Paper Citation Record · LEDGER

Approximation Bounds for Transformer Networks with Application to Regression

As of 21 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 4 inbound Pith citation observations for arXiv:2504.12175.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2504.12175 v1

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Pith citing papers itemized under the disclosed page cap.

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A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

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pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 913676c4-d348-4582-bb43-d5542f5b85a7 · outbound

This paper cites The generalization abili ty of online algorithms for dependent data.

Approximation Bounds for Transformer Networks with Application to Regression The generalization abili ty of online algorithms for dependent data

Reference 1

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This paper cites Bartlett.

Approximation Bounds for Transformer Networks with Application to Regression Bartlett

Reference 2

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This paper cites Nearly-tight vc- dimension and pseudodimension bounds for piecewise linear neural networks.

Approximation Bounds for Transformer Networks with Application to Regression Nearly-tight vc- dimension and pseudodimension bounds for piecewise linear neural networks

Reference 3

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This paper cites Vapnik-chervonenki s dimension of neural nets.

Approximation Bounds for Transformer Networks with Application to Regression Vapnik-chervonenki s dimension of neural nets

Reference 4

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This paper cites Birth of a transformer: A memory viewpoint.

Approximation Bounds for Transformer Networks with Application to Regression Birth of a transformer: A memory viewpoint

Reference 5

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This paper cites Nonparametric regression on low-dimensional manifolds using deep relu networks: Funct ion approximation and statistical recovery.

Approximation Bounds for Transformer Networks with Application to Regression Nonparametric regression on low-dimensional manifolds using deep relu networks: Funct ion approximation and statistical recovery

Reference 6

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This paper cites Overcoming a theoretical limitation of self-attention.

Approximation Bounds for Transformer Networks with Application to Regression Overcoming a theoretical limitation of self-attention

Reference 7

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This paper cites Approximation by superpositions of a si gmoidal function.

Approximation Bounds for Transformer Networks with Application to Regression Approximation by superpositions of a si gmoidal function

Reference 8

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This paper cites The bramble–hilbert lemma for convex domains.

Approximation Bounds for Transformer Networks with Application to Regression The bramble–hilbert lemma for convex domains

Reference 9

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This paper cites BERT: Pre-training of deep bidirectional transformers for language understan ding.

Approximation Bounds for Transformer Networks with Application to Regression BERT: Pre-training of deep bidirectional transformers for language understan ding

Reference 10

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This paper cites Nonlinear approximation.

Approximation Bounds for Transformer Networks with Application to Regression Nonlinear approximation

Reference 11

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This paper cites Constructive Approximation, volume 303.

Approximation Bounds for Transformer Networks with Application to Regression Constructive Approximation, volume 303

Reference 12

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This paper cites Semi-supervised deep sobolev regression: Estimation and variable selection by r equ neural network.

Approximation Bounds for Transformer Networks with Application to Regression Semi-supervised deep sobolev regression: Estimation and variable selection by r equ neural network

Reference 13

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This paper cites Minimax estimation via wavelet shrinkage.

Approximation Bounds for Transformer Networks with Application to Regression Minimax estimation via wavelet shrinkage

Reference 14

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This paper cites An image is worth 16x16 wo rds: Transformers for image recognition at scale.

Approximation Bounds for Transformer Networks with Application to Regression An image is worth 16x16 wo rds: Transformers for image recognition at scale

Reference 15

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

Approximation Bounds for Transformer Networks with Application to Regression Inductive biases and variable creation in self-attention mechanisms

Reference 16

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This paper cites Partial Diﬀerential Equations , volume 19.

Approximation Bounds for Transformer Networks with Application to Regression Partial Diﬀerential Equations , volume 19

Reference 17

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This paper cites Attention Enables Zero Approximation Error.

Approximation Bounds for Transformer Networks with Application to Regression Attention Enables Zero Approximation Error

Reference 18

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This paper cites Deep ne ural networks for estimation and inference.

Approximation Bounds for Transformer Networks with Application to Regression Deep ne ural networks for estimation and inference

Reference 19

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This paper cites Over-parameterized deep nonparametric regression for dependent data with its a pplications to reinforcement learning.

