feat: convergent graph diffusion with exponential-map versor unitization
Replace the divergent rotation-based diffusion operator with a linear blend + exponential-map re-unitization approach that converges in ~28 steps while maintaining vc < 1e-6. Key changes: - GraphDiffusionOperator now averages neighbors in multivector space and re-projects via per-plane exponentials (cos/sin for rotations, cosh/sinh for boosts in Cl(4,1)) - run_pulse V3: per-token graph topology with input-driven output node, recall via VocabManifold.nearest(), --no-glove flag for compiled pack - Tests updated for V3 API Different inputs now produce different recall rankings from the compiled en_core_cognition_v1 vocabulary, completing Threshold 1 (Semantic Encoding). Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
This commit is contained in:
Shay
parent
e1c0b5e758
commit
c9dfad3017
3 changed files with 207 additions and 153 deletions
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@ -2,19 +2,18 @@
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Manifold-level field operators — graph diffusion and protocol.
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Operators transform ManifoldState through algebraic transitions.
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construction_seed_versor is used here as a construction primitive (building new
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versors from damped blends), not as propagation repair.
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Diffusion computes a weighted average of each node with its neighbors
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in Cl(4,1) component space, then re-unitizes to the versor manifold.
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"""
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from __future__ import annotations
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from collections import defaultdict
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from typing import Protocol
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import numpy as np
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from algebra.backend import versor_apply
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from algebra.rotor import word_transition_rotor
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from algebra.versor import construction_seed_versor
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from algebra.cl41 import geometric_product
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from field.state import ManifoldState
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@ -30,11 +29,64 @@ class Operator(Protocol):
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...
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_BOOST_INDICES = frozenset({9, 12, 14, 15})
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def _unitize_f32(v: np.ndarray) -> np.ndarray:
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"""Unitize a multivector to versor condition via the exponential map.
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Builds a proper rotor from the bivector content, ensuring
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R·reverse(R) = 1 exactly in float64, then casts to float32.
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"""
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v64 = np.asarray(v, dtype=np.float64)
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norm = float(np.linalg.norm(v64))
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if norm < 1e-12:
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out = np.zeros(32, dtype=np.float32)
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out[0] = 1.0
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return out
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bv = v64[6:16]
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bv_norm = float(np.linalg.norm(bv))
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if bv_norm < 1e-14:
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out = np.zeros(32, dtype=np.float32)
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out[0] = 1.0 if v64[0] >= 0 else -1.0
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return out
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angle = np.arctan2(bv_norm, abs(float(v64[0])))
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rotor = np.zeros(32, dtype=np.float64)
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rotor[0] = 1.0
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for i in range(10):
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w = float(bv[i]) / bv_norm
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if abs(w) < 1e-14:
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continue
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theta = angle * w
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factor = np.zeros(32, dtype=np.float64)
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blade_idx = 6 + i
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if blade_idx in _BOOST_INDICES:
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factor[0] = np.cosh(theta)
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factor[blade_idx] = np.sinh(theta)
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else:
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factor[0] = np.cos(theta)
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factor[blade_idx] = np.sin(theta)
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rotor = geometric_product(rotor, factor)
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if v64[0] < 0:
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rotor = -rotor
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return rotor.astype(np.float32)
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class GraphDiffusionOperator:
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"""Propagate geometric pressure across graph edges via damped versor transitions.
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"""Propagate geometric pressure across graph edges via damped blending.
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Self-adjoint: adjoint() returns self (symmetric diffusion).
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Uses construction-tier construction_seed_versor for post-damping closure.
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For each node, computes a linear blend with its neighbors in the
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32-component multivector space, then re-projects to the versor
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manifold via the exponential map. The damping factor controls
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the blend weight: 0 = no change, 1 = replace with neighbor average.
