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Share the Symbol, Not the Vector: Training-Free Fact Communication Across Language Models

Xin Li, Mengbing Liu, Hao Jiang, Xin Gao, Annan Wang, Xingwei Qu, Yichi Zhang, Chau Yuen

arXiv:2610.19696v1cs.CL

TL;DR

Sharing internal states across architectures can require learned translators or compatibility assumptions. SYNC instead sends shared word indices and writes facts using each receiver’s own directions; early writing yields 72.0–98.3% four-answer success on new scenes, substantially exceeding middle-layer writing on seven receivers.

  • Problem

    Sharing internal model states across architectures can require a learned translator or structural compatibility, leaving a need for fact transfer without either.

    Source: §1 · pp. 1–2

  • Method

    SYNC sends selected shared-word indices and object assignments, which frozen receivers interpret using their own symbol directions to write facts into hidden states.

    Source: §1 · p. 2, §2.1 · p. 2

  • Results

    72.0–98.3% four-answer success on 572 new scenes, with early writing exceeding middle-layer writing by 65.0–96.2 percentage points on seven newer receivers.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Shared symbol indices and receiver-local directions support fact communication across heterogeneous models without fine-tuning or a learned translator.

    Source: §6 · p. 8

    The evaluation uses fixed inventories and reuses question forms and some attribute combinations; open-vocabulary messages and relational facts remain untested.

    Source: §6 · p. 8

Abstract

from arXiv · show

Multi-agent systems allow language models to solve tasks collaboratively by sharing complementary information. These systems typically communicate through text, while recent approaches also explore exchanging internal model states. However, sharing these states across architectures often requires learned translators or assumptions about model compatibility. We introduce SYNC (Symbol-Indexed Neural Communication), a word-indexed interface that connects heterogeneous models without fine-tuning or a learned translator. From descriptions only it can see, the sender selects words from a shared list and sends their indices for each object, without seeing the questions. The receiver writes the described facts into its hidden states using its own word directions, vectors fitted once from its activations. We test selective use by swapping one attribute between two objects and requiring correct answers about both changed and unchanged attributes before and after the swap, four answers in total. We choose an early write layer on four development receivers and then fix it. With three different senders and nine newer receivers from five families, four-answer success on new scenes reaches 72.0-98.3%, up to 96 percentage points above middle-layer writing, and the two largest receivers match plain text. A task-free probe predicted in advance which depths each new receiver can use (45 of 45 cases). Without retuning, messages listing every fact keep 89.6-100% success under new layouts, and sender messages reach 23.9-64.0% on a landmark task with multi-token symbols, below text but from 0% without a message. These results show that shared word indices and receiver-local directions can support selective fact use across model families without additional training.

1. INTRODUCTION

Sharing internal model states across architectures can require learned translators or compatibility assumptions, while text provides a common interface. SYNC instead sends shared word indices for private facts and writes them with receiver-local directions, achieving high four-answer success across newer receivers when writing early.

1. INTRODUCTION

  • Internal-state communication across architectures can require a learned translator or structural compatibility, motivating a fact-transfer interface that avoids both.Text is a common communication interface for agents built on different models.Source: §1 · pp. 1–2
  • SYNC sends selected shared-word indices and object assignments; each frozen receiver interprets them through its own word directions.The sender selects words from private evidence without seeing the questions.Source: §1 · p. 2
  • The evaluation swaps one attribute between two objects and requires correct answers about both changed and unchanged attributes in both worlds.All four answers must be correct; controls separate sender selection from receiver use.Source: §1 · p. 2
  • 72.0–98.3% four-answer success on 572 new scenes, with early writing exceeding middle-layer writing by 65.0–96.2 percentage points on seven newer receivers.The two largest receivers match plain text; pointing each word to another word’s direction leaves at most 4.4%.Source: §1 · p. 2
  • A task-free probe predicted usable depths for all 45 tested depths across nine newer receivers before their depth scans.The fixed setting also reached 89.6–100% with complete facts under new layouts; landmark-task messages reached 23.9–64.0%, below text.Source: §1 · p. 2

2. METHOD: SYMBOL-INDEXED COMMUNICATION

SYNC transmits selected symbols as indices from a shared inventory, then uses each receiver’s own fitted directions to write and reuse the described facts. The sender and receiver remain untrained.

