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Related papers: Grokking Modular Polynomials

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Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…

Machine Learning · Computer Science 2018-06-08 Samet Oymak

Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on heterophilic graphs, where connected nodes have…

Machine Learning · Computer Science 2021-12-08 Vijay Lingam , Chanakya Ekbote , Manan Sharma , Rahul Ragesh , Arun Iyer , Sundararajan Sellamanickam

For most deep learning algorithms training is notoriously time consuming. Since most of the computation in training neural networks is typically spent on floating point multiplications, we investigate an approach to training that eliminates…

Machine Learning · Computer Science 2016-02-29 Zhouhan Lin , Matthieu Courbariaux , Roland Memisevic , Yoshua Bengio

This paper considers the learning of logical (Boolean) functions with a focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial…

Machine Learning · Computer Science 2024-11-21 Emmanuel Abbe , Samy Bengio , Aryo Lotfi , Kevin Rizk

Markov Logic Networks (MLNs) are well-suited for expressing statistics such as "with high probability a smoker knows another smoker" but not for expressing statements such as "there is a smoker who knows most other smokers", which is…

Artificial Intelligence · Computer Science 2018-08-22 Víctor Gutiérrez-Basulto , Jean Christoph Jung , Ondrej Kuzelka

Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill…

Machine Learning · Computer Science 2024-11-05 Tianyu He , Darshil Doshi , Aritra Das , Andrey Gromov

We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…

Disordered Systems and Neural Networks · Physics 2007-05-23 Leonardo Franco

Empirically, neural networks that attempt to learn programs from data have exhibited poor generalizability. Moreover, it has traditionally been difficult to reason about the behavior of these models beyond a certain level of input…

Machine Learning · Computer Science 2017-04-24 Jonathon Cai , Richard Shin , Dawn Song

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…

Machine Learning · Statistics 2017-10-05 Chihiro Watanabe , Kaoru Hiramatsu , Kunio Kashino

Grokking is a phenomenon where a model trained on an algorithmic task first overfits but, then, after a large amount of additional training, undergoes a phase transition to generalize perfectly. We empirically study the internal structure…

Machine Learning · Computer Science 2023-03-22 William Merrill , Nikolaos Tsilivis , Aman Shukla

Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…

Machine Learning · Computer Science 2018-02-06 Amir Rosenfeld , John K. Tsotsos

Training convolutional neural networks (CNNs) with back-propagation (BP) is time-consuming and resource-intensive particularly in view of the need to visit the dataset multiple times. In contrast, analytic learning attempts to obtain the…

Computer Vision and Pattern Recognition · Computer Science 2022-02-15 Huiping Zhuang , Zhiping Lin , Yimin Yang , Kar-Ann Toh

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this…

Machine Learning · Computer Science 2020-08-21 Tao Li , Vivek Srikumar

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current…

Machine Learning · Computer Science 2019-11-11 Vardaan Pahuja , Jie Fu , Sarath Chandar , Christopher J. Pal

We introduce three memory-augmented Recurrent Neural Networks (MARNNs) and explore their capabilities on a series of simple language modeling tasks whose solutions require stack-based mechanisms. We provide the first demonstration of neural…

Computation and Language · Computer Science 2019-11-11 Mirac Suzgun , Sebastian Gehrmann , Yonatan Belinkov , Stuart M. Shieber

Deep neural networks achieve stellar generalisation on a variety of problems, despite often being large enough to easily fit all their training data. Here we study the generalisation dynamics of two-layer neural networks in a…

Machine Learning · Statistics 2019-06-21 Sebastian Goldt , Madhu S. Advani , Andrew M. Saxe , Florent Krzakala , Lenka Zdeborová

The optimization problem behind neural networks is highly non-convex. Training with stochastic gradient descent and variants requires careful parameter tuning and provides no guarantee to achieve the global optimum. In contrast we show…

Machine Learning · Computer Science 2016-10-31 Antoine Gautier , Quynh Nguyen , Matthias Hein

A major challenge in the use of neural networks both for modeling human cognitive function and for artificial intelligence is the design of systems with the capacity to efficiently learn functions that support radical generalization. At the…

Machine Learning · Computer Science 2025-07-17 Cutter Dawes , Simon Segert , Kamesh Krishnamurthy , Jonathan D. Cohen

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

Machine Learning · Computer Science 2025-09-17 Marcio Nicolau , Anderson R. Tavares , Zhiwei Zhang , Pedro Avelar , João M. Flach , Luis C. Lamb , Moshe Y. Vardi

We introduce a new dataset of logical entailments for the purpose of measuring models' ability to capture and exploit the structure of logical expressions against an entailment prediction task. We use this task to compare a series of…

Neural and Evolutionary Computing · Computer Science 2018-02-26 Richard Evans , David Saxton , David Amos , Pushmeet Kohli , Edward Grefenstette