Reuse exact continuous-time LiDAR finite differences¶

An owned CUDA linearizer retains only its most recent residual/Jacobian arrays. Keys contain the exact FP64 bits of all thirteen transforms and six difference steps. Changing the captured immutable observations invalidates the entry. Each fork owns its lock, stream, payload and cache. Cached host arrays are read-only; public results are independent writable copies. Entries exceeding 64 MiB bypass caching.

The fixed-trajectory optimizer computes only the unweighted initial rank for factors with at least 8,192 residuals when its native compiled factor supports it. Public evaluation hooks and unsupported factors keep full evaluation. Final residual, observability, range and holdout diagnostics remain complete.

Comparisons with the preceding GPU implementation¶

Three dense/standard pairs and five default pairs alternate order. Both methods have independent initially empty persistent Numba/CuPy caches. The first run, compilation and every slow trial are retained. Whole wall includes startup, imports, replay, all clock candidates, refinements, transfers, diagnostics, hashes and saves. Parent audits are outside the timer. CUDA-full scope archives all fourteen preceding geometry, optimizer, query and replay modules.

Workload	Train / holdout targets	Previous GPU median	Candidate median	Ratio of medians	Median paired ratio
120 frames, up to 8,000 points/frame	768,000 / 192,000	81.842589 s	58.798766 s	1.392x	1.392x
120 frames, up to 400 points/frame	38,400 / 9,600	17.541021 s	13.136499 s	1.335x	0.974x
Default sampling caps, CPU dispatch	6,000 / 3,200	7.633336 s	8.759261 s	0.871x	0.911x

These local descriptive ratios do not establish portable performance. Small budgets continue to use CPU dispatch. Ratios from separate cohorts are never multiplied. Standard paired timing does not establish a gain, and final default timing regresses. The cause of variability remains unresolved; no small-workload speedup is claimed.

Workload	API medians	Solver medians	All-thread CPU medians
120 frames, up to 8,000 points/frame	78.120409 -> 54.990135 s (1.421x)	62.428247 -> 42.114281 s (1.482x)	105.421875 -> 82.171875 s (1.283x)
120 frames, up to 400 points/frame	12.341297 -> 9.432027 s (1.308x)	7.003360 -> 6.027572 s (1.162x)	19.062500 -> 15.203125 s (1.254x)
Default sampling caps, CPU dispatch	4.319437 -> 5.300716 s (0.815x)	3.016924 -> 3.841161 s (0.785x)	8.937500 -> 10.562500 s (0.846x)

120 frames, up to 8,000 points/frame¶

Retained status max_iterations, rank 6, train/holdout correspondences 582,119/67,602.

Pair	Order	Previous GPU wall	Candidate wall	Paired ratio
1	baseline -> candidate	86.768432 s	70.049194 s	1.239x
2	candidate -> baseline	81.842589 s	58.798766 s	1.392x
3	baseline -> candidate	64.312364 s	43.094047 s	1.492x

dense definition, aggregate, complete saved result.

120 frames, up to 400 points/frame¶

Retained status max_iterations, rank 6, train/holdout correspondences 29,181/3,451.

Pair	Order	Previous GPU wall	Candidate wall	Paired ratio
1	baseline -> candidate	19.402509 s	57.206190 s	0.339x
2	candidate -> baseline	17.541021 s	13.136499 s	1.335x
3	baseline -> candidate	12.272086 s	12.606016 s	0.974x

full definition, aggregate, complete saved result.

Default sampling caps, CPU dispatch¶

Retained status converged, rank 6, train/holdout correspondences 4,773/2,526.

Pair	Order	Previous GPU wall	Candidate wall	Paired ratio
1	baseline -> candidate	20.496180 s	18.635960 s	1.100x
2	candidate -> baseline	9.138590 s	6.403741 s	1.427x
3	baseline -> candidate	7.633336 s	8.759261 s	0.871x
4	candidate -> baseline	5.465509 s	9.206229 s	0.594x
5	baseline -> candidate	5.338449 s	5.861534 s	0.911x

default definition, aggregate, complete saved result.

