NEAM Guide
What The Sphere Is
This is a DiffusionGemma-derived NEAM probe. DiffusionGemma supplies prompt-conditioned hidden states and directed attention-like couplings; the NEAM layer is a separate mean-field dynamical system run on top of those tensors.
The globe is not a 3D embedding learned by the model. It is an equal-area 2D shell for selected canvas sites. Domain colors are painted directly on that S2 surface, dots are the lattice sites, and arrows are local order vectors projected into the tangent plane at each site.
Simulation Math
\[
\theta_i^{(k)} = x_i^{(k)} + \lambda \sum_j J_{ij}^{(k)}m_j^{(k-1)}
\]
\[
m_i^{(k)} = \phi(\theta_i^{(k)}) =
\frac{\beta\theta_i^{(k)}}{1+\sqrt{1+\beta^2\lVert\theta_i^{(k)}\rVert^2/R^2}}
\]
\[
D_{ij}^{(k)} = J_{ij}^{(k)}
\left(
\frac{m_i^{(k)}\cdot m_j^{(k-1)}}
{\lVert m_i^{(k)}\rVert\lVert m_j^{(k-1)}\rVert+\epsilon}
\right)^2
\]
\[
\sigma_{ij}^{(k)}=(J_{ij}^{(k)}-J_{ji}^{(k)})D_{ij}^{(k)},
\qquad
\sigma_{\mathrm{tot}}(k)=\sum_{ij}\sigma_{ij}^{(k)}
\]
The key point is the weighting: asymmetry alone is not the signal. Directed imbalance becomes NEAM activity only when it is coupled to delayed response.
How To Read Domains
- Color regions are graph communities from susceptibility-weighted site relations.
- Ising-Tracked Dynamic is the primary domain estimator: it adds an observer-side hysteresis margin to the raw framewise susceptibility partition. Raw Dynamic remains available as a no-inertia control; Fixed keeps one run-average partition for comparison.
- The freshness map unwraps the same shell cells as a Mercator-style heat map: hot cells changed domain this step, cold cells have been stable for several denoising steps.
- Bright curved borders mark neighboring shell cells assigned to different communities.
- Domain valence is outgoing signed entropy proxy minus incoming signed entropy proxy.
Why Hysteresis Is Optional
The Ising-like Spin Transformer framing treats denoising step as discrete time, attention as directed coupling, and \(m_i^{(k)}\) as a simulated magnetization. A coarse domain label is therefore a mesoscopic observer state, not a microscopic variable that must instantly follow every spectral-clustering twitch.
Tracked Dynamic does not alter \(x\), \(J\), \(m\), \(D\), \(\Sigma\), or \(\chi\). It only says a site keeps its previous domain unless the new susceptibility-domain affinity beats the old affinity by a local switching margin. This is analogous to a kinetic-Ising switching barrier or domain-wall pinning prior, and should be read as a domain tracker rather than a new physical term.
Barrier Calibration
Calibration diagnostics load with the run payload.
Why This Helps NEAM Work
The shell makes simulation structure inspectable. You can see whether order forms coherent territories, whether those territories move during denoising, and whether high sigma_tot comes from organized domain flow or scattered site noise.
For prompt, seed, or ablation comparisons, watch three quantities together: domain migration, signed sigma_tot, and the D_AB,t heatmap. If symmetrizing J collapses these patterns, the asymmetric couplings are doing visible work in the NEAM layer.
Current Run Last Step
Diagnostics load with the run payload.
mCBAL / Rescue Framing
The NEAM Rescue / mCBAL framing is represented operationally here as market-like directed coupling plus delayed response. The visualization does not claim DiffusionGemma internally exposes thermodynamic variables; it shows how transformer-shaped couplings drive a separate non-equilibrium attention-market simulator.
Implementation Caveats
- The present V0 treats projected hidden states as external fields, not magnetization. Magnetization is simulated after projection.
- PCA whitening is enabled so \(x_i^{(k)}\) lands near the NEAM response scale instead of saturating \(\lVert m_i\rVert\) at \(R=\sqrt{d_\star}\).
- The first rendered magnetization now follows the contract convention \(m_i^{(0)}=0\); delayed correlations start only after there is a previous magnetization state.
- The attention convention is row \(i\), column \(j\): query/site \(i\) attends to key/site \(j\). Changing that convention flips the interpretation of signed flow.
Units And Guardrails
- D_AB,t: unitless delayed alignment averaged over domain site pairs.
- sigma_tot: signed entropy-production proxy units from (J_ij - J_ji) * D_ij.
- migration: fraction of selected sites changing domain labels per denoising step.
- site age: denoising steps since a selected site last changed domain label.
- m_norm: norm of simulated NEAM magnetization in the reduced d_star coordinate system.