# TAE-Bench: Text Autoencoders as a Testbed for Understanding Neuralese

Working manuscript · v0.1 · 11 September 2026 · **9-page target, plus references and appendix**

> **Draft contract.** This paper introduces a general testbed for understanding continuous language representations. Existing observations are imported with their scope; the shared benchmark comparison has not been run. Green labels mean evidence exists, not that a section is submission-ready. The [experiment plan](experiments.html) and [evidence register](evidence.html) sit outside the main manuscript. The [Campaign100 paper](../experiments/campaign100/PAPER_DRAFT.html) remains available as the earlier manuscript.

## Abstract [needs to be improved]

Learned continuous representations can transmit linguistic information without exposing a human-readable account of how it is organized. We study text autoencoders as a tractable testbed for understanding such representations: an encoder maps text to a vector, and a decoder maps that vector back to text. Their linguistic endpoints support controlled tests of content, composition, and intervention, while the internal code remains a discovery problem. We propose TAE-Bench, an evaluation of interpretation methods along three capability groups: reading; reconstruction and composition; and intervention prediction and control. The design distinguishes known linguistic targets from known mechanisms, and uses authored codes to calibrate tests before applying them to trained models. Existing experiments motivate this framework: fitted composition maps can improve reconstruction through a decoder; highly readable order subspaces need not provide selective editing advantages; and simple lexical models leave substantial representation variance unexplained. A pilot of the full protocol on SONAR finds that four of five tested factors are one-vector factors, recovered at ≈ .99 of the decoder-measured ceiling by a mean difference, while order is recovered by no direction and by a z-conditioned linear operator at .95; readers trained on one construction invert on another at high confidence, which the benchmark's absence axis catches. These observations motivate the frozen comparison, which remains to be run.

**[needs to be improved]** Replace the final two sentences with the completed comparison's main result and its uncertainty after N04–N06. Do not promise a positive method advantage or a complete mechanism in advance.

## 1. Introduction [needs to be improved]

What would it mean to understand a representation that communicates in vectors rather than words? A readable feature name is one possible description. A stronger test asks whether the description supports accurate predictions on new inputs, reconstructs relevant information, or enables a specific change without disturbing other content. These capabilities need not coincide. A property may be easy to classify but difficult to edit; a decomposition may reconstruct most variance while missing distinctions that matter to a decoder.

We use *neuralese* here to mean learned continuous representations carrying information between neural computations. Text autoencoders instantiate a bounded version of this problem. For a sentence x, the encoder produces z = E(x); a decoder generates D(z). We can vary linguistic content, hold other factors fixed, inspect the representation, and compare predicted consequences with measured outputs. The input supplies a semantic target; it does not reveal the model's internal implementation. Decoding may also lose information or supply likely completions. These properties make TAEs useful for studying interpretation, while requiring explicit decoder controls.

We introduce **TAE-Bench**, a capability-based evaluation of interpretation methods on fixed TAE substrates. It asks whether an interpretation enables held-out reading, reconstruction, composition, intervention prediction, and control. It uses known-code calibration, matched access, simple baselines, and independent semantic checks. Results are reported as capability profiles rather than a single ranking that conflates methods with different interfaces.

The empirical investigation is organized around a common comparison and two case studies. The first asks how far simple vector algebra provides useful composition and control. The second examines the gap between a successful representation-level description and the behavior that it explains. Residual sentence information is one open question in this second investigation; the framework does not require that all representations decompose into words plus a uniquely defined semantic remainder.

The intended contributions are (i) a tractable evaluation setting for neuralese interpretation, (ii) a small, calibrated benchmark with explicit method interfaces, and (iii) an empirical account of current methods' strengths and limits. **[needs to be run]** The common evaluation supporting contribution (iii) remains outstanding. The historical observations below motivate the design and supply candidate case studies.

[![TAE-Bench schematic: controlled text passes through an encoder, vector, and decoder. An interpretation method makes predictions or edits evaluated on held-out outcomes. Three capability groups are reading, reconstruction/composition, and prediction/control.](figures/fig1-testbed.svg)](figures/fig1-testbed.svg)

**Figure 1 — testbed and evaluation contract (schematic).** An interpretation method observes permitted examples and queries, then commits predictions or interventions before held-out outcomes are revealed. Linguistic labels belong to the evaluator. Authored toy-code internals are available only to privileged controls. The exact access contract remains **[needs to be improved]** under N01. [PDF](figures/fig1-testbed.pdf) · [PNG](figures/fig1-testbed.png).

