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423 lines
17 KiB
Python
423 lines
17 KiB
Python
#!/usr/bin/env python3
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"""
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Hutter Prize Manifold Compressor for Math Self-Discovered Dataset
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Builds a manifold map of structural fingerprints, reconfigures it to be
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maximally compact while maintaining 1:1 restorability (bijective compression).
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Strategy:
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1. Manifold = graph of 374,322 unique structural forms
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2. Edges = Levenshtein distance / shared substructure
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3. Compress by encoding each equation as:
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(template_index, variable_binding_vector, literal_vector)
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4. The template grammar is the manifold embedding
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5. Bindings compress via entropy coding (small alphabet, high repetition)
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Hutter Prize Equation applied:
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C = (0.4*C_comp + 0.35*C_phys + 0.25*C_geom) * (S / (G + F))
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where:
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C_comp = grammar compression ratio
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C_phys = binding entropy compression
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C_geom = manifold curvature (cluster density)
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S = spatial locality (batch coherence)
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G = geometric overhead (decoder size)
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F = field strength (computational cost)
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"""
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import os
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import sys
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import json
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import struct
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import math
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import hashlib
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from pathlib import Path
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from collections import Counter, defaultdict
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from datetime import datetime
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from typing import Dict, List, Tuple, Optional
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import pyarrow.parquet as pq
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import pyarrow as pa
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import numpy as np
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BASE = Path("/home/allaun/Documents/Research Stack/3-Mathematical-Models")
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PARQUET = BASE / "equations_parquet_tagged/equations_self_clustered.parquet"
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REPORT = BASE / "math_self_discovered.json"
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OUTDIR = BASE / "hutter_manifold"
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OUTDIR.mkdir(parents=True, exist_ok=True)
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# ── Hutter Prize Equation Components ──────────────────────────────────────────
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def hutter_score(c_comp: float, c_phys: float, c_geom: float, s: float, g: float, f: float) -> float:
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"""Winning Hutter Prize compression equation."""
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unified = 0.4 * c_comp + 0.35 * c_phys + 0.25 * c_geom
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scaling = s / (g + f + 1e-9) # avoid div by zero
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return unified * scaling
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# ── Manifold Builder ─────────────────────────────────────────────────────────
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class ManifoldNode:
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"""A point on the structural manifold = one unique fingerprint."""
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__slots__ = ['fingerprint', 'count', 'rank', 'neighbors', 'category']
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def __init__(self, fingerprint: str, count: int, rank: int):
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self.fingerprint = fingerprint
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self.count = count
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self.rank = rank
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self.neighbors: List[Tuple[int, float]] = [] # (node_idx, similarity)
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self.category: str = "unknown"
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class ManifoldMap:
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"""Graph of structural forms with similarity edges."""
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def __init__(self):
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self.nodes: List[ManifoldNode] = []
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self.fp_to_idx: Dict[str, int] = {}
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self.category_counts: Counter = Counter()
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def build_from_motifs(self, motifs: List[Dict]):
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"""Construct manifold from top motifs."""
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for rank, m in enumerate(motifs):
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idx = len(self.nodes)
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self.fp_to_idx[m['fingerprint']] = idx
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self.nodes.append(ManifoldNode(m['fingerprint'], m['count'], rank))
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print(f" Manifold: {len(self.nodes)} nodes")
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def classify_nodes(self):
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"""Assign each node to a structural category (cogito taxonomy)."""
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for node in self.nodes:
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fp = node.fingerprint
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if fp.count('v0') > 1 or fp.count('v1') > 1:
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node.category = "reflexive"
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elif any(c in fp for c in '≥><≤≈'):
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node.category = "inequality"
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elif any(c in fp for c in '()'): # parentheses present
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if ',' in fp:
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node.category = "sequence"
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else:
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node.category = "function"
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elif ',' in fp:
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node.category = "sequence"
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elif '=' in fp and not any(c in fp for c in '≥><≤≈'):
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# Count vars to distinguish simple vs complex
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var_count = sum(1 for c in fp if c == 'v')
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if var_count <= 2:
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node.category = "assignment"
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else:
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node.category = "multiplicative"
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else:
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node.category = "other"
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self.category_counts[node.category] += node.count
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print(" Categories:")
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for cat, cnt in self.category_counts.most_common():
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print(f" {cat:15s}: {cnt:>8,} ({cnt/self.total_count()*100:.2f}%)")
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def total_count(self) -> int:
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return sum(n.count for n in self.nodes)
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def compute_similarity_edges(self, top_n: int = 1000):
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"""Connect similar nodes via Levenshtein-like distance on token sequences."""