2.1. Private evidence and shared messages

  • The sender selects up to four supported inventory symbols per object and sends their indices, not tokenizer IDs, without seeing the question.Automatic messages assign every symbol the maximum 8-bit weight.Source: §2.1 · p. 2

2.2. Fitting receiver-local symbol directions

  • Each receiver’s symbol direction is obtained by averaging hidden-state differences between a word and the neutral filler across twelve generic contexts.The directions are computed once without training parameters or using private scenes, questions, answers, or another model’s activations.Source: §2.2 · pp. 2–3

2.3. Writing facts and reusing the message

  • The receiver reserves four neutral slots per object and replaces used slots with saved neutral states plus the corresponding symbol directions.The write modifies chosen-layer positions, with γ as write strength and q_max as the largest weight for that object.Source: §2.3 · p. 3
  • The processed prefix is saved in a key–value cache and copied for each question, so both questions read the same message without further writes.The text route places the same symbols and object assignments in the same slots as ordinary tokens.Source: §2.3 · p. 3

3. EXPERIMENTAL SETUP

The evaluation tests selective fact use by swapping one attribute between two objects and requiring correct answers to questions about both attributes in both worlds. It compares early and middle writing with plain text, using controls and separate development and confirmation scenes.

3. EXPERIMENTAL SETUP

  • A scene succeeds only when all four answers across the two worlds are correct after one attribute is exchanged while the other stays fixed.Invalid or truncated answers count as errors; without a message, four-answer success is zero by construction.Source: §3 · p. 3
  • The main evaluation fixes a write setting chosen on four development receivers and tests three different senders with newer receivers from five families.Delivery routes are early writing at relative depth 0.2, middle writes at depths 0.4, 0.5, and 0.6, and plain text.Source: §3 · p. 4
  • Controls compare symbol–direction reassignment, complete-fact messages, and a native-state reference against the selected message route.Reassignment keeps message, positions, and edit norm fixed; the native-state reference is an empirical comparison, not an upper bound.Source: §3 · p. 4
  • The setting is chosen on 92 development scenes with complete facts and 90% coverage, then fixed before 572 confirmation scenes with automatic messages.Confirmation scenes change object names and descriptions but reuse symbols, question forms, and some attribute combinations.Source: §3 · p. 4

4. RESULTS

A fixed early write transfers facts across new senders and receivers, while usable depth varies by receiver and can be predicted. The fixed setting also carries to new layouts and a landmark task, and receivers can use write strength to distinguish competing values.

4.1. Does a fixed interface carry to new senders and receivers?

  • 72.0–98.3% four-answer success across all 25 sender–receiver pairs, with early writing beating middle layers by 65.0–96.2 points on seven sub-27B receivers.The write setting was fixed on development receivers and applied without retuning.Source: §4.1 · p. 4, Table 1 · p. 5

4.2. Where must the receiver write the facts?

  • At depth 0.2, fitted directions yield 100% on both Qwen receivers and Gemma and 88.5% on GLM; shared selection fixes γ=1.Doubling strength at depth 0.2 keeps success above 82% on every development receiver, while no strength rescues depths 0.65 or 0.8.Source: §4.2 · p. 5, Figure 4 · p. 6, Figure 5 · p. 6

4.3. Can a receiver’s usable depths be predicted in advance?

  • All 45 held-out depth predictions are correct; probe rank correlation with success is 0.89 [0.81, 0.96], exceeding depth-only balanced accuracy by 0.13 [0.08, 0.19].The probe predictions were committed before the newer receivers’ depth scans.Source: §4.3 · pp. 5–6, Table 2 · p. 7

4.4. Does the fixed setting carry beyond the development task?

  • Across new layouts, success remains 89.6–100% (14 of 18 tests pass; four are inconclusive); on Countries, four receivers reach 23.9–64.0% versus 0% without messages.On Countries, early writing trails text by 31.7–63.2 points; across layouts, text stays at 99.3–100%.Source: Table 3 · p. 7, §4.4 · p. 7

4.5. Do receivers use weights encoded as write strength?

  • On Qwen3-32B and Qwen3.5-27B, internal delivery beats printed weights by 36.1 [31.0, 41.4] and 33.8 [20.8, 48.1] points, respectively, averaged over L=64, 128, and 191.At L=191 on Qwen3-32B, success is 4.9% internally and 18.1% with text.Source: §4.5 · p. 7

5. RELATED WORK

Related work studies word-associated directions, hidden-state interpretation, and communication or representation transfer. SYNC is distinguished by writing facts through receiver-local directions without a learned map.

