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Cadence: Error-Bounded Lossy Compression of Demand Time Series with a Time-Series Foundation Model

Roberto Tacconelli

arXiv:2609.06008v1cs.ITcs.DBcs.LG

TL;DR

Foundation-model forecasting improvements provide little lossless-compression benefit because coding gains grow only logarithmically with predictor accuracy. Cadence instead combines TimesFM-3 with closed-loop error-bounded coding, achieving its strongest results on post-cutoff human-demand series while retaining substantial deployment costs and constraints.

  • Problem

    Lossless compression needs a better account of when time-series foundation-model forecasting improvements translate into meaningful coding gains.

  • Method

    Cadence combines TimesFM-3 with closed-loop error-bounded coding and routes residual indices through a shared adaptive arithmetic coder.

  • Results

    +21.4% median gain over the best six classical predictors is achieved across 297 series-tolerance pairs, with all 297 pairs winning on post-cutoff demand corpora.

  • Takeaways & Limitations

    The practical consequence is that foundation models help error-bounded compression within aggregate human-demand data, not numeric time series generally.

  • Takeaways & Limitations

    Cadence remains slow and operationally constrained: it requires a 1.3 GB model, sequential decoding, fixed group sizes, and integer or fixed-point inference for portability.

Abstract

from arXiv · show

We present Cadence, an error-bounded lossy compressor for numeric time series pairing a 330M-parameter time-series foundation model (Google TimesFM-3) with an adaptive arithmetic coder, guaranteeing $|\hat{x}_t-x_t|\leτ$ on every sample. One negative result constrains the design space: for lossless coding a foundation model is worth nothing, because bits saved are logarithmic in predictor accuracy, $Δb=\log_2(\mathrm{MAE_{old}}/\mathrm{MAE_{new}})$. So the $1.51\times$ advantage TimesFM-3 holds over a 32-tap linear predictor buys 0.60 bits of 20.28, a median gain of +0.03%. Error-bounded coding escapes this at one point: once a forecast lands inside the band the residual index is zero and the sample nearly free. Cadence contributes: (1) an adaptive range coder with context-modelled binarization, beating xz/zstd on real indices by 9.7% (15/15) and reversing a finding from a general-purpose back end; (2) a determinism result -- predictions are not bit-identical across batch sizes, and no PyTorch configuration repairs this, forcing group size and execution device into the container format; and (3) domain localization on corpora postdating any plausible training cutoff. On 49 EIA-930 balancing-authority demand series (2026) Cadence gains 13.3% over the best of six classical predictors, and 28.3% on 50 MTA ridership series (2026): 21.4% median over 297 series-tolerance pairs, winning all 297. Against downsampling, what time-series databases deploy for retention, its guaranteed worst-case error is $28$--$56\times$ tighter at equal size. End-to-end, once the context bootstrap is paid for, gains run from 6.8% at six months of hourly data to 15.1% asymptotically. Attempting to falsify the domain claim on SDRBench, theory predicts failure and delivers: -0.8% median, 0 of 27 pairs gaining. Three further negative results and eight retracted claims are reported in full.

1. Introduction

Cadence argues that foundation-model forecasting gains transfer only logarithmically to lossless compression, but error-bounded coding can exploit zero residuals when forecasts fall inside the tolerance band. The paper therefore targets a narrow domain: aggregate human-demand series.

  • Motivation: TimesFM-3’s forecasting advantage transfers logarithmically to lossless compression, limiting the benefit of neural prediction.Code length scales approximately with the logarithm of residual scale.
  • Lossless compression: 0.597 bits out of 20.28, or 2.9%, results from TimesFM-3’s 1.51× MAE improvement over LPC-32 on hourly pageviews.The measured MAEs are 113,608 for TimesFM-3 and 171,507 for LPC-32.
  • Lossless compression: A 1024× better predictor would be required to halve a 20-bit-per-value file.The relationship is shown in Figure 1 across three real series.
  • Error-bounded coding: Error-bounded coding escapes the logarithmic regime when an in-band forecast produces a zero residual costing approximately 0 bits.Cadence uses this discontinuity to motivate a closed-loop error-bounded codec.
  • Evaluation protocol: The identical-coder protocol routes every predictor through one adaptive mixture-of-scales coder and measures exactly +0.00% gain on i.i.d. noise.This avoids attributing back-end differences to predictor quality.
  • Domain localization: Cadence’s domain result is +21.4% across 297 series-tolerance pairs on post-cutoff demand corpora, while the broader numeric-data comparison is −3.4%.The paper frames the gain as belonging to aggregate human-demand series rather than numeric data generally.

