1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
//! Isometry-penalty cache-refresh leaf helpers, split out of `construction.rs`
//! to keep that tracked file under the #780 10k-line gate. These are the two
//! trailing free functions (`refresh_isometry_caches_from_atom` /
//! `refresh_isometry_caches_from_term`); they are re-exported from `mod.rs` via
//! `pub use construction_cache_refresh::*;` so every caller keeps reaching them
//! bare through `use super::*`.
use super::*;
/// Build the per-row Jacobian `J` and Hessian `H` of the decoded output
/// `Z_n = Phi_n B` with respect to the latent coordinates `t_n` of a single
/// SAE atom and install them on the supplied [`IsometryPenalty`].
///
/// Layout follows the convention used by [`IsometryPenalty::grad_target`] and
/// friends:
///
/// * `J ∈ ℝ^{n_obs × (p · d)}`, flattened as `J[n, i*d + a]` —
/// `J[n, i, a] = ∂Z_{n,i} / ∂t_{n,a} = Σ_m dPhi[n, m, a] · B[m, i]`.
/// * `H ∈ ℝ^{n_obs × (p · d · d)}`, flattened as `H[n, (i*d + a)*d + c]` —
/// `H[n, i, a, c] = ∂J[n, i, a] / ∂t_{n, c} = Σ_m d²Phi[n, m, a, c] · B[m, i]`.
/// * `K`, an `Array3` of shape `(n_obs, p, d·d·d)` with last axis packed
/// `((a·d + c)·d + e)` — `K[n, i, a, c, e] = ∂³Z_{n,i} / ∂t_a ∂t_c ∂t_e =
/// Σ_m d³Phi[n, m, a, c, e] · B[m, i]`. Installed via the new third-jet slot
/// whenever the base evaluator's `third_jet_dyn` yields a jet AND the penalty
/// carries no `duchon_radial_source`. This is the residual-curvature source
/// for the exact isometry `hvp`.
///
/// Returns `Ok(true)` when both caches were installed (i.e. the atom was
/// built via [`SaeManifoldAtom::with_basis_second_jet`], so its
/// `basis_second_jet` slot holds a [`SaeBasisSecondJet`] implementation
/// that supplies the analytic Hessian). Returns `Ok(false)` when only the
/// base [`SaeBasisEvaluator`] is installed (no second jet available) — in
/// that case only the first-jet `jacobian_cache` is installed and the
/// penalty's `has_jacobian_second_source` check still has a chance to
/// succeed via a pre-supplied `duchon_radial_source`. Returns `Err` on
/// shape mismatches (which would indicate a buggy evaluator) or when the
/// second-jet implementation itself fails (e.g. wrong latent dimension).
///
/// This entry point takes `&IsometryPenalty` rather than `&mut` because the
/// caches are interior-mutable (see [`IsometryPenalty::refresh_caches`]).
pub fn refresh_isometry_caches_from_atom(
penalty: &IsometryPenalty,
atom: &SaeManifoldAtom,
coords: ArrayView2<'_, f64>,
) -> Result<bool, String> {
let evaluator = atom.basis_evaluator.as_ref().ok_or_else(|| {
format!(
"refresh_isometry_caches_from_atom: atom {} has no basis evaluator",
atom.name
)
})?;
let (_phi, jet) = evaluator.evaluate(coords)?;
let n_obs = coords.nrows();
let d = atom.latent_dim();
let m = atom.basis_size();
let p = atom.decoder_coefficients.ncols();
if penalty.p_out != p {
return Err(format!(
"refresh_isometry_caches_from_atom: penalty.p_out={} but atom.decoder.cols={p}",
penalty.p_out
));
}
if jet.dim() != (n_obs, m, d) {
return Err(format!(
"refresh_isometry_caches_from_atom: evaluator first jet has shape {:?}, expected ({n_obs}, {m}, {d})",
jet.dim()
));
}
// J[n, i*d + a] = Σ_m dPhi[n, m, a] · B[m, i]. One (n×m)·(m×p) GEMM per
// latent axis `a` (jet slice × decoder), scattered into the row-major
// (n, p, d) layout: the m-contraction is a matmul, not a quadruple scalar
// loop of bounds-checked element reads (the profiled BLOCKER-1 hot leaf).
