The capacity of deep learning models is often large enough to both learn the underlying statistical signal and overfit to noise in the training set. This noise memorization can be harmful especially for data with a low signal-to-noise ratio (SNR), leading to poor generalization. Inspired by prior observations that label noise provides implicit regularization that improves generalization, in this work, we investigate whether introducing label noise to the gradient updates can enhance the test performance of neural network (NN) in the low SNR regime. Specifically, we consider training a two-layer NN with a simple label noise gradient descent (GD) algorithm, in an idealized signal-noise data setting. We prove that adding label noise during training suppresses noise memorization, preventing it from dominating the learning process; consequently, label noise GD enjoys rapid signal growth while the overfitting remains controlled, thereby achieving good generalization despite the low SNR. In contrast, we also show that NN trained with standard GD tends to overfit to noise in the same low SNR setting and establish a non-vanishing lower bound on its test error, thus demonstrating the benefit of introducing label noise in gradient-based training.

We demonstrate that architectures which traditionally are considered to be ill-suited for a task can be trained using inductive biases from another architecture. We call a network untrainable when it overfits, underfits, or converges to poor results even when tuning their hyperparameters. For example, fully connected networks overfit on object recognition while deep convolutional networks without residual connections underfit. The traditional answer is to change the architecture to impose some inductive bias, although the nature of that bias is unknown. We introduce guidance, where a guide network steers a target network using a neural distance function.

Advancements in AI for science unlocks capabilities for critical drug discovery tasks such as protein-ligand binding affinity prediction. However, current models overfit to existing oversimplified datasets that does not represent naturally occurring and biologically relevant proteins with modifications. In this work, we curate a complete and modification-aware version of the widely used DAVIS dataset by incorporating 4,032 kinase-ligand pairs involving substitutions, insertions, deletions, and phosphorylation events. This enriched dataset enables benchmarking of predictive models under biologically realistic conditions. Based on this new dataset, we propose three benchmark settings--Augmented Dataset Prediction, Wild-Type to Modification Generalization, and Few-Shot Modification Generalization--designed to assess model robustness in the presence of protein modifications. Through extensive evaluation of both docking-free and docking-based methods, we find that docking-based model generalize better in zero-shot settings. In contrast, docking-free models tend to overfit to wild-type proteins and struggle with unseen modifications but show notable improvement when fine-tuned on a small set of modified examples. We anticipate that the curated dataset and benchmarks offer a valuable foundation for developing models that better generalize to protein modifications, ultimately advancing precision medicine in drug discovery.

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Autoencoders (AE) aim to reproduce the output from the input. They may hence tend to overfit towards learning the identity-function between the input and output, i.e., they may predict each feature in the output from itself in the input. This is not useful, however, when AEs are used for prediction tasks in the presence of noise in the data. It may seem intuitively evident that this kind of overfitting is prevented by training a denoising AE, as the dropped-out features have to be predicted from the other features. In this paper, we consider linear autoencoders, as they facilitate analytic solutions, and first show that denoising / dropout actually prevents the overfitting towards the identity-function only to the degree that it is penalized by the induced L2-norm regularization. In the main theorem of this paper, we show that the emphasized denoising AE is indeed capable of completely eliminating the overfitting towards the identity-function. Our derivations reveal several new insights, including the closed-form solution of the full-rank model, as well as a new (near-)orthogonality constraint in the low-rank model. While this constraint is conceptually very different from the regularizers recently proposed, their resulting effects on the learned embeddings are empirically similar. Our experiments on three well-known data-sets corroborate the various theoretical insights derived in this paper.

We pay special attention to the setting where the sample size n is small. This type of tests carries concrete significance in scientific studies.