7. An adaptive arithmetic coder, and evidence

Cadence replaces general-purpose residual compression with a context-modelled binary range coder. This back end beats xz/zstd on real quantization indices and reverses an earlier qualitative finding.

  • Adaptive arithmetic coding: +9.7% on real indices across 15/15 cases is achieved by Cadence’s context-modelled binary range coder over xz/zstd.The coder uses adaptive arithmetic coding with context-modelled binarization of quantization indices.
  • Evidence: The arithmetic coder reverses an apparent back-end finding and re-explains a negative result previously attributed to the wrong cause.Generic compressors can favor classical predictors when they compress long zero runs especially well.

2. Related Work

Prior work spans error-bounded scientific compressors, lossless monitoring codecs, foundation models, and adaptive entropy coders. Cadence positions its contribution at the intersection while emphasizing that one-dimensional operational telemetry is outside SZ3’s primary design target.

  • Error-bounded compression: SZ and SZ3 quantize prediction residuals and entropy-code indices using Lorenzo, regression, or hierarchical interpolation predictors.Cadence reimplements these predictor families for controlled comparisons.
  • Error-bounded compression: SZ3 is primarily designed for multidimensional simulation fields, not one-dimensional operational telemetry.This scope difference matters when interpreting Cadence’s SZ3 comparison.
  • Time-series databases: Production time-series systems commonly use XOR-style lossless codecs for monitoring workloads and downsample long-term history to coarse aggregates.Downsampling discards extrema and is not itself error-bounded.
  • Time-series foundation models: TimesFM-3 extends time-series foundation-model forecasting with multivariate forecasting, over a trillion training points, nine quantiles, and a 64-step horizon.The paper studies compression consequences that forecasting research has not established.
  • Neural lossless compression: Online adaptation with arithmetic coding has established strong lossless compression at very low throughput, while language-model gains are larger because their predictors greatly outperform short context models.Cadence’s 1.5× advantage over a linear filter is comparatively modest.

3. Method

Cadence is a closed-loop, error-bounded codec that reconstructs a lossy seed, predicts from reconstructed history, quantizes residuals, and entropy-codes the resulting indices. Its tolerance is scaled by series variability, and its neural execution is fixed to preserve decoder synchronization.

  • Tolerance: Cadence sets the absolute tolerance as τ = ρσ(x) and sweeps ρ over 0.01, 0.05, and 0.2.The same ρ produces different relative errors across domains.
  • Tolerance: A ρ of 0.05 corresponds to 1.1% relative error on grid load but 4.5% on station ridership.Cross-domain comparisons should therefore use matched relative error.
  • Closed-loop prediction: The predictor consumes its own reconstruction rather than the original series, enabling the decoder to reproduce predictions exactly.This closed loop makes prediction under injected quantization noise part of the codec behavior.
  • Neural Predictor: TimesFM-3 uses context c, a 64-step horizon, and only the first horizon step, yielding stride-1 median point forecasts.The other eight quantiles are disabled because they are not worth transmitting.
  • Determinism: Batch size is fixed through group size G because model outputs are not bit-identical across batch sizes.The format stores G and decoding one series requires the full group.
  • Context bootstrap: Cadence lossily encodes c seed samples with the best of five classical predictors before feeding the reconstructed seed to TimesFM-3.The seed avoids requiring the neural model to predict without sufficient history.
  • Entropy coding: Quantization indices are encoded with adaptive binary range coding, context-coded zero flags and magnitude prefixes, and bypass sign and tail fields.Contexts derive from recent magnitudes and are reproducible by the decoder.

4. Experimental Setup

Cadence is evaluated on post-cutoff demand corpora and controlled synthetic and operational series, using a strongest-classical baseline with identical entropy coding. The setup accounts for implementation, contamination, licensing, and reproducibility constraints.

  • Implementation: Experiments run on one NVIDIA RTX 5060 with PyTorch 2.12 and timesfm 3.0.0, while TimesFM-3 weights require 1.3 GB and 1.4–1.9 GB of VRAM at reported batch sizes.SZ3 is built from source and ZFP uses zfpy 1.0.1; figures use fp32.
  • Baselines: The primary baseline selects the best of six classical error-bounded predictors under the same tolerance and adaptive entropy coder.The predictors include Lorenzo orders 1–3, 32-tap least-squares LPC, and multilevel linear and cubic interpolation.
  • Corpora: Grid contains hourly EIA-930 demand for 49 US balancing authorities from January–June 2026, while Transit contains MTA ridership for 50 station complexes from January–August 2026.
  • Contamination control: Grid and Transit postdate any plausible training cutoff, supporting the domain evaluation, while contaminated series are excluded when sentinel values would distort tolerance scaling.The SEC balancing authority is excluded because 3 of 4,343 samples contain extreme sentinel values.
  • Reproducibility: All code, experiment registries, result files, and corpus-reconstruction scripts are released, but TimesFM-3 weights remain undistributed under a non-commercial licence.

