Paper Citation Record · LEDGER

Teaching Arithmetic to Small Transformers

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 18 inbound Pith citation observations for arXiv:2307.03381.

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

pith.paper-citation-record.v1
2307.03381 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 18 of 18 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:46:40.211034Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T07:46:46.579171Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 4b8bf036-d2b1-479e-abe5-2a842d7cd143 · inbound

LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code cites this paper.

LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code Teaching Arithmetic to Small Transformers

Reference 93

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T17:34:43.084617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0b49fecf-3d4f-4ea9-b01d-37500a795c5a · inbound

Neuron-Level Differentiation of Memorization and Generalization in Large Language Models cites this paper.

Neuron-Level Differentiation of Memorization and Generalization in Large Language Models Teaching Arithmetic to Small Transformers

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T04:46:40.211034Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4426678-28f4-4e48-88d6-5c03e2af04d5 · inbound

IGC: Integrating a Gated Calculator into an LLM to Solve Arithmetic Tasks Reliably and Efficiently cites this paper.

IGC: Integrating a Gated Calculator into an LLM to Solve Arithmetic Tasks Reliably and Efficiently Teaching Arithmetic to Small Transformers

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:57.653404Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abf5b344-4828-4ab4-aca6-4995bffdc486 · inbound

Rethinking Addressing in Language Models via Contexualized Equivariant Positional Encoding cites this paper.

Rethinking Addressing in Language Models via Contexualized Equivariant Positional Encoding Teaching Arithmetic to Small Transformers

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-10T22:49:44.887238Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 426e010d-1581-4846-8edd-4c488463b9e0 · inbound

Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challenges cites this paper.

Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challenges Teaching Arithmetic to Small Transformers

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-09T14:54:29.200198Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5dcaa1b2-db8b-41b7-a7e3-c8e144101426 · inbound

FoNE: Precise Single-Token Number Embeddings via Fourier Features cites this paper.

FoNE: Precise Single-Token Number Embeddings via Fourier Features Teaching Arithmetic to Small Transformers

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:12:28.720583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a0b6e6fa-3f8f-4697-9da3-2b0f4fe85944 · inbound

Extrapolation by Association: Length Generalization Transfer in Transformers cites this paper.

Extrapolation by Association: Length Generalization Transfer in Transformers Teaching Arithmetic to Small Transformers

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:22.085667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fdea804-aca2-4a6d-ab2e-d2aa5eb6429d · inbound

Scaling Self-Supervised Representation Learning for Symbolic Piano Performance cites this paper.

Scaling Self-Supervised Representation Learning for Symbolic Piano Performance Teaching Arithmetic to Small Transformers

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-06T21:36:14.817089Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d975cf47-cfb7-4719-b38f-ae9e8ed841f5 · inbound

Reverse Browser: Vector-Image-to-Code Generator cites this paper.

Reverse Browser: Vector-Image-to-Code Generator Teaching Arithmetic to Small Transformers

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:43.622820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bcba20c1-3609-46c9-b824-aa3b8e3f6351 · inbound

Reverse Browser: Vector-Image-to-Code Generator cites this paper.

Reverse Browser: Vector-Image-to-Code Generator Teaching Arithmetic to Small Transformers

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:43.737669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e44fd7f8-9e15-4d23-a4b6-e01237b9d9a2 · inbound

From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in LLMs cites this paper.

From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in LLMs Teaching Arithmetic to Small Transformers

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-16T17:11:08.200460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0e64a4cf-d13d-4de7-a17c-027c38f50d46 · inbound

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction cites this paper.

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction Teaching Arithmetic to Small Transformers

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-11T03:45:57.272795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9857c1e8-1912-462b-9cc8-3069e59579a4 · inbound

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction cites this paper.

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction Teaching Arithmetic to Small Transformers

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-01T13:25:44.997513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bc4ac8bf-9eaa-42b7-821d-14afeaaa5198 · inbound

Slower Generalization, Faster Memorization: A Sweet Spot in Algorithmic Learning cites this paper.

Slower Generalization, Faster Memorization: A Sweet Spot in Algorithmic Learning Teaching Arithmetic to Small Transformers

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-06-30T21:35:04.967157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation abca3a7f-162f-4630-b14e-202722446d60 · inbound

LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning cites this paper.

LinAlg-Bench: A Forensic Benchmark Revealing Structural Failure Modes in LLM Mathematical Reasoning Teaching Arithmetic to Small Transformers

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T17:48:48.761927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3ddf70f0-209b-45b6-a966-dad851043b0f · inbound

Arithmetic Pedagogy for Language Models cites this paper.

Arithmetic Pedagogy for Language Models Teaching Arithmetic to Small Transformers

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:46:46.580714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 18ff3aed-c046-4ef3-8d2a-0e471c6b5d7b · inbound

Explaining and Tuning Transformer-based LLMs in Arithmetic Tasks with Human Strategies cites this paper.

Explaining and Tuning Transformer-based LLMs in Arithmetic Tasks with Human Strategies Teaching Arithmetic to Small Transformers

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T18:53:10.165241Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18e0fc23-0ebb-4e57-8f88-754edd3586ce · inbound

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks cites this paper.

Can Transformers Really Do It All? On the Compatibility of Inductive Biases Across Tasks Teaching Arithmetic to Small Transformers

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-01T17:31:48.050944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.