Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective | Paper Citation Record

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This paper cites Vatt: Transformers for multimodal self-sup ervised learning from raw video, audio and text.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Vatt: Transformers for multimodal self-sup ervised learning from raw video, audio and text

Reference 1

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This paper cites On the theory of dynamic programming.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective On the theory of dynamic programming

Reference 2

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This paper cites Is space -time attention all you need for video understanding? In International Conference on Machine Learning.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Is space -time attention all you need for video understanding? In International Conference on Machine Learning

Reference 3

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This paper cites Simplicity bias in transformers and their ability to learn sparse boolean functio ns.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Simplicity bias in transformers and their ability to learn sparse boolean functio ns

Reference 4

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This paper cites Low-rank bottleneck in multi-head attention models.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Low-rank bottleneck in multi-head attention models

Reference 5

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This paper cites Language models are few-shot learners.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Language models are few-shot learners

Reference 6

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This paper cites Decision trans former: Re- inforcement learning via sequence modeling.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Decision trans former: Re- inforcement learning via sequence modeling

Reference 7

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This paper cites What can transformer learn with vary ing depth? case studies on sequence learning tasks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective What can transformer learn with vary ing depth? case studies on sequence learning tasks

Reference 8

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This paper cites Approximation by superpositions of a sigmoidal function.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Approximation by superpositions of a sigmoidal function

Reference 9

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This paper cites BERT: pre- training of deep bidirectional transformers for language underst anding.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective BERT: pre- training of deep bidirectional transformers for language underst anding

Reference 10

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This paper cites A ttention is not all you need: Pure attention loses rank doubly exponentially with depth.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective A ttention is not all you need: Pure attention loses rank doubly exponentially with depth

Reference 11

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This paper cites An image is worth 16x 16 words: Transformers for image recognition at scale.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective An image is worth 16x 16 words: Transformers for image recognition at scale

Reference 12

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This paper cites Inductive biases and variable creation in self-attention mechanisms.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Inductive biases and variable creation in self-attention mechanisms

Reference 13

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This paper cites Attention Enables Zero Approximation Error.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Attention Enables Zero Approximation Error

Reference 14

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This paper cites Switch transfor mers: Scaling to trillion parameter models with simple and eﬃcient sparsity.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Switch transfor mers: Scaling to trillion parameter models with simple and eﬃcient sparsity

Reference 15

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This paper cites On the approximate realization of continu ous mappings by neural networks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective On the approximate realization of continu ous mappings by neural networks

Reference 16

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This paper cites Approximation rates for neur al networks with encodable weights in smoothness spaces.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Approximation rates for neur al networks with encodable weights in smoothness spaces

Reference 17

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This paper cites Error bou nds for approxima- tions with deep relu neural networks in w s, p norms.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Error bou nds for approxima- tions with deep relu neural networks in w s, p norms

Reference 18

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This paper cites On the rate of convergence of a classiﬁer based on a transformer encoder.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective On the rate of convergence of a classiﬁer based on a transformer encoder

Reference 19

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This paper cites Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Data.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Data

Reference 20

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This paper cites Approximation capabilities of multilayer feedforwar d networks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Approximation capabilities of multilayer feedforwar d networks

Reference 21

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This paper cites Fundamental Limits of Prompt Tuning Transformers: Universality, Capacity and Efficiency.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Fundamental Limits of Prompt Tuning Transformers: Universality, Capacity and Efficiency

Reference 22

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This paper cites Oﬄine reinforcem ent learning as one big sequence modeling problem.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Oﬄine reinforcem ent learning as one big sequence modeling problem

Reference 23

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This paper cites Approximation Rate of the Transformer Architecture for Sequence Modeling.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Approximation Rate of the Transformer Architecture for Sequence Modeling

Reference 24

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This paper cites Deep neural networks with relu-sine-exponentia l activations break curse of dimensionality in approximation on h¨ older class.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Deep neural networks with relu-sine-exponentia l activations break curse of dimensionality in approximation on h¨ older class

Reference 25

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This paper cites Convergence Analysis of Flow Matching in Latent Space with Transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Convergence Analysis of Flow Matching in Latent Space with Transformers

Reference 26

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This paper cites Approximation bounds for transformed with application to regression.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Approximation bounds for transformed with application to regression

Reference 27

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This paper cites On the Optimal Memorization Capacity of Transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective On the Optimal Memorization Capacity of Transformers