5. Results

Cadence’s lossless advantage is negligible, whereas its error-bounded gains are concentrated in aggregate human-demand series and remain positive across all tested series-tolerance pairs. The evaluation also shows that coder choice and bootstrap overhead materially affect conclusions and short archives.

  • Lossless coding: +0.03% is the median lossless gain over the best classical predictor across 12 series, with 7/12 nominal wins of negligible size.
  • Error-bounded coding: +28.3% is the reported ridership gain, and all 297 tested series-tolerance pairs gain across the two demand domains.The distribution is concentrated above zero rather than being driven by a tail.
  • Domain localization: The effect is domain-localized, spanning −0.8% on scientific simulation output to +28.3% on ridership rather than applying to numeric data generally.
  • Lossless coding: The harness reproduces true entropy on i.i.d. noise: log2 4096 = 12.000, every predictor reads 12.003, and the gain is exactly zero.An earlier +2.15% result came from mismatched density families rather than predictor skill.
  • Coder sensitivity: The general-purpose back end manufactured a qualitative finding by compressing long zero runs from simple predictors especially well at loose tolerance.With the arithmetic coder, the reported tolerance trend inverts.
  • Evaluation: Figure 3 compares rate–distortion using guaranteed error rather than ρ, providing a cross-domain comparable axis.
  • Error-bounded coding: +13.3% is Cadence’s gain over the best-of-six classical predictors on grid load, while the median gain reaches +36.3% against the real SZ3 binary.The defensible comparison is the best-of-six baseline because classical predictors also beat SZ3 on these data.
  • End-to-end accounting: Container overhead dominates below N ≈4k, and an earlier N = 2048 comparison overstated Cadence’s advantage.

5.3 SDRBench: A Falsification Test

SDRBench tests whether Cadence’s gains localize to aggregate human-demand data rather than numeric data generally. The results falsify broad generalization: Cadence loses on smooth scientific fields, increasingly so at wider tolerances, while the comparison is limited by its one-dimensional setting.

  • Falsification result: 0 of 27 SDRBench field-tolerance pairs gain for Cadence, confirming the predicted loss on scientific simulation output.EXAALT trajectories are near breakeven, while Hurricane scanlines lose heavily.
  • Falsification result: −41.0% is the largest reported Hurricane scanline loss at ρ = 0.2, with losses worsening from −3.5% to −25.4% as tolerance widens.This tolerance trend is the mirror image of the demand-series result.
  • Domain boundary: +21.4% on demand series versus losses on SDRBench makes the domain characterization a tested boundary rather than an observation.The SDRBench evaluation uses six EXAALT trajectories and three Hurricane ISABEL scanlines in a fair 1-D versus 1-D comparison.
  • Caveat: Cadence’s one-dimensional codec cannot exploit the multidimensional structure for which SZ3 is designed, so these results do not evaluate SZ3 in native mode.Within the 1-D setting, both Cadence and the classical family beat SZ3 by a wide margin.

5.5 End-to-End Codec and the Context Bootstrap

Cadence’s end-to-end gains account for neural context seeding and implementation synchronization rather than reporting body-only compression. The bootstrap reduces short-archive gains, while batch-size and device-dependent predictions require metadata in the container; at matched size, the codec provides tighter worst-case fidelity than downsampling.

  • Context bootstrap: 6.8% end-to-end gain at six months of hourly data rises to 15.1% asymptotically after accounting for context-bootstrap cost.The bootstrap dominates short archives because classical baselines do not pay this cost.
  • Determinism: Batch size is not prediction-invariant, and no tested configuration repairs it, so group size must be fixed in the format.A desynchronization probability of approximately 8 × 10^-6 per sample becomes near-certain across a million samples.
  • Determinism: GPU and CPU predictions differ by up to 3.9 × 10^-3 MW, requiring execution device metadata because long archives can desynchronize.The reported expected first desynchronization is approximately 1.44×10^5 samples, and five-year archives fail with approximately 26% probability.
  • Retention comparison: 28.0× to 56.1× tighter worst-case error than downsampling is achieved at matched file size across grid, NAB, and transit workloads.Downsampling does not provide an L∞ guarantee, whereas Cadence’s comparison is based on guaranteed worst-case error.

