gam-sae 0.3.145

use super::*;

// The JumpReLU optimization-inclusion band is the single canonical predicate
// `crate::assignment::jumprelu_in_optimization_band`, whose support is the
// machine-precision cutoff `(logit − threshold)/τ > −36` (`σ(−36) ≈ 2e-16`).
// That band is the support over which the sparsity prior's value/gradient/
// Hessian are assembled in `assignment.rs` (and the logdet third-derivative
// adjoint in `construction.rs`); it defines where the prior is NONZERO.
//
// It is NOT, however, the Newton active set. Putting every in-band atom in the
// joint Arrow-Schur block made the per-token block `K·(1+d)` (at `threshold=0`,
// `τ=1` with sparse logits essentially every atom is in-band), breaking the
// `O(k_active)` contract. The priors are column-SEPARABLE, so a gated-off atom
// contributes a DIAGONAL-only block and never needs the joint (cross-coupling)
// solve: `from_jumprelu` keeps the hard-gated atoms plus the gated-off atoms
// whose separable contribution exceeds a relative cutoff, and drops the
// negligible deep-band tail (bounded gradient error; identical objective value,
// which the loss sums over the full band regardless of this layout). A tighter
// FIXED `−4·τ` band was tried once and STALLED the fit — it dropped coordinates
// in `(−36τ, −4τ]` from the solve while the prior still put O(1) gradient on
// them (objective↔gradient desync). The cutoff here is on the ACTUAL separable
// gradient magnitude, so an atom is only dropped when its contribution is
// already negligible; that desync cannot recur.

/// Per-row active-set layout for sparse SAE assignment (any mode).
///
/// When the assignment is sparse — structurally (JumpReLU gate) or
/// effectively (softmax / IBP-MAP at large `K`, where the assignment mass
/// concentrates on a small support) — only a subset of `K` atoms are active
/// per observation.  The Arrow-Schur row block for observation `i` has dim
/// `q_active_i = |active_atoms_i| + Σ_{k ∈ active_i} d_k` rather than
/// `q = assignment_dim + Σ_k d_k`.  This struct records which atoms are active per row
/// and maps compressed block positions back to full-q positions so that
/// `apply_newton_step` can unpack the compact `delta_t` from the solve.
///
/// For JumpReLU the active set is the hard forward gate (`a_{n,k} ≠ 0`) plus any
/// gated-off atom still carrying a non-negligible column-separable prior
/// gradient; below-cutoff gated-off atoms are diagonal-only and dropped (see
/// [`Self::from_jumprelu`]). For IBP-MAP the active set is the union of a
/// top-`k_active_cap`
/// truncation and a magnitude cutoff on `a_{n,k}`; this is only enabled when
/// `K` is large enough that the dense `(m_total · p)²` data Gram would not
/// fit the host / device working-set budget, and the dropped atoms carry
/// `O(a_{n,k}²)` curvature that is negligible by construction of the cutoff.
///
/// #1408: SOFTMAX engages this compact layout when an explicit `top_k`
/// (`softmax_active_cap`) and/or the in-core memory budget bounds the active
/// set — the `AssignmentMode::Softmax` arm of `assemble_arrow_schur` consults
/// [`crate::manifold::SaeManifoldTerm::softmax_active_plan`] and,
/// on `Some((cap, cutoff))`, builds the active set via
/// [`Self::from_dense_weights`]. The full-`K` dense softmax layout is retained
/// only when neither lever engages (no `top_k`, in-budget `K`). Folding softmax
/// `top_k` into the compact solve required writing the active×active Gershgorin
/// Loewner majorizer sub-block (#1419; the softmax entropy curvature is
/// indefinite, so its raw diagonal cannot be used) AND contracting that SAME
/// majorizer over the compact logit slots in the logdet ρ-trace
/// (`assignment_log_strength_hessian_trace`) and the θ-adjoint, so value,
/// `log|H|`, and Γ differentiate one operator on the compact support. That
/// coordinated change is landed and FD-certified; the FFI's after-the-fit
/// top-`k` projection is then a no-op at the optimum.
#[derive(Debug, Clone)]
pub struct SaeRowLayout {
    /// `active_atoms[row]` — sorted indices of active atoms for that row.
    pub active_atoms: Vec<Vec<usize>>,
    /// For row `i`, active atom `active_atoms[i][j]` has its coord block
    /// starting at compressed position `coord_starts[i][j]`.
    pub coord_starts: Vec<Vec<usize>>,
    /// Full-q coordinate offset for atom `k` (length `k_atoms`).
    pub coord_offsets_full: Vec<usize>,
    /// Per-atom coordinate dimensions, indexed by atom index.
    pub coord_dims: Vec<usize>,
}