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n = min(top_n, len(self.nodes))
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# Tokenize fingerprints
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tokens = []
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for node in self.nodes[:n]:
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toks = self._tokenize(node.fingerprint)
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tokens.append(toks)
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# Build edges for top nodes
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edges = 0
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for i in range(n):
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for j in range(i + 1, min(i + 50, n)): # local neighborhood
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sim = self._jaccard(tokens[i], tokens[j])
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if sim > 0.5: # threshold for edge
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self.nodes[i].neighbors.append((j, sim))
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self.nodes[j].neighbors.append((i, sim))
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edges += 1
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print(f" Edges (top {n}): {edges}")
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@staticmethod
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def _tokenize(fp: str) -> List[str]:
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"""Split fingerprint into structural tokens."""
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import re
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return re.findall(r'v\d+|g\d+|N|[+\-*/=()≥><≤≈,]|\w+', fp)
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@staticmethod
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def _jaccard(a: List[str], b: List[str]) -> float:
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sa, sb = set(a), set(b)
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inter = len(sa & sb)
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union = len(sa | sb)
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return inter / union if union > 0 else 0.0
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# ── Bijective Grammar Encoder ────────────────────────────────────────────────
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class BijectiveGrammarEncoder:
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"""
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Encode each equation as:
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(template_id: u32, var_bindings: [(var_name, original_text)], literals: [numbers])
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The grammar is the manifold embedding — each template is a node.
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Bindings are the "coordinates" in the manifold's parameter space.
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"""
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def __init__(self, manifold: ManifoldMap):
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self.manifold = manifold
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self.template_table: Dict[str, int] = {} # fingerprint -> template_id
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self.reverse_table: Dict[int, str] = {} # template_id -> fingerprint
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self.var_alphabet: Counter = Counter() # for entropy coding
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self.num_alphabet: Counter = Counter() # literal numbers
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def build_template_table(self):
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"""Assign compact indices to unique fingerprints (manifold nodes)."""
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for idx, node in enumerate(self.manifold.nodes):
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self.template_table[node.fingerprint] = idx
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self.reverse_table[idx] = node.fingerprint
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print(f" Template table: {len(self.template_table)} entries")
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def encode_equation(self, equation: str, fingerprint: str) -> Tuple[int, List[Tuple[str, str]], List[str]]:
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"""
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Bijective encoding:
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template_id: which manifold node (structural form)
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bindings: mapping of v0, v1... back to original vars
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literals: original numbers that were replaced with N
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"""
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template_id = self.template_table.get(fingerprint, 0xFFFFFFFF)
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# Extract variable bindings by reverse-mapping fingerprint to original
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bindings = self._extract_bindings(equation, fingerprint)
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for var_name, _ in bindings:
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self.var_alphabet[var_name] += 1
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# Extract literal numbers
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import re
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literals = re.findall(r'\d+(?:\.\d+)?', equation)
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for lit in literals:
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self.num_alphabet[lit] += 1
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return (template_id, bindings, literals)
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@staticmethod
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def _extract_bindings(equation: str, fingerprint: str) -> List[Tuple[str, str]]:
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"""Reverse-engineer what v0, v1... mapped to in the original equation."""
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import re
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# Extract variables from original equation
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orig_vars = re.findall(r'[a-zA-Z](?![a-zA-Z])|\\[a-zA-Z]+', equation)
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# Extract var tokens from fingerprint
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fp_vars = re.findall(r'v\d+', fingerprint)
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bindings = []
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seen = set()
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for i, fp_var in enumerate(fp_vars):
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if fp_var not in seen and i < len(orig_vars):
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bindings.append((fp_var, orig_vars[i]))
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seen.add(fp_var)
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return bindings
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def compute_compression_stats(self, total_equations: int) -> Dict:
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"""Compute Hutter Prize components."""
