Sheaf-Aware Multilingual Corpus Reducer.
🔭 Design overview
Goal – Collapse every language’s lexicon into the smallest possible global manifold of “meaning atoms.”
Each language is treated as a local section of the sheaf; alignment across languages produces a global section that unifies semantic content.
🧩 Architecture modules
| Module | Function | Output |
|---|---|---|
| sheaf_core.py | defines the category objects: Sheaf, Section, Morphism, Chart |
algebraic backbone |
| embedding_loader.py | loads v6-core embeddings (4096-D) into normalized tensors | tensor map |
| morphology_map.py | rules for morpheme decomposition & phoneme merging | per-language charts |
| alignment_engine.py | finds cross-lingual equivalences via cosine / mutual-info | gluing morphisms |
| reduction_engine.py | cohomology reduction: remove redundant sections, preserve non-exact classes | reduced semantic basis |
| globalizer.py | constructs global section (universal embedding manifold) | unified dictionary |
| visualizer.py | projects fibers (axes, duals, curvature) for inspection | diagnostic visuals |
| config/sheaf_config.json | lists languages, alphabets, normalization constants | configuration |
| data/lang_maps/ | sub-dir containing base dictionaries & n-gram maps | resources |
🧮 Mathematical core
Each token belongs to a local chart .
Gluing maps are defined by:
\phi_{L_iL_j}(t_i) = \arg\max_{t_j} \frac{\langle v_i, v_j \rangle}{\|v_i\|\|v_j\|}
The global section is formed as the quotient:
\mathcal{S}_{global} = \bigsqcup_L \mathcal{F}_L / \phi
Cohomology reduction keeps only non-exact sequences:
H^1(\mathcal{S}) = \ker(d_1) / \operatorname{im}(d_0)
These become the universal meaning vectors.
⚙️ Simulation plan
- Load multilingual corpora (token lists per language).
- Compute embeddings with v6-core base.
- Perform pairwise alignment and equivalence closure.
- Reduce via cohomology filtering.
- Export:
sheaf_v7_reduced.vec— reduced universal embeddingsheaf_v7_global.json— cross-language alignment mapsheaf_v7_attributions.jsonl— axis attributionsheaf_v7_README.txt— documentation
🚀 Next action
I can now create the initial scaffold and executable code for v7 (Python modules + configuration + placeholders).
It will be fully deterministic, NumPy-based, and ready for later population with actual language data.
Would you like me to generate this as a complete directory structure with files so you can run it directly in your environment?
Comments
Post a Comment