Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of their inductive biases and how those biases differ from other neural network architectures remains elusive. In this work, we identify the sensitivity of the model to token-wise random perturbations in the input as a unified metric which explains the inductive bias of transformers across different data modalities and distinguishes them from other architectures. We show that transformers have lower sensitivity than MLPs, CNNs, ConvMixers and LSTMs, across both vision and language tasks. We also show that this low-sensitivity bias has important implications: i) lower sensitivity correlates with improved robustness; it can also be used as an efficient intervention to further improve the robustness of transformers; ii) it corresponds to flatter minima in the loss landscape; and iii) it can serve as a progress measure for grokking. We support these findings with theoretical results showing (weak) spectral bias of transformers in the NTK regime, and improved robustness due to the lower sensitivity.

Adam is the de facto optimization algorithm for several deep learning applications, but an understanding of its implicit bias and how it differs from other algorithms, particularly standard first-order methods such as (stochastic) gradient descent (GD), remains limited. In practice, neural networks (NNs) trained with SGD are known to exhibit simplicity bias --- a tendency to find simple solutions. In contrast, we show that Adam is more resistant to such simplicity bias. First, we investigate the differences in the implicit biases of Adam and GD when training two-layer ReLU NNs on a binary classification task with Gaussian data. We find that GD exhibits a simplicity bias, resulting in a linear decision boundary with a suboptimal margin, whereas Adam leads to much richer and more diverse features, producing a nonlinear boundary that is closer to the Bayes' optimal predictor. This richer decision boundary also allows Adam to achieve higher test accuracy both in-distribution and under certain distribution shifts. We theoretically prove these results by analyzing the population gradients. Next, to corroborate our theoretical findings, we present extensive empirical results showing that this property of Adam leads to superior generalization across various datasets with spurious correlations where NNs trained with SGD are known to show simplicity bias and do not generalize well under certain distributional shifts.

In recent research aimed at understanding the strong generalization performance of simple gradient-based methods on overparameterized models, it has been demonstrated that when training a linear predictor on separable data with an exponentially-tailed loss function, the predictor converges towards the max-margin classifier direction, explaining its resistance to overfitting asymptotically. Moreover, recent findings have shown that overfitting is not a concern even in finite-time scenarios (non-asymptotically), as finite-time generalization bounds have been derived for gradient flow, gradient descent (GD), and stochastic GD. In this work, we extend this line of research and obtain new finite-time generalization bounds for other popular first-order methods, namely normalized GD and Nesterov’s accelerated GD. Our results reveal that these methods, as they converge more rapidly in terms of training loss, also exhibit enhanced generalization performance in terms of test error.

Compressed sensing (CS) is extensively used to reduce magnetic resonance imaging (MRI) acquisition time. State-of-the-art deep learning-based methods have proven effective in obtaining fast, high-quality reconstruction of CS-MR images. However, they treat the inherently complex-valued MRI data as real-valued entities by extracting the magnitude content or concatenating the complex-valued data as two real-valued channels for processing. In both cases, the phase content is discarded. To address the fundamental problem of real-valued deep networks, i.e. their inability to process complex-valued data, we propose a complex-valued generative adversarial network (Co-VeGAN) framework, which is the first-of-its-kind generative model exploring the use of complex-valued weights and operations. Further, since real-valued activation functions do not generalize well to the complex-valued space, we propose a novel complex-valued activation function that is sensitive to the input phase and has a learnable profile. Extensive evaluation of the proposed approach1on different datasets demonstrates that it significantly outperforms the existing CS-MRI reconstruction techniques.

Deep metric learning has been effectively used to learn distance metrics for different visual tasks like image retrieval, clustering, etc. In order to aid the training process, existing methods either use a hard mining strategy to extract the most informative samples or seek to generate hard synthetics using an additional network. Such approaches face different challenges and can lead to biased embeddings in the former case, and (i) harder optimization (ii) slower training speed (iii) higher model complexity in the latter case. In order to overcome these challenges, we propose a novel approach that looks for optimal hard negatives (LoOp) in the embedding space, taking full advantage of each tuple by calculating the minimum distance between a pair of positives and a pair of negatives. Unlike mining-based methods, our approach considers the entire space between pairs of embeddings to calculate the optimal hard negatives. Extensive experiments combining our approach and representative metric learning losses reveal a significant boost in performance on three benchmark datasets1.