TransWeave Full

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Responsible: Ben Goertzel

Papers: Goertzel (2025), Hyperon for AGI⇒ASI Whitepaper, §5.8

Status: Proposed. Theoretical framework described in the 2025 whitepaper. Not yet implemented.

This card provides mathematical depth beyond the concise TransWeave index card. TransWeave proposes an 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.

Core Problem

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.

Intertwining Maps

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:

\[\text{update} \circ \text{map} \approx \text{map} \circ \text{update}\]

• Variables: \(\text{update}\) = learning/reasoning step in one paradigm; \(\text{map}\) = transfer mapping between paradigms
• Domain: Stochastic dynamic programming formulations of cognitive algorithms
• Assumptions: Both source and target tasks can be viewed as approximate stochastic dynamic programming
• Meaning: Transfer and learning "almost commute" — the order of operations produces bounded, predictable differences rather than catastrophic divergence
• Source: Goertzel (2025), Whitepaper §5.8.4

Value Suboptimality Bounds

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:

\[w(\text{chain}) = \prod_{i=1}^{n} w_i\]

• Variables: \(w_i\) = weakening factor at transfer step \(i\)
• Meaning: If each step in a transfer chain has a known weakening factor, the total weakening of the chain is the product — providing clean bookkeeping of "how much generality we've spent" as transfers are composed
• Source: Goertzel (2025), Whitepaper §5.8.1

Impossibility Results and Selective Transfer (H-ICA)

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:

• Components that align cleanly are transferred
• Components flagged as non-transferable are marked for relearning in the target domain
• The transfer certificate documents which components transferred, which require relearning, and what monitoring is needed

This prevents the catastrophic negative transfer that plagues naive approaches, where a solution that works perfectly in one domain becomes actively harmful in another.

Braid Composition (Yang-Baxter Structure)

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:

• Predictive-coding learners, PLN inference, MOSES/GEO-EVO, WILLIAM compression, and SubRep options can be woven in any pragmatic order with bounds on order sensitivity
• SubRep admission certificates and MetaMo multi-goal motives ride the same machinery
• Geodesic inference/control properties are preserved under transfer
• Transports that minimize commutators are more freely reorderable
• When the math flags non-commuting or impossible segments, the system falls back to selective transfer rather than forcing brittle reuse

Integration with Geodesic Control

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.

Scope of Application

TransWeave applies across all PRIMUS cognitive paradigms:

• Predictive coding: Updates commute with transfer maps under controlled bounds
• PLN inference: Evidence and truth values transfer with geodesic properties preserved
• MOSES/GEO-EVO: Evolutionary search operators and deme statistics transfer between related program spaces
• WILLIAM compression: Patterns discovered in one context inform other contexts via transfer
• ECAN attention: Learned attention flow patterns transfer to new but related problems, preserving transport structure while adjusting for domain-specific features
• SubRep options: Admission certificates propagate through the same intertwining machinery — if options are certified safe in one domain, TransWeave identifies which safety aspects transfer to new domains

Key References

• Goertzel, B. (2025). Hyperon for AGI⇒ASI Whitepaper, §5.8: TransWeave: Intelligence Through Intertwining

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Related cards: PRIMUS Full · PLN Full · MOSES Full