We will incorporate the answers/other feedback into the revised manuscript. The general quality of samples seems to be negatively impacted. We agree other wavelets could be potentially interesting. SR is not claimed as our primary goal/contribution. Rather, it is a fortuitous byproduct of the conditional structure that WF enables. A more thorough exploration of WF for SR is a promising direction for future work.

Wavelets have emerged as a cutting edge technology in a number of fields. Concrete results of their application in Image and Signal processing suggest that wavelets can be effectively applied to Natural Language Processing (NLP) tasks that capture a variety of linguistic properties. In this paper, we leverage the power of applying Discrete Wavelet Transforms (DWT) to word and sentence embeddings. We first evaluate, intrinsically and extrinsically, how wavelets can effectively be used to consolidate important information in a word vector while reducing its dimensionality. We further combine DWT with Discrete Cosine Transform (DCT) to propose a non-parameterized model that compresses a sentence with a dense amount of information in a fixed size vector based on locally varying word features. We show the efficacy of the proposed paradigm on downstream applications models yielding comparable and even superior (in some tasks) results to original embeddings.

Deep learning-based weather forecasting models have recently demonstrated significant performance improvements over gold-standard physics-based simulation tools. However, these models are vulnerable to adversarial attacks, which raises concerns about their trustworthiness. In this paper, we first investigate the feasibility of applying existing adversarial attack methods to weather forecasting models. We argue that a successful attack should (1) not modify significantly its original inputs, (2) be faithful, i.e., achieve the desired forecast at targeted locations with minimal changes to non-targeted locations, and (3) be geospatio-temporally realistic. However, balancing these criteria is a challenge as existing methods are not designed to preserve the geospatio-temporal dependencies of the original samples. To address this challenge, we propose a novel framework called FABLE (Forecast Alteration By Localized targeted advErsarial attack), which employs a 3D discrete wavelet decomposition to extract the varying components of the geospatio-temporal data. By regulating the magnitude of adversarial perturbations across different components, FABLE can generate adversarial inputs that maintain geospatio-temporal coherence while remaining faithful and closely aligned with the original inputs. Experimental results on multiple real-world datasets demonstrate the effectiveness of our framework over baseline methods across various metrics.

Summary and Contributions: This paper introduces a hierarchical structure for normalizing flows for density estimation and data generation based on wavelet transforms, allowing for a natural factorization of the data distribution based on different resolutions of the data. For density estimation, each image is fed into a sequence of wavelet transforms. Each wavelet transform takes an image and outputs a lower resolution image (obtained by a low-pass filter) and a tensor of detail coefficients (obtained by a high-pass filter). Repeatedly applying wavelet transforms to the output images leads to a set of detail coefficient tensors for each scale and a final 1x1x3 "image" representing the average intensity per channel. The original representation can be recovered from this representation with a sequence of inverse wavelet transforms.

Artifact detection algorithms are crucial to correcting the output generated by diffusion models. However, because of the variety of artifact forms, existing methods require substantial annotated data for training. This requirement limits their scalability and efficiency, which restricts their wide application. This paper shows that the similarity of denoised images between consecutive time steps during the sampling process is related to the severity of artifacts in images generated by diffusion models. Building on this observation, we introduce the concept of Similarity Trajectory to characterize the sampling process and its correlation with the image artifacts presented. Using an annotated data set of 680 images, which is only 0.1% of the amount of data used in the prior work, we trained a classifier on these trajectories to predict the presence of artifacts in images. By performing 10-fold validation testing on the balanced annotated data set, the classifier can achieve an accuracy of 72.35%, highlighting the connection between the Similarity Trajectory and the occurrence of artifacts. This approach enables differentiation between artifact-exhibiting and natural-looking images using limited training data.

How to best develop foundational models for time series forecasting remains an important open question. Tokenization is a crucial consideration in this effort: what is an effective discrete vocabulary for a real-valued sequential input? To address this question, we develop WaveToken, a wavelet-based tokenizer that allows models to learn complex representations directly in the space of time-localized frequencies. Our method first scales and decomposes the input time series, then thresholds and quantizes the wavelet coefficients, and finally pre-trains an autoregressive model to forecast coefficients for the forecast horizon. By decomposing coarse and fine structures in the inputs, wavelets provide an eloquent and compact language for time series forecasting that simplifies learning. Empirical results on a comprehensive benchmark, including 42 datasets for both in-domain and zero-shot settings, show that WaveToken: i) provides better accuracy than recently proposed foundation models for forecasting while using a much smaller vocabulary (1024 tokens), and performs on par or better than modern deep learning models trained specifically on each dataset; and ii) exhibits superior generalization capabilities, achieving the best average rank across all datasets for three complementary metrics. In addition, we show that our method can easily capture complex temporal patterns of practical relevance that are challenging for other recent pre-trained models, including trends, sparse spikes, and non-stationary time series with varying frequencies evolving over time.

An increasing number of applications require processing of signals defined on weighted graphs. While wavelets provide a flexible tool for signal processing in the classical setting of regular domains, the existing graph wavelet constructions are less flexible - they are guided solely by the structure of the underlying graph and do not take directly into consideration the particular class of signals to be processed. This paper introduces a machine learning framework for constructing graph wavelets that can sparsely represent a given class of signals. Our construction uses the lifting scheme, and is based on the observation that the recurrent nature of the lifting scheme gives rise to a structure resembling a deep auto-encoder network. Particular properties that the resulting wavelets must satisfy determine the training objective and the structure of the involved neural networks. The training is unsupervised, and is conducted similarly to the greedy pre-training of a stack of auto-encoders. After training is completed, we obtain a linear wavelet transform that can be applied to any graph signal in time and memory linear in the size of the graph. Improved sparsity of our wavelet transform for the test signals is confirmed via experiments both on synthetic and real data.

The use of deep learning for radio modulation recognition has become prevalent in recent years. This approach automatically extracts high-dimensional features from large datasets, facilitating the accurate classification of modulation schemes. However, in real-world scenarios, it may not be feasible to gather sufficient training data in advance. Data augmentation is a method used to increase the diversity and quantity of training dataset and to reduce data sparsity and imbalance. In this paper, we propose data augmentation methods that involve replacing detail coefficients decomposed by discrete wavelet transform for reconstructing to generate new samples and expand the training set. Different generation methods are used to generate replacement sequences. Simulation results indicate that our proposed methods significantly outperform the other augmentation methods.