Paper Citation Record · LEDGER

Observability conditions for neural state-space models with eigenvalues and their roots of unity

As of 17 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2504.15758.

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2504.15758 v2

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measured 47 of 47 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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47 of 47 outbound references displayed

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Outbound references

Observation 17339ceb-d535-4217-97d2-180789f44082 · outbound

This paper cites StackExchange.

Observability conditions for neural state-space models with eigenvalues and their roots of unity StackExchange

Reference 1

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This paper cites MathOverflow.

Observability conditions for neural state-space models with eigenvalues and their roots of unity MathOverflow

Reference 2

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This paper cites URL https://mast.queensu.ca/~math211/m211oh/ m211oh96.pdf.

Observability conditions for neural state-space models with eigenvalues and their roots of unity URL https://mast.queensu.ca/~math211/m211oh/ m211oh96.pdf

Reference 3

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This paper cites URL https://en.wikipedia.org/wiki/Bauer%E2%80%93Fike_ theorem.

Observability conditions for neural state-space models with eigenvalues and their roots of unity URL https://en.wikipedia.org/wiki/Bauer%E2%80%93Fike_ theorem

Reference 4

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Observation e689b83f-9d97-44f6-81ea-208c6e46c7b8 · outbound

This paper cites State Space Models as Foundation Models: A Control Theoretic Overview.

Observability conditions for neural state-space models with eigenvalues and their roots of unity State Space Models as Foundation Models: A Control Theoretic Overview

Reference 5

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Observation 115616dc-0c12-4d69-8a11-6b10cd22c6c3 · outbound

This paper cites BlackMamba: Mixture of Experts for State-Space Models.

Observability conditions for neural state-space models with eigenvalues and their roots of unity BlackMamba: Mixture of Experts for State-Space Models

Reference 6

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This paper cites Lower Bounds for Non-Convex Stochastic Optimization.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Lower Bounds for Non-Convex Stochastic Optimization

Reference 7

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This paper cites Convex Optimization: Algorithms and Complexity.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Convex Optimization: Algorithms and Complexity

Reference 8

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Observation d7ed6122-9a6c-48cb-9ced-518e0089bd23 · outbound

This paper cites Lower Bounds for Finding Stationary Points II: First-Order Methods.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Lower Bounds for Finding Stationary Points II: First-Order Methods

Reference 9

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This paper cites Lower Bounds for Finding Stationary Points I.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Lower Bounds for Finding Stationary Points I

Reference 10

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This paper cites The hoffman-wielandt inequality.

Observability conditions for neural state-space models with eigenvalues and their roots of unity The hoffman-wielandt inequality

Reference 11

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Observation 92562911-bf6d-47df-ab28-70c95fedf825 · outbound

This paper cites Doubly stochastic matrix.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Doubly stochastic matrix

Reference 12

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Observation e42ff50f-9212-4249-8db1-efb23b2a2845 · outbound

This paper cites Dahleh, and George Verghese.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Dahleh, and George Verghese

Reference 13

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Observation b68c29bb-bef8-444c-9657-b2a6c2f4f96f · outbound

This paper cites Distances between subspaces.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Distances between subspaces

Reference 14

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Observability conditions for neural state-space models with eigenvalues and their roots of unity Unresolved cited work

Reference 15

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Observation 3abc41ba-7b7d-4250-ba48-6c2694e55fa8 · outbound

This paper cites Neural State-Space Models: Empirical Evaluation of Un- certainty Quantification.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Neural State-Space Models: Empirical Evaluation of Un- certainty Quantification

Reference 16

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Observation e1a7d4e7-8c3e-4b73-bc9a-d3d37f336a30 · outbound

This paper cites Influence of the singular manifold of nonobservable states in reconstructing chaotic attractors.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Influence of the singular manifold of nonobservable states in reconstructing chaotic attractors

Reference 17

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Observation dbce29ca-cc27-4b4e-be56-4a4e7592588a · outbound

This paper cites Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming

Reference 18

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This paper cites Mamba: Linear-time sequence modeling with selective state spaces,.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Mamba: Linear-time sequence modeling with selective state spaces,

Reference 19

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This paper cites Efficiently Modeling Long Sequences with Structured State Spaces.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Efficiently Modeling Long Sequences with Structured State Spaces

Reference 20

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This paper cites The distance between orthogonal matrices induced by the frobenius norm.