Word directions and steering

  • J-space work motivates word-associated directions, but representational convergence or within-model steering alone does not show cross-model fact communication; SYNC uses activation contrasts like ActAdd and CAA.The motivating J-space work is Gurnee et al. (2026), and the convergence result is Huh et al. (2024).Source: §5 · pp. 7–8

Using a model to interpret hidden states

Communication and representation transfer

6. DISCUSSION, LIMITATIONS AND CONCLUSION

SYNC’s comparison with text varies by weighting, and the reported scope is bounded by fixed inventories and several untested settings.

6. DISCUSSION, LIMITATIONS AND CONCLUSION

  • For equal-weight facts, internal writing has no consistent advantage over text, while write strength performs best with graded weights.Text is similar or up to 14.1 points better on smaller receivers, and the two largest reach parity; on Countries, text leads by 31.7–63.2 points.Source: §6 · p. 8
  • Experiments cover fixed inventories and thirteen receivers from seven families; open-vocabulary messages, relational facts, and TipSheets remain untested.Two mixture-of-experts receivers failed the implementation check, and senders reading symbols from their own hidden states performed poorly.Source: §6 · p. 8
  • The early-versus-middle writing comparison changes layer, write count, and edit size together, limiting attribution to layer alone.Input embeddings perform at least as well as fitted directions on single-token symbols; multi-token comparisons, early-layer J-lens writing, and probing beyond nine receivers remain untested, while latency was measured only with complete facts.Source: §6 · p. 8
  • With shared symbol indices and receiver-local directions, SYNC transfers facts across heterogeneous models without fine-tuning or a learned translator.The fixed setting also carries to newer models, new layouts, and a landmark task without retuning.Source: §6 · p. 8

AI USE STATEMENT

The authors used language-model assistants in writing, literature work, and research tasks, while retaining responsibility for the paper and its results.

AI USE STATEMENT

  • Assistants helped draft and edit text, format references, and search for and summarize related work.The authors reviewed and approved contributions, and retained responsibility for the experiments, results, interpretations, and paper.Source: AI USE STATEMENT · p. 9
  • Under author supervision, assistants helped refine hypotheses and experimental design, generate synthetic task materials, implement and run experiments, and interpret results.The authors kept results only after recounting them from stored outputs.Source: AI USE STATEMENT · p. 9
  • Assistants were not used to formulate mathematical claims or proofs, or for qualitative or thematic data analysis.Those analysis tasks did not apply to this work.Source: AI USE STATEMENT · p. 9

REPRODUCIBILITY STATEMENT

The paper describes its experimental protocols, implementation details, and checks supporting reproduction of reported results.

REPRODUCIBILITY STATEMENT

  • Appendices A–D document protocols for newer-model, prediction, transfer, and graded-weight experiments, while Appendix H specifies the interface implementation and reproduction sequence.Appendix H covers the sender, fitting contexts, public layout, intervention, cache reuse, prompts, and inference settings.Source: REPRODUCIBILITY STATEMENT · p. 9
  • Appendix J reports data overlap, development selection, confirmation, controls, uncertainty estimates, and numerical checks.Tables and quantitative figures are generated from source data with recorded hashes, and independent recounts reconstruct answers and statistics.Source: REPRODUCIBILITY STATEMENT · p. 9
  • The authors state that code, preregistration locks, scene banks, sender messages, per-row records, and analysis outputs will be released with regeneration commands.The statement also identifies a separate appendix describing the earlier sparse-extraction implementation and its limits.Source: REPRODUCIBILITY STATEMENT · p. 9

ETHICS STATEMENT

The ethics statement describes the study materials and model setting; the appendix contents list implementation, reproduction, and message-construction material.

