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Related papers: Length Generalization Bounds for Transformers

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This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the…

Machine Learning · Computer Science 2023-10-17 Jingwen Fu , Nanning Zheng

In this paper, we propose a new covering technique localized for the trajectories of SGD. This localization provides an algorithm-specific complexity measured by the covering number, which can have dimension-independent cardinality in…

Machine Learning · Statistics 2022-09-20 Sejun Park , Umut Şimşekli , Murat A. Erdogdu

Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the…

Information Theory · Computer Science 2026-01-13 Qinshan Zhang , Bin Chen , Yong Jiang , Shu-Tao Xia

One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…

Machine Learning · Computer Science 2024-07-23 Chengli Tan , Jiangshe Zhang , Junmin Liu

Information-theoretic (IT) generalization bounds have been used to study the generalization of learning algorithms. These bounds are intrinsically data- and algorithm-dependent so that one can exploit the properties of data and algorithm to…

Machine Learning · Computer Science 2026-01-06 Ze Peng , Jian Zhang , Yisen Wang , Lei Qi , Yinghuan Shi , Yang Gao

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…

Disordered Systems and Neural Networks · Physics 2020-01-08 Francesco Borra , Marco Cosentino Lagomarsino , Pietro Rotondo , Marco Gherardi

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

Machine Learning · Computer Science 2025-05-09 Haiyun He , Ziv Goldfeld

We prove linear convergence of gradient descent to a global optimum for the training of deep residual networks with constant layer width and smooth activation function. We show that if the trained weights, as a function of the layer index,…

Machine Learning · Computer Science 2023-01-26 Rama Cont , Alain Rossier , RenYuan Xu

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…

Machine Learning · Computer Science 2020-08-06 Yuheng Bu , Shaofeng Zou , Venugopal V. Veeravalli

We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…

Machine Learning · Computer Science 2020-10-22 Nicolas Gontier , Koustuv Sinha , Siva Reddy , Christopher Pal

Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can…

Computation and Language · Computer Science 2020-06-03 Xingyuan Pan , Maitrey Mehta , Vivek Srikumar

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

Machine Learning · Computer Science 2023-05-16 Huayi Tang , Yong Liu

Whether language models can systematically generalize remains actively debated. Yet empirical performance is jointly shaped by multiple factors such as training data, training paradigms, and inference-time strategies, making failures…

Artificial Intelligence · Computer Science 2026-04-17 Yao Tong , Jiayuan Ye , Anastasia Borovykh , Reza Shokri

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…

Machine Learning · Statistics 2018-02-27 Fredrik D. Johansson , Nathan Kallus , Uri Shalit , David Sontag

In Transformers, Position Embeddings (PEs) significantly influence Length Generalization (LG) performance, yet their fundamental role remains unclear. In this work, we investigate the limitations and capabilities of PEs in achieving LG. We…

Machine Learning · Computer Science 2025-10-07 Yang Chen , Yitao Liang , Zhouchen Lin

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on…

Statistics Theory · Mathematics 2021-08-16 Arash Behboodi , Holger Rauhut , Ekkehard Schnoor

The generalization gap of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature.…

Machine Learning · Computer Science 2024-09-12 Mireille Boutin , Evzenie Coupkova

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…

Machine Learning · Computer Science 2015-03-17 Huan Xu , Shie Mannor

Despite the success of Transformers on language understanding, code generation, and logical reasoning, they still fail to generalize over length on basic arithmetic tasks such as addition and multiplication. A major reason behind this…

Machine Learning · Computer Science 2024-06-05 Mahdi Sabbaghi , George Pappas , Hamed Hassani , Surbhi Goel
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