Related papers: Normalization Layer Per-Example Gradients are Suff…

The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are…

In this paper we show that simple noise regularisation can be an effective way to address GNN oversmoothing. First we argue that regularisers addressing oversmoothing should both penalise node latent similarity and encourage meaningful node…

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit…

Adversarially robust models are locally smooth around each data sample so that small perturbations cannot drastically change model outputs. In modern systems, such smoothness is usually obtained via Adversarial Training, which explicitly…

Adversarial training is the most successful empirical method for increasing the robustness of neural networks against adversarial attacks. However, the most effective approaches, like training with Projected Gradient Descent (PGD) are…

Recently, DeepNorm scales Transformers into extremely deep (i.e., 1000 layers) and reveals the promising potential of deep scaling. To stabilize the training of deep models, DeepNorm (Wang et al., 2022) attempts to constrain the model…

Sparse auto-encoders are useful for extracting low-dimensional representations from high-dimensional data. However, their performance degrades sharply when the input noise at test time differs from the noise employed during training. This…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Building on our prior explorations of convolutional neural networks (CNNs) for financial data processing, this paper introduces two significant enhancements to refine our CNN model's predictive performance and robustness for financial…

In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schr\"odinger equation). In this paper, we aim to reduce the generalization error without…

Over-parameterized deep neural networks trained by simple first-order methods are known to be able to fit any labeling of data. Such over-fitting ability hinders generalization when mislabeled training examples are present. On the other…

Transformers trained in low precision can suffer forward-error amplification. We give a first-order, module-wise theory that predicts when and where errors grow. For self-attention we derive a per-layer bound that factorizes into three…

Embedding layers in transformer-based NLP models typically account for the largest share of model parameters, scaling with vocabulary size but not yielding performance gains proportional to scale. We propose an alternative approach in which…

Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of…

Fine-tuning over large pretrained language models (PLMs) has established many state-of-the-art results. Despite its superior performance, such fine-tuning can be unstable, resulting in significant variance in performance and potential risks…

Large language models (LLMs) have transformed natural-language processing, yet their scale makes real-world deployment costly. Post-training quantization reduces memory and computation but often degrades accuracy, while quantization-aware…

Gradient clipping has long been considered essential for ensuring the convergence of Stochastic Gradient Descent (SGD) in the presence of heavy-tailed gradient noise. In this paper, we revisit this belief and explore whether gradient…

Solid results from Transformers have made them prevailing architectures in various natural language and vision tasks. As a default component in Transformers, Layer Normalization (LN) normalizes activations within each token to boost the…

Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple,…

Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…