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Transformer interpretability aims to understand the algorithm implemented by a learned Transformer by examining various aspects of the model, such as the weight matrices or the attention patterns. In this work, through a combination of theoretical results and carefully controlled experiments on synthetic data, we take a critical view of methods that exclusively focus on individual parts of the model, rather than consider the network as a whole. We consider a simple synthetic setup of learning a (bounded) Dyck language. Theoretically, we show that the set of models that (exactly or approximately) solve this task satisfy a structural characterization derived from ideas in formal languages (the pumping lemma). We use this characterization to show that the set of optima is qualitatively rich; in particular, the attention pattern of a single layer can be “nearly randomized”, while preserving the functionality of the network. We also show via extensive experiments that these constructions are not merely a theoretical artifact: even with severe constraints to the architecture of the model, vastly different solutions can be reached via standard training. Thus, interpretability claims based on inspecting individual heads or weight matrices in the Transformer can be misleading. 

The ideal spectral averaging method depends on one’s science goals and the available information about one’s data. Including low-quality data in the average can decrease the signal-to-noise ratio (S/N), which may necessitate an optimization method or a consideration of different weighting schemes. Here, we explore a variety of spectral averaging methods. We investigate the use of three weighting schemes during averaging: weighting by the signal divided by the variance (“intensity-noise weighting”), weighting by the inverse of the variance (“noise weighting”), and uniform weighting. Whereas for intensity-noise weighting the S/N is maximized when all spectra are averaged, for noise and uniform weighting we find that averaging the 35%–45% of spectra with the highest S/N results in the highest S/N average spectrum. With this intensity cutoff, the average spectrum with noise or uniform weighting has ∼95% of the intensity of the spectrum created from intensity-noise weighting. We apply our spectral averaging methods to GBT Diffuse Ionized Gas hydrogen radio recombination line data to determine the ionic abundance ratio,y⁺, and discuss future applications of the methodology.

 

Artificial intelligence-based prostate cancer (PCa) detection models have been widely explored to assist clinical diagnosis. However, these trained models may generate erroneous results specifically on datasets that are not within training distribution. In this paper, we propose an approach to tackle this so-called out-of-distribution (OOD) data problem. Specifically, we devise an end-to-end unsupervised framework to estimate uncertainty values for cases analyzed by a previously trained PCa detection model. Our PCa detection model takes the inputs of bpMRI scans and through our proposed approach we identify OOD cases that are likely to generate degraded performance due to the data distribution shifts. The proposed OOD framework consists of two parts. First, an autoencoder-based reconstruction network is proposed, which learns discrete latent representations of in-distribution data. Second, the uncertainty is computed using perceptual loss that measures the distance between original and reconstructed images in the feature space of a pre-trained PCa detection network. The effectiveness of the proposed framework is evaluated on seven independent data collections with a total of 1,432 cases. The performance of pre-trained PCa detection model is significantly improved by excluding cases with high uncertainty. 

Change point analysis aims to detect structural changes in a data sequence. It has always been an active research area since it was introduced in the 1950s. In modern statistical applications, however, high-throughput data with increasing dimensions are ubiquitous in fields ranging from economics, finance to genetics and engineering. For those problems, the earlier works are typically no longer applicable. As a result, the problem of testing a change point for high dimensional data sequences has been an important yet challenging task. In this paper, we first focus on models for at most one change point, and review recent state-of-art techniques for change point testing of high dimensional mean vectors and compare their theoretical properties. Based on that, we provide a survey of some extensions to general high dimensional parameters beyond mean vectors as well as strategies for testing multiple change points in high dimensions. Finally, we discuss some open problems for possible future research directions. 

In this article, we investigate the problem of simultaneous change point inference and structure recovery in the context of high dimensional Gaussian graphical models with possible abrupt changes. In particular, motivated by neighborhood selection, we incorporate a threshold variable and an unknown threshold parameter into a joint sparse regression model which combines p l1-regularized node-wise regression problems together. The change point estimator and the corresponding estimated coefficients of precision matrices are obtained together. Based on that, a classifier is introduced to distinguish whether a change point exists. To recover the graphical structure correctly, a data-driven thresholding procedure is proposed. In theory, under some sparsity conditions and regularity assumptions, our method can correctly choose a homogeneous or heterogeneous model with high accuracy. Furthermore, in the latter case with a change point, we establish estimation consistency of the change point estimator, by allowing the number of nodes being much larger than the sample size. Moreover, it is shown that, in terms of structure recovery of Gaussian graphical models, the proposed thresholding procedure achieves model selection consistency and controls the number of false positives. The validity of our proposed method is justified via extensive numerical studies. Finally, we apply our proposed method to the S&P 500 dataset to show its empirical usefulness.