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"""
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def __init__(self, damping: float = 0.5) -> None:
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@ -44,20 +96,20 @@ class GraphDiffusionOperator:
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def forward(self, state: ManifoldState) -> tuple[ManifoldState, float]:
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old_fields = state.fields
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new_fields = old_fields.copy()
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neighbors: dict[int, list[int]] = defaultdict(list)
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for edge_idx in range(state.edges.shape[0]):
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src, dst = int(state.edges[edge_idx, 0]), int(state.edges[edge_idx, 1])
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try:
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V = word_transition_rotor(old_fields[src], old_fields[dst])
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except ValueError:
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continue
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diffused = versor_apply(V, old_fields[dst])
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blended = self._damping * diffused + (1.0 - self._damping) * old_fields[dst]
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try:
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new_fields[dst] = construction_seed_versor(blended)
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except ValueError:
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new_fields[dst] = old_fields[dst]
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neighbors[dst].append(src)
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new_fields = old_fields.copy()
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for node, srcs in neighbors.items():
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f = old_fields[node].astype(np.float64)
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neighbor_avg = np.mean(
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[old_fields[s].astype(np.float64) for s in srcs], axis=0,
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)
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blended = (1.0 - self._damping) * f + self._damping * neighbor_avg
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new_fields[node] = _unitize_f32(blended)
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delta = float(np.linalg.norm(new_fields - old_fields))
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return ManifoldState(fields=new_fields, edges=state.edges, step=state.step + 1), delta
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@ -1,23 +1,25 @@
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"""
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Vertical slice: one cognitive pulse from injection to token recall.
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V2 — live semantic manifold.
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V3 — per-token manifold topology with input-driven output node.
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Uses the English Supervised Seeding Epoch (language_packs.en_seeder) to
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replace the mock 10-word hash vault. Every word is a geometrically valid
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Cl(4,1) unit versor derived from a GloVe-50 embedding via the structured
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CGA lift, so vault_recall now returns semantically meaningful neighbours.
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Each input token becomes a graph node initialised from the vocabulary
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manifold (compiled pack or GloVe seeder). An output node is initialised
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from the centroid of the input tokens — not from a fixed hash — so
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diffusion pressure actually encodes input semantics into the output.
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Recall searches the full VocabManifold by CGA inner product.
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Usage:
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# First run downloads GloVe (~822 MB) and caches it.
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python -m scripts.run_pulse
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python -m scripts.run_pulse "what is truth"
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python -m scripts.run_pulse --top-k 5 "grace and peace"
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python -m scripts.run_pulse "What is truth?"
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python -m scripts.run_pulse --top-k 10 "Compare knowledge and wisdom"
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python -m scripts.run_pulse --no-glove "light" # compiled pack only, no download
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Flags:
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--top-k N Return N nearest vault words (default 5)
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--max-words N Load at most N words from GloVe (default 50000)
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--no-glove Fall back to deterministic hash vault (no download)
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--no-glove Use compiled en_core_cognition_v1 pack (70 words, no download)
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-v Verbose logging
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"""
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from __future__ import annotations
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@ -25,124 +27,130 @@ from __future__ import annotations
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import argparse
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import logging
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import sys
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from typing import List, Tuple
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import numpy as np
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from algebra.backend import vault_recall
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from algebra.backend import cga_inner
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from algebra.versor import construction_seed_versor
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from field.operators import GraphDiffusionOperator
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from field.state import ManifoldState
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from sensorium.adapters.text import deterministic_hash_versor
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from vocab.manifold import VocabManifold
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log = logging.getLogger(__name__)
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CONVERGENCE_THRESHOLD = 1e-6
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MAX_STEPS = 2000
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# ---------------------------------------------------------------------------
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# Hash-based mock vault (kept for --no-glove fallback)
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# ---------------------------------------------------------------------------
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_MOCK_VOCAB = [
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"truth", "light", "wisdom", "peace", "knowledge",
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"word", "path", "life", "grace", "hope",
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]
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TOP_K = 5
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COMPILED_PACK_ID = "en_core_cognition_v1"
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def _build_mock_vault() -> Tuple[List[np.ndarray], List[str]]:
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versors = [deterministic_hash_versor(w) for w in _MOCK_VOCAB]
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return versors, list(_MOCK_VOCAB)
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def _load_manifold(use_glove: bool, max_words: int) -> VocabManifold:
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if use_glove:
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from language_packs.en_seeder import seed_english_manifold
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log.info("[pulse] Seeding English manifold (max_words=%d) …", max_words)
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manifold = seed_english_manifold(max_words=max_words)
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log.info("[pulse] Manifold ready: %d words", len(manifold))
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return manifold
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# ---------------------------------------------------------------------------
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# Live semantic vault from VocabManifold
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# ---------------------------------------------------------------------------
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def _build_live_vault(max_words: int = 50_000):
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"""Return a seeded VocabManifold for use in nearest() recall."""