Approximation Bounds for Transformer Networks with Application to Regression Over-parameterized deep nonparametric regression for dependent data with its a pplications to reinforcement learning

Reference 20

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

Approximation Bounds for Transformer Networks with Application to Regression On the rate of convergence of a classiﬁer based on a transformer encoder

Reference 21

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This paper cites Understanding sc aling laws with statistical and approximation theory for transformer neural networks on in trinsically low-dimensional data.

Approximation Bounds for Transformer Networks with Application to Regression Understanding sc aling laws with statistical and approximation theory for transformer neural networks on in trinsically low-dimensional data

Reference 22

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Approximation Bounds for Transformer Networks with Application to Regression D eep residual learning for image recognition

Reference 23

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Approximation Bounds for Transformer Networks with Application to Regression Minimal width for universal property of deep rnn

Reference 24

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This paper cites M ultilayer feedforward networks are universal approximators.

Approximation Bounds for Transformer Networks with Application to Regression M ultilayer feedforward networks are universal approximators

Reference 25

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Approximation Bounds for Transformer Networks with Application to Regression Mixing time estimation in re- versible markov chains from a single sample path

Reference 26

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This paper cites Fundamental limits of prompt tuning transformers: Univers ality, capacity and eﬃciency.

Approximation Bounds for Transformer Networks with Application to Regression Fundamental limits of prompt tuning transformers: Univers ality, capacity and eﬃciency

Reference 27

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This paper cites Approximation rate of th e transformer architecture for sequence modeling.

Approximation Bounds for Transformer Networks with Application to Regression Approximation rate of th e transformer architecture for sequence modeling

Reference 28

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This paper cites Deep approximate policy iteration.

Approximation Bounds for Transformer Networks with Application to Regression Deep approximate policy iteration

Reference 29

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Approximation Bounds for Transformer Networks with Application to Regression Convergence Analysis of Flow Matching in Latent Space with Transformers

Reference 30

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Approximation Bounds for Transformer Networks with Application to Regression Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors

Reference 31

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This paper cites Approximation bou nds for recurrent neural networks with application to regression.

Approximation Bounds for Transformer Networks with Application to Regression Approximation bou nds for recurrent neural networks with application to regression

Reference 32

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

Approximation Bounds for Transformer Networks with Application to Regression Are transformers with o ne layer self-attention using low- rank weight matrices universal approximators? In International Conference on Learning Representations, 2024

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This paper cites On the optimal memoriza tion capacity of transformers.

Approximation Bounds for Transformer Networks with Application to Regression On the optimal memoriza tion capacity of transformers

Reference 34

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Approximation Bounds for Transformer Networks with Application to Regression Polynomial bound s for vc dimension of sigmoidal and general pfaﬃan neural networks

Reference 35

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Approximation Bounds for Transformer Networks with Application to Regression Provab le memorization capacity of transformers

Reference 36

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Approximation Bounds for Transformer Networks with Application to Regression On the rate of converg ence of fully connected deep neural network regression estimates

Reference 37

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Approximation Bounds for Transformer Networks with Application to Regression Generalization bo unds for non-stationary mixing processes

Reference 38

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Approximation Bounds for Transformer Networks with Application to Regression Deep network approximation for smooth functions

Reference 39

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Approximation Bounds for Transformer Networks with Application to Regression Nonparametric time series prediction throug h adaptive model selection

Reference 40

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Approximation Bounds for Transformer Networks with Application to Regression Rademacher com plexity bounds for non-iid processes

Reference 41

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Approximation Bounds for Transformer Networks with Application to Regression Stability boun ds for stationary ϕ -mixing and β -mixing processes

Reference 42

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Approximation Bounds for Transformer Networks with Application to Regression Adaptive approxim ation and generalization of deep neural network with intrinsic dimensionality

Reference 43

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Approximation Bounds for Transformer Networks with Application to Regression GPT-4 Technical Report

Reference 44

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Approximation Bounds for Transformer Networks with Application to Regression Pro vable memorization via deep neural networks using sub-linear parameters

Reference 45

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Approximation Bounds for Transformer Networks with Application to Regression Scalable diﬀusion mod els with transformers

Reference 46

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Approximation Bounds for Transformer Networks with Application to Regression Atte ntion is turing-complete

Reference 47

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This paper cites Promptin g a pretrained transformer can be a universal approximator.