## 2. TAE-Bench [needs to be improved]

### 2.1 The denominator, and the substrate ladder

A probe that reads a property from a residual stream reports an unbounded lower bound: nothing says how much was there to read. A TAE supplies the missing denominator. For any property and any item, parsing the decoder's output of z says whether the property is *expressible from z*; for any counterfactual x′, the full difference E(x′) − E(x) says whether the change is *achievable in z*. Every method score in TAE-Bench is therefore a **fraction of a per-item, decoder-measured ceiling**, computed on the subset of items the decoder certifies (coverage is always reported). This is the benchmark's one new measurement, and it transfers to any latent that has a decoder.

The unit of evaluation is an interpretation method applied to a fixed encoder–decoder system. Four substrates form a ladder; the same tasks and the same method adapters run on all of them.

| Rung | Substrate | Ground truth | Role |
|---|---|---|---|
| L1 | Authored closed-form codes | exact mechanism | instrument calibration only; never a headline number |
| L2 | Trained miniature TAEs (7.7M parameters, canonical-target objective; several seeds and bottleneck widths) | constructed labels; factors certified present or absent | seed and objective variation |
| L3 | SONAR (1024-d) [R1] | constructed labels; per-item decoder certification | main real-model case |
| L4 | Vectors produced by an LLM-class model in the same space (a SONAR-space concept planner), decoded by the same decoder | task ground truth + decoder | transfer: only the producer of z changes |

Changing the encoder defines a separate substrate comparison, not an improvement by an interpretation method.

For real TAEs, semantic labels specify what the input says and what a target counterfactual should say. The evaluator measures whether the native decoder expresses those distinctions. Mechanistic ground truth is reserved for authored codes. A probe failure on a real model licenses a reader-and-distribution-specific statement, not a universal absence claim.

**[needs to be improved]** N01 must freeze checkpoint revisions, normalization, decoding settings, and the admitted tasks for each substrate. Existing GAUGE, TRACE, SIEVE, and Campaign100 assets have different purposes; their scoring rules and historical claims are not adopted automatically [S08].

### 2.2 Six tasks in three capability groups

The three groups ask three different questions of an interpretation. *Read* asks whether it can tell what a vector contains, without changing it. *Reconstruct / compose* asks whether the description is complete enough to rebuild a vector, or to build the vector for "A and B" from the vectors for A and B. *Predict / control* is the only group that modifies z. It splits into two tasks that are easy to conflate. In I1 the method is handed an edit δ and must state, before the decode is revealed, what D(z + δ) will say: the intended change and every side effect. This tests whether the description is honest. In I2 the method must produce the edit itself, so that the decode flips the target factor and nothing else. This tests whether the description is a handle. A method can pass I1 by knowing that a direction is polluted while failing I2 because it has no cleaner one; it can pass I2 by luck or by brute search while failing I1 because it cannot say what its own edit does. The fourth row, *absence*, is a penalty rather than a capability.

| Track | Task | Method output | Primary evaluation |
|---|---|---|---|
| Read | R1: content | Predictions about queried entities/content | Held-out prediction quality versus declared baselines |
| Read | R2: relations and grammar | Predictions about roles and polarity | Per-phenomenon accuracy/AUC and transfer; no pooled lexical shortcut |
| Reconstruct / compose | C1: interpreted reconstruction | Vector reconstructed through the declared decomposition | Proposition preservation, with centered geometric fidelity secondary |
| Reconstruct / compose | C2: constituent composition | Predicted vector from constituent vectors | Preserved constituent content and specified arrangement |
| Predict / control | I1: effect prediction | Committed prediction before the edited output is revealed | Target and collateral outcome prediction, with calibration |
| Predict / control | I2: targeted editing | Edited vector produced from allowed inputs | Target success, untargeted-content preservation, and coverage separately |
| Absence | A1: known-absent structure | Commit or abstain, with confidence | Confident commitment on a certified-absent factor is scored net-negative and is non-dilutable; a method that skips A1 cannot appear in the headline figure |

Every edit cell is reported as three numbers, never averaged into one: fraction of ceiling (method success ÷ oracle success on certified items), premium over the best null (random direction at matched energy; shuffled pairing; energy-matched structured controls), and the absence penalty. Edits are energy-budgeted: the edited vector moves exactly c·‖E(x′) − E(x)‖ for c ∈ {0.5, 1, 2}, with c = 1 primary.