Reference 28

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This paper cites Are transformers with one lay er self-attention using low-rank weight matrices universal approximators? In International Conference on Learning Representations, 2024.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Are transformers with one lay er self-attention using low-rank weight matrices universal approximators? In International Conference on Learning Representations, 2024

Reference 29

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This paper cites The lipschitz constant of self-attention.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective The lipschitz constant of self-attention

Reference 30

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This paper cites Provable memor ization ca- pacity of transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Provable memor ization ca- pacity of transformers

Reference 31

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This paper cites On the representation of cont inuous functions of many variables by superposition of continuous functions of one var iable and addi- tion.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective On the representation of cont inuous functions of many variables by superposition of continuous functions of one var iable and addi- tion

Reference 32

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This paper cites Univer- sal approximation under constraints is possible with transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Univer- sal approximation under constraints is possible with transformers

Reference 33

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This paper cites On the expressive ﬂexibility of self-attention matrices.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective On the expressive ﬂexibility of self-attention matrices

Reference 34

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This paper cites RoBERTa: A Robustly Optimized BERT Pretraining Approach.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective RoBERTa: A Robustly Optimized BERT Pretraining Approach

Reference 35

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Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective De ep network ap- proximation for smooth functions

Reference 36

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This paper cites The ex- pressive power of neural networks: A view from the width.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective The ex- pressive power of neural networks: A view from the width

Reference 37

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This paper cites Your transformer may not be as powerful as you expect.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Your transformer may not be as powerful as you expect

Reference 38

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This paper cites Upper and lower mem- ory capacity bounds of transformers for next-token prediction.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Upper and lower mem- ory capacity bounds of transformers for next-token prediction

Reference 39

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This paper cites Memor ization capacity of multi-head attention in transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Memor ization capacity of multi-head attention in transformers

Reference 40

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Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Stabilizing transformers for reinforcement learning

Reference 41

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This paper cites Scalable diﬀusion models with transfor mers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Scalable diﬀusion models with transfor mers

Reference 42

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This paper cites Prompting a pre trained trans- former can be a universal approximator.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Prompting a pre trained trans- former can be a universal approximator

Reference 43

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Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Sutsk ever

Reference 44

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This paper cites Language models are unsupervised multitask learners.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Language models are unsupervised multitask learners

Reference 45

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This paper cites Represe ntational strengths and limitations of transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Represe ntational strengths and limitations of transformers

Reference 46

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This paper cites The kolmogorov–arnold represent ation theorem revisited.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective The kolmogorov–arnold represent ation theorem revisited

Reference 47

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This paper cites Deep network a pproximation char- acterized by number of neurons.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Deep network a pproximation char- acterized by number of neurons

Reference 48

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Observation 20bb7d9f-f9a7-4078-9d93-55c27adb4cf3 · outbound

This paper cites Deep network w ith approximation error being reciprocal of width to power of square root of depth.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Deep network w ith approximation error being reciprocal of width to power of square root of depth

Reference 49

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Observation eb945735-2a54-48b7-8abf-88d6e8529536 · outbound

This paper cites Neural networ k approximation: Three hidden layers are enough.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Neural networ k approximation: Three hidden layers are enough

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.923400Z

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Observation 198c7600-5d2d-481d-b621-c6e90a362200 · outbound

This paper cites Optimal approx imation rate of relu networks in terms of width and depth.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Optimal approx imation rate of relu networks in terms of width and depth

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.906104Z

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Observation 0ab4e756-b007-4950-8f38-d49f2a5b3733 · outbound

This paper cites Sharp bounds on the approx imation rates, metric entropy, and n-widths of shallow neural networks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Sharp bounds on the approx imation rates, metric entropy, and n-widths of shallow neural networks

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.889911Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0a0d7df0-a005-49cd-862f-718ac7b32302 · outbound

This paper cites Adaptivity of deep relu network for learning in beso v and mixed smooth besov spaces: optimal rate and curse of dimensionality.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Adaptivity of deep relu network for learning in beso v and mixed smooth besov spaces: optimal rate and curse of dimensionality

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.874019Z

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Observation bf6de93d-7d02-4bd3-99e2-08fc02b34eff · outbound

This paper cites Approximation and estimat ion ability of trans- formers for sequence-to-sequence functions with inﬁnite dimens ional input.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Approximation and estimat ion ability of trans- formers for sequence-to-sequence functions with inﬁnite dimens ional input

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.858018Z

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Observation 615463b2-5879-4925-aaee-d985aac6d416 · outbound