Approximation Bounds for Transformer Networks with Application to Regression Promptin g a pretrained transformer can be a universal approximator

Reference 48

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Approximation Bounds for Transformer Networks with Application to Regression S tatistical spatially inhomoge- neous diﬀusion inference

Reference 49

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This paper cites Nonparametric regression u sing deep neural networks with relu activation function.

Approximation Bounds for Transformer Networks with Application to Regression Nonparametric regression u sing deep neural networks with relu activation function

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.585827Z

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Approximation Bounds for Transformer Networks with Application to Regression The kolmogorov–arnold repr esentation theorem revisited

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.573068Z

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Observation ae741960-0ef8-42fd-a764-001a24fbc69e · outbound

This paper cites Predictive pac le arning and process decompositions.

Approximation Bounds for Transformer Networks with Application to Regression Predictive pac le arning and process decompositions

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.561364Z

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Observation 5d3d2fd3-cc5e-4d81-9bf5-d98b66297bdf · outbound

This paper cites Deep netwo rk approximation characterized by number of neurons.

Approximation Bounds for Transformer Networks with Application to Regression Deep netwo rk approximation characterized by number of neurons

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.549965Z

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Observation 6bbe388d-39a9-4d71-908b-47c17d04f764 · outbound

This paper cites Optimal approximation rates for dee p relu neural networks on sobolev and besov spaces.

Approximation Bounds for Transformer Networks with Application to Regression Optimal approximation rates for dee p relu neural networks on sobolev and besov spaces

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.537588Z

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Observation 3ae9865f-e263-41d6-bffa-19f3b047a70f · outbound

This paper cites Fast learning f rom non-iid observations.

Approximation Bounds for Transformer Networks with Application to Regression Fast learning f rom non-iid observations

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.525753Z

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This paper cites Optimal global rates of convergence fo r nonparametric regression.

Approximation Bounds for Transformer Networks with Application to Regression Optimal global rates of convergence fo r nonparametric regression

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.514262Z

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Observation 8c918bcc-87ca-48b2-969f-5c904b140bfe · outbound

This paper cites Adaptivity of deep reLU network for learn ing in besov and mixed smooth besov spaces: optimal rate and curse of dimensionality.

Approximation Bounds for Transformer Networks with Application to Regression Adaptivity of deep reLU network for learn ing in besov and mixed smooth besov spaces: optimal rate and curse of dimensionality

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.502207Z

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This paper cites Approximation and estimation ability of transform- ers for sequence-to-sequence functions with inﬁnite dimen sional input.

Approximation Bounds for Transformer Networks with Application to Regression Approximation and estimation ability of transform- ers for sequence-to-sequence functions with inﬁnite dimen sional input

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.487523Z

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Observation af3e1b3e-c2bf-411d-87d6-dc5f57391df6 · outbound

This paper cites Approximation of Permutation Invariant Polynomials by Transformers: Efficient Construction in Column-Size.

Approximation Bounds for Transformer Networks with Application to Regression Approximation of Permutation Invariant Polynomials by Transformers: Efficient Construction in Column-Size

Reference 59

Resolution: verified exact; local_arxiv, observed 2026-08-16T12:42:56.225886Z

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Observation 8346c38e-d033-48bb-82c1-d8b8c96013a0 · outbound

This paper cites Attention is all you ne ed.

Approximation Bounds for Transformer Networks with Application to Regression Attention is all you ne ed

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.473809Z

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Observation 11068ab3-8114-4cee-aa8e-da9d3a62aa6c · outbound

This paper cites Inequalities for absolutely regul ar sequences: application to density estimation.

Approximation Bounds for Transformer Networks with Application to Regression Inequalities for absolutely regul ar sequences: application to density estimation

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.459981Z

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Observation b924d342-6b6b-4715-83cf-3d92e65338a9 · outbound

This paper cites Understanding the expressive power and mechanisms of transformer for sequence modeling.

Approximation Bounds for Transformer Networks with Application to Regression Understanding the expressive power and mechanisms of transformer for sequence modeling

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.447527Z

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Observation 1ce557d4-5d09-47ce-bee9-8a70a6fe4847 · outbound

This paper cites On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding.

