# S^2-KD: Semantic-Spectral Knowledge Distillation Spatiotemporal Forecasting

arXiv: https://arxiv.org/abs/2512.00366 · HTML: https://mlsanity.com/paper/2512.00366/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 29 Nov 2025.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [DeepSeek-VL: Towards Real-World Vision-Language Understanding](https://mlsanity.com/paper/2403.05525/) (2024)
- [Improved Knowledge Distillation via Teacher Assistant](https://mlsanity.com/paper/1902.03393/) (2019)
- [Distilling Knowledge via Knowledge Review](https://mlsanity.com/paper/2104.09044/) (2021)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [SimVP: Simpler yet Better Video Prediction](https://mlsanity.com/paper/2206.05099/) (2022)
- [PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2103.09504/) (2021)
- [Towards Understanding Knowledge Distillation](https://mlsanity.com/paper/2105.13093/) (2021)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction](https://mlsanity.com/paper/2305.11421/) (2023)
- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [Earthfarseer: Versatile Spatio-Temporal Dynamical Systems Modeling in One Model](https://mlsanity.com/paper/2312.08403/) (2023)
- [Turb-L1: Achieving Long-term Turbulence Tracing By Tackling Spectral Bias](https://mlsanity.com/paper/2505.19038/) (2025)
- [DynST: Dynamic Sparse Training for Resource-Constrained Spatio-Temporal Forecasting](https://mlsanity.com/paper/2403.02914/) (2024)
- [An Effective Information Theoretic Framework for Channel Pruning](https://mlsanity.com/paper/2408.16772/) (2024)

## Built on by (most cited first, 2 of 2)

- [GraphiContact: Pose-aware Human-Scene Robust Contact Perception for Interactive Systems](https://mlsanity.com/paper/2603.20310/) (2026)
- [TAM: Task-Aware Memory Distillation for Efficient Spatiotemporal Prediction](https://mlsanity.com/paper/2610.11617/) (2026)

## Abstract (arXiv)

Spatiotemporal forecasting often relies on computationally intensive models to capture complex dynamics. Knowledge distillation (KD) has emerged as a key technique for creating lightweight student models, with recent advances like frequency-aware KD successfully preserving spectral properties (i.e., high-frequency details and low-frequency trends). However, these methods are fundamentally constrained by operating on pixel-level signals, leaving them blind to the rich semantic and causal context behind the visual patterns. To overcome this limitation, we introduce S^2-KD, a novel framework that unifies Semantic priors with Spectral representations for distillation. Our approach begins by training a privileged, multimodal teacher model. This teacher leverages textual narratives from a Large Multimodal Model (LMM) to reason about the underlying causes of events, while its architecture simultaneously decouples spectral components in its latent space. The core of our framework is a new distillation objective that transfers this unified semantic-spectral knowledge into a lightweight, vision-only student. Consequently, the student learns to make predictions that are not only spectrally accurate but also semantically coherent, without requiring any textual input or architectural overhead at inference. Extensive experiments on benchmarks like WeatherBench and TaxiBJ+ show that S^2-KD significantly boosts the performance of simple student models, enabling them to outperform state-of-the-art methods, particularly in long-horizon and complex non-stationary scenarios.