Paper Citation Record · LEDGER

How Do Transformers Learn Variable Binding in Symbolic Programs?

As of 22 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 5 inbound Pith citation observations for arXiv:2505.20896.

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

pith.paper-citation-record.v1
2505.20896 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:50:10.446055Z

measured 48 of 48 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 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T22:57:08.127769Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T13:09:51.104464Z

Reference resolution

43 of 43 outbound references displayed

verified exact1
verified fuzzy20
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 790663cc-956d-4ca4-83d9-283c2770bb8c · outbound

This paper cites write newline.

How Do Transformers Learn Variable Binding in Symbolic Programs? write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:04.962041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2da02e3a-c05b-4b16-9a50-70e86586493f · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:50:15.537294Z

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 8209d497-689d-47bb-9492-a5a77e8b1112 · outbound

This paper cites Layer Normalization.

How Do Transformers Learn Variable Binding in Symbolic Programs? Layer Normalization

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:05.267517Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 485dad34-ecc5-4738-b6d9-902590a27cf9 · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:05.386622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7146ba49-059f-49cd-88f1-51961cd36b84 · outbound

This paper cites D., Schlichtkrull, M.

How Do Transformers Learn Variable Binding in Symbolic Programs? D., Schlichtkrull, M

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:05.503814Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 886a3397-8170-4ba7-9d6b-316069b3459e · outbound

This paper cites D., Schmid, L., Hupkes, D., and Titov, I.

How Do Transformers Learn Variable Binding in Symbolic Programs? D., Schmid, L., Hupkes, D., and Titov, I

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:05.690384Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54bae7f5-2152-4eea-87b5-02ce0dfe1bd0 · outbound

This paper cites Causal scrubbing, a method for rigorously testing interpretability hypotheses.

How Do Transformers Learn Variable Binding in Symbolic Programs? Causal scrubbing, a method for rigorously testing interpretability hypotheses

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:15.334410Z

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 d2f30315-43b8-467d-a715-d7ea4fce2871 · outbound

This paper cites Are neural nets modular? inspecting functional modularity through differentiable weight masks.

How Do Transformers Learn Variable Binding in Symbolic Programs? Are neural nets modular? inspecting functional modularity through differentiable weight masks

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:15.235491Z

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 b7fd3691-7c91-44c4-96f5-8f9ec9f1614e · outbound

This paper cites Representational Analysis of Binding in Language Models.

How Do Transformers Learn Variable Binding in Symbolic Programs? Representational Analysis of Binding in Language Models

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:15.047630Z

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 755b4f8f-ac79-4b01-bef7-2381e9a7d276 · outbound

This paper cites Discovering Variable Binding Circuitry with Desiderata.

How Do Transformers Learn Variable Binding in Symbolic Programs? Discovering Variable Binding Circuitry with Desiderata

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:06.347611Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 861ab519-de3c-499f-adcc-a734b20a7117 · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:50:14.883112Z

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 4b07a2d2-e807-40a7-9c27-abd2d94b61ec · outbound

This paper cites and Steinhardt, J.

How Do Transformers Learn Variable Binding in Symbolic Programs? and Steinhardt, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:14.744930Z

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 1034321e-acb8-4785-8960-2fdd6297720a · outbound

This paper cites and Steinhardt, J.

How Do Transformers Learn Variable Binding in Symbolic Programs? and Steinhardt, J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:14.609552Z

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 3796cca7-0046-44af-9df7-74711e434061 · outbound

This paper cites Monitoring Latent World States in Language Models with Propositional Probes , June 2024.

How Do Transformers Learn Variable Binding in Symbolic Programs? Monitoring Latent World States in Language Models with Propositional Probes , June 2024

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:14.388149Z

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 5136d1c0-a587-475c-811c-b1e34a5153af · outbound

This paper cites and King, A.

How Do Transformers Learn Variable Binding in Symbolic Programs? and King, A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:14.162893Z

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 390edfd7-026a-476e-85bc-14b6fde05e00 · outbound

This paper cites Neural natural language inference models partially embed theories of lexical entailment and negation.

How Do Transformers Learn Variable Binding in Symbolic Programs? Neural natural language inference models partially embed theories of lexical entailment and negation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:07.368506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33082fb5-34c6-47b9-a166-640058c08c7a · outbound

This paper cites Causal abstractions of neural networks.

