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Fixed-Capacity Causal Models with Parallel Recovery for GPU Lossless Compression

Zeyu Jia

arXiv:2610.02236v3cs.AR

TL;DR

GPU compression must balance dense complete frames against encoding and checked-recovery costs. The paper compares fixed-capacity causal models and aligns entropy states with byte-bank dependencies; selection reduces original GPX size by 11.65%, while mode results vary across inputs.

  • Problem

    GPU compression must balance complete-frame density against encoding and encode-plus-recovery cost because transfers, models, state records, and checked recovery can erase payload savings.

    Source: §1 · p. 1

  • Method

    The paper compares three causal representations under a shared 512-row budget, selects before encoding one payload, and aligns entropy states with causal byte-bank dependencies.

    Source: §1 · p. 1, §7 · p. 9

  • Results

    Selection reduces original GPX size by 11.65%, while high-first loses on five inputs and mode winners vary across the seven inputs.

    Source: §5 · p. 4, §5.1 · p. 4

  • Takeaways & Limitations

    The measured contribution is a bounded density–execution point using established components, not an optimum established for unseen inputs.

    Source: §1 · p. 1, §7 · p. 9

    Reused cohorts, finite training, derived controls, unequal resources, concentrated gains, and unmeasured energy and broad scaling limit inference.

    Source: §6 · p. 9

Abstract

from arXiv · show

GPU compression needs both dense complete frames and inexpensive checked recovery. We compare three causal representations under the same 512-row model budget, select before encoding one payload, and align entropy states with causal byte banks. Same-lane and residual banks decode concurrently; high-first banks decode in causal order. On ten reused structured/electrophysiology inputs, split-bank execution lowers aggregate median encode-plus-recovery time 13.10% for 0.18% more frame bytes. A separate twelve-configuration GPU comparison places it on the measured median frontier: 5.75% and 7.11% smaller frames than transformed nvCOMP Zstd at 35.14/19.03% lower paired cost for 64/8 KiB requests. A matched native-CPU model control isolates a 44.16% reduction in complete encoding cost; a CUDA-free CPU receiver restores the same frames. Three whole EEG recordings retain a separate Zstd-1--16 curve, while fixed ECG fixtures expose transformed-Zstd counterexamples. Model overhead, concentrated gains, technical ranges and adverse outcomes bound these operating points. ANS interleaving and transforms are established; reused inputs, unequal resources and fixed controls do not establish codec optima or population superiority.

1 Introduction

The paper treats GPU compression as a complete-frame and checked-recovery trade-off, comparing density with encoding and encode-plus-recovery cost. It evaluates three causal representations under a shared model budget and aligns entropy states with byte-bank dependencies.

1 Introduction

  • Transfers, model costs, state records, and checked recovery can erase GPU payload savings, motivating comparison of complete density and encoding-plus-recovery cost.The proposed design compares three representations under the same 512-row budget, selects before encoding one payload, and aligns entropy states with causal byte banks.Source: §1 · p. 1
  • The contribution is a bounded density–execution operating point using established components, with complete-cost curves retaining controls, concentrated gains, reversals, and counterexamples.Ancillary classic certificates provide neither practical acceleration nor split-format guarantees.Source: §1 · p. 1

2 Related work

The paper builds on established entropy coding, transforms, codec selection, and GPU context modeling, while distinguishing its controls from claims of optimality or imported throughput.

2 Related work

  • ANS interleaving and transforms are established components; the paper aligns banks with candidate dependencies rather than claiming new coding priority.The passage cites Zstandard, typed transforms, and parallel description-length modeling as component sources.Source: §2 · p. 2
  • OpenZL composes graphs and selects codecs, MANS supplies integer ANS, and CuCM performs GPU context mixing.Pinned and derived controls do not establish their optima, and CuCM remains unmatched.Source: §2 · p. 2
  • Serialized-byte pruning [15] and codec cost selection predate this work; its ancillary bound preserves one unchanged selector without generic selection priority.Earlier GPX [17] shares ancestry and data, but its routing and throughput claims are not imported.Source: §2 · p. 2

3 Fixed-capacity representations

Three fixed-capacity representations change causal dependencies while retaining 512 model rows per candidate. The paper fits and compresses models, selects one payload before encoding, and aligns entropy-bank execution with those dependencies.

