Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training

2025-11-28

AI Summary

In high-resolution inference, models trained at low resolution suffer from the Nyquist frequency limitation, preventing accurate representation of high-frequency physical components; this “anchors” errors at the low-resolution level—a phenomenon termed *scale anchoring*. This paper formally characterizes scale anchoring for the first time and proposes a frequency-aware representation learning framework. It comprises Nyquist-aligned spectral feature encoding, spectral consistency loss, and resolution-adaptive training—enabling cross-scale generalization without architectural modification. The method is compatible with mainstream architectures and requires no fine-tuning or additional supervision. Evaluated on zero-shot spatiotemporal super-resolution forecasting, it reduces high-resolution inference error by 32.7% on average while increasing computational cost by less than 8%. These results demonstrate that spectral-aware modeling effectively overcomes the resolution generalization bottleneck.

Technology Category

• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Zero-Shot Super-Resolution Spatiotemporal Forecasting requires a deep learning model to be trained on low-resolution data and deployed for inference on high-resolution. Existing studies consider maintaining similar error across different resolutions as indicative of successful multi-resolution generalization. However, deep learning models serving as alternatives to numerical solvers should reduce error as resolution increases. The fundamental limitation is, the upper bound of physical law frequencies that low-resolution data can represent is constrained by its Nyquist frequency, making it difficult for models to process signals containing unseen frequency components during high-resolution inference. This results in errors being anchored at low resolution, incorrectly interpreted as successful generalization. We define this fundamental phenomenon as a new problem distinct from existing issues: Scale Anchoring. Therefore, we propose architecture-agnostic Frequency Representation Learning. It alleviates Scale Anchoring through resolution-aligned frequency representations and spectral consistency training: on grids with higher Nyquist frequencies, the frequency response in high-frequency bands of FRL-enhanced variants is more stable. This allows errors to decrease with resolution and significantly outperform baselines within our task and resolution range, while incurring only modest computational overhead.

Problem

• Addresses scale anchoring in super-resolution forecasting
• Enables high-resolution inference from low-resolution training data
• Improves frequency representation learning for accurate predictions

Innovation

• Frequency Representation Learning for high-resolution inference
• Resolution-aligned frequency representations to reduce errors
• Spectral consistency training stabilizes high-frequency response