Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training
Wenshuo Wang, Fan Zhang
TL;DR
This paper introduces Frequency Representation Learning to address Scale Anchoring in Zero-Shot Super-Resolution Spatiotemporal Forecasting, enabling models to better generalize to high-resolution data by aligning frequency representations.
Contribution
It proposes a novel, architecture-agnostic method that improves high-resolution inference accuracy by mitigating frequency representation limitations inherent in low-resolution training data.
Findings
Frequency response in high-frequency bands is more stable with FRL.
Errors decrease as resolution increases with FRL.
FRL significantly outperforms baseline methods within tested resolutions.
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…
Peer Reviews
Decision·ICLR 2026 Poster
- This paper looks into spectral bias-related stuff, which is important in scientific machine learning. - This paper proposes a new concept, called scale anchoring, in zero-shot super-resolution. - This paper provided a theoretical and empirical analysis of this scale anchoring phenomenon. - This paper is generally well-written and well-presented.
I have several major concerns listed below. - First, what is the difference between the defined scale anchoring and the prior concepts, such as spectral bias / discretization-invariance? To me, scale anchoring refers to a failure mode in which a model trained on low-resolution data fails to get good accuracy at finer resolutions, due to missing high-frequency information beyond the coarse data’s Nyquist limit. Spectral bias also refers to the same things that a NN model cannot learn high-frequ
1、Novel: The paper is the first to clearly identify the "Scale Anchoring" phenomenon and provides a theoretical analysis of its mechanism (frequency blindness and high-frequency error dominance), addressing an under-recognized limitation in existing zero-shot super-resolution research. 2、Strong Generalizability: FRL is architecture-agnostic and can be seamlessly integrated into various mainstream models such as GNNs, Transformers, and CNNs. Experiments show that it significantly improves high-re
1、Insufficient Computational Overhead Analysis: Although a training complexity increase of approximately 1.1–1.4× is mentioned, the paper lacks detailed discussions on actual training time and memory usage comparisons across different architectures, as well as the storage requirements for multi-resolution data construction. 2、Limited Generalization in Extreme Physical Scenarios: The authors note in the appendix that FRL fails in high-Reynolds-number turbulence (e.g., Re=10^5), but they do not de
1. The identification of the “scale anchoring” problem is interesting and relevant in several fields, such as neural operators. 2. The proposed method (FRL) is architecture‐agnostic in principle. 3. The experiments show that the inference error can be even lower for zero-shot super resolution. Existing works usually consider the same error as a success.
Some of these weaknesses below fall somewhere between questions and weaknesses, so I’ve included them here. 1. A central conceptual concern is that the zero-shot high-resolution inference task itself appears ill-posed under the stated assumptions. If the model is trained purely on low-resolution data, its training distribution is inherently band-limited by the Nyquist frequency of that grid. Consequently, the high-frequency components present in the high-resolution domain are unobserved and uni
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Taxonomy
TopicsDomain Adaptation and Few-Shot Learning · Gaussian Processes and Bayesian Inference · Generative Adversarial Networks and Image Synthesis