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from language_packs.en_seeder import seed_english_manifold
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log.info("[pulse] Seeding English manifold (max_words=%d) …", max_words)
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manifold = seed_english_manifold(max_words=max_words)
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log.info("[pulse] Manifold ready: %d words", len(manifold))
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from language_packs.compiler import load_pack
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_, manifold = load_pack(COMPILED_PACK_ID)
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return manifold
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# ---------------------------------------------------------------------------
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# Manifold construction and pulse loop
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# ---------------------------------------------------------------------------
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def _build_initial_manifold(prompt_versor: np.ndarray) -> ManifoldState:
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context_versor = deterministic_hash_versor("__context__")
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output_versor = deterministic_hash_versor("__output__")
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fields = np.stack([prompt_versor, context_versor, output_versor], axis=0)
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edges = np.array([[0, 1], [1, 2], [0, 2]], dtype=np.int32)
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return ManifoldState(fields=fields, edges=edges)
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def _inject_token(token: str, manifold: VocabManifold) -> np.ndarray:
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"""Project one token into Cl(4,1). Manifold lookup first, hash fallback."""
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try:
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return manifold.get_versor(token.lower()).astype(np.float64)
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except KeyError:
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return deterministic_hash_versor(token).astype(np.float64)
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def _inject_prompt(text: str, manifold=None) -> np.ndarray:
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def _build_manifold(
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text: str,
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manifold: VocabManifold,
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) -> tuple[ManifoldState, list[str]]:
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"""Build a per-token graph with an input-driven output node.
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Topology:
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- Each input token → one node (versor from manifold or hash fallback)
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- One output node → initialised from centroid of input versors
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- Star edges: every input node → output node
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- Chain edges: sequential input nodes for adjacency pressure
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"""
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Project the prompt text into Cl(4,1).
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tokens = text.strip().lower().split()
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if not tokens:
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tokens = ["__empty__"]
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If a seeded VocabManifold is provided, tokenise by whitespace and average
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the per-token versors that exist in the manifold. Tokens absent from the
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manifold fall back to deterministic_hash_versor so no word is silently
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dropped.
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"""
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if manifold is None:
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return deterministic_hash_versor(text)
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token_versors = [_inject_token(t, manifold) for t in tokens]
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tokens = text.lower().split()
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versors = []
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for tok in tokens:
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try:
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versors.append(manifold.get_versor(tok).astype(np.float64))
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except KeyError:
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log.debug("[pulse] OOV token %r — using hash versor", tok)
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versors.append(deterministic_hash_versor(tok).astype(np.float64))
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if not versors:
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return deterministic_hash_versor(text)
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# Centroid in embedding space, then re-close onto versor manifold.
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from algebra.versor import construction_seed_versor
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centroid = np.mean(versors, axis=0)
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# Scale to (-0.9, 0.9) before seed construction.
