Signal Model & Math
Nomentum models market microstructure as synaptic plasticity. The core state is a bounded conductance composed of fast and slow components, updated by signed spike trains from net flow.
State
Let Gf and Gs denote fast and slow conductance components. The synaptic state is G = w_f·Gf + w_s·Gs with w_f=0.6, w_s=0.4.
Continuous-time dynamics
dGf/dt = -Gf/τ_fast + k_f·S(t),
dGs/dt = -Gs/τ_slow + k_s·S(t).
Liquidity scales τ_slow monotonically; τ_fast is short to reject noise. Saturation terms and bounded nonlinearities ensure G ∈ [0,1].
Discrete update
// per tick Δt
Gf ← clip( Gf·e^{-Δt/τ_f,eff} + α_f·ϕ(Gf) + β_f·sgn·w(pct)·M )
Gs ← clip( Gs·e^{-Δt/τ_s,eff} + α_s·ϕ(Gs) + β_s·sgn·w(pct)·M )
G ← 0.6·Gf + 0.4·Gs
ϕ(·) is a saturation/variability correction; w(pct) scales impulses by trade fraction; M is a momentum-derived gain in [~0.7, 1.4].
Timing sensitivity (STDP-like)
Short inter-spike intervals amplify learning within a bounded window, favoring consistent sequences and de-emphasizing isolated flips.
Momentum coupling
Multi-timeframe momentum uses tanh-normalized deltas across short/medium/long horizons (e.g., 5m/1h/1d) combined as a convex blend. M scales learning strength; it does not directly overwrite G.
Risk damping
A composite scalar in [0,1] derived from microstructure/holder distributions down-weights M in adverse regimes. Final gain uses M' = M·(1 - R).
Discrete Decay Formulations
G_f^{t+1} = \mathrm{clip}(G_f^t e^{-\Delta t/\tau_f^*} + α_fϕ(G_f^t) + β_f σ w(p) M)G_s^{t+1} = \mathrm{clip}(G_s^t e^{-\Delta t/\tau_s^*} + α_sϕ(G_s^t) + β_s σ w(p) M)
Parameters: σ ∈ {-1,+1} (buy/sell), w(p) saturates trade fraction p, τₛ* scales with liquidity
Saturation & Variability
Bounded mappings ensure stable dynamics:
- Saturation function: φ(G) = 1 - e⁻ᶜᴳ
- Organic noise: ε ∼ N(0, η√G)
Momentum Blend
M = Σ λᵢ [1 + tanh(Δᵢ/sᵢ)]Σ λᵢ = 1, weights favor short horizons
Risk Damping
R = Σ ωⱼ rⱼM' = M(1 - R)Factors: concentration, bundle intensity, large-holder turnover, new-holder velocity
Score Calculation
Monotone function of G and regime flags with clipping and hysteresis to prevent flicker.