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.

Understanding neural network's (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches a near-perfect level, offers a unique window to investigate the underlying mechanisms of NNs' generalizability. Here we propose an interpretation for grokking by framing it as a computational glass relaxation: viewing NNs as a physical system where parameters are the degrees of freedom and train loss is the system energy, we find memorization process resembles a rapid cooling of liquid into non-equilibrium glassy state at low temperature and the later generalization is like a slow relaxation towards a more stable configuration. This mapping enables us to sample NNs' Boltzmann entropy (density of states) landscape as a function of training loss and test accuracy.

When do diffusion models reproduce their training data, and when are they able to generate samples beyond it?

Learning rate is widely regarded as crucial for effective foundation model pretraining. Recent research explores and demonstrates the transferability of learning rate configurations across varying model and dataset sizes, etc. Nevertheless, these approaches are constrained to specific training scenarios and typically necessitate extensive hyperparameter tuning on proxy models. In this work, we propose AdaLRS, a plug-in-and-play adaptive learning rate search algorithm that conducts online optimal learning rate search via optimizing loss descent velocities. We provide theoretical and experimental analyzes to show that foundation model pretraining loss and its descent velocity are both convex and share the same optimal learning rate. Relying solely on training loss dynamics, AdaLRS involves few extra computations to guide the search process, and its convergence is guaranteed via theoretical analysis. Experiments on both LLM and VLM pretraining show that AdaLRS adjusts suboptimal learning rates to the neighborhood of optimum with marked efficiency and effectiveness, with model performance improved accordingly. We also show the robust generalizability of AdaLRS across varying training scenarios, such as different model sizes, training paradigms, base learning rate scheduler choices, and hyperparameter settings.

Transformers have become the de facto architecture for a wide range of machine learning tasks, particularly in large language models (LLMs). Despite their remarkable performance, many challenges remain in training deep transformer networks, especially regarding the position of the layer normalization. While Pre-Norm structures facilitate more stable training owing to their stronger identity path, they often lead to suboptimal performance compared to Post-Norm. In this paper, we propose HybridNorm, a simple yet effective hybrid normalization strategy that integrates the advantages of both Pre-Norm and Post-Norm. Specifically, HybridNorm employs QKV normalization within the attention mechanism and Post-Norm in the feed-forward network (FFN) of each transformer block. We provide both theoretical insights and empirical evidence to demonstrate that HybridNorm improves the gradient flow and the model robustness. Extensive experiments on large-scale transformer models, including both dense and sparse variants, show that HybridNorm consistently outperforms both Pre-Norm and Post-Norm approaches across multiple benchmarks.

Generative Flow Networks (GFlowNets) learn to sample states proportional to an unnormalized reward. Despite their theoretical promise, practical training is often unstable, exhibiting severe loss spikes and mode collapse. To tackle this, we first assess the sensitivity of GFlowNet objectives, demonstrating that a small Total Variation (TV) distance between the learned and target distributions does not preclude unbounded training loss. Motivated by this mismatch, we establish converse guarantees by deriving loss-to-TV bounds that certify global fidelity from bounded trajectory balance losses. Lastly, we propose Stable GFlowNets, an algorithm that leverages our theoretical results to stabilize training, and empirically demonstrate improved training behavior and superior distributional fidelity.

What can linearized neural networks actually say about generalization? As mentioned in the main text, all our models are trained using the same scheme which was selected without any hyperparameter tuning, besides ensuring a good performance on CIFAR2 for the neural networks. Namely, we train using stochastic gradient descent (SGD) to optimize a binary crossentropy loss, with a decaying learning rate starting at 0.05 and momentum set to 0.9. Furthermore, we use a batch size of 128and train for a 100epochs. This is enough to obtain close-to-zero training losses for the neural networks, and converge to a stable test accuracy in the case of the linearized models1.