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Related papers: Outlier-Efficient Hopfield Layers for Large Transf…

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Transformer models have been widely adopted in various domains over the last years, and especially large language models have advanced the field of AI significantly. Due to their size, the capability of these networks has increased…

Machine Learning · Computer Science 2023-11-10 Yelysei Bondarenko , Markus Nagel , Tijmen Blankevoort

Out-of-distribution (OOD) detection is critical when deploying machine learning models in the real world. Outlier exposure methods, which incorporate auxiliary outlier data in the training process, can drastically improve OOD detection…

Machine Learning · Computer Science 2025-01-09 Claus Hofmann , Simon Schmid , Bernhard Lehner , Daniel Klotz , Sepp Hochreiter

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one…

We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…

Machine Learning · Computer Science 2024-06-04 Jerry Yao-Chieh Hu , Thomas Lin , Zhao Song , Han Liu

We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval…

Machine Learning · Statistics 2025-06-10 Jerry Yao-Chieh Hu , Bo-Yu Chen , Dennis Wu , Feng Ruan , Han Liu

Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…

Machine Learning · Computer Science 2025-04-11 Saul Santos , António Farinhas , Daniel C. McNamee , André F. T. Martins

Associative memory models are content-addressable memory systems fundamental to biological intelligence and are notable for their high interpretability. However, existing models evaluate the quality of retrieval based on proximity, which…

Machine Learning · Computer Science 2025-11-26 Shurong Wang , Yuqi Pan , Zhuoyang Shen , Meng Zhang , Hongwei Wang , Guoqi Li

The Hopfield model is a pioneering neural network model with associative memory retrieval. The analytical solution of the model in mean field limit revealed that memories can be retrieved without any error up to a finite storage capacity of…

Disordered Systems and Neural Networks · Physics 2017-10-31 Do-Hyun Kim , Jinha Park , B. Kahng

Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…

Machine Learning · Computer Science 2024-12-02 Xueyan Niu , Bo Bai , Lei Deng , Wei Han

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

Hadamard transforms have become a key tool for stabilizing low-precision training, but existing methods apply them uniformly across tensors and computation paths. We show that this one-size-fits-all strategy is inherently limited: Hadamard…

Machine Learning · Computer Science 2026-05-11 Seonggon Kim , Alireza Khodamoradi , Pranathi Vasireddy , Kristof Denolf , Eunhyeok Park

Associative memory models based on Hopfield networks and self-attention based on key-value mechanisms have been popular approaches in the study of memory mechanisms in deep learning. It has been pointed out that the state update rule of the…

Machine Learning · Computer Science 2025-11-27 Tsubasa Masumura , Masato Taki

We propose and analyze a new variation of the so-called {\em exponential Hopfield model}, a recently introduced family of associative neural networks with unprecedented storage capacity. Our construction is based on a cost function defined…

Disordered Systems and Neural Networks · Physics 2025-09-09 Linda Albanese , Andrea Alessandrelli , Adriano Barra , Peter Sollich

We propose a two-stage memory retrieval dynamics for modern Hopfield models, termed $\mathtt{U\text{-}Hop}$, with enhanced memory capacity. Our key contribution is a learnable feature map $\Phi$ which transforms the Hopfield energy function…

Machine Learning · Computer Science 2024-11-12 Dennis Wu , Jerry Yao-Chieh Hu , Teng-Yun Hsiao , Han Liu

Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…

Neural and Evolutionary Computing · Computer Science 2017-07-26 Huiling Zhen , Shang-Nan Wang , Hai-Jun Zhou

Outlier detection (OD) has received continuous research interests due to its wide applications. With the development of deep learning, increasingly deep OD algorithms are proposed. Despite the availability of numerous deep OD models,…

Machine Learning · Computer Science 2023-05-29 Yihong Huang , Yuang Zhang , Liping Wang , Xuemin Lin

Outlier detection (OD) literature exhibits numerous algorithms as it applies to diverse domains. However, given a new detection task, it is unclear how to choose an algorithm to use, nor how to set its hyperparameter(s) (HPs) in…

Machine Learning · Computer Science 2022-10-20 Xueying Ding , Lingxiao Zhao , Leman Akoglu

Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…

Disordered Systems and Neural Networks · Physics 2024-06-12 Ángel Poc-López , Miguel Aguilera

Our work combines aspects of three promising paradigms in machine learning, namely, attention mechanism, energy-based models, and associative memory. Attention is the power-house driving modern deep learning successes, but it lacks clear…

Outlier detection is one of the most important processes taken to create good, reliable data in machine learning. The most methods of outlier detection leverage an auxiliary reconstruction task by assuming that outliers are more difficult…

Computer Vision and Pattern Recognition · Computer Science 2022-11-23 Ning Huyan , Dou Quan , Xiangrong Zhang , Xuefeng Liang , Jocelyn Chanussot , Licheng Jiao
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