neurons creating cyberlinks on the same vimputer — learning together
in ML, one entity trains one model. in cyber, millions of neurons train one shared graph. each cyberlink is a signed economic commitment — a weight update to the cybergraph. every link encodes implicit knowledge: what the neuron inferred from observing explicit knowledge
the sum of all learning acts is the cybergraph — knowledge as collective memory
the tru runs inference over this memory, producing explicit knowledge. neurons observe it, derive meaning, and link again. the observation loop at scale is egregore
learning incentives reward agents whose links increase the system's syntropy
mathematical foundations
the system state evolves as each cyberlink updates the cybergraph:
$$S(t+1) = F(S(t), W(t), T(t))$$
weight updates follow a Hebbian rule modulated by consensus:
$$w_{ij}(t+1) = w_{ij}(t) + \alpha \cdot f(x_i, x_j) + \beta \cdot g(\pi_i, \pi_j)$$
where the first term captures local co-activation and the second aligns with global focus $\pi$. the resulting weight change per cyberlink:
$$\Delta w_{ij} = \alpha \cdot r_{ij} \cdot \pi_j$$
where $r_{ij}$ is the information-theoretic value exchanged and $\pi_j$ is the consensus-based importance of each particle
exploration and exploitation
the system balances exploration and exploitation through adaptive rate:
$$\varepsilon = \beta \cdot (1 - C_{\text{local}}) \cdot S_{\text{global}}$$
weak local consensus or high global stability drives exploration. strong local consensus drives exploitation. this prevents premature convergence while preserving discovered structure
temporal scales
neurons operate on two timescales. short-term memory responds to recent observations:
$$M_s(t) = (1 - \alpha_s) \cdot M_s(t-1) + \alpha_s \cdot x(t)$$
long-term memory captures persistent structure:
$$M_l(t) = (1 - \alpha_l) \cdot M_l(t-1) + \alpha_l \cdot x(t)$$
the cybergraph stores both: recent cyberlinks shift fast weights, accumulated structure forms slow weights. see collective focus theorem for the convergence proof
buy energy for collective learning
see egregore for the broader framework