3.4 Interaction Probability: Beyond Frequency---Contextual Resonance and Predictive Entanglement
In traditional large language models (LLMs), probability is derived primarily from statistical co-occurrence and token-level prediction. While effective for surface-level generation, this probabilistic grounding is insufficient to model the nuanced, emergent semantics arising from multi-word interactions, particularly those involving cultural, artistic, or idiomatic content. The CAS-6 framework proposes a richer interpretation of interaction probability---one that incorporates contextual resonance and predictive entanglement.
A. Limitations of Token-Level Frequency Models
Most transformer-based architectures (e.g., BERT, GPT) rely on masked language modeling or autoregressive decoding, where the likelihood of a word is estimated based on linear or partially bidirectional context windows. This formulation:
Assumes independence or limited-order Markov dependencies.
Fails to account for nonlinear entanglement of meaning across permutations (e.g., "crocodile tears" "tears crocodile").
Overrepresents literal frequency while underrepresenting conceptual salience or artistic resonance.
B. Redefining Probability in CAS-6: Three Axes
We redefine interaction probability as a multidimensional construct, composed of the following interacting factors:
1. Statistical Frequency (f)
Conventional co-occurrence in corpora.
Still useful, but considered only one axis of semantic relevance.
2. Contextual Resonance (r)
A measure of how semantically "stable" or "meaningful" the interaction is across diverse contexts.
For example, the dyad "crocodile tears" maintains its figurative connotation across domains (media, literature, politics), giving it high contextual resonance.
3. Predictive Entanglement (e)
A dynamic measure capturing how strongly the presence of one token (or structure) activates or modulates another's interpretation.
For instance, "eyes" when preceded by "tears" has a different affective and semantic projection than when preceded by "crocodile."
Thus, we define an augmented interaction probability P as:
Pij=fij+rij+eijP = f + r + e
Where:
,,, , are tunable weights depending on application domain.
fijf: normalized co-occurrence frequency
rijr: resonance score, derived from contextual variability tests or semantic stability estimators.
eije: entanglement coefficient, measured via attention heads, mutual information, or transformer gradient analysis.
C. Applications in Model Design and Interpretation
Semantic Disambiguation: High entanglement + low frequency suggests idiomatic or poetic expressions.
Figurative Language Detection: High resonance + asymmetry in directional entanglement can mark metaphors.
Low-Resource Semantics: Enables reasoning over rare but meaning-rich combinations that are underrepresented in training data.
D. Computational Implementation