3 Fixed-capacity representations

  • The three candidates use the same 512-row capacity but different dependencies: same-lane preserves byte order, high-first emits high then low bytes, and residual codes reversible modular differences.Residual values are converted to signed differences and then reversible unsigned zigzag values before same-lane prediction.Source: §3 · p. 2, Table 1 · p. 2
  • Same-lane and high-first share the high-byte bank after reindexing on all seven inputs, but their low-byte conditionals differ and neither dominates generally.Table compression and finite-state overhead affect complete size, so entropy alone cannot guarantee the smallest frame.Source: §3 · p. 2

3.1 Support-exact static probabilities

  • Each model fits the current complete tile with positive integer frequencies summing to 4096, then compresses and transmits the full 512 × 256 table.Full-input support does not justify out-of-sample reuse.Source: §3.1 · p. 3

3.2 Selecting before payload encoding

  • A fused GPU pass builds and compresses all three candidate models, scores them before payload encoding, and emits exactly one selected payload.The score is a coding-cost proxy, not an exact frame-size guarantee, because finite rANS overhead can reverse its ordering.Source: §3.2 · p. 3
  • The complete format records representation, model, chunk metadata, literal prefixes, payload, and digest; its CPU receiver reconstructs, decodes, inverts, and verifies without GPU operations.The matched native multithreaded CPU control must produce an inner frame byte-for-byte identical to the GPU frame.Source: §3.2 · p. 3

3.3 Causal-bank execution and CPU reception

  • Same-lane and residual banks decode independently, while high-first recovery runs its dependent high and low phases in causal order.The split format uses two states per chunk and replaces each 10-byte classic chunk record with an 18-byte record; residual restoration still requires a whole-tile modular prefix sum.Source: §3.3 · pp. 3–4
  • A standalone Windows/x64 CPU package restored 30 GPU-produced source frames and 112 fixtures, and rejected 42 malformed frames without CUDA libraries.This demonstrates a tested receiver dependency boundary, not portability or CPU optimality.Source: §3.3 · p. 4
  • Classic single-state selector bounds require stated finite-state assumptions and strict complete-size separation; setup costs prevent practical acceleration, and no guarantee applies to split format..Source: §3.3 · p. 4

4 Experimental protocol

The evaluation uses reused development inputs and charges specified codec operations while excluding startup and I/O from codec timings. Its CT instances cover selected slices rather than independent patients or whole Carp/Tree volumes.

4 Experimental protocol

  • Seven reused development inputs total 48.20 MB, combining whole Silesia MR and X-ray, historical 4 MiB lily and kidney prefixes, and complete published arrays.Brain is a ten-slice subset rather than a full patient volume; the evaluation is reused internal data, not independent confirmation.Source: §4 · p. 4
  • Codec timings charge models, transfers, fitting, transforms, assembly, and checked inverses, while excluding imports, I/O, warmup, pre-sync, and offline assets.Resources are unequal, technical repetitions are not independent datasets, and task-memory and GPU admission budgets are not measured peaks.Source: §4 · p. 4
  • CT instances include complete 113-slice UNC CThead and central 128/32 Carp/Tree slices, not independent patients or whole Carp/Tree volumes.The Tree parent SHA512 remains unverified.Source: §4 · p. 4

5 Complete-frame results

The complete-frame results show that selecting among causal representations can reduce GPX size, but outcomes vary by input and comparison. Split-bank execution and GPU controls define measured operating points, while the EEG, ECG, and other fixed-input results bound their scope.

