les_alpha: latent polarizability head + induced-dipole LES term

[alacour]

Summary

Adds an optional latent polarizability head to the LES edge read-out, feeding upstream les's non-self-consistent induced-dipole term. This is the Allegro-LES construction from the polarizable-multipole LES paper (Kim, King, Park et al. 2026, arXiv 2605.05746), transplanted onto ECENet's edge frames.

• les_alpha='iso': one scalar per edge, scatter-summed to a per-atom α_i.
• les_alpha='aniso': two scalars per edge, a_e·I + b_e·(r̂r̂ᵀ − I/3) — an isotropic part plus a traceless bond-axial part. Symmetric and equivariant by construction; a lone bond gives the uniaxial α_∥/α_⊥ of a diatomic.
• Packed l0 = [q | u | α]; ecenet.les.unpack_l0 is the one place that knows the layout, model.les_flags carries the flag. α slots are zero-init (not a saddle: E_lr is linear in α); les_charge_scale doesn't touch α.

Energy. The periodic path passes latent_alphas straight to upstream's Ewald. The vectorized isolated path forms the field of the fixed multipoles from the already-built masked f_qu/f_uu kernels and adds −½ E_i·α_i·E_i.

Read-outs. LESLongRange.born_charges() is now the single Z* implementation behind the calculator and eval_spice_bec, going through upstream's forward when α is present so the induced dipoles are part of the polarization. total_polarizability() sums α_i per structure (paper Eq. 29 — exactly dP/dE_ext for this model). The calculator stashes results['les_alphas'] and gains compute_polarizability(atoms). All four trainers and predict_charges take/handle the flag.

Test plan

• tests/test_les.py: packed layout, α = 0 at init, 'iso' invariant / 'aniso' RαRᵀ-equivariant and symmetric, lone bond uniaxial with r̂ as principal axis, les_charge_scale leaves α alone, batched variants consistent, bad configs rejected
• tests/test_les.py: vectorized isolated path == upstream loop for iso/aniso × dipoles on/off (energies and gradients, worst 2e-15), FD forces 5e-11, periodic path exact, α = 0 reduces to the no-α energy, born_charges α = 0 == direct BEC call
• tests/test_xyz_trainer.py: xyz-trained 'aniso' checkpoint through load_calculator — joint-graph forces, stress FD 2e-13 through the periodic α path, α stashed, compute_polarizability == Σα_i == dP/dE_ext via upstream e_ext (autograd), BEC finite with a non-zero induced part, α-less checkpoint refused
• tests/test_trainer_les.py: rMD17 smoke with les_alpha='iso'
• All other test scripts and ruff clean

Notes

• Physical α needs the ε_e unscaling of the paper (Eqs. 23–24): ε_e = 1 for isolated molecules, ε_∞/(1 + χ^les) for bulk. Left to the caller.
• No positivity constraint on α (the paper found it unnecessary); trivially addable if it turns out to matter.
• Validation against reference polarizabilities (e.g. a Psi4 subset of SPICE) is the open follow-up — SPICE carries no α labels, so the head trains from energies/forces only, as in the paper.

🤖 Generated with Claude Code

https://claude.ai/code/session_019oREKbosSjju8EEuuPhHea