let b = &atom.decoder_coefficients;
let mut jac3d = ndarray::Array3::<f64>::zeros((n_obs, p, d));
for a in 0..d {
let basis_axis: ndarray::ArrayView2<'_, f64> = jet.slice(ndarray::s![.., .., a]);
let slab = basis_axis.dot(b);
jac3d.slice_mut(ndarray::s![.., .., a]).assign(&slab);
}
let jac = jac3d
.into_shape_with_order((n_obs, p * d))
.map_err(|err| format!("refresh_isometry_caches_from_atom: J reshape failed: {err}"))?;
// The second jet is sourced from the optional `basis_second_jet`
// slot. The trait split (`SaeBasisEvaluator` vs `SaeBasisSecondJet`)
// encodes "no closed-form Hessian" as trait absence: when the atom
// was built with `with_basis_evaluator` (base trait only) the slot
// is `None` and the `H` cache is not installed. When the atom was
// built with `with_basis_second_jet` the slot holds the same Arc
// upcast to the supertrait, and `second_jet` returns the analytic
// Hessian here.
let jac2_opt = if let Some(second_eval) = atom.basis_second_jet.as_ref() {
let hess = second_eval.second_jet(coords)?;
if hess.dim() != (n_obs, m, d, d) {
return Err(format!(
"refresh_isometry_caches_from_atom: evaluator second jet has shape {:?}, expected ({n_obs}, {m}, {d}, {d})",
hess.dim()
));
}
// H[n, (i*d + a)*d + c]: one (n×m)·(m×p) GEMM per (a, c) pair,
// scattered into the row-major (n, p, d, d) layout (same GEMM-not-
// scalar-loop rewrite as J above).
let mut jac2_4d = ndarray::Array4::<f64>::zeros((n_obs, p, d, d));
for a in 0..d {
for c in 0..d {
let basis_axes: ndarray::ArrayView2<'_, f64> =
hess.slice(ndarray::s![.., .., a, c]);
let slab = basis_axes.dot(b);
jac2_4d.slice_mut(ndarray::s![.., .., a, c]).assign(&slab);
}
}
let jac2 = jac2_4d
.into_shape_with_order((n_obs, p * d * d))
.map_err(|err| format!("refresh_isometry_caches_from_atom: H reshape failed: {err}"))?;
Some(Arc::new(jac2))
} else {
None
};
// Third jet K[n, i, ((a·d + c)·d + e)] = Σ_m d³Phi[n, m, a, c, e] · B[m, i]
// feeds the residual-curvature term of the exact isometry Hessian
// B_{ab,cd} = K_{a,cd}^T W J_b + H_{a,c}^T W H_{b,d}
// + H_{a,d}^T W H_{b,c} + J_a^T W K_{b,cd}.
// Sourced from the base evaluator's object-safe `third_jet_dyn` forwarder
// (closed-form analytic override for every basis with an analytic Hessian:
// sphere/circle/torus/affine/euclidean/duchon; `None` otherwise — no
// finite-difference fallback). Installed only when the penalty
// has no `duchon_radial_source` — a Duchon penalty already carries its own
// analytic third source and `jacobian_third` would shadow it with this
// cache. Always written (Some or None) so a stale K from a prior outer step
// never survives a refresh.
let jac3_opt = if penalty.duchon_radial_source.is_none() {
match evaluator.third_jet_dyn(coords) {
Some(third) => {
let t3 = third?;
if t3.dim() != (n_obs, m, d, d, d) {
return Err(format!(
"refresh_isometry_caches_from_atom: evaluator third jet has shape {:?}, expected ({n_obs}, {m}, {d}, {d}, {d})",
t3.dim()
));
}
// K[n, i, ((a·d + c)·d + e)]: one (n×m)·(m×p) GEMM per
// (a, c, e) triple into the row-major (n, p, d, d, d) layout,
// then flattened — the last axis packing ((a·d + c)·d + e) IS
// the row-major order of (a, c, e).
