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Chaotic-Differential Information Fields: A Framework for Emergent Semantic Dynamics in Language…
- The paper introduces a theoretical framework called Chaotic-Differential Information Fields (CDIF) for language models, departing from traditional linear-algebraic approaches.
- CDIF represents tokens as initial conditions in a high-dimensional phase space, evolving them through non-linear dynamical systems based on chaos theory.
- Semantic meaning and token sequences emerge from trajectories converging upon context-dependent strange attractors, with token generation defined by mapping to attractor regions.
- The model aims to address limitations of current transformer architectures, providing a formalism for semantic ambiguity, phase transitions, and non-repetitive generative flows.
- The mathematical framework involves token representation as phase space initial conditions, context-modulated evolution equations, attractor formation, token generation via attractor partitioning, and stability considerations.
- Training components include initial condition embeddings, context parameter maps, and attractor partition classifiers, with a training objective combining language modeling loss and stability regularization.
- Theoretical advantages of the CDIF framework include emergent non-linearity, compressed memory representation, context-sensitive dynamics, natural ambiguity modeling, and robustness/stability.
- Computational considerations involve complexity analysis, parallel implementation possibilities, and suitability for specialized hardware supporting ODE integration.
- Future directions include empirical validation, exploring architectural variations, theoretical analysis of attractor topology, and potential hybrid models combining linear and non-linear approaches.
- In conclusion, CDIF offers a radical rethinking of language model architecture, aligning with dynamical systems theory to capture complex linguistic phenomena and potentially enhancing AI reasoning processes.
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