/// Inputs to [`SaeRowLayout::from_jumprelu`], grouped into one bundle so the
/// per-row active-set construction takes a single parameter rather than a long
/// positional argument list. Borrowed matrices (`logits`, `contribution`) stay
/// by reference; the owned `coord_dims` / `coord_offsets_full` are moved on into
/// the resulting layout.
pub(crate) struct JumpReluLayoutParams<'a> {
    /// Number of observation rows.
    pub n: usize,
    /// Number of dictionary atoms.
    pub k_atoms: usize,
    /// JumpReLU hard-gate threshold `θ`.
    pub threshold: f64,
    /// Gate temperature `τ`.
    pub temperature: f64,
    /// `(n × k_atoms)` per-row logits.
    pub logits: &'a Array2<f64>,
    /// `(n × k_atoms)` per-row separable-diagonal gradient magnitudes.
    pub contribution: &'a Array2<f64>,
    /// Cap on the per-row active-set size.
    pub k_active_cap: usize,
    /// Relative (per-row-peak) cutoff below which gated-off atoms are dropped.
    pub relative_cutoff: f64,
    /// Per-atom coordinate dimensions (length `k_atoms`).
    pub coord_dims: Vec<usize>,
    /// Full-q coordinate offset for each atom (length `k_atoms`).
    pub coord_offsets_full: Vec<usize>,
}