let mut jac3_5d = ndarray::Array5::<f64>::zeros((n_obs, p, d, d, d));
for a in 0..d {
for c in 0..d {
for e in 0..d {
let basis_axes: ndarray::ArrayView2<'_, f64> =
t3.slice(ndarray::s![.., .., a, c, e]);
let slab = basis_axes.dot(b);
jac3_5d
.slice_mut(ndarray::s![.., .., a, c, e])
.assign(&slab);
}
}
}
let jac3 = jac3_5d
.into_shape_with_order((n_obs, p, d * d * d))
.map_err(|err| {
format!("refresh_isometry_caches_from_atom: K reshape failed: {err}")
})?;
Some(Arc::new(jac3))
}
None => None,
}
} else {
None
};
let installed = jac2_opt.is_some();
penalty.refresh_caches(Some(Arc::new(jac)), jac2_opt);
penalty.set_third_decoder_derivative(jac3_opt);
Ok(installed)
}
/// Walk an [`AnalyticPenaltyRegistry`] and refresh every Isometry penalty
/// against the SAE atom it owns. The alignment rule is positional within each
/// `(latent_dim, p_out)` signature: the penalty's `target.latent_dim` must
/// equal the atom's `latent_dim` AND the penalty's `p_out` must equal the
/// atom's decoder column count `p`. Multi-atom configurations install one
/// isometry penalty per atom, so the *k*-th isometry penalty matching a given
/// signature is paired with the *k*-th atom matching that same signature. This
/// reduces to the unambiguous single-atom/single-penalty case wired by
/// `solver/workflow.rs`, and never collapses multiple penalties onto the first
/// matching atom (which would leave every later atom's coords un-refreshed).
///
/// Returns the number of penalties that got both caches populated (i.e. the
/// number of atoms whose `basis_second_jet` slot holds a
/// [`SaeBasisSecondJet`] implementation supplying the analytic Hessian).
pub fn refresh_isometry_caches_from_term(
registry: &AnalyticPenaltyRegistry,
term: &SaeManifoldTerm,
coords_per_atom: &[Array2<f64>],
) -> Result<usize, String> {
if coords_per_atom.len() != term.atoms.len() {
return Err(format!(
"refresh_isometry_caches_from_term: coords_per_atom length {} != number of atoms {}",
coords_per_atom.len(),
term.atoms.len()
));
}
let mut refreshed_with_second = 0usize;
// Per-signature cursor: how many atoms matching a given (latent_dim, p_out)
// have already been consumed by earlier isometry penalties. Pairing the
// k-th penalty of a signature with the k-th atom of that signature gives a
// stable one-to-one mapping for multi-atom configs.
let mut consumed_per_signature: std::collections::HashMap<(usize, usize), usize> =
std::collections::HashMap::new();
for entry in registry.penalties.iter() {
let AnalyticPenaltyKind::Isometry(p) = entry else {
continue;
};
let Some(p_latent_dim) = p.target.latent_dim else {
continue;
};
let signature = (p_latent_dim, p.p_out);
let already_consumed = consumed_per_signature.entry(signature).or_insert(0);
// Advance to the (already_consumed)-th atom matching this signature.
let mut seen = 0usize;
let mut paired: Option<usize> = None;
for (atom_idx, atom) in term.atoms.iter().enumerate() {
let matches = atom.latent_dim() == p_latent_dim
&& atom.decoder_coefficients.ncols() == p.p_out
&& atom.basis_evaluator.is_some();
if !matches {
continue;
}
if seen == *already_consumed {
paired = Some(atom_idx);
break;
}
seen += 1;
}
let Some(atom_idx) = paired else {
continue;
};
*already_consumed += 1;
let atom = &term.atoms[atom_idx];
let coords = coords_per_atom[atom_idx].view();
if refresh_isometry_caches_from_atom(p, atom, coords)? {
refreshed_with_second += 1;
}
}
Ok(refreshed_with_second)
}