Paper Citation Record · LEDGER

The Effect of Depth on the Expressivity of Deep Linear State-Space Models

As of 20 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2506.19296.

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

pith.paper-citation-record.v1
2506.19296 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:47:32.341686Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

25 of 25 outbound references displayed

verified exact2
verified fuzzy9
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 86e636fc-f8b6-49d0-820e-0345d89c3db8 · outbound

This paper cites A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.236866Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a297545-a7ec-4d02-aa14-93297ad227aa · outbound

This paper cites Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.240877Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae343118-4a2a-452b-9bfd-8a94532c6d7f · outbound

This paper cites The emergence of clusters in self-attention dynamics.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models The emergence of clusters in self-attention dynamics

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.639252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 718384d2-a47e-4f76-a363-101f027c2539 · outbound

This paper cites It’s raw! audio generation with state-space models.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models It’s raw! audio generation with state-space models

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.629000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e4e7bf59-8a4c-4f71-8c70-db6f769920d9 · outbound

This paper cites On the Role of Initialization on the Implicit Bias in Deep Linear Networks.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models On the Role of Initialization on the Implicit Bias in Deep Linear Networks

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:47:32.466796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 706e4111-df2f-4098-a10b-e79ceaf55921 · outbound

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

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Mamba: Linear-Time Sequence Modeling with Selective State Spaces

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.256418Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 296defea-5b93-4f8e-b57c-f74e03cef716 · outbound

This paper cites Hippo: Recurrent memory with optimal polynomial projections.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Hippo: Recurrent memory with optimal polynomial projections

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.260421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c479e6da-9db0-42c7-9431-ece42a83c9eb · outbound

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

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Efficiently Modeling Long Sequences with Structured State Spaces

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.264558Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 96cd470d-b095-4d68-b698-b7dab0cd3a6e · outbound

This paper cites Combining recurrent, convolutional, and continuous-time models with linear state space layers.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Combining recurrent, convolutional, and continuous-time models with linear state space layers

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.270611Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fa34a9c-b7f7-4801-8140-c867178ad775 · outbound

This paper cites Diagonal state spaces are as effective as structured state spaces.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Diagonal state spaces are as effective as structured state spaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.276270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d423aa82-939b-489b-8fa4-ab47606ea229 · outbound

This paper cites Estimation and inference of impulse responses by local projections.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Estimation and inference of impulse responses by local projections

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.597470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f6f9bc0b-e762-426b-bfba-641d5164961f · outbound

This paper cites Videomamba: State space model for efficient video understanding.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Videomamba: State space model for efficient video understanding

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.585479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5f70a085-1791-44d0-8cfb-dc5bedd56a72 · outbound

This paper cites The geometry of the deep linear network.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models The geometry of the deep linear network

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.294872Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c890cb7-6baa-4995-9d10-c4183bfda84b · outbound

This paper cites Theoretical foundations of deep selective state-space models.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Theoretical foundations of deep selective state-space models

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.574240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 60f43a7f-a57e-43e6-8255-d4a5807b1df0 · outbound

This paper cites S4nd: Modeling images and videos as multidimensional signals with state spaces.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models S4nd: Modeling images and videos as multidimensional signals with state spaces

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.303121Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46dcfbe3-c308-473a-9c36-642ffcb95518 · outbound

This paper cites On the difficulty of training recurrent neural networks.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models On the difficulty of training recurrent neural networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.550935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 565ed52d-8365-49f8-84e0-50144aa8ce72 · outbound

This paper cites Diagonal state space augmented transformers for speech recognition.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Diagonal state space augmented transformers for speech recognition

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.537720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 102085a0-27ce-4a7b-b36b-47a4602a0530 · outbound

This paper cites On the interplay between learning and memory in deep state space models.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models On the interplay between learning and memory in deep state space models

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.524560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a5ef6ef3-6415-4dd8-aab8-01428eec7e97 · outbound

This paper cites Simplified State Space Layers for Sequence Modeling.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Simplified State Space Layers for Sequence Modeling

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.317786Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c1db194-6c8c-4118-b25e-61d7f5945696 · outbound

This paper cites Long Range Arena: A Benchmark for Efficient Transformers.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Long Range Arena: A Benchmark for Efficient Transformers

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.322669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a38a5ab-0637-4d18-8d90-687de92bc76d · outbound

This paper cites Attention is all you need.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Attention is all you need

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.327280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e29e40e-6659-4bee-8390-a14186ad8d7d · outbound

This paper cites Demystifying the Token Dynamics of Deep Selective State Space Models.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Demystifying the Token Dynamics of Deep Selective State Space Models

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:47:32.394459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2a9c99ef-4063-4efc-80f3-7538db777b71 · outbound

This paper cites State-space models with layer-wise nonlinearity are universal approximators with exponential decaying memory.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models State-space models with layer-wise nonlinearity are universal approximators with exponential decaying memory

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:47:32.501187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e8cc808a-3140-47e3-aad9-b25a716c41b4 · outbound

This paper cites Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.338280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d74579bf-e112-4569-b110-282d22745439 · outbound

This paper cites write newline.

The Effect of Depth on the Expressivity of Deep Linear State-Space Models write newline

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T18:47:32.341686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.