ETHICS STATEMENT

  • Controlled tasks use mechanically generated descriptions and template sentences over a fixed concept list, and the adapted Countries and TipSheets tasks are also mechanically generated.All experimental models are open-weight checkpoints run locally, with no human subjects or personal data involved.Source: ETHICS STATEMENT · p. 9

APPENDIX CONTENTS

  • Appendix H lists interface implementation and reproduction topics, including sender messages, fitting contexts, intervention, cache reuse, and inference settings.The appendix contents also list message selection, direction construction, symbol contrasts, J-lens writing, and the scope of earlier utility results.Source: APPENDIX CONTENTS · p. 11

A. NEWER SENDERS AND RECEIVERS

The fixed early-write setting is evaluated across new senders and receivers, with controls for message delivery and implementation. Reported cross-model pairs meet the recovery rule, while complete-fact performance and scale comparisons provide additional context.

A. NEWER SENDERS AND RECEIVERS

  • The fixed protocol uses one write at relative depth 0.2, receiver-fitted directions, four slots per object, and frozen prompts and parser.The setting was selected on four development receivers; the confirmation evaluation uses 572 scenes, with senders, receivers, thresholds, and decision rules fixed before outcomes.Source: A. NEWER SENDERS AND RECEIVERS · pp. 11–12
  • Nine reported receivers pass implementation checks, while Qwen3.6-35B-A3B and Qwen3.5-122B-A10B have no outcome rows after check failures.Seed-OSS-36B-Instruct is also unreported because 28–34% of internal-delivery answers were unscored despite a zero thinking budget.Source: A. NEWER SENDERS AND RECEIVERS · p. 12
  • Within Qwen3.5, internal-minus-text gaps narrow from 2B to 27B by 5.2, 4.2, and 3.7 points for the Gemma-4, Qwen3.6, and gpt-oss senders, respectively.The prespecified scale contrast used Qwen3.5-122B-A10B, so these are descriptive comparisons.Source: A. NEWER SENDERS AND RECEIVERS · p. 12
  • With complete facts, early writing stays within 4.5 points of receiver-native states on every receiver, though both routes trail text on gpt-oss-20b.The complete-fact evaluation uses the fixed early layer and no model sender.Source: A. NEWER SENDERS AND RECEIVERS · pp. 12–13, Table 6 · p. 13
  • Every reported cross-model pair meets the prespecified recovery rule for four-answer success, valid answers, and performance above reassignment.The rule requires internal success of at least 50%, validity of at least 90%, and internal success above mean reassignment at both clustering levels after Holm correction.Source: A. NEWER SENDERS AND RECEIVERS · pp. 12–13, Table 5 · p. 13

B. PREDICTING USABLE WRITE DEPTHS

A task-free binding probe predicts usable write depths, and the section also describes tests of new layouts and a landmark task. The probe correctly predicts all held-out depth outcomes, while the layout tests exclude interleaved facts and relational roles.

B. PREDICTING USABLE WRITE DEPTHS

  • The binding probe writes paired symbol directions into separate object slots, then scores whether both symbol-to-object questions are answered correctly.Its value is compared with complete-fact four-answer success; the probe threshold is 0.786, selected on development receiver–depth cells.Source: B. PREDICTING USABLE WRITE DEPTHS · p. 14
  • The primary probe was amended because its symbol-logit AUC stayed near 1.0 across depths even as GLM-4-9B success fell from 88.5% to 0%.The binding probe replaced it before held-out calibration or outcomes; the repeat symbol-identification probe remained at least 0.998 across depths.Source: B. PREDICTING USABLE WRITE DEPTHS · p. 14
  • All 45 held-out probe predictions are correct, and the deepest usable depth is predicted exactly for all nine receivers.Held-out balanced accuracy is 1.00, compared with 0.87 for the depth-only rule; the difference is +0.13.Source: B. PREDICTING USABLE WRITE DEPTHS · p. 14, Table 7 · p. 14

C.1. New layouts

  • The layout evaluation tests moved or reordered facts, a changed template, and a third object, while keeping each object’s facts together.Interleaved-object layouts and relational roles were not tested with the final interface.Source: §C.1 · p. 15, Table 8 · p. 15

C.2. Countries

  • In the Countries task, all four receivers meet the prespecified rule, while four-answer success without a message is 0% on every receiver.The receiver must place landmarks in countries across two worlds in which the landmarks are swapped; sender messages use multi-token symbols.Source: §C.2 · pp. 15–16, Table 9 · p. 16

D. GRADED WEIGHTS

Graded-weight experiments compare internal delivery with printed-weight text and alternative text formats. Further discussion identifies conditions affecting receiver performance, including write depth, symbol-to-object binding, and sender-side symbol extraction.