Observability conditions for neural state-space models with eigenvalues and their roots of unity The distance between orthogonal matrices induced by the frobenius norm

Reference 21

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Observation a9dbe6e4-455e-45d6-aeed-89d12488856e · outbound

This paper cites How to prove that the singular value of product of two orthonormal matrix is related to the principal angles between their columns space, 2019.

Observability conditions for neural state-space models with eigenvalues and their roots of unity How to prove that the singular value of product of two orthonormal matrix is related to the principal angles between their columns space, 2019

Reference 22

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Observation cfdc9e84-d1a0-4504-b93c-1a454e9511c5 · outbound

This paper cites Sparse Mamba: Introducing Controllability, Observability, And Stability To Structural State Space Models.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Sparse Mamba: Introducing Controllability, Observability, And Stability To Structural State Space Models

Reference 23

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This paper cites State-space models are accurate and efficient neural operators for dynamical systems.

Observability conditions for neural state-space models with eigenvalues and their roots of unity State-space models are accurate and efficient neural operators for dynamical systems

Reference 24

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Observability conditions for neural state-space models with eigenvalues and their roots of unity MambaLRP: Explaining Selective State Space Sequence Models

Reference 25

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This paper cites Showing when a permutation matrix is diagonizable over r and over c.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Showing when a permutation matrix is diagonizable over r and over c

Reference 26

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Observation 8ece8429-61bd-434a-b21a-87e7e6fdd5de · outbound

This paper cites Observability of complex systems via conserved quantities.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Observability of complex systems via conserved quantities

Reference 27

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Observability conditions for neural state-space models with eigenvalues and their roots of unity Unresolved cited work

Reference 28

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Observation aea7c4fa-203d-4bcf-baa6-002a0e48dd3d · outbound

This paper cites Stochastic gradient descent for nonconvex learning without bounded gradient assumptions, 2019.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Stochastic gradient descent for nonconvex learning without bounded gradient assumptions, 2019

Reference 29

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Observation 72b7ac97-8382-4a60-91ad-13d00b51ad8f · outbound

This paper cites The proof for worst-case convergence rate of non-smooth convex optimization.

Observability conditions for neural state-space models with eigenvalues and their roots of unity The proof for worst-case convergence rate of non-smooth convex optimization

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.357315Z

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Observation 54c51585-8bdf-457d-b555-0d84da1e5843 · outbound

This paper cites Observability of complex systems.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Observability of complex systems

Reference 31

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Observation c4c7c384-8a27-4793-9057-4fcdd16ff1be · outbound

This paper cites Montanari, Chao Duan, Luis A.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Montanari, Chao Duan, Luis A

Reference 32

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This paper cites Montanari, Leandro Freitas, Daniele Proverbio, and Jorge Gon¸ calves.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Montanari, Leandro Freitas, Daniele Proverbio, and Jorge Gon¸ calves

Reference 33

Resolution: verified exact; doi, observed 2026-08-16T11:25:46.040053Z

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Observation 6b355241-1d1c-4eb4-bc8a-081ef45711e6 · outbound

This paper cites Dynamic Sensor Selection for Biomarker Discovery.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Dynamic Sensor Selection for Biomarker Discovery

Reference 35

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Observation c034f03f-eaae-4038-ba28-aadb0e1eaf29 · outbound

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Observability conditions for neural state-space models with eigenvalues and their roots of unity Unresolved cited work

Reference 36

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This paper cites Simplified State Space Layers for Sequence Modeling.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Simplified State Space Layers for Sequence Modeling

