Long-horizon multivariate time series forecasting (LTSF) remains challenging due to non-stationarity, regime shifts, and error accumulation. The Variability-Aware Recursive Neural Network (VARNN) is designed to track such variability by maintaining a residual-memory state driven by one-step prediction errors. However, its original formulation is limited to one-step sequence regression and does not directly support multi-step forecasting. In this work, we extend VARNN to long-horizon forecasting and introduce StateFlow, a recurrent forecasting framework that uses VARNN as a dual-state recurrent backbone to capture two complementary signals from the lookback sequence: a hidden-state trajectory representing primary temporal dynamics, including trend, seasonality, level changes, and recurring patterns, and a residual-memory trajectory representing structured local prediction deviations, driven from a nonlinear recurrent transformation of errors between one-step base predictions and observed values. A chunk-based decoder separately summarizes these trajectories and maps them to the future horizon for direct multi-step forecasting. We further employ a two-stage optimization strategy that first trains the VARNN encoder through a one-step base prediction objective to optimize the internal representations over the lookback sequence, and then trains a horizon-specific decoder for direct multi-step forecasting. Experiments on standard LTSF benchmarks show that StateFlow achieves competitive performance against strong linear, recurrent, convolutional, and Transformer-based baselines while preserving linear recurrent encoding and a compact model design.
We introduce the context-ready transformer, a new recurrent neural network architecture built from a D-layer transformer block that pre-contextualizes each token before it enters the block. During left-to-right generation, a correction network combines the previous position's block output -- a cached summary of past context -- with the current token embedding, so the tokenenters the block already contextualized rather than as a raw embedding. At sequential inference, the correction chain makes the architecture a recurrent neural network. For training, we unroll the correction process K times over the full sequence, processing all positions in parallel at each step. A pretrained transformer can also be converted to a context-ready model by adding a zero-initialized correction FFN and fine-tuning. We evaluate across widths, depths, block sizes, and two datasets, with all comparisons against standard transformers, variants, and ablations. A D=5 model beats a 12-layer transformer while generating 1.7x faster on an A100. With K=10, a single-layermodel (D=1) beats a 6-layer transformer with a 2.6x inference speedup, and sequential inference matches parallel K=10 to within 0.01 PPL. The architecture benefits most from wide representations and long contexts. On a pointer-chasing task, D=1 trained with BPTT solves all 10 composition levels, while standard transformers exhibit staircase-like depth dependence.