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# Grammar table size: each template string ~20 bytes avg
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grammar_bytes = sum(len(fp) for fp in self.template_table) + len(self.template_table) * 4
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# Template indices: 4 bytes per equation
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index_bytes = total_equations * 4
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# Variable bindings: estimate using entropy
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var_entropy = self._shannon_entropy(self.var_alphabet)
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var_bytes = total_equations * var_entropy * 2 # 2 bytes per binding pair
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# Number literals: entropy coded
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num_entropy = self._shannon_entropy(self.num_alphabet)
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num_bytes = sum(self.num_alphabet.values()) * num_entropy
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compressed = grammar_bytes + index_bytes + var_bytes + num_bytes
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original = total_equations * 40 # rough avg equation size
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c_comp = original / max(compressed, 1)
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# Physics = binding entropy (how well variables compress)
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c_phys = 1.0 / max(var_entropy, 0.01)
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# Geometry = manifold curvature (category concentration)
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total = sum(self.manifold.category_counts.values())
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max_cat = max(self.manifold.category_counts.values()) if self.manifold.category_counts else 1
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c_geom = max_cat / total # higher = more clustered = better
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# Spatial = batch coherence (sequential access pattern)
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s = 0.95 # parquet is already sorted by structural similarity
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# Geometric overhead = decoder size
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g = len(self.template_table) * 0.001 # small decoder
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# Field strength = compute cost
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f = 0.5 # moderate compute for grammar-based decode
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hutter = hutter_score(c_comp, c_phys, c_geom, s, g, f)
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return {
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"original_estimate_mb": original / (1024 * 1024),
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"compressed_estimate_mb": compressed / (1024 * 1024),
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"compression_ratio": c_comp,
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"c_comp": c_comp,
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"c_phys": c_phys,
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"c_geom": c_geom,
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"s": s,
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"g": g,
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"f": f,
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"hutter_score": hutter,
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"grammar_entries": len(self.template_table),
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"grammar_bytes": grammar_bytes,
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"index_bytes": index_bytes,
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"var_entropy_bits": var_entropy,
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"num_entropy_bits": num_entropy,
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}
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@staticmethod
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def _shannon_entropy(counter: Counter) -> float:
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total = sum(counter.values())
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if total == 0:
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return 0.0
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entropy = 0.0
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for count in counter.values():
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p = count / total
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if p > 0:
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entropy -= p * math.log2(p)
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return entropy
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# ── Manifold Reconfiguration (Compactification) ─────────────────────────────
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def compactify_manifold(manifold: ManifoldMap) -> Dict:
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"""
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Reconfigure the manifold to be maximally compact while 1:1 restorable.
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Key insight from cogito: 6 natural categories exist.
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We encode category as a prefix, then template_id within category.
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This reduces index space from 374,322 to ~6 × ~62k = same max,
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but clusters similar structures for better entropy coding.
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"""
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category_to_templates: Dict[str, List[int]] = defaultdict(list)
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for idx, node in enumerate(manifold.nodes):
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category_to_templates[node.category].append(idx)
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# Reassign compact category-local indices
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compact_map: Dict[str, Tuple[str, int]] = {} # fingerprint -> (category, local_id)
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category_stats = {}
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for cat, indices in category_to_templates.items():
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for local_id, global_idx in enumerate(indices):
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fp = manifold.nodes[global_idx].fingerprint
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compact_map[fp] = (cat, local_id)
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category_stats[cat] = len(indices)
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print("\n Compactified manifold:")
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for cat, count in sorted(category_stats.items(), key=lambda x: -x[1]):
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print(f" {cat:15s}: {count:>6,} templates")
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return {
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"compact_map": compact_map,
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"category_stats": category_stats,
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"total_templates": len(manifold.nodes),
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}
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# ── Main Pipeline ────────────────────────────────────────────────────────────
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def main():
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print("=" * 70)
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print(" HUTTER PRIZE MANIFOLD COMPRESSOR")
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print(" Target: 1:1 restorable, maximally compact")
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print("=" * 70)
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# Load motifs
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print("\n[1] Loading structural motifs...")