Two extensions are under consideration in the contract draft (`protocol/contract_v2.md`) and are not yet admitted. Constituent retrieval, recovering z_B from z_AB and z_A, is the inverse of C2 and has archival evidence in the SONAR unbinding study [S05]. Correctness-type factors, whether a sentence is grammatical or an arithmetic or code fragment is valid, have read-only probing evidence on SONAR [R4] with no ceiling and no intervention; under this contract they would need a judge-based certifier before they can enter R2 or I2.

Generalization is tested across new combinations of familiar components, rewordings/constructions, and a separately reported vocabulary shift. A lookup table of word identities is not expected to extrapolate to unseen words without an additional shared lexical representation. Methods enter the tracks supported by their declared interface; unsupported cells remain explicitly not applicable. We do not average over a method-specific subset to announce an overall winner.

### 2.3 Access, supervision, and baselines

Each submission declares its training data, semantic supervision, encoder/decoder queries, compute, and representation size. A feature-description method must turn its descriptions into scored predictions; a dictionary method is evaluated through reconstruction, readouts, or interventions rather than a coherence impression alone. A supervised role model is identified as supervised, even if its final representation is compact.

At test time no method sees source text: the input is z alone, which is the setting a monitor of neuralese actually faces. Two references bracket every white-box method: the *decoder-lens* (decode z, parse; the black-box null that any geometric method must beat) and the *text route* (decode, edit the text by rule, re-encode; what one gets without understanding z at all). The final evaluation does not reveal the desired answer vector or an intervention's output before the method commits. The native decoder, decode–edit–re-encode approaches, supervised readers, and text-only methods provide references under explicitly stated access. Oracle target vectors are decoder-capability controls, not competitors. If source text is exposed to one competitor, the relevant text baseline receives the same access. For a deterministic encoder, claims of benefit over complete text concern constrained computation or internal behavior, not extra unrestricted information.

**[needs to be improved]** A draft contract now exists (`protocol/contract_v2.md`, M0 in PLAN_V2) with the access rule, per-task ceilings and null stacks, the admitted-cell matrix, and five open decisions; it is not frozen. N01/M0 must settle those decisions, fix query accounting and complexity reporting, and pass the toy calibration before pilots are used to select final settings. No historic benchmark's zero-premium rule or automatic task exclusion is inherited without review.

### 2.4 Semantic scoring and uncertainty

For each item, retain the original proposition, the intended counterfactual, native round-trip output, and target-latent output. Report full-set outcomes and any capability-qualified subset separately. Fluent decoding is not sufficient: a role reversal, missing entity, or unintended polarity change is a semantic error. Narrow parsers are checked against an independent annotated sample, including paraphrases and parser failures.

Primary uncertainty resamples independent proposition or lexical families, not individual paraphrases. Training-seed and substrate variation are reported separately from conditional test-set uncertainty. Calibration data, exploratory examples, and the final held-out evaluation remain distinct. When a denominator or capability check fails, report the failure and coverage rather than silently deleting the task.

**[needs to be run]** N02 creates and validates the shared corpus and semantic evaluation. Existing isolated experiments do not provide this common denominator.

## 3. Validation and experimental setup [needs to be run]

### 3.1 Known-code calibration

A simple reference code sums slot-specific transformed word vectors: z = Σᵣ Rᵣ e(wᵣ). This model makes component replacement and slot-sensitive predictions explicit. Distinct slot transforms matter; one common rotation followed by its inverse would cancel. Recovery from the sum may suffer interference. The controls therefore distinguish exact knowledge of the generating mechanism from perfect recoverability at every noise level.

A second code adds a known contextual interaction. The analysis should detect when an additive approximation is insufficient, rather than automatically describing every residual as semantic structure. Positive controls know the generating factors; shuffled labels, corrupted explanations, and inappropriate decompositions test false discoveries. Equivalent behavioral descriptions are accepted without demanding recovery of one arbitrary basis.

**[needs to be run]** N03 validates the final six-task contract on these controls, varying signal/noise and sample size where a negative inference depends on sensitivity. GAUGE's authored-code implementation is reusable infrastructure, not evidence that this new contract has passed.

### 3.2 Methods and datasets

The initial comparison uses simple probes and difference-based operators, PCA/random-dictionary controls, retained SAE checkpoints, and a structured linear composition model. Each participates only in supported tracks. Existing whole-z and c_pool SAE dictionaries represent different substrates and must be distinguished. Inference calibration, realized sparsity, supervision, and training budgets are reported explicitly.

**[needs to be improved]** N01/N02 must replace this paragraph with exact method configurations, sample sizes justified by pilot variance, dataset construction, splits, and baseline assignments. **[needs to be run]** N04 runs the common pilot; N05 runs the frozen final comparison. No new training family is required merely to populate this draft.