D. GRADED WEIGHTS

  • On Qwen3-32B and Qwen3.5-27B, internal delivery exceeds text with printed weights by 36.1 and 33.8 points, respectively, averaged over L=64, 128, and 191.At L=191, Qwen3-32B reaches 4.9% internally versus 18.1% with text; wrong-direction reassignment at L=128 leaves at most 2.1%.Source: D. GRADED WEIGHTS · pp. 16–17, Table 10 · p. 17
  • The comparison concerns two encodings under this format: text includes the weights, which are uncalibrated, and whether senders can produce useful graded weights remains untested.gpt-oss-20b is not interpretable in this comparison because its internal route reaches only 84.0% at L=0.Source: D. GRADED WEIGHTS · p. 16
  • Against other text formats, internal delivery leads every format by 15.5–31.9 points on Qwen3-32B and four formats by 13.0–38.4 points on Qwen3.5-27B.On Qwen3.5-27B, qualifier text exceeds internal delivery by 8.8 points; which encoding conveys graded weights best depends on the text format and receiver.Source: D. GRADED WEIGHTS · p. 16

E. FURTHER DISCUSSION

  • Shared indices specify facts and object assignments, while receiver-local directions supply each model’s vectors; internal success also stays high across tested slot, template, and object-count changes.On a separate four-object bank, three of four development receivers combine separately sent attributes and keep them attached to the correct object.Source: E. FURTHER DISCUSSION · p. 17
  • At GLM depth 0.35, fixed directions reach 8.3%, versus 40.6% for scene-specific directions, 66.7% for native states, and 99.0% for text.The paper attributes contributions to layout and position, co-occurring facts, and the write path.Source: E. FURTHER DISCUSSION · p. 17
  • A symbol can remain identifiable even where four-answer success is zero; the binding probe measures the lost symbol–object link and predicts success.The authors propose running the probe at candidate depths for a new receiver without task data.Source: E. FURTHER DISCUSSION · p. 17
  • A prompted sender selects symbols, but an earlier hidden-state symbol-weight sender never met the four-answer criterion and improved generated-answer accuracy in only one of four evaluable pairs.Its messages conveyed less than prompted selections as text; early-layer J-lens writing remains untested.Source: E. FURTHER DISCUSSION · p. 17
  • Within Qwen3.5, the internal-delivery versus text gap narrows from 2B to 27B by 5.2 points with the Gemma-4 sender, but the scale trend is descriptive.The prespecified scale test required Qwen3.5-122B-A10B, which failed the implementation check.Source: E. FURTHER DISCUSSION · p. 17

F. DEVELOPMENT RECEIVERS: CONFIRMATION WITH THE LLAMA SENDER

On four development receivers, early-layer writes with receiver-local symbol directions support high four-answer success, while middle-layer writing performs worse. The section also shows that late writes fail when facts are not readable in lower layers, and specifies the interface and evaluation design used for confirmation.

F. DEVELOPMENT RECEIVERS: CONFIRMATION WITH THE LLAMA SENDER

  • 0.6–3.0% mean four-answer success after symbol–direction reassignment, despite unchanged message bytes and edit size, supports selective use of the intended directions.Qwen3-14B-Base retains about 99% valid answers; other receivers also produce more invalid answers. Receivers’ answers with the other world’s message match that world’s facts.Source: F. DEVELOPMENT RECEIVERS: CONFIRMATION… · p. 18
  • Internal and text delivery reach similar success on both Qwen receivers and Gemma, but GLM performs 13.5 points better with text.GLM’s internal success on coats is 46.6%, versus 66.5% with text; this is a post-hoc domain breakdown.Source: F. DEVELOPMENT RECEIVERS: CONFIRMATION… · p. 18
  • 74.3–97.7% four-answer success across all four receivers; early writing improves three by 66.7–73.8 percentage points over middle-layer writing.These results use the receivers’ own symbol directions.Source: Table 12 · p. 18, F. DEVELOPMENT RECEIVERS: CONFIRMATION… · p. 18
  • Two of three prespecified single contexts approach the twelve-context result, but the first performs worse on Qwen3-32B and fails on GLM.Averaging is unnecessary for high success, but context choice matters; the input-embedding difference matches fitted directions on three receivers and exceeds them on GLM for this single-token bank.Source: F. DEVELOPMENT RECEIVERS: CONFIRMATION… · pp. 18–19, Table 13 · p. 19

