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In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

Numerical Analysis · Mathematics 2026-03-04 Alexander Keller , Frances Y. Kuo , Dirk Nuyens , Ian H. Sloan

Pretraining large language models (LLMs) with next-token prediction has led to remarkable advances, yet the context-dependent nature of token embeddings in such models results in high intra-class variance and inter-class similarity, thus…

Computation and Language · Computer Science 2026-05-12 Yan Sun , Guoxia Wang , Jinle Zeng , JiaBin Yang , Shuai Li , Li Shen , Dacheng Tao , DianHai Yu , Haifeng Wang

Deep neural networks are learning models with a very high capacity and therefore prone to over-fitting. Many regularization techniques such as Dropout, DropConnect, and weight decay all attempt to solve the problem of over-fitting by…

Machine Learning · Computer Science 2016-12-06 Armen Aghajanyan

Language models with the Transformers structure have shown great performance in natural language processing. However, there still poses problems when fine-tuning pre-trained language models on downstream tasks, such as over-fitting or…

Computation and Language · Computer Science 2023-05-12 Hongyi Yuan , Zheng Yuan , Chuanqi Tan , Fei Huang , Songfang Huang

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…

Machine Learning · Computer Science 2024-06-05 Hongkang Li , Meng Wang , Tengfei Ma , Sijia Liu , Zaixi Zhang , Pin-Yu Chen

Vision Transformer (ViT) and its variants (e.g., Swin, PVT) have achieved great success in various computer vision tasks, owing to their capability to learn long-range contextual information. Layer Normalization (LN) is an essential…

Computer Vision and Pattern Recognition · Computer Science 2022-10-17 Wenqi Shao , Yixiao Ge , Zhaoyang Zhang , Xuyuan Xu , Xiaogang Wang , Ying Shan , Ping Luo

Deep neural networks struggle to continually learn multiple sequential tasks due to catastrophic forgetting of previously learned tasks. Rehearsal-based methods which explicitly store previous task samples in the buffer and interleave them…

Machine Learning · Computer Science 2022-07-12 Prashant Bhat , Bahram Zonooz , Elahe Arani

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences,…

Machine Learning · Computer Science 2020-06-16 Sinong Wang , Belinda Z. Li , Madian Khabsa , Han Fang , Hao Ma

Transformer-based architectures achieve state-of-the-art performance across a wide range of tasks in natural language processing, computer vision, and speech processing. However, their immense capacity often leads to overfitting, especially…

Computer Vision and Pattern Recognition · Computer Science 2025-09-22 Mirza Samad Ahmed Baig , Syeda Anshrah Gillani , Abdul Akbar Khan , Shahid Munir Shah , Muhammad Omer Khan

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear…

Computer Vision and Pattern Recognition · Computer Science 2023-09-04 Dongchen Han , Xuran Pan , Yizeng Han , Shiji Song , Gao Huang

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…

Computation and Language · Computer Science 2025-05-06 Henry Ndubuaku , Mouad Talhi

Sound classification models' performance suffers from generalizing on out-of-distribution (OOD) data. Numerous methods have been proposed to help the model generalize. However, most either introduce inference overheads or focus on…

Sound · Computer Science 2023-07-20 Honglin Mu , Wentian Xia , Wanxiang Che

Transformer models typically calculate attention matrices using dot products, which have limitations when capturing nonlinear relationships between embedding vectors. We propose Neural Attention, a technique that replaces dot products with…

Machine Learning · Computer Science 2025-11-10 Andrew DiGiugno , Ausif Mahmood

Large-scale transformers achieve impressive results on program synthesis benchmarks, yet their true generalization capabilities remain obscured by data contamination and opaque training corpora. To rigorously assess whether models are truly…

Machine Learning · Computer Science 2026-05-01 Henrik Voigt , Michael Habeck , Joachim Giesen

Noise is ubiquitous in data used to train large language models, but it is not well understood whether these models are able to correctly generalize to inputs generated without noise. Here, we study noise-robust learning: are transformers…

Machine Learning · Computer Science 2026-02-10 Evan Peters , Ando Deng , Matheus H. Zambianco , Devin Blankespoor , Achim Kempf

We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In…

Machine Learning · Computer Science 2026-04-09 Chris Kolb , Christian L. Müller , Bernd Bischl , David Rügamer

Smoothness is a key inductive bias in machine learning and is closely related to generalization. Existing smoothness-inducing methods typically rely either on explicit gradient regularization, which often incurs substantial computational…

Machine Learning · Computer Science 2026-05-11 Parsa Moradi , Tayyebeh Jahaninezhad , Hanzaleh Akbarinodehi , Mohammad Ali Maddah-Ali

We study the effect of normalization schemes on token representations in deep transformers. Modeling their evolution as interacting particles on the sphere, we show that normalization acts as a form of speed regulation. This perspective…

Machine Learning · Computer Science 2025-11-12 Nikita Karagodin , Shu Ge , Yury Polyanskiy , Philippe Rigollet

Many sequence-to-sequence tasks in natural language processing are roughly monotonic in the alignment between source and target sequence, and previous work has facilitated or enforced learning of monotonic attention behavior via specialized…

Computation and Language · Computer Science 2021-04-09 Annette Rios , Chantal Amrhein , Noëmi Aepli , Rico Sennrich

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means…

Machine Learning · Computer Science 2025-05-28 Hemanth Saratchandran , Damien Teney , Simon Lucey