Paper Citation Record · LEDGER

Scaling Probabilistic Circuits via Monarch Matrices

As of 15 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2506.12383.

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

pith.paper-citation-record.v1
2506.12383 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T01:02:34.708820Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

13 of 13 outbound references displayed

verified exact2
verified fuzzy7
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3fdd1c60-64cd-4368-b9fd-befd241ec300 · outbound

This paper cites •B(i, D)is a block-diagonal matrix with block size D 2i−1 × D 2i−1 , where each block is aB 1, D 2i−1 butterfly factor.

Scaling Probabilistic Circuits via Monarch Matrices •B(i, D)is a block-diagonal matrix with block size D 2i−1 × D 2i−1 , where each block is aB 1, D 2i−1 butterfly factor

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:35.368833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 672d8034-897e-4b99-9496-6041666d9388 · outbound

This paper cites Notice that the delta functions require (for a non-zero entry) that j(i) c =j (i+1) c whenever c̸=i.

Scaling Probabilistic Circuits via Monarch Matrices Notice that the delta functions require (for a non-zero entry) that j(i) c =j (i+1) c whenever c̸=i

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:35.228639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 677c8c57-d6b6-486c-83e7-3658458fdfd3 · outbound

This paper cites KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI.

Scaling Probabilistic Circuits via Monarch Matrices KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-07T01:02:34.999378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 38fda189-99d3-42c5-a9cc-81a66f310931 · outbound

This paper cites One Billion Word Benchmark for Measuring Progress in Statistical Language Modeling.

Scaling Probabilistic Circuits via Monarch Matrices One Billion Word Benchmark for Measuring Progress in Statistical Language Modeling

Reference 1970

Resolution: unresolved; no resolver link, observed 2026-08-07T01:02:33.661816Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08299f58-a6dc-46db-b107-70a10a0e366a · outbound

This paper cites On the latent variable interpretation in sum-product networks.

Scaling Probabilistic Circuits via Monarch Matrices On the latent variable interpretation in sum-product networks

Reference 1995

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:35.970058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d9e7c3d5-a427-4027-ab3b-98de74135178 · outbound

This paper cites Accessed: 2024-12-1.

Scaling Probabilistic Circuits via Monarch Matrices Accessed: 2024-12-1

Reference 2011

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:36.186734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7717dc48-9b4b-41fb-a835-d52fc7cfa999 · outbound

This paper cites Tractable learning for structured probability spaces: A case study in learning preference distributions.

Scaling Probabilistic Circuits via Monarch Matrices Tractable learning for structured probability spaces: A case study in learning preference distributions

Reference 2013

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:36.417151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 35cac194-764e-4423-8fef-6863103aea13 · outbound

This paper cites Auto-Encoding Variational Bayes.

Scaling Probabilistic Circuits via Monarch Matrices Auto-Encoding Variational Bayes

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-07T01:02:33.962789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff58e531-db7c-4230-ae26-4fea52fd4e1a · outbound

This paper cites Interpolating Butterfly and Monarch Matrices Butterfly matrices (Dao et al., 2019; Meng et al.,.

Scaling Probabilistic Circuits via Monarch Matrices Interpolating Butterfly and Monarch Matrices Butterfly matrices (Dao et al., 2019; Meng et al.,

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:35.770609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3afe4318-3094-4fb5-9f2f-98b4d3dfbc16 · outbound

This paper cites What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?.

Scaling Probabilistic Circuits via Monarch Matrices What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T01:02:34.081854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77ecbc51-04c3-45b4-889f-8af44a6b1d7f · outbound

This paper cites They are constructed as the product of sparse matrices known as butterfly factor matrices (Parker, 1995).

Scaling Probabilistic Circuits via Monarch Matrices They are constructed as the product of sparse matrices known as butterfly factor matrices (Parker, 1995)

Reference 2022

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:02:35.511016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7a17d95a-4c41-4809-8588-ffcaf6563a89 · outbound

This paper cites Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions.

Scaling Probabilistic Circuits via Monarch Matrices Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T01:02:33.848281Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4006c374-94fe-4da8-95f7-e55f6b6ff229 · outbound

This paper cites Restructuring Tractable Probabilistic Circuits.

Scaling Probabilistic Circuits via Monarch Matrices Restructuring Tractable Probabilistic Circuits

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-07T01:02:34.870777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.