Recently, emergence has received widespread attention from the research community along with the success of large-scale models.Different from the literature, we hypothesize a key factor that promotes the performance during the increase of scale: the reduction of monosemantic neurons that can only form one-to-one correlations with specific features.Monosemantic neurons tend to be sparser and have negative impacts on the performance in large models.Inspired by this insight, we propose an intuitive idea to identify monosemantic neurons and inhibit them.However, achieving this goal is a non-trivial task as there is no unified quantitative evaluation metric and simply banning monosemantic neurons does not promote polysemanticity in neural networks.Therefore, we first propose a new metric to measure the monosemanticity of neurons with the guarantee of efficiency for online computation, then introduce a theoretically supported method to suppress monosemantic neurons and proactively promote the ratios of polysemantic neurons in training neural networks.We validate our conjecture that monosemanticity brings about performance change at different model scales on a variety of neural networks and benchmark datasets in different areas, including language, image, and physics simulation tasks.Further experiments validate our analysis and theory regarding the inhibition of monosemanticity.

Unsupervised image denoising has been proposed to alleviate the widespread noise problem without requiring clean images. Existing works mainly follow the self-supervised way, which tries to reconstruct each pixel x of noisy images without the knowledge of x. More recently, some pioneer works further emphasize the importance of x and propose to weigh the information extracted from x and other pixels when recovering x. However, such a method is highly sensitive to the standard deviation σnof noise injected to clean images, where σnis inaccessible without knowing clean images. Thus, it is unrealistic to assume that σnis known for pursuing high model performance.To alleviate this issue, we propose Noise2Info to extract the critical information, the standard deviation σnof injected noise, only based on the noisy images. Specifically, we first theoretically provide an upper bound on σn, while the bound requires clean images. Then, we propose a novel method to estimate the bound of σnby only using noisy images. Besides, we prove that the difference between our estimation with the true deviation goes smaller as the model training. Empirical studies show that Noise2Info is effective and robust on benchmark data sets and closely estimates the standard deviation of noise during model training.

The acquisition of accurate rainfall distribution in space is an important task in hydrological analysis and natural disaster pre-warning. However, it is impossible to install rain gauges on every corner. Spatial interpolation is a common way to infer rainfall distribution based on available raingauge data. However, the existing works rely on some unrealistic pre-settings to capture spatial correlations, which limits their performance in real scenarios. To tackle this issue, we propose the SSIN, which is a novel data-driven self-supervised learning framework for rainfall spatial interpolation by mining latent spatial patterns from historical observation data. Inspired by the Cloze task and BERT, we fully consider the characteristics of spatial interpolation and design the SpaFormer model based on the Transformer architecture as the core of SSIN. Our main idea is: by constructing rich self-supervision signals via random masking, SpaFormer can learn informative embeddings for raw data and then adaptively model spatial correlations based on rainfall spatial context. Extensive experiments on two real-world raingauge datasets show that our method outperforms the state-of-the-art solutions. In addition, we take traffic spatial interpolation as another use case to further explore the performance of our method, and SpaFormer achieves the best performance on one large real-world traffic dataset, which further confirms the effectiveness and generality of our method.

Precipitation forecasting, modeled as an important chaotic system in earth system science, is not explicitly solved with theory-driven models. In recent years, deep learning models have achieved great success in various applications including rainfall prediction. However, these models work in an image processing manner regardless of the nature of a physical system. We found that the non-linearity relationships learned by deep learning models, which mostly rely on the activation functions, are commonly weighted piecewise continuous functions with bounded first-order derivatives. In contrast, the polynomial is one of the most widely used classes of functions for theory-driven models, applied to numerical approximation, dynamic system modeling, etc.. Researchers started to use the polynomial activation functions (Pacs in short) for neural networks from the 1990s. In recent years, with bloomed researches that apply deep learning to scientific problems, it is weird that such a powerful class of basis functions is rarely used. In this paper, we investigate it and argue that, even though polynomials are good at information extraction, it is too fragile to train stably. We finally solve its serious data flow explosion problem with Chebyshev polynomials and prepended normalization, which enables networks to go deep with Pacs. To enhance the robustness of training, a normalization called Range Norm is further proposed. Performance on synthetic dataset and summer precipitation prediction task validates the necessity of such a class of activation functions to simulate complex physical mechanisms. The new tool for deep learning enlightens a new way of automatic theoretical physics analysis.