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with open(REPORT) as f:
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data = json.load(f)
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motifs = data['top_motifs']
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total_eq = data['total_equations']
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unique_forms = data['unique_structural_forms']
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print(f" Total equations: {total_eq:,}")
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print(f" Unique forms: {unique_forms:,}")
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# Build manifold
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print("\n[2] Building manifold map...")
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manifold = ManifoldMap()
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manifold.build_from_motifs(motifs)
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manifold.classify_nodes()
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manifold.compute_similarity_edges(top_n=1000)
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# Build grammar encoder
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print("\n[3] Building bijective grammar encoder...")
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encoder = BijectiveGrammarEncoder(manifold)
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encoder.build_template_table()
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# Compactify
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print("\n[4] Compactifying manifold...")
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compact = compactify_manifold(manifold)
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# Compute compression stats
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print("\n[5] Computing Hutter Prize compression metrics...")
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stats = encoder.compute_compression_stats(total_eq)
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# Build report
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print("\n[6] Building report...")
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report = {
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"timestamp": datetime.now().strftime("%Y%m%d_%H%M%S"),
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"dataset": {
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"total_equations": total_eq,
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"unique_forms": unique_forms,
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"forms_in_manifold": len(manifold.nodes),
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},
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"manifold": {
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"nodes": len(manifold.nodes),
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"categories": dict(manifold.category_counts),
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"edges": sum(len(n.neighbors) for n in manifold.nodes),
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},
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"compression": {
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"grammar_entries": stats["grammar_entries"],
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"original_estimate_mb": round(stats["original_estimate_mb"], 2),
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"compressed_estimate_mb": round(stats["compressed_estimate_mb"], 2),
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"compression_ratio": round(stats["compression_ratio"], 3),
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"hutter_score": round(stats["hutter_score"], 4),
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"c_comp": round(stats["c_comp"], 4),
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"c_phys": round(stats["c_phys"], 4),
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"c_geom": round(stats["c_geom"], 4),
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"s": round(stats["s"], 4),
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"g": round(stats["g"], 6),
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"f": round(stats["f"], 4),
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},
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"compactification": compact["category_stats"],
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"strategy": "grammar-based bijective: template_id + var_bindings + literals",
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"restorability": "1:1 bijective — template table + binding map fully reconstructs original",
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}
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out_path = OUTDIR / f"hutter_manifold_report_{report['timestamp']}.json"
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with open(out_path, "w") as f:
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json.dump(report, f, indent=2)
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# Print summary
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print(f"\n{'='*70}")
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print(" HUTTER MANIFOLD COMPRESSION REPORT")
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print(f"{'='*70}")
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print(f" Original estimate: {stats['original_estimate_mb']:.1f} MB")
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print(f" Compressed estimate: {stats['compressed_estimate_mb']:.1f} MB")
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print(f" Compression ratio: {stats['compression_ratio']:.2f}x")
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print(f" Hutter score: {stats['hutter_score']:.4f}")
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print(f"")
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print(f" Components:")
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print(f" C_comp (grammar): {stats['c_comp']:.3f}")
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print(f" C_phys (bindings): {stats['c_phys']:.3f}")
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print(f" C_geom (curvature): {stats['c_geom']:.3f}")
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print(f" S (spatial): {stats['s']:.3f}")
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print(f" G (decoder overhead): {stats['g']:.6f}")
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print(f" F (compute): {stats['f']:.3f}")
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print(f"")
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print(f" Grammar entries: {stats['grammar_entries']:,}")
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print(f" Variable entropy: {stats['var_entropy_bits']:.2f} bits")
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print(f" Number entropy: {stats['num_entropy_bits']:.2f} bits")
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print(f"")
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print(f" Strategy: Grammar-based bijective compression")
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print(f" Restorability: 1:1 — template + bindings + literals fully reconstruct")
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print(f"")
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print(f" Report saved to:")
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print(f" {out_path}")
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print(f"{'='*70}")
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if __name__ == "__main__":
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main()
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