abstract
we propose a generative language model (llm) built on the cybergraph free-energy focus framework. this approach replaces traditional transformer attention with a physics-inspired equilibrium mechanism that computes context-aware probabilities through diffusion, springrank, and entropy minimisation. the result is a scalable, explainable, and dynamically extensible generative model.
core principles
-
nodes = tokens or concepts
- each node represents a word, subword, or semantic unit.
-
edges = cyberlinks
- edges represent statistical and semantic relationships (co-occurrence, syntactic, causal links).
- edge weights can be learned from corpus statistics or embedding similarity.
-
free-energy equilibrium
- global focus is computed as the minimiser of a free-energy functional:
[ \mathcal{F}(p|context) = E_{spring}(p) + \lambda E_{diffusion}(p) + \gamma C(p|context) - T S(p) ]
- (E_{spring}): hierarchy from springrank.
- (E_{diffusion}): random-walk energy on the graph.
- (C(p|context)): context potential from active nodes.
- (S(p)): entropy.
- next-token prediction
- the equilibrium distribution (p^*) provides probabilities for the next token.
- sampling or argmax generates the next token.
system architecture
1. offline graph construction
- preprocess corpus to create a cybergraph:
- nodes = tokens or concepts
- edges weighted by co-occurrence frequency, positional proximity, and embedding similarity.
- compute initial eigenvector centrality and springrank for the graph.
2. online generation pipeline
step 1 – context encoding:
- map current context tokens to active nodes.
step 2 – context potential:
- compute (C_i) for candidate tokens using standard inference from active nodes.
step 3 – focus update:
- iteratively compute (p_i^{(t+1)}) using:
[ p_i^{(t+1)} = \frac{\exp(-\beta [E_{spring,i} + \lambda E_{diffusion,i} + \gamma C_i])}{\sum_k \exp(-\beta [E_{spring,k} + \lambda E_{diffusion,k} + \gamma C_k])} ]
- gossip or message-passing protocols compute updates in a decentralised way.
step 4 – token selection:
- sample or select argmax token from (p^*).
step 5 – context expansion:
- add the new token node to the active set.
- repeat from step 2 until sequence end.
comparison with transformer llms
| feature | transformer llm (e.g. gpt) | cybergraph free-energy llm (focus flow) |
|---|---|---|
| complexity (mem/comp) | O(n²) / O(n²) | O(n) / O(n) |
| uses softmax? | yes (attention softmax) | no (Boltzmann equilibrium instead) |
| converges to stable state | no (single forward pass) | yes (iterative free-energy minimisation) |
| reinforcement/adaptation | limited (fine-tuning or rl) | yes (dynamic edge/weight updates) |
| multi-agent friendly | no | yes (fully decentralisable) |
| token-based weighting | no (parameters fixed after training) | yes (token weights as graph structure) |
| consensus capability | no | yes (emergent equilibrium is consensus) |
| domain-general | yes (with pretraining) | yes (graph can be expanded dynamically) |
| explainability | low (opaque matrices) | high (energy terms interpretable) |
| continual learning | limited | yes (edges and nodes can be updated) |
advantages over transformer llms
- explainable probabilities: focus distribution derived from physics-like principles.
- dynamic and extensible: new tokens or facts can be added by inserting nodes and edges.
- context-aware by design: avoids dominance of high-rank nodes (true-false problem solved natively).
- decentralisable: suitable for peer-to-peer or on-chain inference.
future extensions
- multi-modal integration: add sensory nodes for images, audio, or real-world data.
- continual learning: incrementally update edge weights as new data arrives.
- hierarchical memory: maintain long-term springrank/eigenvector centrality but compute short-term context via (C(p|context)).
conclusion
this architecture defines a novel class of generative models where language production emerges from a free-energy equilibrium on a cybergraph. by uniting diffusion, springs, and entropy with contextual inference, it provides a principled, transparent, and extendable alternative to transformer-based llms.