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centroid = np.mean(token_versors, axis=0)
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max_abs = float(np.max(np.abs(centroid)))
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if max_abs > 1e-9:
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centroid = centroid * (0.9 / max_abs)
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return construction_seed_versor(centroid).astype(np.float32)
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output_versor = construction_seed_versor(centroid).astype(np.float64)
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node_labels = list(tokens) + ["__output__"]
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fields = np.stack(
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[np.asarray(v, dtype=np.float32) for v in token_versors]
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+ [output_versor.astype(np.float32)],
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axis=0,
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)
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output_idx = len(tokens)
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edges: list[list[int]] = []
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for i in range(len(tokens)):
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edges.append([i, output_idx])
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for i in range(len(tokens) - 1):
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edges.append([i, i + 1])
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edge_array = (
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np.array(edges, dtype=np.int32)
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if edges
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else np.empty((0, 2), dtype=np.int32)
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)
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return ManifoldState(fields=fields, edges=edge_array), node_labels
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def _recall_from_manifold(
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output_versor: np.ndarray,
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manifold: VocabManifold,
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top_k: int,
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) -> list[tuple[str, float]]:
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"""Top-k words from VocabManifold by CGA inner product."""
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exclude: set[int] = set()
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results: list[tuple[str, float]] = []
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for _ in range(top_k):
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try:
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word, idx = manifold.nearest(
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output_versor, exclude_indices=frozenset(exclude),
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)
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except ValueError:
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break
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score = float(cga_inner(output_versor, manifold.get_versor_at(idx)))
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exclude.add(idx)
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results.append((word, score))
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return results
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def run_pulse(
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text: str,
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*,
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top_k: int = 5,
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top_k: int = TOP_K,
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max_words: int = 50_000,
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use_glove: bool = True,
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) -> List[str]:
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"""
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Execute a single cognitive pulse over the manifold and return the
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top-k nearest vault words to the stabilised output-node versor.
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Returns
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-------
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List of resolved word strings, length <= top_k.
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"""
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# --- Build vault ---------------------------------------------------------
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if use_glove:
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manifold = _build_live_vault(max_words=max_words)
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else:
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manifold = None
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# --- Inject prompt -------------------------------------------------------
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prompt_versor = _inject_prompt(text, manifold)
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state = _build_initial_manifold(prompt_versor)
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) -> list[str]:
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"""Execute one cognitive pulse and return top-k recalled words."""
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manifold = _load_manifold(use_glove, max_words)
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state, node_labels = _build_manifold(text, manifold)
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op = GraphDiffusionOperator(damping=0.5)
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print(f"[pulse] input : {text!r}")
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print(f"[pulse] nodes : {state.fields.shape[0]}, edges: {state.edges.shape[0]}")
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n_input = len(node_labels) - 1
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print(f"[pulse] input : {text!r}")
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print(f"[pulse] vocab : {len(manifold)} words")
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print(f"[pulse] graph : {len(node_labels)} nodes ({n_input} token + output), {state.edges.shape[0]} edges")
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# --- Propagation loop ----------------------------------------------------
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step = 0
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step = 0
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delta = float("inf")
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while step < MAX_STEPS:
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state, delta = op.forward(state)
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else:
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print(f"[pulse] WARNING: max_steps ({MAX_STEPS}) reached — delta={delta:.2e}")
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# --- Recall --------------------------------------------------------------
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output_versor = state.fields[2] # output node
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resolved: List[str] = []
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output_idx = len(node_labels) - 1
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output_versor = state.fields[output_idx]
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results = _recall_from_manifold(output_versor, manifold, top_k)
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if manifold is not None:
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# Use VocabManifold.nearest() directly — semantically grounded.
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exclude: set[int] = set()
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for rank in range(top_k):
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try:
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word, idx = manifold.nearest(output_versor, exclude_indices=frozenset(exclude))
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exclude.add(idx)
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resolved.append(word)
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except ValueError:
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break
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else:
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vault_versors, vault_words = _build_mock_vault()
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results = vault_recall(vault_versors, output_versor, top_k=top_k)
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for idx, score in results:
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resolved.append(vault_words[idx])
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print(f"[pulse] output -> top-{top_k} recall:")
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for rank, (word, score) in enumerate(results, 1):
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marker = " <-" if word in [t.lower() for t in node_labels[:-1]] else ""
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print(f"[pulse] {rank}. {word!r:20s} score={score:+.6f}{marker}")
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print(f"[pulse] top-{top_k} recall: {resolved}")
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return resolved
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return [w for w, _ in results]
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# ---------------------------------------------------------------------------
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@ -184,12 +180,12 @@ def run_pulse(
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# ---------------------------------------------------------------------------
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def _parse_args() -> argparse.Namespace:
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p = argparse.ArgumentParser(description="CORE cognitive pulse (V2 — live manifold)")
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p.add_argument("text", nargs="*", default=["hello world"])
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p.add_argument("--top-k", type=int, default=5, metavar="N")
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p.add_argument("--max-words",type=int, default=50_000, metavar="N")
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p = argparse.ArgumentParser(description="CORE cognitive pulse (V3)")
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p.add_argument("text", nargs="*", default=["What is truth?"])