5 Complete-frame results

  • 11.65%: selection reduces original GPX size; high-first, the strongest fixed mode, loses on five inputs.The selector’s score is a coding-cost proxy, not an exact frame-size guarantee.Source: §5 · p. 4

5.1 Dependency effects and placement

  • High-first saves 19.17% on cells3d and 18.81% on Brain but worsens five inputs; MR and nickel show model and payload savings can oppose.Residual wins MR, X-ray and kidney, while same-lane wins lily and nickel; neither component alone predicts the smaller complete frame.Source: §5.1 · pp. 4–5

5.2 Concentration and earlier scope tests

  • Cells3d supplies 93.09% of earlier net savings; excluding it leaves 1.56%, while MR, kidney and nickel lose, and a reused Carp slab reverses raw-Zstd-1 on its first repetition.A separate warmed study wins only once against transformed Zstd-1.Source: §5.2 · p. 5

5.3 Whole-file electrophysiology

  • On three reused EDF files, split emits 71.845 MB at 1.014 seconds encoding and 1.574 seconds paired; it beats requested-20-worker raw Zstd-16 on density, but transformed Zstd-1 is faster.Split is on the aggregate paired median envelope, yet loses to classic GPU lookup in two of three repetitions; these results do not establish stable-speed superiority.Source: §5.3 · pp. 5–6, Figure 1 · p. 6

5.4 Endpoint costs are a separate question

  • Local TCP GPU encoding emits 33.46% and 3.06% fewer bytes than raw and transformed Zstd pipelines, respectively, at 1.46 and 1.35 times validated endpoint cost.A later shared-GPU study lowers endpoint median only 2.81% and fails practical admission.Source: §5.4 · p. 6

5.5 Optional GPU recovery and fixed GPU controls

  • 13.10%: split-bank execution lowers GPU paired median on ten reused inputs, with 0.18% more frame bytes.Separate results include a 44.16% lower complete-encoding median for GPU versus native-CPU modeling, and split GPX frames 5.75% and 7.11% smaller than zigshuffle plus Zstd at 35.14% and 19.03% lower paired medians. Other controls trade smaller frames for higher costs, including FP16 ANS and Bitcomp/Cascaded comparisons.Source: §5.5 · pp. 7–8

5.6 Prospectively fixed ECG waveform files

  • On three fixed ECG records, classic 8 KiB GPX is 11.70% smaller than raw Zstd-16, but transformed Zstd-1 is 17.02% smaller and costs 45.05% as much paired.The split format was not tested in this study.Source: §5.6 · p. 8

5.7 Prospectively fixed small external fixtures

  • On fixed small external fixtures, OpenZL-9 is smaller and faster on all three Nibabel inputs, while unchanged LibriSpeech frames cost more to encode and recover than CPU20.Entropy-only encoding enlarges two Nibabel outputs by 17.72% and 15.97%; these fixtures do not provide broad confirmation.Source: §5.7 · p. 9

6 Discussion and limitations

The reported operating points are bounded by reused and limited controls, concentrated gains, and unmeasured technical ranges. Adverse outcomes and external reversals also constrain the findings.

  • Imaging/speech losses and source/clock reversals limit scope; gains concentrate and include earlier prefixes.Source: §6 · p. 9
  • Classic certificates offer no practical acceleration; shared-statistics and batched-preparation each yield 120 exact recoveries but fail net-benefit admission.Source: §6 · p. 9
  • The fourth equalbudget context saves lily/kidney 2.49/1.19%, but aggregate bytes fall only 0.09% at 1.04 paired cost.It records 240 exact recoveries without a certificate.Source: §6 · p. 9
  • Reused cohorts, finite OpenZL training, derived MANS controls, and unmatched CuCM limit inference.Source: §6 · p. 9
  • Energy, GPU peaks, and broad scaling remain unmeasured; EDF file diagnostics report 543–559 MiB encoding and 157–168 MiB CPU-decoding peak Windows working sets.CPU encoders use less; historical V15 best results are not pooled.Source: §6 · p. 9

7 Conclusion

Fixed-capacity causal models produce dense complete frames, while dependency-aligned entropy states reduce measured execution cost. The conclusion is bounded by distinct operating points, tested CPU recovery, and limits on inference.

  • Fixed-capacity causal models yield dense complete frames, and dependency-aligned entropy states reduce measured execution cost.Source: §7 · p. 9
  • Original and split formats occupy distinct matched-GPU operating points, with tested standalone CPU recovery.Source: §7 · p. 9
  • Unequal resources, reuse, concentrated gains, and external reversals bound the findings; classic certificates do not apply to split banks.Source: §7 · p. 9
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