Recent work has proposed adding biologically-inspired components to visual neural networks as a way to improve their adversarial robustness. One surprisingly effective component for reducing adversarial vulnerability is response stochasticity, like that exhibited by biological neurons.

In the AutoML domain, test accuracy is heralded as the quintessential metric for evaluating model efficacy, underpinning a wide array of applications from neural architecture search to hyperparameter optimization. However, the reliability of test accuracy as the primary performance metric has been called into question, notably through research highlighting how label noise can obscure the true ranking of state-of-the-art models. We venture beyond, along another perspective where the existence of hard samples within datasets casts further doubt on the generalization capabilities inferred from test accuracy alone. Our investigation reveals that the distribution of hard samples between training and test sets affects the difficulty levels of those sets, thereby influencing the perceived generalization capability of models. We unveil two distinct generalization pathways-toward easy and hard samples-highlighting the complexity of achieving balanced model evaluation. Finally, we propose a benchmarking procedure for comparing hard sample identification methods, facilitating the advancement of more nuanced approaches in this area. Our primary goal is not to propose a definitive solution but to highlight the limitations of relying primarily on test accuracy as an evaluation metric, even when working with balanced datasets, by introducing the in-class data imbalance problem. By doing so, we aim to stimulate a critical discussion within the research community and open new avenues for research that consider a broader spectrum of model evaluation criteria. The anonymous code is available at https://github.com/PawPuk/CurvBIM blueunder the GPL-3.0 license.

Supervised deep learning excels in the baffling task of disentangling the training data, so as to reach near-zero training error, while still achieving good accuracy on the classification of unseen data. How this feat is achieved, particularly in relation to the geometry and structure of the training data, is currently a topic of debate and partly still an open question [1-6]. Activations of hidden layers in response to input examples, i.e., the internal representations of the data, evolve during training to facilitate eventual linear separation in the last layer. This requires a gradual segregation of points belonging to different classes, in what can be pictured as a disentangling motion between their class manifolds. Segregation of class manifolds is a powerful conceptualisation that informs the design of distancebased losses in metric learning and contrastive learning [7-11] and underlies several approaches aimed at quantifying expressivity and generalisation, in artificial neural networks as well as in neuroscience [12-17]. Several recent efforts have leveraged this picture to characterise information processing along the layers of a deep network, particularly focusing on metrics such as intrinsic dimensionality and curvature [18-22]. In Ref. [19], for instance, two descriptors of manifold geometry, related to the intrinsic dimension and to the extension of the manifolds, are shown to undergo dramatic reduction as a result of training in deep convolutional neural networks. Such shrinking (together with intermanifold correlations, which we neglect in this manuscript) decisively supports the model's capacity in a memorisation task. Yet, this appears to be just one side of the coin.

The geometry of these class manifolds (CMs) is widely studied and intimately related to model performance; for example, the margin depends on CM boundaries. We exploit the notions of Gaussian width and Gordon's escape theorem to tractably estimate the effective dimension of CMs and their boundaries through tomographic intersections with random affine subspaces of varying dimension. We show several connections between the dimension of CMs, generalization, and robustness. In particular we investigate how CM dimension depends on 1) the dataset, 2) architecture (including ResNet, WideResNet & Vision Transformer), 3) initialization, 4) stage of training, 5) class, 6) network width, 7) ensemble size, 8) label randomization, 9) training set size, and 10) robustness to data corruption. Together a picture emerges that higher performing and more robust models have higher dimensional CMs. Moreover, we offer a new perspective on ensembling via intersections of CMs. Our code is on Github.

The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as vision and speech. Multiple methods have been proposed to explicitly incorporate the manifold hypothesis as a prior in modern Deep Neural Networks (DNNs), with varying success. In this paper, we propose a new method, Distance Learner, to incorporate this prior for DNN-based classifiers. Distance Learner is trained to predict the distance of a point from the underlying manifold of each class, rather than the class label. For classification, Distance Learner then chooses the class corresponding to the closest predicted class manifold. Distance Learner can also identify points as being out of distribution (belonging to neither class), if the distance to the closest manifold is higher than a threshold. We evaluate our method on multiple synthetic datasets and show that Distance Learner learns much more meaningful classification boundaries compared to a standard classifier. We also evaluate our method on the task of adversarial robustness, and find that it not only outperforms standard classifier by a large margin, but also performs at par with classifiers trained via state-of-the-art adversarial training.