted(hot, key=lambda n: -n.access_count)[:10]:
print(f" {node.path:<42} {node.access_count:>5} accesses")
if cold:
print(f"\n Coldest nodes:")
for node in sorted(cold, key=lambda n: n.access_count)[:5]:
print(f" {node.path:<42} {node.access_count:>5} accesses")
# Edge summary
strong_edges = [(k, e) for k, e in self.edges.items() if e.weight >= 2.0]
print(f"\n Edges: {len(self.edges)} total, {len(strong_edges)} strong (weight >= 2.0)")
if strong_edges:
print(f"\n Strongest causal edges (A β B):")
print(f" {'Source':<25} {'β Target':<25} {'Count':>5} {'Ξt(ms)':>7} {'Wt':>6}")
print(f" {'-'*25} {'-'*25} {'-'*5} {'-'*7} {'-'*6}")
sorted_edges = sorted(strong_edges, key=lambda x: -x[1].weight)
for (src, tgt), edge in sorted_edges[:15]:
src_short = src if len(src) <= 25 else "..." + src[-22:]
tgt_short = tgt if len(tgt) <= 25 else "..." + tgt[-22:]
print(f" {src_short:<25} {tgt_short:<25} "
f"{edge.count:>5} {edge.mean_delta_ns/1e6:>7.3f} {edge.weight:>6.1f}")
# Cluster summary
if self.clusters:
print(f"\n Clusters (proto-hyperedges): {len(self.clusters)}")
for cluster in sorted(self.clusters, key=lambda c: -len(c.members)):
print(f"\n Cluster {cluster.cluster_id} "
f"({len(cluster.members)} members, "
f"{cluster.total_coaccesses} co-accesses):")
for member in sorted(cluster.members):
node = self.nodes.get(member)
temp = getattr(node, '_temp_class', '?') if node else '?'
count = node.access_count if node else 0
print(f" [{temp:>4}] {member:<40} {count:>4}x")
else:
print(f"\n Clusters: none found (threshold: {self.cluster_threshold})")
# Causal chains
chains = self.get_causal_chains()
if chains:
print(f"\n Causal chains discovered: {len(chains)}")
for i, chain in enumerate(chains[:5]):
parts = []
for path, delta_ms in chain:
short = path.split(".")[-1] if "." in path else path
if delta_ms > 0:
parts.append(f"--({delta_ms:.2f}ms)--> {short}")
else:
parts.append(short)
print(f" Chain {i}: {' '.join(parts)}")
if len(chains) > 5:
print(f" ... and {len(chains) - 5} more chains")
# Condensation potential
if hot and cold:
hot_accesses = sum(n.access_count for n in hot)
total_accesses = sum(n.access_count for n in self.nodes.values())
hot_pct = hot_accesses / total_accesses * 100
print(f"\n Condensation potential:")
print(f" {len(hot)} hot nodes handle {hot_pct:.0f}% of all accesses")
print(f" {len(cold)} cold nodes could be compressed/paged")
if self.clusters:
print(f" {len(self.clusters)} clusters enable batch promote/demote")
if chains:
print(f" {len(chains)} causal chains enable predictive prefetch")
print(f"\n{'='*60}\n")
def save(self, filepath):
"""Save the graph to JSON for later analysis."""
data = {
"nodes": {p: n.to_dict() for p, n in self.nodes.items()},
"edges": [e.to_dict() for e in self.edges.values() if e.weight >= 1.0],
"clusters": [c.to_dict() for c in self.clusters],
"chains": self.get_causal_chains(),
"summary": {
"total_nodes": len(self.nodes),
"total_edges": len(self.edges),
"strong_edges": sum(1 for e in self.edges.values() if e.weight >= 2.0),
"clusters": len(self.clusters),
"chains": len(self.get_causal_chains()),
}
}
class NumpyEncoder(json.JSONEncoder):
def default(self, obj):
if isinstance(obj, (np.integer,)):
return int(obj)
if isinstance(obj, (np.floating,)):
return float(obj)
return super().default(obj)
with open(filepath, 'w') as f:
json.dump(data, f, indent=2, cls=NumpyEncoder)
print(f" Saved graph ({len(self.nodes)} nodes, "
f"{len(self.edges)} edges) to {filepath}")
|