Separate dense CPU/hybrid comparison¶

Three fresh alternating pairs compare the earlier packed/parallel CPU version with the current hybrid. This is a separate cohort; its first compilation and all slower runs remain. Compiled scope archives ten CPU modules. The current packed builder is shared with its GPU callback disabled for CPU, preserving the existing numeric selection.

Whole-process medians 149.580531 -> 52.385271 s (2.855x); median paired ratio 3.231x.

Pair	Order	CPU wall	Hybrid wall	Paired ratio
1	CPU -> hybrid	148.058603 s	52.385271 s	2.826x
2	hybrid -> CPU	149.580531 s	46.301385 s	3.231x
3	CPU -> hybrid	256.507218 s	62.293333 s	4.118x

CPU/hybrid definition, aggregate.

Actual-device diagnostics outside formal timing¶

Of 129 requested finite differences, 56 launch GPU work and 73 reuse exact host results. Actual launched rows: 32,768,988. Largest retained per-context entry: 33,398,792 bytes, below the 67,108,864-byte limit. Initial compiled rank calls: 26 of 26. GPU query batches: 52; uniform/adaptive query rows: 24,960,000/24,960,000; payload uploads: 26. CPU standalone residual calls: 207; ordered normal reductions: 129; GPU standalone residual calls: 0; CPU finite-difference fallback calls: 0. Compiled CPU replay: 120 batches, 960,000 points. Query boundary/tie repair stays on CPU.

The complete diagnostic result matches the first final dense candidate artifact. Instrumented call sums overlap across concurrent/nested calls and are not critical-path fractions. Actual counts, diagnostic launcher.

The separate preceding-version profile found 73 identical repeats in 129 GPU requests. It binds the exact source and input hashes. Its historical comparison excludes only the provenance Git commit and explicitly bound execution notes. Full original results remain. Preceding profile, profile result.

Stopped first comparison¶

The initial twelve-module comparison stopped after the first baseline worker completed. The older parent binding checks rejected the preceding GPU association/replay imports. No speedup is reported for this incomplete attempt. Its complete worker result, exact source snapshots, launcher and path-portable failure logs remain under attempts/v1. The final cohort uses a new output directory and new empty caches after the binding fix.

Retained preceding candidate and aborted secondary cohort¶

Before the 8,192-residual crossover, a complete five-pair cohort showed a dense median ratio of 1.290x (paired median 1.163x), standard 1.006x (paired 1.056x), and a default regression: 6.101217 -> 11.804868 seconds, 0.517x (paired 0.815x). Its full 30 trials are preserved separately. Timing variation does not identify the cause of the slower default runs. The final dispatch leaves small factors on native complete evaluation. The first secondary CPU cohort was explicitly stopped before its first worker completed to apply this dispatch guard. Its logs, archived baseline modules, termination record and source/input bindings remain under attempts/v2/cpu_stopped. Preceding index, abort record.

Result and lineage checks¶

Every complete final API/saved artifact matches all numeric fields, iterations, status, correspondence counts, holdout results and logical interpolation counters. Comparison only normalizes path separators and excludes strictly validated execution identity notes. No sampling, physical settings, robust loss, solver or holdout budget is reduced. The AIST GLIM source recording is copied into two topics as an execution parity control; it provides no independent two-sensor calibration accuracy evidence. The stopped trial and both instrumented diagnostics are separate from the 28 final formal trials. Complete result YAML stays byte-identical. Only location metadata is made portable; original hashes and changed fields are recorded in the index. Measured sources retain actual bytes.

Publication index, benchmark launcher, CPU launcher.

Preceding GPU source 9f68d3d165385fa6a3f154d5e14fe31676b40a85; measured candidate 1bf71e2668e3ff790a427d9c5d6ea66df90d22e3. CPU source eb50c99878706a45eb0e584f3573507313cdc172. Schema-valid complete measurements, definitions and aggregates are archived.