[sarlinpe]

Summary

In Caspar kernels, factors write to multiple distinct output parameter groups (e.g., residual out_res, camera pose out_pose_*, camera calibration out_calib_*, and 3D point out_point_*). Between these parameter groups, the kernel emits barrier synchronizations and shared memory reduction flushes (FlushSumShared).

Previously, Common Subexpression Elimination (CSE) in make_dabseg and do_cpse operated globally across the entire factor DAG. When a subexpression (such as -(1 + k*r^2)) computed during the camera pose Jacobian was reused hundreds of lines later in the calibration Jacobian across 12 FlushSumShared barriers, the variable remained live throughout all intermediate reductions. Under __launch_bounds__(1024, 1) (which limits threads to 64 registers), this extreme register pressure (>1.8 KB stack spill) caused registers to be spilled to local memory and corrupted in kernels with high occupancy.

In COLMAP's Caspar bundle adjustment integration (see colmap/colmap#4799), this register corruption caused double-precision calibration Jacobians to evaluate to wildly inaccurate values (~10^4 instead of fractional derivatives).

Proposed Solution

Rather than relying on string heuristics, this PR scopes subexpression elimination by output parameter group:

1. Accessor: Added group: str | None = None parameter.
2. Factor.make_kernels: Explicitly tags output accessors with their parameter group (group=k for node variables and group="res" for residual outputs).
3. CallData & Dabseg: Included group in CallData's hash and equality, preventing Dabseg.data_to_id from deduplicating expressions across group boundaries.
4. make_dabseg: Resets expr_map across out.group transitions during DAG construction.
5. do_cpse: Partitions associative/commutative calls by call.group so partial CSE reductions only combine terms within the same group.
6. function_fixers: Preserves call.group across DAG transformations.

Verification

• test_generate_solver in symforce_caspar_codegen_test.py passes, confirming that cross-barrier live ranges are eliminated in the test Rosenbrock factor as well (reducing register pressure from 9 to 8 registers in kernel_rosenbrock_res_jac_first.cu).
• Regenerated all 488 single- and double-precision Caspar kernels in COLMAP. All 17 unit tests in bundle_adjustment_caspar_test pass cleanly in both f32 and f64 without needing any manual kernel workarounds.