This paper cites Sequence length independen t norm-based gener- alization bounds for transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Sequence length independen t norm-based gener- alization bounds for transformers

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.841564Z

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Observation 74052132-839c-41ea-a55e-bd85921f705d · outbound

This paper cites Gomez, Lukasz Kaiser, and Illia Polosukhin.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Gomez, Lukasz Kaiser, and Illia Polosukhin

Reference 56

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Observation 1dbad732-fc51-40dc-9652-6dacad3f1092 · outbound

This paper cites A Mathematical Theory of Attention.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective A Mathematical Theory of Attention

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-16T12:19:04.173444Z

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Observation ba3ab9b3-6dcd-47d4-a030-7f953a6b827b · outbound

This paper cites Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling

Reference 58

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Observation b189ae16-3a17-464e-a952-661551978161 · outbound

This paper cites Don’t fear peculiar activation functions: Eu af and beyond.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Don’t fear peculiar activation functions: Eu af and beyond

Reference 59

Resolution: verified exact; raw_fallback, observed 2026-08-16T12:19:04.402054Z

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Observation 43a8d2bd-0325-4494-8186-da3b05dcbd25 · outbound

This paper cites Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-16T12:19:04.190498Z

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Observation a05e3f37-be23-4845-ad90-fce1f30d088d · outbound

This paper cites Statistically meaningful app roximation: a case study on approximating turing machines with transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Statistically meaningful app roximation: a case study on approximating turing machines with transformers

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.816457Z

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Observation 57349ba1-68cf-4356-a546-7641e56f9b57 · outbound

This paper cites Whic h transformer architecture ﬁts my data? a vocabulary bottleneck in self-attent ion.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Whic h transformer architecture ﬁts my data? a vocabulary bottleneck in self-attent ion

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.801118Z

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Observation 9ee46c1b-00a4-4b87-9df9-48eb2c16f4da · outbound

This paper cites Carbonell, Ruslan Salak hutdinov, and Quoc V.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Carbonell, Ruslan Salak hutdinov, and Quoc V

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.786289Z

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Observation caa4cfcf-42a4-47fd-b917-383990be018f · outbound

This paper cites Error bounds for approximations with deep r elu networks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Error bounds for approximations with deep r elu networks

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.770148Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation be7643b8-1f3f-4b7e-ae12-1240ea4cc897 · outbound

This paper cites Optimal approximation of continuous functio ns by very deep relu networks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Optimal approximation of continuous functio ns by very deep relu networks

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.754503Z

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Observation f3347c92-8afa-4a9f-a9b9-5b788eecbee1 · outbound

This paper cites Elementary superexpressive activations.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Elementary superexpressive activations

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.738981Z

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Observation 19007ddd-4229-48d2-95c5-45619b3630c5 · outbound

This paper cites The phase diagram o f approximation rates for deep neural networks.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective The phase diagram o f approximation rates for deep neural networks

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.722334Z

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Observation 9edcb588-19b4-4753-a27b-e3ae4b73e43f · outbound

This paper cites Do transformers really perform badly fo r graph repre- sentation? In Advances in Neural Information Processing Systems , 2021.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Do transformers really perform badly fo r graph repre- sentation? In Advances in Neural Information Processing Systems , 2021

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.705752Z

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Observation 2d642a86-509e-4c3c-80d0-6108feb628e5 · outbound

This paper cites Reddi, and Sanjiv Kumar.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Reddi, and Sanjiv Kumar

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.688423Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 856a2c67-5713-4123-b9cd-a85339088395 · outbound

This paper cites O (n) connections are expressive enough : Universal ap- proximability of sparse transformers.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective O (n) connections are expressive enough : Universal ap- proximability of sparse transformers

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.672541Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bba17ba0-1e4d-48cf-a49d-a1394fede61a · outbound

This paper cites Big bird: Transformers for longer sequences.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Big bird: Transformers for longer sequences

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.655986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 45055737-d76b-4a81-92b7-2391c4e29e95 · outbound

This paper cites Deep network a pproximation: Achieving arbitrary accuracy with ﬁxed number of neurons.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Deep network a pproximation: Achieving arbitrary accuracy with ﬁxed number of neurons

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.640237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8bf1d0da-acde-4aab-b299-3d681bc1e659 · outbound

This paper cites The space Cm consists of all functions whose ﬁrst m derivatives exist and are continuous, and C0 denotes the space of continuous functions.

Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective The space Cm consists of all functions whose ﬁrst m derivatives exist and are continuous, and C0 denotes the space of continuous functions

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:19:04.622766Z

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