impl SaeRowLayout {
    /// JumpReLU compact active set, sized by the HARD FORWARD GATE plus the
    /// gated-off atoms that still carry a NON-NEGLIGIBLE column-separable prior
    /// contribution — NOT the whole machine-precision optimization band.
    ///
    /// The joint (cross-coupling) Newton row block only ever needs the atoms
    /// that actually couple: the atoms with nonzero assignment mass
    /// (`logit > threshold`, i.e. the hard forward gate `a_k ≠ 0`), whose
    /// data-fit reconstruction Jacobian cross-couples with the decoder and with
    /// every other on atom. Every OTHER in-band atom is gated OFF (`a_k = 0`),
    /// so its reconstruction contribution and data-fit logit JVP are hard-zero
    /// and its ONLY footprint in the Newton system is a DIAGONAL block from the
    /// column-SEPARABLE priors (the assignment sparsity prior on its own logit,
    /// and the ARD prior on its own coords). A diagonal-only atom never needed
    /// the joint block.
    ///
    /// The former layout put EVERY atom in the band
    /// `(logit − threshold)/τ > −36` (see
    /// [`crate::assignment::jumprelu_in_optimization_band`]) into the joint
    /// block. That band is the smooth prior's machine-precision support
    /// (`σ(−36) ≈ 2e-16`), so at `threshold = 0`, `τ = 1` with typical (sparse)
    /// logits essentially ALL `K` atoms qualified and the per-token block was
    /// `K·(1+d)`, violating the `O(k_active)` contract on the very lane meant
    /// for large `K`.
    ///
    /// `contribution[row, k]` is the exact magnitude of atom `k`'s separable
    /// diagonal GRADIENT sub-vector at that row (`|∂P/∂logit| + Σ_axis
    /// |∂ARD/∂t|`) — i.e. precisely the piece of `g_t` that leaves the row block
    /// when `k` is dropped. Atoms are kept when they are hard-gated OR their
    /// contribution exceeds `relative_cutoff · row_peak`, capped at
    /// `k_active_cap` (hard-gated atoms are never dropped; the remaining budget
    /// is filled by the highest-contribution gated-off atoms). Dropping an atom
    /// therefore changes the assembled gradient by less than the cutoff, and
    /// leaves the OBJECTIVE VALUE bit-identical (the loss's
    /// `assignment_prior_value` / `ard_value` sum the full −36 band
    /// independently of this layout). This mirrors the softmax / IBP-MAP
    /// [`Self::from_dense_weights`] truncation, which likewise keeps a row's
    /// top-`k` atoms above a relative cutoff and drops the negligible tail.
    pub(crate) fn from_jumprelu(params: JumpReluLayoutParams<'_>) -> Self {
        let JumpReluLayoutParams {
            n,
            k_atoms,
            threshold,
            temperature,
            logits,
            contribution,
            k_active_cap,
            relative_cutoff,
            coord_dims,
            coord_offsets_full,
        } = params;
        use std::cmp::Ordering::Equal;
        let cap = k_active_cap.max(1);
        let mut per_row = Vec::with_capacity(n);
        for row in 0..n {
            let row_logits = logits.row(row);
            let row_contrib = contribution.row(row);
            let in_band = |k: usize| {
                crate::assignment::jumprelu_in_optimization_band(
                    row_logits[k],
                    threshold,
                    temperature,
                )
            };
            // Hard forward gate: nonzero assignment mass ⇒ data-fit coupling in
            // the joint block. Always retained.
            let hard: Vec<usize> = (0..k_atoms).filter(|&k| row_logits[k] > threshold).collect();
            // Relative-cutoff base: the largest separable contribution over all
            // in-band atoms in this row.
            let peak = (0..k_atoms)
                .filter(|&k| in_band(k))
                .fold(0.0_f64, |m, k| m.max(row_contrib[k].abs()));
            let cutoff = relative_cutoff * peak;
            // Gated-off, still-in-band atoms whose separable diagonal gradient is
            // non-negligible (> cutoff). The negligible deep-band tail is dropped.
            let mut extra: Vec<usize> = (0..k_atoms)
                .filter(|&k| {
                    row_logits[k] <= threshold && in_band(k) && row_contrib[k].abs() > cutoff
                })
                .collect();
            // Cap the total active set; hard-gated atoms are never dropped, so the
            // gated-off `extra` set absorbs the truncation.
            let budget = cap.saturating_sub(hard.len());
            if extra.len() > budget {
                if budget == 0 {
                    extra.clear();
                } else {
                    extra.select_nth_unstable_by(budget - 1, |&i, &j| {
                        row_contrib[j]
                            .abs()
                            .partial_cmp(&row_contrib[i].abs())
                            .unwrap_or(Equal)
                    });
                    extra.truncate(budget);
                }
            }
            let mut active: Vec<usize> = hard;
            active.extend(extra);
            if active.is_empty() {
                // Never emit an empty row block (a degenerate empty block zeroes
                // the row). Retain the single most-contributing in-band atom, or
                // — if the row has no band atom at all — the largest-logit atom.
                let best = (0..k_atoms)
                    .filter(|&k| in_band(k))
                    .max_by(|&i, &j| {
                        row_contrib[i]
                            .abs()
                            .partial_cmp(&row_contrib[j].abs())
                            .unwrap_or(Equal)
                    })
                    .or_else(|| {
                        (0..k_atoms).max_by(|&i, &j| {
                            row_logits[i].partial_cmp(&row_logits[j]).unwrap_or(Equal)
                        })
                    });
                if let Some(b) = best {
                    active.push(b);
                }
            }
            active.sort_unstable();
            per_row.push(active);
        }
        Self::from_active_atoms(per_row, coord_dims, coord_offsets_full)
    }

