# When Do Autoregressive Sequence Models Forecast Physical Wavefields? A Controlled Study on Synthetic Seismograms

arXiv: https://arxiv.org/abs/2606.10868 · HTML: https://mlsanity.com/paper/2606.10868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Parallel WaveGAN: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram](https://mlsanity.com/paper/1910.11480/) (2019)
- [ProphetNet: Predicting Future N-gram for Sequence-to-Sequence Pre-training](https://mlsanity.com/paper/2001.04063/) (2020)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [DDSP: Differentiable Digital Signal Processing](https://mlsanity.com/paper/2001.04643/) (2020)
- [Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation](https://mlsanity.com/paper/2204.01171/) (2022)
- [Neural Speech Phase Prediction based on Parallel Estimation Architecture and Anti-Wrapping Losses](https://mlsanity.com/paper/2211.15974/) (2022)
- [Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecasts](https://mlsanity.com/paper/2302.11101/) (2023)
- [Harnessing Loss Decomposition for Long-Horizon Wave Predictions via Deep Neural Networks](https://mlsanity.com/paper/2412.02924/) (2024)
- [Data-Driven Forecasting of three-Component Seismograms Using Transformer Architectures](https://mlsanity.com/paper/2606.02912/) (2026)

## Abstract (arXiv)

Long-horizon autoregressive forecasting of oscillatory physical signals, such as seismograms, gravitational-wave strain, and similar wavefields is limited by error accumulation: as a causal model is fed its own outputs over hundreds of steps, small per-step errors compound into phase drift that pointwise metrics fail to detect. We ask when such rollout stays stable, using synthetic three-component seismograms as a physically structured testbed and the textscSeismoGPT autoregressive forecaster as the model under study. Through controlled architecture ablations evaluated on free rollout with paired significance tests, we isolate the contribution of each design choice. Multi-token prediction is the dominant stabilizer, accounting for almost the entire improvement over a single-token baseline (+0.042 median NCC); a horizon-embedding hybrid prediction head and a cross-horizon STFT-magnitude coherence loss each add a small but consistent further gain. Performance depends sharply on a context-ratio threshold near one, roughly the full P-S interval of observed signal, below which rollout generalization collapses. The dominant residual failure is a polarity inversion: a magnitude-based spectral loss reduces its incidence but, by construction, cannot penalize an inverted segment once it occurs, identifying phase-aware objectives as the natural next step. We frame this as a controlled study of rollout stability on oscillatory wavefields, not a benchmark of forecasting architectures.