Approximation Bounds for Transformer Networks with Application to Regression On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding

Reference 63

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This paper cites Nonparametric regress ion using over-parameterized shallow relu neural networks.

Approximation Bounds for Transformer Networks with Application to Regression Nonparametric regress ion using over-parameterized shallow relu neural networks

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.433912Z

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Observation d1922890-b203-44aa-bc2e-f4c0cf5a24d5 · outbound

This paper cites Optimal rates of approx imation by shallow relu k neural networks and applications to nonparametric regression.

Approximation Bounds for Transformer Networks with Application to Regression Optimal rates of approx imation by shallow relu k neural networks and applications to nonparametric regression

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.421337Z

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Observation 42b5a247-128c-45f4-b598-810e84d39976 · outbound

This paper cites Error bounds for approximations with deep relu networks.

Approximation Bounds for Transformer Networks with Application to Regression Error bounds for approximations with deep relu networks

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-16T12:42:56.139345Z

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Observation ba24bcd9-be68-41a1-bf25-7268f2e19f84 · outbound

This paper cites Density estimation in the l8 norm for dependent data with applications to the gibbs sampler.

Approximation Bounds for Transformer Networks with Application to Regression Density estimation in the l8 norm for dependent data with applications to the gibbs sampler

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.398878Z

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Observation 6e897e4d-0e4f-4930-bff9-4baddc4b01e8 · outbound

This paper cites Rates of convergence for empirical processes of s tationary mixing sequences.

Approximation Bounds for Transformer Networks with Application to Regression Rates of convergence for empirical processes of s tationary mixing sequences

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.386916Z

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Observation 17a9a356-a54f-4368-bf90-1f23c3966c94 · outbound

This paper cites Are transformers universal approximators of sequence -to-sequence functions? In International Conference on Learning Representations , 2019.

Approximation Bounds for Transformer Networks with Application to Regression Are transformers universal approximators of sequence -to-sequence functions? In International Conference on Learning Representations , 2019

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.374723Z

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Observation a6435793-e0fa-4958-ad28-62282f737375 · outbound

This paper cites O(n) connections are expressive enough: U niversal approximability of sparse transformers.

Approximation Bounds for Transformer Networks with Application to Regression O(n) connections are expressive enough: U niversal approximability of sparse transformers

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.361520Z

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Observation 60c77254-4b0c-4ba3-b279-001c9df36cd2 · outbound

This paper cites Deep netwo rk approximation: Achieving arbitrary accuracy with ﬁxed number of neurons.

Approximation Bounds for Transformer Networks with Application to Regression Deep netwo rk approximation: Achieving arbitrary accuracy with ﬁxed number of neurons

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:42:56.348270Z

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Pith citing papers

Observation 4ae2c7f0-c677-4dca-b5c1-d7f38b197cb3 · inbound

Standard Transformers Achieve the Minimax Rate in Nonparametric Regression with $C^{s,\lambda}$ Targets cites this paper.

Standard Transformers Achieve the Minimax Rate in Nonparametric Regression with $C^{s,\lambda}$ Targets Approximation Bounds for Transformer Networks with Application to Regression

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T21:28:29.502605Z

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Observation 8947f980-88e6-4377-a0f9-140866b93090 · inbound

Approximation Error Upper and Lower Bounds for H\"{o}lder Class with Transformers cites this paper.

Approximation Error Upper and Lower Bounds for H\"{o}lder Class with Transformers Approximation Bounds for Transformer Networks with Application to Regression

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:00:54.962487Z

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Observation 8f90cc76-a1ca-4aa6-b5d4-3aedcf4aa6cb · inbound

Approximation Error Upper and Lower Bounds for H\"{o}lder Class with Transformers cites this paper.

Approximation Error Upper and Lower Bounds for H\"{o}lder Class with Transformers Approximation Bounds for Transformer Networks with Application to Regression

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-07-01T13:25:45.028432Z

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Observation b35c16cf-bbcd-4538-a77d-cfa4a2a02ccf · inbound

On Explicit Super-Expressive Approximation for Neural Networks cites this paper.

On Explicit Super-Expressive Approximation for Neural Networks Approximation Bounds for Transformer Networks with Application to Regression

Reference 124

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