Generalizable autoregressive modeling of time series through functional narratives

Time series data are inherently functions of time, yet current transformers often learn time series by modeling them as mere concatenations of time periods, overlooking their functional properties. In this work, we propose a novel objective for transformers that learn time series by re-interpreting them as temporal functions. We build an alternative sequence of time series by constructing degradation operators of different intensity in the functional space, creating augmented variants of the original sample that are abstracted or simplified to different degrees. Based on the new set of generated sequence, we train an autoregressive transformer that progressively recovers the original sample from the most simplified variant. Analogous to the next word prediction task in languages that learns narratives by connecting different words, our autoregressive transformer aims to learn the Narratives of Time Series (NoTS) by connecting different functions in time. Theoretically, we justify the construction of the alternative sequence through its advantages in approximating functions. When learning time series data with transformers, constructing sequences of temporal functions allows for a broader class of approximable functions (e.g., differentiation) compared to sequences of time periods, leading to a 26\% performance improvement in synthetic feature regression experiments. Experimentally, we validate NoTS in 3 different tasks across 22 real-world datasets, where we show that NoTS significantly outperforms other pre-training methods by up to 6\%. Additionally, combining NoTS on top of existing transformer architectures can consistently boost the performance. Our results demonstrate the potential of NoTS as a general-purpose dynamic learner, offering a viable alternative for developing foundation models for time series analysis.

Struggle with Adversarial Defense? Try Diffusion

Adversarial attacks induce misclassification by introducing subtle perturbations. Recently, diffusion models are applied to the image classifiers to improve adversarial robustness through adversarial training or by purifying adversarial noise. However, diffusion-based adversarial training often encounters convergence challenges and high computational expenses. Additionally, diffusion-based purification inevitably causes data shift and is deemed susceptible to stronger adaptive attacks. To tackle these issues, we propose the Truth Maximization Diffusion Classifier (TMDC), a generative Bayesian classifier that builds upon pre-trained diffusion models and the Bayesian theorem. Unlike data-driven classifiers, TMDC, guided by Bayesian principles, utilizes the conditional likelihood from diffusion models to determine the class probabilities of input images, thereby insulating against the influences of data shift and the limitations of adversarial training. Moreover, to enhance TMDC's resilience against more potent adversarial attacks, we propose an optimization strategy for diffusion classifiers. This strategy involves post-training the diffusion model on perturbed datasets with ground-truth labels as conditions, guiding the diffusion model to learn the data distribution and maximizing the likelihood under the ground-truth labels. The proposed method achieves state-of-the-art performance on the CIFAR10 dataset against heavy white-box attacks and strong adaptive attacks. Specifically, TMDC achieves robust accuracies of 82.81% against $l_{\infty}$ norm-bounded perturbations and 86.05% against $l_{2}$ norm-bounded perturbations, respectively, with $\epsilon=0.05$.

Balanced Data, Imbalanced Spectra: Unveiling Class Disparities with Spectral Imbalance

Classification models are expected to perform equally well for different classes, yet in practice, there are often large gaps in their performance. This issue of class bias is widely studied in cases of datasets with sample imbalance, but is relatively overlooked in balanced datasets. In this work, we introduce the concept of spectral imbalance in features as a potential source for class disparities and study the connections between spectral imbalance and class bias in both theory and practice. To build the connection between spectral imbalance and class gap, we develop a theoretical framework for studying class disparities and derive exact expressions for the per-class error in a high-dimensional mixture model setting. We then study this phenomenon in 11 different state-of-the-art pretrained encoders and show how our proposed framework can be used to compare the quality of encoders, as well as evaluate and combine data augmentation strategies to mitigate the issue. Our work sheds light on the class-dependent effects of learning, and provides new insights into how state-of-the-art pretrained features may have unknown biases that can be diagnosed through their spectra.