How Do Transformers Learn Variable Binding in Symbolic Programs? Causal abstractions of neural networks

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:13.935220Z

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 c47790f2-5683-4dac-8f9c-dbdcddadee20 · outbound

This paper cites C., and Potts, C.

How Do Transformers Learn Variable Binding in Symbolic Programs? C., and Potts, C

Reference 18

Resolution: verified exact; doi, observed 2026-08-07T13:50:10.692843Z

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 60b65955-83ca-44f0-98ca-bf7a822f87cd · outbound

This paper cites Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability.

How Do Transformers Learn Variable Binding in Symbolic Programs? Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:07.811798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c20c7ce7-2c68-48ee-8504-30bb4edc5fd0 · outbound

This paper cites Gaussian Error Linear Units (GELUs).

How Do Transformers Learn Variable Binding in Symbolic Programs? Gaussian Error Linear Units (GELUs)

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:07.945135Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41c31ea3-b8a6-42b9-907f-ec071cbe9237 · outbound

This paper cites S., Michaud, E., Tegmark, M., and Williams, M.

How Do Transformers Learn Variable Binding in Symbolic Programs? S., Michaud, E., Tegmark, M., and Williams, M

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:13.717023Z

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 180baef2-2efe-4477-9efd-3bcd7ed26d21 · outbound

This paper cites Decoupled Weight Decay Regularization.

How Do Transformers Learn Variable Binding in Symbolic Programs? Decoupled Weight Decay Regularization

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:08.265504Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65211d17-79fe-43a4-870e-a943ca65811c · outbound

This paper cites Predicting inductive biases of pre-trained models.

How Do Transformers Learn Variable Binding in Symbolic Programs? Predicting inductive biases of pre-trained models

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:13.538841Z

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 7f23c211-e615-4ab1-8f78-281645e158d1 · outbound

This paper cites Hashhop: Long context evaluation.

How Do Transformers Learn Variable Binding in Symbolic Programs? Hashhop: Long context evaluation

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:13.345630Z

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 69d65ec7-5e79-4622-8c04-a27a7248d3cf · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:50:13.213801Z

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 ad4afa0d-b1e5-4f9d-943e-d2b83c296ff6 · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:08.875560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38362840-46e8-4301-8216-8c286c3e5dcd · outbound

This paper cites F., Vijayan, S., Rao, S.

How Do Transformers Learn Variable Binding in Symbolic Programs? F., Vijayan, S., Rao, S

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:13.026695Z

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 1ba7672e-6891-44c6-9660-f9c64078a08c · outbound

This paper cites UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction.

How Do Transformers Learn Variable Binding in Symbolic Programs? UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:09.050519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b1da28c-5298-4e06-bbe9-9400cda60024 · outbound

This paper cites J., and Belinkov, Y.

How Do Transformers Learn Variable Binding in Symbolic Programs? J., and Belinkov, Y

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:12.860371Z

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 191bb10d-048d-410c-8264-9b0467b3801c · outbound

This paper cites A tale of two circuits: Grokking as competition of sparse and dense subnetworks.

How Do Transformers Learn Variable Binding in Symbolic Programs? A tale of two circuits: Grokking as competition of sparse and dense subnetworks

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:12.681514Z

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 9b666188-da79-4e2c-ac65-58ffca101649 · outbound

This paper cites S., Sun, J., Todd, E., Bau, D., and Belinkov, Y.

How Do Transformers Learn Variable Binding in Symbolic Programs? S., Sun, J., Todd, E., Bau, D., and Belinkov, Y

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:09.330362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f7f1153-0400-4a86-b9db-fba564f26305 · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

How Do Transformers Learn Variable Binding in Symbolic Programs? Progress measures for grokking via mechanistic interpretability

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:12.526060Z

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 504870ea-af48-4bfd-af8b-5e25884db169 · outbound

This paper cites R., Haklay, T., Belinkov, Y., and Bau, D.

How Do Transformers Learn Variable Binding in Symbolic Programs? R., Haklay, T., Belinkov, Y., and Bau, D

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:12.339552Z

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 8559864f-e3aa-47bd-979e-5d33e1a01751 · outbound

This paper cites Language models are unsupervised multitask learners.

