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ARXIV:2606.06772 · DEEP LEARNING THEORY · SUBMITTED 08 JUN · 20:22 UTC · FRESHNESS FRESH
ARXIV:2606.06772DEEP LEARNING THEORYSUBMITTED 08 JUN · 20:22 UTCFRESHNESS FRESHJunyu Zhou · Puyu Wang · Yunwen Lei · Marius Kloft · Yiming Ying · arXiv
Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates.
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Pain Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates.
Evidence 0 refs | 3 sources | 50% coverage
Blocker Evidence unverified
Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of…
Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the…
ScienceToStartup currently rates this 0.0/10 on the public viability pass. Our results demonstrate that, with sufficient width, DNNs trained by GD or SGD can achieve generalization performance comparable to kernel-based methods. Code availability is…
Deep Learning Theory moved forward this cycle; last verified June 2026. Public score 0.0/10. Production flags indicate code availability.
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Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates.
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10.48550/arXiv.2606.06772Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates.
Abstract
Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of shallow architectures, the statistical generalization properties of deep neural networks (DNNs), especially in regression tasks, remain far less understood. In this paper, we make significant progress toward closing this gap by providing a comprehensive generalization analysis of DNNs trained using gradient-based methods. First, we establish, for the first time, a crucial connection between the learning dynamics of a DNN with smooth activation functions trained via gradient-based methods and those of kernel methods, showing that gradient-based methods on over-parameterized DNNs can fully inherit the favorable learning dynamics of their kernel counterparts. Building on this connection and the well-established optimality of kernel methods, we derive the first known minimax-optimal rates for the excess population risk of both gradient descent (GD) and stochastic gradient descent (SGD), under the assumption that network width scales polynomially with the sample size. Our results demonstrate that, with sufficient width, DNNs trained by GD or SGD can achieve generalization performance comparable to kernel-based methods.
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Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of shallow architectures, the...
METHOD
Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of shallow architectures...
RESULT
ScienceToStartup currently rates this 0.0/10 on the public viability pass. Our results demonstrate that, with sufficient width, DNNs trained by GD or SGD can achieve generalization performance comparable to kernel-based methods. Code availability is flagged in the production rec...
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Deep Learning Theory moved forward this cycle; last verified June 2026. Public score 0.0/10. Production flags indicate code availability.
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Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of shallow architectures, the statistical generalization properties of deep neural networks (DNNs), especially in regression tasks, remain far less understood.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Understanding the generalization performance of over-parameterized neural networks has become a central topic in deep learning theory. While recent advances, particularly works under the Neural Tangent Kernel (NTK) regime, have shed light on the behavior of shallow architectures, the statistical generalization properties of deep neural networks (DNNs), especially in regression tasks, remain far less understood.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 0.0/10 on the public viability pass. Our results demonstrate that, with sufficient width, DNNs trained by GD or SGD can achieve generalization performance comparable to kernel-based methods. Code availability is flagged in the production record; the public repository link still needs proof alignment.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Deep Learning Theory moved forward this cycle; last verified June 2026. Public score 0.0/10. Production flags indicate code availability.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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Theoretical analysis of generalization in deep neural networks trained with gradient methods, establishing minimax-optimal rates.
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