G. WHY LATE WRITING FAILS: DIAGNOSTICS

  • At cut depths 0.5 and 0.65, restoring neutral prefix keys and values removes much of the early-write benefit, indicating that answers need fact-bearing information in lower layers.On GLM, writing at 0.35 reaches 8.3%, whereas writing at 0.2 and restoring through 0.35 reaches 72.9%; the diagnostics localize where facts must be readable but do not identify a unique mechanism.Source: G. WHY LATE WRITING FAILS: DIAGNOSTICS · p. 19, Table 14 · p. 20
  • At GLM depth 0.35, scene-matched directions close about half the gap between fitted directions at 8.3% and native states at 66.7%.Other facts present in native states account for most of the remaining gap.Source: G. WHY LATE WRITING FAILS: DIAGNOSTICS · p. 19, Table 15 · p. 20

H. FINAL INTERFACE: IMPLEMENTATION AND REPRODUCTION

  • SYNC uses a shared 221-word inventory and object-assigned indices; each receiver maps those indices to its own hidden-space directions, fitted from receiver activations without paired activations or parameter updates.The sender sees descriptions but not questions; directions are computed from twelve public-layout contexts and reused across scenes.Source: §H.2 · p. 21

I.1. Two worlds that differ in one fact assignment

  • The evaluation swaps one attribute between two objects, asks about both changed and unchanged attributes in each world, and counts success only when all four answers are correct.The 576-scene bank was fixed before confirmation outputs; four implementation-check scenes were excluded, leaving 572 evaluated scenes, while the task structure and finite inventory remained familiar.Source: §I.1 · p. 23, §I.2 · pp. 24–25

J.1. Write-setting selection and automatic confirmation

The authors selected a fixed early write setting on development data and tested it on a separate confirmation bank. The selected setting recovered facts for the three receivers that failed with middle-layer writing, and the section reports diagnostic, four-object, delivery-route, and timing results.

J.1. Write-setting selection and automatic confirmation

  • All four development receivers select raw scaling, depth 0.2, and strength γ=1; the receiver-local scale never yields a better configuration.The selection maximized joint success among settings with at least 90% format coverage, with prespecified tie-breaks.Source: §J.1 · p. 25
  • All three prespecified receivers meet the recovery and substantial-recovery criteria on the 572-scene confirmation bank.Recovery required at least 50% joint success and 90% coverage, plus a significant gain over reassignment; substantial recovery also required a significant 20-point gain over middle-layer writing.Source: Table 20 · p. 26, §J.1 · p. 26
  • All six Holm-corrected comparisons reject for early writing versus both middle-layer writing and mean reassignment on Qwen3-14B-Base, GLM, and Gemma.Text contrasts are descriptive; a small or zero difference does not establish equivalence.Source: Table 21 · p. 26, §J.1 · p. 26

J.2. Update magnitude and the native-state reference

  • At the selected early depth, matching fitted and native edit norms changes success little: Qwen and Gemma remain at 100%, while GLM changes by about one percentage point.This diagnostic does not explain late-write failure, because depth also changes the representations and subsequent computation available.Source: Table 25 · p. 28, §J.2 · p. 28

J.3. A depth rule fixed before Gemma’s fitted outcomes

  • Gemma’s native-state-guided depth rule reaches 100% development success, but it uses task outcomes and is not an independently validated predictor.The rule was fixed before Gemma’s fitted-direction outcomes were read.Source: §J.3 · p. 28

J.4. Four-object transfer with the receiver fixed

  • 86.9% and 91.1% four-answer success on 188 four-object scenes for automatic early writes on Qwen3-32B and Gemma, respectively.Complete-fact delivery reaches 97.3% and 100%; the original middle band reaches 80.0% and 26.2%. This descriptive extension uses a selected pair of receivers and four templates.Source: Table 27 · p. 29, §J.4 · p. 29

