FROM 1D TO 4D: A UNIFIED SEQUENCE PREDICTION FRAMEWORK WITH THE KUN-V2 ARCHITECTURE

Sequence prediction is central to modern deep learning. In recent general-purpose time-series models, sequence completion and reconstruction, predicting the hid- den part of a sequence from its visible part, have become the common basis of forecasting, imputation and anomaly detection. These models, however, are gener- ally hard to extend to higher dimensionalities. Neural operators such as FNO and U-NO can be extended, but at a comparatively high complexity. To address the or- der in which subspaces are processed and the efficiency on high-dimensional data, we propose KUN-V2, a unified encoder–decoder framework that processes inputs of arbitrary spatial dimensionality via two ingredients: an auto-factorization that splits each spatial axis into balanced chunks, and a compact spec language that selects in what order and grouping the chunks are reduced. We show that the time complexity is linear in the product of all input dimensions and invariant under any reordering or regrouping of the chunk schedule. We validate the framework in-distribution on a single task, masked-half sequence completion, across all four targeted dimensionalities and, on synthetic data, a fifth with a single shared code- base: only the input shape, spec string, and chunk multiplicities change between settings. The evaluation covers 21 datasets, comprising synthetic and real data at N = 1 . . . 4 and the two synthetic families at N = 5. Against eleven learned baselines, KUN-V2 places in the top three on 17 and first on 11, and on a synthetic cost ladder its measured training time and peak memory stay within the linear-in- element-count bound. KUN-V2 thus reduces the cost of moving to a new dimen- sionality from architectural re-design to a configuration change. Code is available at https://github.com/jccxfgj-beep/kun-v2/tree/main.