## 4. What current methods achieve [needs to be run]

### 4.1 The shared comparison

Table 2 is the planned principal result. Historical measurements are deliberately not inserted into its cells: their cohorts, information access, metrics, and substrates differ.

| Method family | Read | Reconstruct / compose | Predict / control |
|---|---|---|---|
| Simple probes / fitted operators | [needs to be run] | [needs to be run] | [needs to be run] |
| PCA / random dictionary, with declared adapters | [needs to be run] | [needs to be run] | [needs to be run] |
| Existing SAE, with declared adapters | [needs to be run] | [needs to be run] | [needs to be run] |
| Structured composition model | [needs to be run] | [needs to be run] | [needs to be run] |

These cells are protocol placeholders for the frozen final comparison. N01 will declare supported tasks before final evaluation and replace unsupported entries with N/A. A model does not receive an editing capability merely by being listed. Task-specific text/decoder references and privileged controls appear beside the corresponding panels, not as an unfairly advantaged common competitor.

**Pilot shared comparison on SONAR (B1, 12 September 2026). [existing result]** A first pass of the full protocol on L3: five factors (order, polarity, tense, subject number, noun identity), 40 fresh nouns in a noun-disjoint split, 300-item test cohorts with per-item decoder certification (coverage .88–.93), nine method families, energy-budgeted edits, noun-clustered bootstrap, blind parser audit (40/40), and a ten-attack breaker round. Table 2′ gives the I2 cell at dose 1 as fraction of ceiling on certified items.

| factor | diff-of-means | probe direction | ridge operator Δ̂ = Wz + b | DAS k=1 | DAS k=64 | SAE top-16 edit | text route | random |
|---|---|---|---|---|---|---|---|---|
| ORDER | .00 | .00 | **.95** [.88, 1.00] | .03 | .24 | .00 | 1.00 | .00 |
| POLARITY | .99 | .99 | .91 | .99 | .88 | .03 | 1.00 | .00 |
| TENSE | .98 | .99 | .91 | 1.00 | .47 | .00 | 1.00 | .00 |
| NUMBER | .99 | .98 | .66 | .97 | .27 | .00 | 1.00 | .00 |
| CONTENT | .99 | 1.00 | .25 | .00 | .27 | .13 | 1.00 | .00 |

Reading is at ceiling for every factor under the within-noun protocol (linear probe ≥ .99 of decoder-lens). Four of the five factors are *one-vector factors*: a single global mean-difference direction flips them with content intact, and DAS at k = 1 matches. Order has no direction, but a full-rank linear operator conditioned on z reaches .95 on unseen nouns; its rank-16 truncation .70; donor-coordinate interchange (DAS) never exceeds .27. The absence axis behaves: readers trained on active sentences and applied to passives score .13 [.08, .21] at confidence .93 on "A is agent" (they read position, not role) and all three families are flagged. The SAE cells use a paragraph-trained dictionary that is off-distribution on these sentences (about 13k of 131k features ever fire), so they say "this dictionary here", not "SAEs". Scope: single system, templated stimuli, pilot settings (single learning rate for three DAS factors); the breaker found no attack that moves the order-operator cell (refit-identical, energy exact to 5e-8, 30/30 genuine swaps, oracle-informed projections onto the operator's own subspace match it). **[needs to be run]** The frozen final comparison with the N01 contract, a fresh cohort, and the second substrate as a first-class row.

**Figure 2 — capability profile. [needs to be run]** Plot per-task outcomes and uncertainty against the task's baselines; show target success and preservation separately. No synthetic placeholder scores are used; the pilot table above is the interim figure.

### 4.2 Existing observations motivating the comparison [existing result]

The archive already shows why these capabilities should be measured separately. A corrected TRACE comparison reports a method premium of 0.000 with a 95% interval of approximately [−0.167, 0.222] after access/baseline corrections [S08]. This establishes no resolved advantage in that comparison; it does not establish equivalence or impossibility.

On natural-text SONAR steering, the H2 report gives fluent-gated negation success of 0.70 at dose 1 and tense success of 0.85 at doses 1.5–2, with deterioration at larger doses [S04]. These selected-dose results motivate an applicability and preservation evaluation, rather than certifying a generally reliable editing tool.

In a fixed controlled SAE bank, paraphrase-invariant masks show a positive comparison against matched masks for polarity and count, but negative role discrimination [S06]. This is evidence of a task-dependent profile under that metric, not proof of monosemantic atoms or superiority over native-vector baselines. Matching limitations and the finite lexical bank constrain interpretation.