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p.add_argument("--top-k", type=int, default=5, metavar="N")
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p.add_argument("--max-words", type=int, default=50_000, metavar="N")
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p.add_argument("--no-glove", action="store_true",
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help="Use deterministic hash vault instead of GloVe manifold")
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help="Use compiled pack only (no GloVe download)")
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p.add_argument("-v", "--verbose", action="store_true")
|
||||
return p.parse_args()
|
||||
|
||||
|
|
|
|||
|
|
@ -2,33 +2,39 @@
|
|||
|
||||
import numpy as np
|
||||
|
||||
from scripts.run_pulse import build_initial_manifold, build_mock_vault, run_pulse
|
||||
from sensorium.adapters.text import deterministic_hash_versor
|
||||
from scripts.run_pulse import run_pulse, _build_manifold
|
||||
from language_packs.compiler import load_pack
|
||||
|
||||
|
||||
class TestPulseIntegration:
|
||||
def test_full_cycle_completes(self) -> None:
|
||||
word = run_pulse("hello world")
|
||||
assert isinstance(word, str)
|
||||
assert len(word) > 0
|
||||
words = run_pulse("hello world", use_glove=False)
|
||||
assert isinstance(words, list)
|
||||
assert len(words) > 0
|
||||
assert all(isinstance(w, str) for w in words)
|
||||
|
||||
def test_output_node_changes(self) -> None:
|
||||
prompt = deterministic_hash_versor("test input")
|
||||
state = build_initial_manifold(prompt)
|
||||
initial_output = state.fields[2].copy()
|
||||
_, manifold = load_pack("en_core_cognition_v1")
|
||||
state, labels = _build_manifold("test input", manifold)
|
||||
output_idx = len(labels) - 1
|
||||
initial_output = state.fields[output_idx].copy()
|
||||
|
||||
from field.operators import GraphDiffusionOperator
|
||||
op = GraphDiffusionOperator(damping=0.5)
|
||||
for _ in range(20):
|
||||
state, _ = op.forward(state)
|
||||
assert not np.allclose(state.fields[2], initial_output, atol=1e-7)
|
||||
assert not np.allclose(state.fields[output_idx], initial_output, atol=1e-7)
|
||||
|
||||
def test_vault_recall_returns_known_word(self) -> None:
|
||||
word = run_pulse("wisdom seeker")
|
||||
vault_versors, vault_words = build_mock_vault()
|
||||
assert word in vault_words
|
||||
def test_different_inputs_produce_different_output(self) -> None:
|
||||
w1 = run_pulse("alpha", use_glove=False)
|
||||
w2 = run_pulse("omega", use_glove=False)
|
||||
assert isinstance(w1, list) and isinstance(w2, list)
|
||||
|
||||
def test_different_inputs_may_differ(self) -> None:
|
||||
w1 = run_pulse("alpha")
|
||||
w2 = run_pulse("omega")
|
||||
assert isinstance(w1, str) and isinstance(w2, str)
|
||||
def test_recall_returns_known_vocab(self) -> None:
|
||||
_, manifold = load_pack("en_core_cognition_v1")
|
||||
words = run_pulse("wisdom seeker", use_glove=False)
|
||||
for w in words:
|
||||
try:
|
||||
manifold.get_versor(w)
|
||||
except KeyError:
|
||||
raise AssertionError(f"{w!r} not in compiled vocab")
|
||||
|
|
|
|||
Loading…
Reference in a new issue