Neural networks are known to exploit spurious artifacts (or shortcuts) that co-occur with a target label, exhibiting heuristic memorization. On the other hand, networks have been shown to memorize training examples, resulting in example-level memorization. These kinds of memorization impede generalization of networks beyond their training distributions. Detecting such memorization could be challenging, often requiring researchers to curate tailored test sets. In this work, we hypothesize -- and subsequently show -- that the diversity in the activation patterns of different neurons is reflective of model generalization and memorization. We quantify the diversity in the neural activations through information-theoretic measures and find support for our hypothesis on experiments spanning several natural language and vision tasks. Importantly, we discover that information organization points to the two forms of memorization, even for neural activations computed on unlabeled in-distribution examples. Lastly, we demonstrate the utility of our findings for the problem of model selection. The associated code and other resources for this work are available at //linktr.ee/InformationMeasures .
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Calibration is a popular framework to evaluate whether a classifier knows when it does not know - i.e., its predictive probabilities are a good indication of how likely a prediction is to be correct. Correctness is commonly estimated against the human majority class. Recently, calibration to human majority has been measured on tasks where humans inherently disagree about which class applies. We show that measuring calibration to human majority given inherent disagreements is theoretically problematic, demonstrate this empirically on the ChaosNLI dataset, and derive several instance-level measures of calibration that capture key statistical properties of human judgements - class frequency, ranking and entropy.
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based R\'enyi's entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank R\'enyi's entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2 s)$ or even $\mathcal{O}(ns^2)$, where $n$ is the number of data samples and $s \ll n$. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based R\'enyi's entropy in terms of both performance and computational efficiency.
Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of their ability to model interactions is lacking. The current paper aims to address this gap. Formalizing strength of interactions through an established measure known as separation rank, we quantify the ability of certain GNNs to model interaction between a given subset of vertices and its complement, i.e. between sides of a given partition of input vertices. Our results reveal that the ability to model interaction is primarily determined by the partition's walk index -- a graph-theoretical characteristic that we define by the number of walks originating from the boundary of the partition. Experiments with common GNN architectures corroborate this finding. As a practical application of our theory, we design an edge sparsification algorithm named Walk Index Sparsification (WIS), which preserves the ability of a GNN to model interactions when input edges are removed. WIS is simple, computationally efficient, and markedly outperforms alternative methods in terms of induced prediction accuracy. More broadly, it showcases the potential of improving GNNs by theoretically analyzing the interactions they can model.
Data scarcity is a notable problem, especially in the medical domain, due to patient data laws. Therefore, efficient Pre-Training techniques could help in combating this problem. In this paper, we demonstrate that a model trained on the time direction of functional neuro-imaging data could help in any downstream task, for example, classifying diseases from healthy controls in fMRI data. We train a Deep Neural Network on Independent components derived from fMRI data using the Independent component analysis (ICA) technique. It learns time direction in the ICA-based data. This pre-trained model is further trained to classify brain disorders in different datasets. Through various experiments, we have shown that learning time direction helps a model learn some causal relation in fMRI data that helps in faster convergence, and consequently, the model generalizes well in downstream classification tasks even with fewer data records.
This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local problems. Regarding local problems, a specific scheduling strategy is introduced. Then, to measure correctly the convergence of the iterative process, we introduce a reference solution that revisits the product of classical and enriched functions. As a consequence, we are able to propose a purely matrix-based implementation of the global-local problem. The distributed approach is then compared to other parallel solvers either direct or iterative with domain decomposition. The comparison addresses the scalability as well as the elapsed time. Numerical examples deal with linear elastic problems: a polynomial exact solution problem, a complex micro-structure, and, finally, a pull-out test (with different crack extent). 1: C. A. Duarte, D.-J. Kim, and I. Babu\v{s}ka. A global-local approach for the construction of enrichment functions for the generalized fem and its application to three-dimensional cracks. In Advances in Meshfree Techniques, Dordrecht, 2007. Springer
In many task settings, text classification models are likely to encounter examples from novel classes on which they cannot predict correctly. Selective prediction, in which models abstain on low-confidence examples, provides a possible solution, but existing models are often overly confident on OOD examples. To remedy this overconfidence, we introduce Contrastive Novelty-Augmented Learning (CoNAL), a two-step method that generates OOD examples representative of novel classes, then trains to decrease confidence on them. First, we generate OOD examples by prompting a large language model twice: we prompt it to enumerate relevant novel labels, then generate examples from each novel class matching the task format. Second, we train our classifier with a novel contrastive objective that encourages lower confidence on generated OOD examples than training examples. When trained with CoNAL, classifiers improve in their ability to detect and abstain on OOD examples over prior methods by an average of 2.3% AUAC and 5.5% AUROC across 4 NLP datasets, with no cost to in-distribution accuracy.
Reliable application of machine learning-based decision systems in the wild is one of the major challenges currently investigated by the field. A large portion of established approaches aims to detect erroneous predictions by means of assigning confidence scores. This confidence may be obtained by either quantifying the model's predictive uncertainty, learning explicit scoring functions, or assessing whether the input is in line with the training distribution. Curiously, while these approaches all state to address the same eventual goal of detecting failures of a classifier upon real-life application, they currently constitute largely separated research fields with individual evaluation protocols, which either exclude a substantial part of relevant methods or ignore large parts of relevant failure sources. In this work, we systematically reveal current pitfalls caused by these inconsistencies and derive requirements for a holistic and realistic evaluation of failure detection. To demonstrate the relevance of this unified perspective, we present a large-scale empirical study for the first time enabling benchmarking confidence scoring functions w.r.t all relevant methods and failure sources. The revelation of a simple softmax response baseline as the overall best performing method underlines the drastic shortcomings of current evaluation in the abundance of publicized research on confidence scoring. Code and trained models are at //github.com/IML-DKFZ/fd-shifts.
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.
For deploying a deep learning model into production, it needs to be both accurate and compact to meet the latency and memory constraints. This usually results in a network that is deep (to ensure performance) and yet thin (to improve computational efficiency). In this paper, we propose an efficient method to train a deep thin network with a theoretic guarantee. Our method is motivated by model compression. It consists of three stages. In the first stage, we sufficiently widen the deep thin network and train it until convergence. In the second stage, we use this well-trained deep wide network to warm up (or initialize) the original deep thin network. This is achieved by letting the thin network imitate the immediate outputs of the wide network from layer to layer. In the last stage, we further fine tune this well initialized deep thin network. The theoretical guarantee is established by using mean field analysis, which shows the advantage of layerwise imitation over traditional training deep thin networks from scratch by backpropagation. We also conduct large-scale empirical experiments to validate our approach. By training with our method, ResNet50 can outperform ResNet101, and BERT_BASE can be comparable with BERT_LARGE, where both the latter models are trained via the standard training procedures as in the literature.
While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.
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