Cadence: Error-Bounded Lossy Compression of Demand Time Series with a Time-Series Foundation Model
Abstract
Cadence pairs a time-series foundation model with an adaptive arithmetic coder for error-bounded lossy compression, achieving substantial gains over classical predictors while reporting negative results on lossless coding and cross-batch determinism.
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 |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(MAE_{old}/MAE_{new}). So the 1.51times 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--56times 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.
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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 |x^t−xt|≤τ on every sample.
The lossless number is the one that matters for anyone shipping this: a 330M foundation model nets 0.03% median gain over a 32-tap linear predictor. That's a hard sell on a microcontroller where the predictor is free and the model needs an accelerator. The error-bounded regime is where the real value lives, but I'd want to see the bound hold on series with regime shifts — demand data isn't smooth, it jumps when a factory line goes down or a tariff lands. And the inference cost of TimesFM-3 has to be weighed against just running a cheap predictor and accepting the error. Show me the bound surviving a structural break and I'm interested.
Thanks, the structural-break question is the right one to push on, so I ran it.
One framing note first: the paper is a lossy compression paper. The +0.03% lossless result isn't a headline being oversold, it's the negative result that motivates everything else - it's there to explain why the work moves to the error-bounded regime, via the log2 law (a 1.51× better forecaster buys 0.60 bits of 20.28). And I agree with your microcontroller point entirely: at 224 values/s and 1.3 GB of weights, this is an archival codec. The paper says so in Limitations. It is not competing with a free linear predictor on an MCU and shouldn't be read as trying to.
On the bound. It survives by construction, not by luck. With k = round((x−p)/D) and x̂ = p + kD, you get |x̂−x| ≤ τ for any prediction p, however wrong. A regime shift makes p bad, which costs bits, not correctness. Verified anyway on 27 closed loops - 6 grid series × {none, +3σ level shift, volatility burst, both} plus 3 NAB series with documented real failures. Bound held on every sample of every series, worst ratio 1.000.
On the bitrate, which is the real question. Gain vs the best classical predictor, in 100-sample windows around the break:
| window | +3σ level shift | volatility burst | real NAB failure |
|---|---|---|---|
| −100..0 | +5.1% | +13.1% | +3.9% |
| 0..+100 | +7.7% | −210% | +3.6% |
| +100..+200 | −3.7% | −203% | +1.9% |
| +200..+300 | +1.9% | −37% | 0.0% |
| +600..+900 | +8.4% | +0.2% | +1.0% |
So: level shifts - your factory-line and tariff cases - barely dent it. One window at −3.7%, then full recovery. Real documented failures in NAB stay positive throughout.
But you've found a genuine failure mode: volatility bursts. During a 2σ noise burst Cadence costs three times the classical predictor, and takes 300–400 samples to recover. That is consistent with a mechanism already in the paper (§5.4): TimesFM-3 has a measured noise gain up to G=2.12 in the closed loop, where Lorenzo-1 has G=1. Injected volatility is exactly the input that penalises a high-gain predictor. A level shift is a one-off prediction error; a volatility burst is sustained noise amplification.
That's a real limitation and it isn't in the paper. It should be. Thanks.
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