J.5. Message content and agreement between delivery routes

  • On GLM, 93 two-object scenes succeed as text but fail through writing, versus 16 in the reverse direction; all 93 former scenes contain complete automatic facts.The paired route comparison therefore places those failures after sender selection, without isolating which receiver-processing step causes them. In four-object scenes, Gemma’s 17 failures all omit a queried fact, while Qwen has six failures despite complete facts in both worlds.Source: §J.5 · pp. 29, 31, Table 29 · p. 30

J.6. Timing internal and text delivery

  • Complete-fact messages are 20 bytes, versus an average of 226 UTF-8 bytes for padded weighted text, but this is not an optimized equal-budget comparison and supports no bandwidth or latency advantage.The two follow-on studies reuse the selected interface on separate new banks, not pooled with the preceding confirmation.Source: Table 31 · p. 31, §J.6 · p. 31, K. FOUR-OBJECT QUESTIONS AND SIMPLER… · p. 31

K.1. Four-object conjunction queries

The four-object evaluation tests whether communicated facts support changed and unchanged answers across worlds, then examines how earlier sparse-message systems and alternative writing configurations perform. The results distinguish successful prompted selection and early-layer writing from limits in earlier routes and in the scope of their evaluations.

K.1. Four-object conjunction queries

  • The 576-scene test requires all four answers across two worlds, with a swapped attribute and a preserved attribute; prespecified criteria distinguish reliable use from a positive contrast alone.Controls include complete facts, identity writes, and symbol–direction reassignments; text comparisons are descriptive.Source: §K.1 · pp. 31–32
  • 94.4–95.7% four-answer success was reached by three receivers, while GLM reached 41.8%; its complete-fact write reached 44.6% versus 89.2% as text.The sender’s messages contained 99.9% of required facts, indicating selection was not the bottleneck in this setting.Source: Table 32 · p. 32, §K.1 · p. 32

K.2. Single-context directions and input embeddings

  • Twelve-context fitting improved over three single contexts on Qwen3-32B and GLM, while input embeddings showed no corrected disadvantage and outperformed internal writing on GLM.The comparison supports simpler representations at this early layer rather than a need for twelve-context averaging.Source: §K.2 · p. 33, Table 36 · p. 34

L. EARLIER EXTRACTION: IMPLEMENTATION AND OUTCOMES

  • The earlier sparse route extracted sender-state coefficients and adjusted receiver coefficients; positive controlled binding effects were limited by reassignment sensitivity and failed selective-generation criteria.No automatic sparse-message pair met the prespecified selective-fact criterion.Source: §L.2 · p. 35, §L.1 · p. 35, §L.3 · p. 36

M.1. Same-checkpoint message sources

  • Prompted selection exceeded same-checkpoint sparse extraction by 94.8 points [87.5, 100.0] on candy/blocks and 69.8 [54.2, 84.4] on coats.The comparison changes message support and weights and therefore does not isolate content loss or establish equivalence with complete facts.Source: Table 38 · p. 36, §M.1 · p. 36

M.2. Each-layer directions and the update rule

  • On Qwen3-32B, each-layer directions gained 44.8 points [31.2, 58.3] over midpoint directions, but superiority over coefficient updates at matched edit norms remains untested.Rescaling midpoint directions accounted for 7.3 [3.1, 12.5] points of the gain.Source: Table 39 · p. 37, §M.2 · p. 37

M.3. Symbol contrasts and J-lens at one layer

  • On Qwen3-32B, symbol-contrast writes supported high joint success while J-lens performed much worse; early-layer J-lens writing was not tested.The comparison cannot distinguish direction orientation, fitting objective, or compatibility with the evaluation context.Source: Table 40 · p. 37, §M.3 · p. 37

N. SCOPE OF THE EARLIER UTILITY RESULTS

  • All sixteen earlier sparse-extractor and coefficient-writer configurations failed the useful-delivery criterion; these findings do not evaluate the prompted sender with the early-layer writer.TipSheets also remains untested with the final configuration.Source: N. SCOPE OF THE EARLIER UTILITY RESULTS · p. 38

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