Cadence：基於時間序列基礎模型的需求時間序列誤差有界有損壓縮

摘要

我們提出 Cadence，一款用於數值時間序列的誤差有界有損壓縮器，將 3.3 億參數的時間序列基礎模型（Google TimesFM-3）與自適應算術編碼器配對，並保證每個樣本滿足 |x_t-x_t|≤τ。一項負面結果限制了設計空間：對於無損編碼，基礎模型毫無價值，因為節省的位元數與預測器準確度呈對數關係，Δb=log_2(MAE_{old}/MAE_{new})。因此，TimesFM-3 相較於 32 抽頭線性預測器所擁有的 1.51 倍優勢，僅換得 20.28 位元中的 0.60 位元，中位數增益為 +0.03%。誤差有界編碼在一點上擺脫了此限制：一旦預測落於誤差帶內，殘差索引即為零，樣本幾乎免費。Cadence 的貢獻包括：（1）具上下文建模二值化的自適應範圍編碼器，在真實索引上以 9.7%（15/15）勝過 xz/zstd，並推翻了一項來自通用後端的發現；（2）一項確定性結果——預測在不同批次大小下並非位元完全一致，且沒有任何 PyTorch 組態能修復此問題，迫使將群組大小與執行裝置寫入容器格式；以及（3）在晚於任何合理訓練截止點的語料庫上進行領域局部化。在 49 條 EIA-930 平衡機構需求序列（2026）上，Cadence 相較於六種經典預測器中的最佳者提升 13.3%；在 50 條 MTA 載客量序列（2026）上提升 28.3%：在 297 個序列-容差配對上中位數為 21.4%，且全數 297 個勝出。相對於時間序列資料庫為保留資料所部署的降採樣，在相同大小下，其保證的最壞情況誤差縮小 28--56 倍。端到端而言，一旦支付了上下文自舉成本，增益從六個月每小時資料的 6.8% 到漸近的 15.1%。嘗試在 SDRBench 上否證領域主張時，理論預測會失敗，而結果正是如此：中位數 -0.8%，27 個配對中 0 個獲得增益。另外三項負面結果與八項撤回的主張均有完整報告。

English

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.