    /// Mode-agnostic effective active set for dense-weight modes (softmax /
    /// IBP-MAP) at large `K`: keep, per row, the top-`k_active_cap` atoms by
    /// `|a_{n,k}|` whose magnitude also exceeds `relative_cutoff · rowpeak`.
    ///
    /// #1414: the cutoff is RELATIVE TO EACH ROW'S OWN PEAK `max_k |a_{n,k}|`,
    /// matching the documented `sparse_active_plan` contract
    /// (`construction.rs:1763-1766`). A global cutoff (one threshold from the
    /// whole-dataset peak) would wrongly drop both atoms of a uniformly-small row
    /// `[0.0009, 0.0008]` just because another row peaks at `1.0`, changing the
    /// high-`K` compact model.
    ///
    /// `assignments[row]` is the dense length-`K` assignment vector `a_{n,·}`.
    /// The active set is always non-empty (the single largest-magnitude atom is
    /// retained even if below cutoff) so every row keeps a valid block.
    pub(crate) fn from_dense_weights(
        assignments: &[Array1<f64>],
        k_active_cap: usize,
        relative_cutoff: f64,
        coord_dims: Vec<usize>,
        coord_offsets_full: Vec<usize>,
    ) -> Self {
        let cap = k_active_cap.max(1);
        let mut per_row = Vec::with_capacity(assignments.len());
        for a in assignments {
            let k = a.len();
            // #1411: select the top-`cap` atoms by |a_k| in O(K) with a PARTIAL
            // select (`select_nth_unstable_by`), not a full O(K log K) sort. Only
            // the cap-sized active prefix matters; its internal order is
            // irrelevant (sorted at the end). The row peak is a separate O(K) max
            // scan. End-to-end this keeps support proposal O(K) (single pass +
            // partial select), the contracted per-token cost the high-K plan
            // claims, instead of sorting all K per row.
            let row_peak = a.iter().fold(0.0_f64, |m, &v| m.max(v.abs()));
            let cutoff = relative_cutoff * row_peak;
            let mut idx: Vec<usize> = (0..k).collect();
            // Partition so the `cap` largest-|a| indices occupy `idx[..cap]`
            // (unordered within); cheaper than a full sort when `cap << k`.
            if cap < k {
                idx.select_nth_unstable_by(cap - 1, |&i, &j| {
                    a[j].abs()
                        .partial_cmp(&a[i].abs())
                        .unwrap_or(std::cmp::Ordering::Equal)
                });
                idx.truncate(cap);
            }
            let mut active: Vec<usize> = idx
                .into_iter()
                .filter(|&k_idx| a[k_idx].abs() > cutoff)
                .collect();
            if active.is_empty() {
                // Retain the single largest-magnitude atom so the row block is
                // never empty (a degenerate empty block would zero the row).
                let top = (0..k).fold(None::<usize>, |best, i| match best {
                    Some(b) if a[b].abs() >= a[i].abs() => Some(b),
                    _ => Some(i),
                });
                if let Some(top) = top {
                    active.push(top);
                }
            }
            active.sort_unstable();
            per_row.push(active);
        }
        Self::from_active_atoms(per_row, coord_dims, coord_offsets_full)
    }

    /// Build from explicit per-row active-atom index lists.
    pub(crate) fn from_active_atoms(
        active_atoms: Vec<Vec<usize>>,
        coord_dims: Vec<usize>,
        coord_offsets_full: Vec<usize>,
    ) -> Self {
        let mut coord_starts_all = Vec::with_capacity(active_atoms.len());
        for active in &active_atoms {
            let mut starts = Vec::with_capacity(active.len());
            let mut cursor = active.len();
            for &k in active {
                starts.push(cursor);
                cursor += coord_dims[k];
            }
            coord_starts_all.push(starts);
        }
        Self {
            active_atoms,
            coord_starts: coord_starts_all,
            coord_offsets_full,
            coord_dims,
        }
    }

    /// Per-row compressed dim.
    pub fn row_q_active(&self, row: usize) -> usize {
        let active = &self.active_atoms[row];
        let coord_sum: usize = active.iter().map(|&k| self.coord_dims[k]).sum();
        active.len() + coord_sum
    }