5.8 Throughput

Cadence’s measured throughput and ablations expose batching, precision, context, and side-information trade-offs. Several seemingly promising enhancements either add no compression value or fail because they fragment or dilute the adaptive coder.

  • Throughput: Every series-tolerance pair advances in lockstep on one forward pass, so the initial throughput figure was a batching artifact.The independent closed loops share a forward pass rather than establishing a model property.
  • Throughput: bf16 roughly doubles throughput but perturbs predictions by 288 MW, or 51% of the 565 MW model error, inflating residuals by roughly 12%.The authors retain fp32 to avoid conflating a speed choice with a compression result.
  • Context length: Context length is worth about two points at long archive lengths, while c=256 costs only 3.1% against c=1024 and quarters inference cost.The authors characterize this as a systems result rather than a compression result.
  • Quantile ablation: Quantile conditioning yields a median +0.3% in 10/15 configurations but is negative at ρ = 0.2, so the quantile output can be disabled.A flat adaptive coder already tracks residual scale causally.
  • Context length: Context accuracy saturates early: c=256 costs only 1.6% of body rate versus c=1024 while quartering inference cost.The end-to-end optimum is c=256 for six months of hourly data and c=512 beyond one year.
  • Quantile ablation: Spread-context coding still gives −13.8% in 0/15 configurations because context dilution slows adaptive-model convergence.The result attributes the failure to diluted contexts rather than stream fragmentation.
  • Covariates and hybrid prediction: Cross-series conditioning reduced MAE from 113.6k to 111.4k but increased code length from 19.045 to 19.054 bpv.This shows that better forecast accuracy did not improve coding in this test.
  • Covariates and hybrid prediction: Foundation-model interpolation failed in every tested configuration, ranging from −0.7% to −210%.The authors provisionally conclude that this covariate pathway is not usable side information for coding.

6. Discussion

The discussion localizes Cadence’s gains to aggregate human-demand series and emphasizes measurement discipline, deployment costs, and scope boundaries. It also argues that real-byte evaluation and the entropy back end are part of the experimental design.

  • Domain localization: Aggregate human-demand series share many independent decisions, hourly sampling, and strong daily and weekly periodicity, whereas per-machine metrics are often near-optimal for simple predictors.SDRBench represents the opposite regime, where Cadence loses by up to 41%.
  • Domain localization: No tested cheap statistic reliably separates winners from losers; practitioners should measure a sample of their own data rather than rely on a proxy.The tested correlations were r = −0.37 and r = +0.44 with n = 49.
  • Measurement discipline: Idealized code lengths overstated gains by roughly a quarter, and a projected +9.9% end-to-end figure measured +2.9%.The discussion recommends reporting real bytes and treating idealized lengths strictly as upper bounds.
  • Measurement discipline: Using xz or Zstandard understated every predictor by approximately 10% and manufactured a tolerance trend that reversed under the real coder.The entropy back end is therefore part of the experimental design.
  • Deployment boundaries: Cadence runs at 224 values/s in fp32, versus MB/s for classical codecs, making it an archival codec with strictly sequential decoding.The 1.3 GB model must be present at both endpoints, and its weights carry a non-commercial licence.
  • Deployment boundaries: The 1.3 GB model and group-size coupling constrain deployment: decoding one series costs a full group.A self-contained archive would need approximately 54 GB of payload to amortize the model.
  • Deployment boundaries: Integer or fixed-point inference could make the bitstream portable across hardware and remove the group-size constraint, while distillation could address throughput.The discussion frames downsampling replacement in time-series databases as the most useful deployment comparison.

7. Conclusion

Cadence helps error-bounded lossy compression on aggregate human-demand series, but not lossless coding and not all numeric domains. Its practical advantage is strongest against downsampling, while end-to-end gains are reduced by context-bootstrap costs.

  • Conclusion: A 1.5× better forecaster buys 0.6 bits of a 20-bit budget in lossless coding, producing a median gain of +0.03%.The paper reports +21.4% over the best of six classical predictors across 297 series-tolerance pairs, winning all 297, for aggregate human-demand series.
  • Conclusion: Cadence achieves +21.4% across 297 series-tolerance pairs on two uncontaminated 2026 corpora, winning all 297.The deliverable end-to-end gain is +6.8% at six months and rises to +15.1% asymptotically after paying the context bootstrap.
  • Conclusion: At equal file size, Cadence offers a worst-case error 28–56× tighter than downsampling.The paper identifies downsampling as the retention mechanism used by time-series databases.
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