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A general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for…

Machine Learning · Statistics 2020-01-29 Daniel Krefl , Stefano Carrazza , Babak Haghighat , Jens Kahlen

The concept of conditional computation for deep nets has been proposed previously to improve model performance by selectively using only parts of the model conditioned on the sample it is processing. In this paper, we investigate…

Computer Vision and Pattern Recognition · Computer Science 2019-04-02 Zhourong Chen , Yang Li , Samy Bengio , Si Si

We introduce a new method for training deep Boltzmann machines jointly. Prior methods of training DBMs require an initial learning pass that trains the model greedily, one layer at a time, or do not perform well on classification tasks. In…

Machine Learning · Statistics 2013-05-02 Ian J. Goodfellow , Aaron Courville , Yoshua Bengio

We introduce a Deep Boltzmann Machine model suitable for modeling and extracting latent semantic representations from a large unstructured collection of documents. We overcome the apparent difficulty of training a DBM with judicious…

Machine Learning · Computer Science 2013-09-27 Nitish Srivastava , Ruslan R Salakhutdinov , Geoffrey E. Hinton

Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have…

Machine Learning · Computer Science 2026-03-13 Rajdeep Pathak , Rahul Goswami , Madhurima Panja , Palash Ghosh , Tanujit Chakraborty

The functions of proteins and RNAs are determined by a myriad of interactions between their constituent residues, but most quantitative models of how molecular phenotype depends on genotype must approximate this by simple additive effects.…

Quantitative Methods · Quantitative Biology 2017-12-19 Adam J. Riesselman , John B. Ingraham , Debora S. Marks

The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space…

Machine Learning · Computer Science 2026-03-03 Han Guo , Songlin Yang , Tarushii Goel , Eric P. Xing , Tri Dao , Yoon Kim

Transformer models have recently attracted much interest from computer vision researchers and have since been successfully employed for several problems traditionally addressed with convolutional neural networks. At the same time, image…

Computer Vision and Pattern Recognition · Computer Science 2021-07-13 Ricard Durall , Stanislav Frolov , Jörn Hees , Federico Raue , Franz-Josef Pfreundt , Andreas Dengel , Janis Keupe

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

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the…

Machine Learning · Computer Science 2024-01-30 Tokio Kajitsuka , Issei Sato

Modern autoregressive models rely on attention, yet the Softmax full attention in Transformers scales quadratically with sequence length. Sliding Window Attention (SWA) achieves linear-time encoding/decoding by constraining the attention…

Machine Learning · Computer Science 2026-01-08 Jiaxu Liu , Yuhe Bai , Xiangyu Yin , Christos-Savvas Bouganis

Many studies have been conducted to improve the efficiency of Transformer from quadric to linear. Among them, the low-rank-based methods aim to learn the projection matrices to compress the sequence length. However, the projection matrices…

Machine Learning · Computer Science 2022-11-30 Bosheng Qin , Juncheng Li , Siliang Tang , Yueting Zhuang

Deep Boltzmann machines (DBMs), one of the first ``deep'' learning methods ever studied, are multi-layered probabilistic models governed by a pairwise energy function that describes the likelihood of all variables/nodes in the network. In…

Machine Learning · Computer Science 2023-07-12 Zhili Feng , Ezra Winston , J. Zico Kolter

Molecular structure-property relationships are key to molecular engineering for materials and drug discovery. The rise of deep learning offers a new viable solution to elucidate the structure-property relationships directly from chemical…

Machine Learning · Computer Science 2018-10-09 Seongok Ryu , Jaechang Lim , Seung Hwan Hong , Woo Youn Kim

We introduce the Genetic-Gated Networks (G2Ns), simple neural networks that combine a gate vector composed of binary genetic genes in the hidden layer(s) of networks. Our method can take both advantages of gradient-free optimization and…

Neural and Evolutionary Computing · Computer Science 2019-03-06 Simyung Chang , John Yang , Jaeseok Choi , Nojun Kwak

\textit{Attention} computes the dependency between representations, and it encourages the model to focus on the important selective features. Attention-based models, such as Transformer and graph attention network (GAT), are widely utilized…

Machine Learning · Computer Science 2021-03-02 Kyungwoo Song , Yohan Jung , Dongjun Kim , Il-Chul Moon

There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…

Machine Learning · Computer Science 2025-07-04 Yu-Hsiang Lan , Eric K. Oermann

Attention mechanisms, particularly softmax attention, have been instrumental in the success of transformer-based models such as GPT. However, the quadratic memory complexity of softmax attention with respect to sequence length poses…

Machine Learning · Computer Science 2026-02-20 Gabriel Mongaras , Trevor Dohm , Eric C. Larson

Learning representations of molecular structures using deep learning is a fundamental problem in molecular property prediction tasks. Molecules inherently exist in the real world as three-dimensional structures; furthermore, they are not…

Machine Learning · Computer Science 2024-01-22 Daiki Koge , Naoaki Ono , Shigehiko Kanaya

The Transformer architecture has significantly advanced deep learning, particularly in natural language processing, by effectively managing long-range dependencies. However, as the demand for understanding complex relationships grows,…

Computation and Language · Computer Science 2024-06-18 Qian Chen , Wen Wang , Qinglin Zhang , Siqi Zheng , Shiliang Zhang , Chong Deng , Hai Yu , Jiaqing Liu , Yukun Ma , Chong Zhang