    /// Expand a compact `delta_t` row slice back into full-q, zeros for inactive.
    pub fn expand_row(&self, row: usize, delta_t_row: &[f64], out: &mut [f64]) {
        for v in out.iter_mut() {
            *v = 0.0;
        }
        let active = &self.active_atoms[row];
        let starts = &self.coord_starts[row];
        for (j, &k) in active.iter().enumerate() {
            out[k] = delta_t_row[j];
            let d = self.coord_dims[k];
            let full_off = self.coord_offsets_full[k];
            for axis in 0..d {
                out[full_off + axis] = delta_t_row[starts[j] + axis];
            }
        }
    }
}

#[cfg(test)]
mod jumprelu_hard_gate_tests {
    // #5 — JumpReLU joint block sized by the hard forward gate plus the gated-off
    // atoms with a non-negligible column-separable prior gradient; the negligible
    // deep-band tail is dropped (see [`SaeRowLayout::from_jumprelu`]).
    use super::{JumpReluLayoutParams, SaeRowLayout};
    use crate::assignment::{assignment_prior_grad_hdiag, AssignmentMode, SaeAssignment};
    use crate::manifold::{
        SaeAtomBasisKind, SaeManifoldAtom, SaeManifoldRho, SaeManifoldTerm,
        SAE_DENSE_BETA_PENALTY_PROBE_MAX_DIM,
    };
    use gam_terms::latent::LatentManifold;
    use ndarray::{Array1, Array2, Array3};

    // Exact sparsity-prior separable diagonal gradient magnitude used as the
    // per-atom selection score: |P'(logit)| = λ·σ(1−σ)/τ at (threshold=0, τ=1, λ=1).
    fn logit_slope(logit: f64) -> f64 {
        let a = 1.0 / (1.0 + (-logit).exp());
        a * (1.0 - a)
    }

    /// GATE (i): with logits where most atoms are IN-BAND (all `> −36`) but only
    /// a few are hard-gated or near the threshold, the built block tracks the
    /// hard-gate + near-threshold count `n_active·(1+d)`, NOT `K·(1+d)`. Pins the
    /// exact retained set, the deep-band drop, and the cap truncation.
    #[test]
    fn from_jumprelu_block_size_tracks_hard_gate_not_band() {
        let n = 2usize;
        let k = 6usize;
        let (threshold, temperature) = (0.0_f64, 1.0_f64);
        // Two hard-gated (>0), one near-threshold gated-off (retained), three deep
        // gated-off (in the −36 band but negligible separable gradient → dropped).
        let logits = Array2::from_shape_vec(
            (n, k),
            vec![
                1.0, 0.5, -0.3, -20.0, -25.0, -30.0, // row 0
                0.8, 0.2, -0.4, -22.0, -26.0, -31.0, // row 1
            ],
        )
        .unwrap();
        // Every logit is inside the −36 optimization band, so the OLD full-band
        // layout would put all K=6 atoms in the joint block.
        for &l in logits.iter() {
            assert!(crate::assignment::jumprelu_in_optimization_band(l, threshold, temperature));
        }
        let contribution = logits.mapv(logit_slope);
        let coord_dims = vec![1usize; k];
        // Full-q coord offsets: assignment_dim (=K logits) then one axis per atom.
        let coord_offsets_full: Vec<usize> = (0..k).map(|i| k + i).collect();

        // No cap (cap = K): the relative cutoff is the sole lever.
        let layout = SaeRowLayout::from_jumprelu(JumpReluLayoutParams {
            n,
            k_atoms: k,
            threshold,
            temperature,
            logits: &logits,
            contribution: &contribution,
            k_active_cap: k,
            relative_cutoff: 1.0e-3,
            coord_dims: coord_dims.clone(),
            coord_offsets_full: coord_offsets_full.clone(),
        });
        for row in 0..n {
            // Hard-gated {0,1} plus the near-threshold gated-off atom 2; deep atoms
            // {3,4,5} dropped.
            assert_eq!(layout.active_atoms[row], vec![0, 1, 2], "row {row}");
            // Block dim = 3·(1+d) = 6, versus the full-band 6·(1+d) = 12.
            assert_eq!(layout.row_q_active(row), 3 * (1 + 1));
            assert!(layout.row_q_active(row) < k * (1 + 1));
        }