Reference 37

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This paper cites Quantitative measure of observability for linear stochastic systems.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Quantitative measure of observability for linear stochastic systems

Reference 38

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Observation 940ac330-eca3-47d8-94d6-f4c03da0670f · outbound

This paper cites Derivative of eigenvectors of a matrix with respect to its components.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Derivative of eigenvectors of a matrix with respect to its components

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.347604Z

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Observation 7d8cdfdf-5239-44ae-a3d5-24924af7b5b8 · outbound

This paper cites Undermind ai-powered search for scientific literature.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Undermind ai-powered search for scientific literature

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.338163Z

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Observation f56c0832-1bab-4f6a-8b4c-49b196bf0e8a · outbound

This paper cites Observability gramian for nonlinear systems.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Observability gramian for nonlinear systems

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.328572Z

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Observation a48df05a-7806-4445-af7b-4be3fdbb5e13 · outbound

This paper cites Technical communique: Impulse observability and impulse controllability of linear time-varying singular systems.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Technical communique: Impulse observability and impulse controllability of linear time-varying singular systems

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.319272Z

Source-reported events for the cited work

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Observation ee265c17-eaf2-4a52-9f8d-1b11072368ac · outbound

This paper cites AdaGrad stepsizes: Sharp convergence over nonconvex landscapes.

Observability conditions for neural state-space models with eigenvalues and their roots of unity AdaGrad stepsizes: Sharp convergence over nonconvex landscapes

Reference 43

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This paper cites On the impulse response of singular discrete lti systems and three fourier transform pairs.

Observability conditions for neural state-space models with eigenvalues and their roots of unity On the impulse response of singular discrete lti systems and three fourier transform pairs

Reference 44

Resolution: verified exact; doi, observed 2026-08-16T11:25:46.019397Z

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Observation 2d539c9e-1137-47b0-b742-7255a9b3262e · outbound

This paper cites LY k=1 (I− ∆ 2·A)−1(I + ∆ 2·A) # exp{−2πij} ! (I− ∆ 2·A)−1∆B (181) =C I− [V (I− ∆ 2· Λ)V−1]−1(I + ∆ 2·A) exp{−2πij L} −1 (182) × I−.

Observability conditions for neural state-space models with eigenvalues and their roots of unity LY k=1 (I− ∆ 2·A)−1(I + ∆ 2·A) # exp{−2πij} ! (I− ∆ 2·A)−1∆B (181) =C I− [V (I− ∆ 2· Λ)V−1]−1(I + ∆ 2·A) exp{−2πij L} −1 (182) × I−

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.309718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8ca34874-582d-487b-916a-f97aa7e9a40a · outbound

This paper cites Define A(Q,U, Λ) = (Q⊗Ip)T (U⊗Ip)T diag(λ1,...,λ n)(U⊗Ip)(Q⊗Ip) (243) B(Λ,U,S ) =f(diag(λ1,...,λ n))1/2(U⊗I)S.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Define A(Q,U, Λ) = (Q⊗Ip)T (U⊗Ip)T diag(λ1,...,λ n)(U⊗Ip)(Q⊗Ip) (243) B(Λ,U,S ) =f(diag(λ1,...,λ n))1/2(U⊗I)S

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.299898Z

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Observation ed6c3936-fa87-40e4-8079-380c1adfdb38 · outbound

This paper cites Returning to the proof of the Lemma, Now, we denote D =I +O(||A1−A2||2)E for some matrix E.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Returning to the proof of the Lemma, Now, we denote D =I +O(||A1−A2||2)E for some matrix E

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:46.290356Z

Source-reported events for the cited work

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Observation 910c84de-3cc7-4861-ae16-93100936164b · outbound

This paper cites Mamba: Linear-Time Sequence Modeling with Selective State Spaces.

Observability conditions for neural state-space models with eigenvalues and their roots of unity Mamba: Linear-Time Sequence Modeling with Selective State Spaces

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:45.901235Z

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