How Do Transformers Learn Variable Binding in Symbolic Programs? Language models are unsupervised multitask learners

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:09.633083Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f09fcbb4-94b3-47cd-8c17-00a19976dbbc · outbound

This paper cites and Wiegreffe, S.

How Do Transformers Learn Variable Binding in Symbolic Programs? and Wiegreffe, S

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:12.124086Z

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 7942d6b8-edfb-4f21-b091-d9f10c7b3e3f · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:50:11.896762Z

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 205d12fc-a0fd-49b2-8b6b-d2f7078670b5 · outbound

This paper cites an unresolved cited work.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:50:11.740324Z

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 4591e58e-693c-4a8d-b7f6-dc5599d4d472 · outbound

This paper cites Open Problems in Mechanistic Interpretability.

How Do Transformers Learn Variable Binding in Symbolic Programs? Open Problems in Mechanistic Interpretability

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:09.978542Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35eb6fb9-dc93-4c74-892a-57204211c392 · outbound

This paper cites Tensor product variable binding and the representation of symbolic structures in connectionist systems.

How Do Transformers Learn Variable Binding in Symbolic Programs? Tensor product variable binding and the representation of symbolic structures in connectionist systems

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:10.121182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c1eb90f-87b5-4781-893b-7e16ef55176c · outbound

This paper cites Roformer: Enhanced transformer with rotary position embedding.

How Do Transformers Learn Variable Binding in Symbolic Programs? Roformer: Enhanced transformer with rotary position embedding

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T13:50:10.184696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e7571e4-657e-46a0-9ed6-599debba5df0 · outbound

This paper cites N., Kaiser, ., and Polosukhin, I.

How Do Transformers Learn Variable Binding in Symbolic Programs? N., Kaiser, ., and Polosukhin, I

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:11.567779Z

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 8c1cdd81-da35-47f5-bcd8-5288b82e5799 · outbound

This paper cites Investigating gender bias in language models using causal mediation analysis.

How Do Transformers Learn Variable Binding in Symbolic Programs? Investigating gender bias in language models using causal mediation analysis

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:11.345955Z

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 6b568520-53f4-4172-b43a-cfc80959e6ab · outbound

This paper cites Unveiling transformers with LEGO : A synthetic reasoning task, 2023.

How Do Transformers Learn Variable Binding in Symbolic Programs? Unveiling transformers with LEGO : A synthetic reasoning task, 2023

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:50:11.153216Z

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.

Pith citing papers

Observation faa8ded1-7880-4a76-9615-01489e70ff03 · inbound

Do Transformers Use their Depth Adaptively? Evidence from a Relational Reasoning Task cites this paper.

Do Transformers Use their Depth Adaptively? Evidence from a Relational Reasoning Task How Do Transformers Learn Variable Binding in Symbolic Programs?

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-11T10:16:07.537276Z

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 c5c6d36a-4c53-48d0-8fea-ee20128a7f39 · inbound

When Symbol Names Should Not Matter: A Logistic Theory of Fresh-Symbol Classification cites this paper.

When Symbol Names Should Not Matter: A Logistic Theory of Fresh-Symbol Classification How Do Transformers Learn Variable Binding in Symbolic Programs?

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-11T01:45:52.261329Z

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 a57121f8-a65e-4fe4-a363-5fbacde6e7f0 · inbound

Assign and Add: A Mechanistic Study of Compositional Arithmetic cites this paper.

Assign and Add: A Mechanistic Study of Compositional Arithmetic How Do Transformers Learn Variable Binding in Symbolic Programs?

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:02:46.908260Z

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 13e0fe76-b9fb-4612-a7a8-90d33989f234 · inbound

Formalizing the Binding Problem cites this paper.

Formalizing the Binding Problem How Do Transformers Learn Variable Binding in Symbolic Programs?

Reference 93

Resolution: verified exact; arxiv_id, observed 2026-07-02T03:06:29.847762Z

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 867b183c-e7f6-40d8-b8c5-d48ab4ca12f3 · inbound

Radical AI Interpretability cites this paper.

Radical AI Interpretability How Do Transformers Learn Variable Binding in Symbolic Programs?

Reference 101

Resolution: verified exact; arxiv_id, observed 2026-07-04T13:09:51.105712Z

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.