        // Cap = 2: hard-gated atoms are never dropped, so the budget for gated-off
        // atoms is 0 and only the two hard-gated atoms remain.
        let capped = SaeRowLayout::from_jumprelu(JumpReluLayoutParams {
            n,
            k_atoms: k,
            threshold,
            temperature,
            logits: &logits,
            contribution: &contribution,
            k_active_cap: 2,
            relative_cutoff: 1.0e-3,
            coord_dims,
            coord_offsets_full,
        });
        for row in 0..n {
            assert_eq!(capped.active_atoms[row], vec![0, 1], "capped row {row}");
        }
    }

    /// GATE (ii) — LOAD-BEARING value/grad parity. Assembles the SAME JumpReLU
    /// term two ways: dense full-band (`Some(None)`) and the compact hard-gate
    /// layout (`Some(Some(layout))`). The compact per-row gradient `gt`, expanded
    /// back to full-q, must equal the dense gradient to tight tolerance — the
    /// retained atoms (hard-gated AND the near-threshold gated-off atom, whose
    /// separable sparsity-prior diagonal `assignment_grad` is the load-bearing
    /// term) reproduce it EXACTLY, and the dropped deep-band atoms differ only by
    /// their own (negligible, sub-cutoff) separable contribution. The compact
    /// block is strictly smaller, and the DEFAULT assembly path (`None`, which
    /// runs the production `from_jumprelu` wiring in construction.rs) yields the
    /// same compact dimensions. The objective VALUE is layout-independent by
    /// construction (the loss sums the full band), so value parity is structural.
    #[test]
    fn jumprelu_compact_gradient_matches_dense_full_band() {
        let n = 3usize;
        let k = 5usize;
        let p = 2usize;
        let (threshold, temperature) = (0.0_f64, 1.0_f64);
        // Per row: 2 hard-gated (>0), 1 near-threshold gated-off (retained), 2 deep
        // gated-off (in-band but negligible → dropped).
        let logits = Array2::from_shape_vec(
            (n, k),
            vec![
                1.0, 0.3, -0.4, -30.0, -34.0, // row 0
                0.8, 0.1, -0.6, -28.0, -33.0, // row 1
                1.2, 0.5, -0.2, -31.0, -35.0, // row 2
            ],
        )
        .unwrap();
        // Euclidean atoms (identity geometry, so no Riemannian projection mixes
        // the gradient across the scatter); coords at the origin so the ARD
        // separable gradient is zero and `contribution` is purely the sparsity
        // prior — isolating the column-separable term the fix must preserve.
        let atoms: Vec<SaeManifoldAtom> = (0..k)
            .map(|i| {
                let f = (i as f64) + 1.0;
                SaeManifoldAtom::new(
                    format!("atom{i}"),
                    SaeAtomBasisKind::EuclideanPatch,
                    1,
                    Array2::<f64>::from_elem((n, 2), 1.0),
                    Array3::<f64>::zeros((n, 2, 1)),
                    Array2::<f64>::from_shape_vec((2, p), vec![0.1 * f, -0.2 * f, 0.15 * f, 0.3 * f])
                        .unwrap(),
                    Array2::<f64>::eye(2),
                )
                .unwrap()
            })
            .collect();
        let coords: Vec<Array2<f64>> = (0..k).map(|_| Array2::<f64>::zeros((n, 1))).collect();
        let manifolds = vec![LatentManifold::Euclidean; k];
        let assignment = SaeAssignment::from_blocks_with_mode_and_manifolds(
            logits.clone(),
            coords,
            manifolds,
            AssignmentMode::jumprelu(temperature, threshold),
        )
        .unwrap();
        let mut term = SaeManifoldTerm::new(atoms, assignment).unwrap();
        let target =
            Array2::<f64>::from_shape_fn((n, p), |(r, c)| 0.1 * (r as f64) - 0.05 * (c as f64));
        // λ_sparse = 1 (log 0), small smoothness, α = 1 ARD on the single axis.
        let rho = SaeManifoldRho::new(0.0, -6.0, vec![Array1::<f64>::from_elem(1, 0.0); k]);

