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. 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=log2(MAEold/MAEnew). So the 1.51× 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× 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× accuracy advantage yields 0.41 – 0.60 bits. Halving a 20-bit-per-value file requires a 1024× 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)
+13.3%
147/147
no
Transit (2026)
+28.3%
150/150
no
Demand combined
+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, ρ ) 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.
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. ρ
EXAALT (MD traj.)
−0.6%
0/18
flat
Hurricane (smooth)
−25.4%
0/9
deepens
All SDRBench
−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 ×
Table 6: End-to-end container, G=16 , n=4300 , ρ=0.05 , grid load. Classical end-to-end on the same series, same coder, is 2.244bpv .
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, ρ=0.05 , grid load, at the best context for each length.
Condition
Identical
Max diff
Same batch, repeated ×3
yes
0
Batch reordered
yes
0
Batch 1 vs. batch 8
no
3.9×10−3
Batch 8 vs. batch 9
no
7.8×10−3
+ TF32 disabled
no
7.8×10−3
+ use_sdpa=False
no
7.8×10−3
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
Δ 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
+6.0%
+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 τ .
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.
Large language models (LLMs) have enabled time series (TS) analysis by jointly modeling numerical observations and textual context through a shared token interface. However, TS tokens and prompt tokens exhibit fundamentally different information structures, making uniform token processing inefficient. In this paper, we study token efficiency in TS language modeling from an asymmetric-token perspective. We show that TS tokens have highly uneven spectral contributions, where many tokens share redundant frequency patterns while a small subset preserves critical temporal evidence. We also observe that prompt-token influence attenuates with model depth, suggesting that full prompt retention across all layers is unnecessary. Based on these findings, we develop an adaptive token budgeting framework that compresses TS tokens via frequency-domain structure and progressively reduces prompt tokens across layers. Experiments across forecasting, classification, imputation, and anomaly detection demonstrate up to \textit{\textbf{7.68×}} inference acceleration and performance gains in 78% of evaluated settings, showing the effectiveness of asymmetric token compression for scalable TS foundation models.
Jialin Gan, Xin Qiu, Guangzhe Chen +1
Zhejiang University · Harbin Institute of Technology · Shandong University
Time series foundation models (TSFMs) are pretrained on series from diverse domains, where demand series make up only a small fraction. Demand data has properties that such corpora rarely contain: Short histories, frequent zeros, censoring by stock-outs, and exogenous events that the series does not record. To this end, we propose EXAONE Demand, built on 1) a demand-specific corpus and 2) a demand-aware adapter. For the corpus, we assemble 11.3M series and 48.4B observations from 73 sources, and a synthetic generator supplies the behaviour that open demand data under-represents. For the adapter, we attach low-rank branches to a frozen general-domain backbone, one for each of the four demand classes (smooth, intermittent, erratic, and lumpy), and a router that reads eight scale-free statistics of the input series decides how much each branch contributes. We build EXAONE Demand in two versions, one trained on real-world and synthetic demand together and one trained on the synthetic corpus alone. On 22 held-out datasets, both versions outperform 36 TSFMs, and real-world demand adds a gain over synthetic data alone.
Time series foundation models must preserve multi-domain breadth, probabilistic output, and multiple temporal scales, but parameter count grows when each scale receives a separate representation. We introduce Fracast-0, a probabilistic forecasting foundation model that exploits temporal self-similarity to reuse one operator across scales. A parameter-free detector extracts significant seasonal structure. The encoder applies a shared local block along a geometric dilation ladder with scale conditioning, while the decoder combines context-gathered states with an explicit seasonal future state and reuses a second block along another ladder before emitting nine quantiles. Pretraining across six corpora preserves multi-domain breadth within 85,001 parameters. On 97 GIFT-Eval configurations without per-dataset fine-tuning, Fracast-0 is the smallest of 28 evaluated checkpoints and remains non-dominated in the aggregate parameter-accuracy plane with MASE 0.808 and WQL 0.564. It uses 42.0% fewer parameters than TinyCast, whose MASE and WQL are 4.2% and 3.3% lower. These results support cross-scale weight reuse as a practical route to further time series foundation model compression.
Tianxiang Zhan, Huanyao Zhang, Yuanpeng He
University of Electronic Science and Technology of China · Peking University