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

Roberto Tacconelli

cs.ITSep 5, 2026

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

Authors: Roberto Tacconelli

Organizations: Independent Researcher

Abstract

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.

Figures & tables

Figure 1: Compression gain is logarithmic in forecasting gain (Eq. 1 ). Points are measured TimesFM-3-versus-LPC-32 accuracy ratios on three real series; the inset zooms the observed regime, where a

1.33

–

1.51\times

accuracy advantage yields

0.41

–

0.60

bits. Halving a 20-bit-per-value file requires a

1024\times

better predictor.

Series	xz	Classic	TimesFM-3	Gain
ecg_like	9.586	7.999	7.094	$+11.3\%$
sparse_spiky	11.818	9.276	9.078	$+2.1\%$
wikihr_en	23.858	19.758	19.288	$+2.4\%$
wikihr_de	21.733	17.462	17.074	$+2.2\%$
regime_switch	13.413	12.151	12.100	$+0.4\%$
poisson_counts	4.035	3.608	3.606	$+0.1\%$

Table 1: Lossless coding, bits/value. Classic is the best of {LPC-32, LPC-256, seasonal-lag LS, 16-tap stack}; all residuals pass through the identical adaptive coder, so differences reflect prediction skill alone.

Corpus	Median	Wins	Contam.
SDRBench (sci.)	$-0.8\%$	0/27	n/a
Synthetic	$+2.9\%$	7/12	n/a
NAB operational	$+6.4\%$	21/24	no
Grid load (2026)	$\mathbf{+13.3\%}$	147/147	no
Transit (2026)	$\mathbf{+28.3\%}$	150/150	no
Demand combined	$\mathbf{+21.4\%}$	297/297	no

Table 2: Median gain over best-of-six classical predictors, real bytes. Grid and Transit postdate any plausible training cutoff.

Figure 2: Per-series-tolerance gain by corpus, real bytes. Each point is one (series,

\rho

) pair; the bar marks the median. The effect is localized in aggregate human-demand series, not in numeric data generally: it spans

-0.8\%

on scientific simulation output to

+28.3\%

on ridership.

$\boldsymbol{\rho}$	Median	Wins	Classic	Cadence
0.01	$+6.4\%$	49/49	4.356	4.009
0.05	$+13.3\%$	49/49	2.398	2.056
0.20	$+21.2\%$	49/49	1.265	0.980
All	$\mathbf{+13.3\%}$	147/147

Table 3: Grid load, 49 balancing authorities (EIA-930, 2026).

$\boldsymbol{\rho}$	Median	Wins	Classic	Cadence
0.01	$+19.9\%$	50/50	5.942	4.734
0.05	$+27.7\%$	50/50	3.324	2.374
0.20	$+51.2\%$	50/50	1.834	0.926
All	$\mathbf{+28.3\%}$	150/150

Table 4: Subway ridership, 50 station complexes (MTA, 2026).

Figure 3: Rate–distortion on the two uncontaminated demand corpora, plotted against the guaranteed error bound as a percentage of series mean. Medians over 49 balancing authorities (left) and 50 station complexes (right); annotations give Cadence ’s gain over best-of-six classical. SZ3 is the real binary and is included for calibration, not as the primary bar (Section 5.2 ).

Subset	Median	Wins	vs. $\rho$
EXAALT (MD traj.)	$-0.6\%$	0/18	flat
Hurricane (smooth)	$-25.4\%$	0/9	deepens
All SDRBench	$\mathbf{-0.8\%}$	0/27

Table 5: SDRBench, bits/value, real bytes. The predicted loss is confirmed; on the smooth field it deepens as the tolerance widens—the mirror image of Table 4 .

Component	bpv	Share
Seed ( $c=512$ , coded lossily)	0.412	20%
Body (3,788 samples)	1.906	80%
Total	2.111	15.2 $\times$

Table 6: End-to-end container,

G=16

n=4300

\rho=0.05

, grid load. Classical end-to-end on the same series, same coder, is

2.244~\text{bpv}{}

Length	Span	Best $c$	Gain
4,300	6 months	512	$+6.8\%$
8,760	1 year	512	$+11.0\%$
17,520	2 years	512	$+13.0\%$
43,800	5 years	512	$+14.2\%$

Table 7: End-to-end gain by series length,

\rho=0.05

, grid load, at the best context for each length.

Condition	Identical	Max diff
Same batch, repeated $\times 3$	yes	$0$
Batch reordered	yes	$0$
Batch 1 vs. batch 8	no	$3.9\times 10^{-3}$
Batch 8 vs. batch 9	no	$7.8\times 10^{-3}$
+ TF32 disabled	no	$7.8\times 10^{-3}$
+ use_sdpa=False	no	$7.8\times 10^{-3}$

Table 8: Bit-identity of TimesFM-3 predictions, and attempts to force batch-size invariance. Differences in MW on grid load.

Batch	Ctx	Prec.	Values/s
6	1024	fp32	45
64	1024	fp32	113
256	1024	fp32	123
256	512	fp32	224
256	512	bf16	442

Table 9: Throughput. The model is compute-bound and saturates near batch 128–256.

Ctx	Body	$\Delta$ body	Seed	$n{=}4300$	$n{=}43800$
64	2.183	$-11.6\%$	6.367	$-0.0\%$	$+2.5\%$
128	2.071	$-5.9\%$	4.582	$+4.4\%$	$+7.4\%$
256	2.017	$-3.1\%$	3.611	$+5.9\%$	$+9.7\%$
512	1.959	$-0.2\%$	3.214	$\mathbf{+6.0\%}$	$\mathbf{+12.0\%}$
1024	1.956	—	2.980	$+2.0\%$	$+11.8\%$

Table 10: Context-length ablation, grid load, 16 series, identical scored window. Seed cost is priced with the best-of-five classical coder at the same

\tau

Figure 4: Context ablation. (a) Model accuracy saturates early:

c{=}256

costs only

1.6\%

of body rate against

c{=}1024

while quartering inference cost. (b) End-to-end gain against series length. Short contexts amortize their seed quickly but code the body worse; long contexts are the reverse. The crossing puts the optimum at

c{=}256

for six months of hourly data and

c{=}512

beyond one year.

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