        // Reproduce the production `contribution` (construction.rs): the sparsity
        // prior separable gradient magnitude (ARD is zero at the origin).
        let (assignment_grad, _) =
            assignment_prior_grad_hdiag(&term.assignment, &rho).unwrap();
        let contribution =
            Array2::from_shape_fn((n, k), |(r, c)| assignment_grad[r * k + c].abs());
        let coord_dims = vec![1usize; k];
        let coord_offsets = term.assignment.coord_offsets();
        let layout = SaeRowLayout::from_jumprelu(JumpReluLayoutParams {
            n,
            k_atoms: k,
            threshold,
            temperature,
            logits: &logits,
            contribution: &contribution,
            k_active_cap: k,
            relative_cutoff: 1.0e-3,
            coord_dims,
            coord_offsets_full: coord_offsets,
        });
        // The near-threshold gated-off atom 2 is retained (non-negligible
        // separable diagonal); the deep atoms 3,4 are dropped.
        for row in 0..n {
            assert_eq!(layout.active_atoms[row], vec![0, 1, 2], "layout row {row}");
        }

        let probe = SAE_DENSE_BETA_PENALTY_PROBE_MAX_DIM;
        let dense = term
            .assemble_arrow_schur_inner(target.view(), &rho, None, 1.0, probe, Some(None))
            .unwrap();
        let compact = term
            .assemble_arrow_schur_inner(
                target.view(),
                &rho,
                None,
                1.0,
                probe,
                Some(Some(layout.clone())),
            )
            .unwrap();
        // DEFAULT path: no override → construction.rs runs the real `from_jumprelu`
        // wiring. Its compact row dims must match the hand-built layout.
        let default = term
            .assemble_arrow_schur_inner(target.view(), &rho, None, 1.0, probe, None)
            .unwrap();

        let q = term.assignment.row_block_dim();
        assert_eq!(dense.rows.len(), n);
        assert_eq!(compact.rows.len(), n);
        assert_eq!(default.rows.len(), n);
        let mut max_diff = 0.0_f64;
        let mut saw_drop = false;
        for row in 0..n {
            let dgt = &dense.rows[row].gt;
            assert_eq!(dgt.len(), q, "dense row {row} must be full-q");
            // The compact block is strictly smaller (deep-band atoms dropped).
            assert!(
                compact.rows[row].gt.len() < dgt.len(),
                "row {row}: compact block ({}) must be smaller than dense ({})",
                compact.rows[row].gt.len(),
                dgt.len()
            );
            saw_drop = true;
            // The production default path reproduces the compact dimensions.
            assert_eq!(
                default.rows[row].gt.len(),
                compact.rows[row].gt.len(),
                "row {row}: default (production) path must match the compact layout"
            );
            // Expand the compact gradient to full-q and compare to dense.
            let compact_gt: Vec<f64> = compact.rows[row].gt.iter().copied().collect();
            let mut expanded = vec![0.0_f64; q];
            layout.expand_row(row, &compact_gt, &mut expanded);
            for i in 0..q {
                let diff = (expanded[i] - dgt[i]).abs();
                max_diff = max_diff.max(diff);
                assert!(
                    diff < 1.0e-8,
                    "row {row} coord {i}: compact gt {} vs dense {} (diff {diff:e})",
                    expanded[i],
                    dgt[i]
                );
            }
            // Load-bearing: the near-threshold gated-off atom's separable
            // sparsity-prior gradient is present and non-trivial in BOTH assemblies
            // (dropping it would blow past the tolerance).
            assert!(
                dgt[2].abs() > 1.0e-2,
                "row {row}: near-threshold band-only prior gradient must be O(0.1), got {}",
                dgt[2]
            );
        }
        assert!(saw_drop, "the compact layout must actually drop deep-band atoms");
        // Tolerance is met with margin: dropped atoms' separable contribution
        // (~e^{-28..-35}) is far below the 1e-8 gate.
        assert!(max_diff < 1.0e-8, "max full-q gradient diff {max_diff:e}");
    }
}