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feat: kernel-density CDF meshes RectangularKernelAdaptDensity/Image - #374
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…ants Opt-in adaptive rectangular meshes whose per-axis CDF transform is a smooth kernel-density CDF F(x) = sum_i w_i * Phi((x - x_i)/h) (Enzi et al. arXiv:2606.30620 RTU formulation) instead of the empirical point-rank CDF. Strictly monotone by construction, C-infinity in interp queries and traced point positions (no ranks, no sorts), duplicate-safe — so mass/shear gradients are smooth in every configuration, including imaging at pixelization over-sampling 1 and the interferometer sparse path where the empirical CDF makes the likelihood exactly piecewise-constant. Forward transform is evaluated exactly (unit square <-> data bounding box, matching the linear convention); inverse is a fixed n_knots table lookup whose queries are unit-grid constants, so gradients flow through the table values. Bandwidth defaults to the mesh pixel scale and is exposed as a mesh kwarg. Linear and spline meshes are untouched. Closes nothing; certification via autolens_workspace_test jax_grad scripts follows on the workspace leg (#373). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
The bilinear interpolation mapper places reconstruction value (row r, col c) at node U_y=(n_y-r-1)/(n_y-3), U_x=(c-1)/(n_x-3) in unit CDF space (guard ring at the border, rows flipped by the mapper's row = n - i), but edges_transformed drew a uniform [0,1] partition — pcolormesh plots put flux up to ~1.5 mesh pixels from where the mapper scatters it (the "small offsets" of issue #372, confirmed by a delta-function reproduction). The edges are now the node midpoints pushed through the same CDF machinery (guard-safe denominator for degenerate n<=3 meshes; border guard cells clamp to the data span). Both consumers inherit the fix: the pcolormesh plot path and rectangular_rotated's warped-centre reconstruction; spline and linear CDFs share the upstream index convention. Plot geometry only — the mapper is untouched, so inversions and likelihoods are byte-identical. #372 Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…/rectangular-kernel-cdf-mesh
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Summary
Adds opt-in kernel-density-CDF variants of the adaptive rectangular meshes:
RectangularKernelAdaptDensity/RectangularKernelAdaptImage(issue #373). The per-axis transform is the smooth kernel CDFF(x) = Σᵢ wᵢ·Φ((x−xᵢ)/h)(Enzi et al. arXiv:2606.30620 RTU formulation) instead of the empirical point-rank CDF, which the 2026-07-09 JAX gradient audit proved makes the likelihood exactly piecewise-constant in mass/shear at pixelization over-sampling 1 and on the interferometer sparse path.Properties by construction: strictly monotone (no jitter hack), C^∞ in interp queries and traced-point positions (no ranks, no sorts, no argsort anywhere), duplicate-safe (no 1/Δknot terms). The forward transform is evaluated exactly and maps the data bounding box onto the unit square (matching the linear convention); the inverse is a fixed
n_knotstable lookup whose queries are unit-grid constants, so gradients flow smoothly through the table values.bandwidthdefaults to the mesh pixel scale and is exposed as a mesh kwarg. The linear and spline meshes are untouched.Function-level JAX sanity (local, x64): eager == JIT to 1e-13; AD grad matches central FD to ~5e-10 relative through both the bilinear-weights path and the inverse-table path.
API Changes
Added only — two new opt-in mesh classes (
aa.mesh.RectangularKernelAdaptDensity,aa.mesh.RectangularKernelAdaptImage), their interpolator, and additive default-Nonekwargs onAbstractMeshGeometry. No existing symbol removed, renamed, or changed in behaviour.See full details below.
Test Plan
pytest test_autoarray/— 892 passed (16 new tests intest_rectangular_kernel.py: monotonicity, bounding-box mapping, round-trip, duplicate safety, large-bandwidth limit, mapper shape/consistency vs linear, areas totals vs linear, interpolator/geometry plumbing)autolens_workspace_test/scripts/jax_grad/imaging_pixelization.pykernel variants at os_pix=1 AND 4 with strict FD on ALL params;interferometer.pysparse path; eager-vs-JIT; figure-of-merit parity within a few e-4 of the linear meshesFull API Changes (for automation & release notes)
Added
aa.mesh.RectangularKernelAdaptDensity(shape=, bandwidth=1.0, n_knots=64)— density-adaptive rectangular mesh with kernel-density CDF transform (opt-in).aa.mesh.RectangularKernelAdaptImage(shape=, weight_power=1.0, weight_floor=0.0, bandwidth=1.0, n_knots=64)— image-adaptive variant; adapt-image weights become the kernel weights.autoarray.inversion.mesh.interpolator.rectangular_kernel— new module:create_transforms_kernel(),adaptive_rectangular_mappings_weights_via_interpolation_from_kernel(),adaptive_rectangular_areas_from_kernel(),adaptive_rectangular_transformed_grid_from_kernel(),InterpolatorRectangularKernel,KERNEL_CDF_DEFAULT_BANDWIDTH,KERNEL_CDF_DEFAULT_KNOTS.Changed Signature (additive, backwards-compatible)
AbstractMeshGeometry.__init__(..., kernel_bandwidth=None, kernel_knots=None)— new optional kwargs;MeshGeometryRectangular.areas_transformed/edges_transformedroute through the kernel helpers whenkernel_bandwidthis set (mirrors the existingspline_degdispatch).Migration
Coordination note
Adjacent to #372 (rect-adapt, parked at sign-off): both touch
mesh_geometry/rectangular.pyin distinct hunks (itsedges_transformedbody vs this PR's dispatch branches) — clean merge in either order; if #372 lands first the kernel path inherits the corrected edges automatically.Merge gate: do not merge until the workspace-leg certification PR (jax_grad strict-FD assertions) is green — that is this task's success criterion.
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