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Reasoning is an integral part of many tasks performed by language models (LMs). However, the effects of scaling model sizes and data on reasoning abilities at pretraining time remain understudied. To rigorously investigate this problem, we…

Artificial Intelligence · Computer Science 2025-09-30 Xinyi Wang , Shawn Tan , Shenbo Xu , Mingyu Jin , William Yang Wang , Rameswar Panda , Yikang Shen

Associative memory, traditionally modeled by Hopfield networks, enables the retrieval of previously stored patterns from partial or noisy cues. Yet, the local computational principles which are required to enable this function remain…

Transformers use the dense self-attention mechanism which gives a lot of flexibility for long-range connectivity. Over multiple layers of a deep transformer, the number of possible connectivity patterns increases exponentially. However,…

Machine Learning · Computer Science 2023-06-05 Md Shamim Hussain , Mohammed J. Zaki , Dharmashankar Subramanian

Scientific research faces high costs and inefficiencies with traditional methods, but the rise of deep learning and large language models (LLMs) offers innovative solutions. This survey reviews transformer-based LLM applications across…

Machine Learning · Computer Science 2025-09-16 Kaiyuan Tian , Linbo Qiao , Baihui Liu , Gongqingjian Jiang , Shanshan Li , Dongsheng Li

Transformer-based architectures have been the subject of research aimed at understanding their overparameterization and the non-uniform importance of their layers. Applying these approaches to Automatic Speech Recognition, we demonstrate…

Machine Learning · Computer Science 2022-02-07 Lillian Zhou , Dhruv Guliani , Andreas Kabel , Giovanni Motta , Françoise Beaufays

Transformer architecture has become ubiquitous in the natural language processing field. To interpret the Transformer-based models, their attention patterns have been extensively analyzed. However, the Transformer architecture is not only…

Computation and Language · Computer Science 2021-09-16 Goro Kobayashi , Tatsuki Kuribayashi , Sho Yokoi , Kentaro Inui

Deep neural networks have been successful in many reinforcement learning settings. However, compared to human learners they are overly data hungry. To build a sample-efficient world model, we apply a transformer to real-world episodes in an…

Machine Learning · Computer Science 2023-03-14 Jan Robine , Marc Höftmann , Tobias Uelwer , Stefan Harmeling

The transformer is the most popular neural architecture for language modeling. The cornerstone of the transformer is its global attention mechanism, which lets the model aggregate information from all preceding tokens before generating the…

Computation and Language · Computer Science 2026-05-20 Jiaoda Li , Ryan Cotterell

It is widely acknowledged that the performance of Transformer models is logarithmically related to their number of parameters and computational complexity. While approaches like Mixture of Experts (MoE) decouple parameter count from…

Machine Learning · Computer Science 2025-02-07 Zihao Huang , Qiyang Min , Hongzhi Huang , Defa Zhu , Yutao Zeng , Ran Guo , Xun Zhou

Adaptive optimizers, most notably Adam, have become the default standard for training large-scale neural networks such as Transformers. These methods maintain running estimates of gradient first and second moments, incurring substantial…

Machine Learning · Computer Science 2026-05-12 Yao Lu , Dengdong Fan , Shixun Zhang , Yonghong Tian

Understanding the fundamental mechanism behind the success of transformer networks is still an open problem in the deep learning literature. Although their remarkable performance has been mostly attributed to the self-attention mechanism,…

Machine Learning · Computer Science 2022-11-23 Tolga Ergen , Behnam Neyshabur , Harsh Mehta

Neural networks encounter the challenge of Catastrophic Forgetting (CF) in continual learning, where new task learning interferes with previously learned knowledge. Existing data fine-tuning and regularization methods necessitate task…

Machine Learning · Computer Science 2024-05-17 Yuwei Sun , Ippei Fujisawa , Arthur Juliani , Jun Sakuma , Ryota Kanai

Transformer networks, driven by self-attention, are central to Large Language Models. In generative Transformers, self-attention uses cache memory to store token projections, avoiding recomputation at each time step. However, GPU-stored…

Neural and Evolutionary Computing · Computer Science 2024-11-26 Nathan Leroux , Paul-Philipp Manea , Chirag Sudarshan , Jan Finkbeiner , Sebastian Siegel , John Paul Strachan , Emre Neftci

Training Transformer language models is expensive, as performance typically improves with increasing dataset size and computational budget. Although scaling laws describe this trend at large scale, their implications in controlled,…

An essential component of modern recurrent sequence models is the forget gate. While Transformers do not have an explicit recurrent form, we show that a forget gate can be naturally incorporated into Transformers by down-weighting the…

Machine Learning · Computer Science 2025-04-02 Zhixuan Lin , Evgenii Nikishin , Xu Owen He , Aaron Courville

Transformer-based deep learning models have achieved state-of-the-art performance across numerous language and vision tasks. While the self-attention mechanism, a core component of transformers, has proven capable of handling complex data…

Machine Learning · Computer Science 2025-08-05 Laziz Abdullaev , Tan M. Nguyen

Recent studies have put into question the belief that emergent abilities in language models are exclusive to large models. This skepticism arises from two observations: 1) smaller models can also exhibit high performance on emergent…

Computation and Language · Computer Science 2025-01-16 Zhengxiao Du , Aohan Zeng , Yuxiao Dong , Jie Tang

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…

Machine Learning · Computer Science 2026-03-04 Linyan Gu , Lihua Yang , Feng Zhou

The Hopfield model provides a mathematically idealized yet insightful framework for understanding the mechanisms of memory storage and retrieval in the human brain. This model has inspired four decades of extensive research on learning and…

Neurons and Cognition · Quantitative Biology 2025-05-14 Simone Betteti , Giacomo Baggio , Francesco Bullo , Sandro Zampieri

Recent studies point to the potential storage of a large number of patterns in the celebrated Hopfield associative memory model, well beyond the limits obtained previously. We investigate the properties of new fixed points to discover that…

Disordered Systems and Neural Networks · Physics 2017-11-22 Jacopo Rocchi , David Saad , Daniele Tantari