TransWeave is a proposed algebraic framework for transferring and composing knowledge across cognitive paradigms — with formal guarantees on what transfers, what must be relearned, and how much order-sensitivity each operation introduces. This card provides mathematical depth beyond the concise TransWeave index card.
Last verified: 2026-06-05
Papers: Goertzel (2025), Hyperon for AGI⇒ASI Whitepaper, §5.8
Status: Proposed. Theoretical framework described in the 2025 whitepaper. Not yet implemented.
In a multi-paradigm system like PRIMUS, different learning algorithms produce different kinds of knowledge — neural weights, logical proofs, evolved programs, compressed patterns. Naive transfer between paradigms fails because operation order matters: learn→transfer can produce different results than transfer→learn. TransWeave formalizes this order sensitivity and bounds it.
TransWeave formalizes cross-paradigm transfer as task morphisms — structure-preserving transformations called intertwining maps that approximately maintain key relationships between source and target domains.
Formal definition:
An intertwining map between tasks is a transformation that satisfies:
\[\text{update} \circ \text{map} \approx \text{map} \circ \text{update}\]The critical advance is proving that transferred solutions won't be worse than a specified threshold. When a solution is transferred from task \(A\) to task \(B\) via an intertwining map, the framework provides a value suboptimality bound — a guarantee on how far the transferred solution can deviate from optimal in the target domain.
Weakness (the quantale-based simplicity metric) propagates multiplicatively across chains of transfer:
\[w(\text{chain}) = \prod_{i=1}^{n} w_i\]Not everything can transfer — and knowing what cannot is as important as knowing what can. TransWeave includes a Hierarchical Independent Component Analysis (H-ICA) that identifies when solution components fundamentally cannot align between domains.
When H-ICA signals impossibility or near-singularity in the intertwining map, the system automatically falls back to selective transfer:
This prevents the catastrophic negative transfer that plagues naive approaches, where a solution that works perfectly in one domain becomes actively harmful in another.
TransWeave's "almost commutative" operations don't just chain — they braid. The operator calculus shows how composite transfers obey braid-like laws (a Yang-Baxter style structure), so multi-step pipelines can be reordered along different strands with predictable, bounded change.
This means PRIMUS components plug into a single operator layer where:
TransWeave extends naturally to the geodesic framework (the \(f \cdot g\) forward/backward product structure). The product structure of forward/backward factors is preserved under transfer, as are evidence conservation properties. Transferred solutions maintain the same efficient proof/planning characteristics as native solutions.
MORK stores H-ICA components and learned mappings as Merkle-DAG objects with content identifiers (CIDs), enabling similarity search and verification through Merkle proofs.
TransWeave operates across both PRIMUS meta-loops: in the goal-directed loop it determines what existing knowledge can be reused for the current goal, and in the ambient (background) loop it transfers background discoveries across paradigms — for example, patterns discovered by WILLIAM informing other cognitive processes, or attention-flow patterns transferring to new contexts.
TransWeave applies across all PRIMUS cognitive paradigms:
Related cards: PRIMUS · PLN · MOSES