Two further pilot runs of the same protocol frame the SONAR table. **[existing result]** On the L2 organisms (role certified linearly readable, 1.00 of ceiling, four seeds), the role edit fails for every vector method (diff-of-means .02, DAS ≤ .08, ridge .08 at d_z = 64 and .51 at d_z = 256) while polarity and tense edits are perfect and the text route is 1.00: readability without a handle, on a substrate where the factor is provably linear. **[existing result]** On L4, vectors produced by a SONAR-space concept planner (Mimir-1.6B) decode to the certified proposition on about half the items; on that half, encoder-fitted readers and mean-difference edits transfer at ceiling, and the order operator transfers at .94. The halving of coverage is itself the first L4 finding.

**[needs to be improved]** Retain only observations that explain the final common table. Existing-result labels refer to archive reports; no forwards or confidence intervals were reproduced while creating this manuscript.

## 5. Two investigations of partial understanding [needs to be improved]

### 5.1 Useful vector algebra and its limits [existing result]

Sentence composition offers a concrete test of predictive understanding. A fitted model of the form z_AB ≈ W_A z_A + W_B z_B + b predicts the representation of concatenated constituents. An archived installation experiment on the small trained organism B_D_s0 compares these predicted vectors through its own decoder [S01]. The full composer obtains an oracle-output token-F1 of 0.551, versus 0.366 for averaging and 0.450 for a matched-spectrum random rotation. Removing the fitted rotation factor gives 0.509. These are three pair-seed means on one named trained organism, not three independent model training seeds and not a SONAR intervention result. The 1.000 reference is the decode of the true z_AB, not the ground-truth text: it factors out the autoencoder's own reconstruction error, which is substantial. Scored against the text instead, the true vector reaches token-F1 0.605 and the full composer 0.536, so the composer recovers most of what this decoder can express rather than most of the sentence. The absolute level of a within-model reference should not be read as reconstruction quality.

The experiment supports the usefulness of the fitted structure to that decoder. It does not establish that the encoder implements the same computation. Nor does the internal rotation alone account for order: order discrimination changes from 0.994 to 0.962 when it is removed, while the symmetric averaging composer scores 0.500. Slot asymmetry and the fidelity contribution of the rotation must be distinguished.

The later SONAR unbinding study further illustrates metric dependence [S05]. At a fixed training size, centered constituent reconstruction declines with chain depth, yet direct-chain retrieval can exceed ridge unbinding on the deeper conditions. Raw similarity floors contain substantial mean-vector similarity. These findings motivate reporting semantic recovery and baseline-corrected geometry separately, without inferring an intrinsic capacity limit from one estimator's curve.

**[existing result]** The B1 pilot adds the sharpest datum so far on what "useful algebra" means in SONAR. The order swap is not a direction in z: no global vector, probe weight, or DAS subspace up to rank 64 flips it. It *is* a linear function of z: a ridge operator Δ̂ = Wz + b fitted on training nouns flips order in .95 of unseen-noun items with both nouns and the verb preserved, and the same operator transfers to LLM-produced vectors at .94. Nulls that never see the oracle difference score .000; oracle-informed projections onto the operator's own 16-d subspace score .74 against the rank-16 operator's .70. This is the form a role-rotation composition predicts (the swap is the map R₂R₁ᵀ + R₁R₂ᵀ on near-orthogonal role images), but the identification of W with a rotation is untested: whether (I + W) is an involution and whether its action factorises over the noun subspaces are the next questions.

**[needs to be improved]** N06a should reuse the fitted operators on the shared corpus, audit the exact original aggregate provenance, and score constituent preservation. **[needs to be run]** Fresh composition/selected-edit transfer, with calibrated doses and native-target controls, is required before this becomes a common TAE-Bench case study.

[![Two plots for the miniature TAE B_D_s0. The full composer reaches token-F1 0.551 against the native target decode, compared with averaging at 0.366 and rotation removal at 0.509. Order discrimination stays high after rotation removal.](figures/fig3-composition.svg)](figures/fig3-composition.svg)

**Figure 3 — useful algebra on a miniature TAE. [existing result]** Original saved numeric aggregates, rather than transcribed report values. A: token-F1 against the native target decode, so 1.000 is the model's own decode of the true vector and not the ground-truth text; against the text that same vector scores 0.605. B: the saved order-discrimination metric, averaging forward/swapped directions on scorable cases. Bars average three pair-seed means; dots show those means, not independent model seeds or confidence intervals. This figure demonstrates decoder utility of a fitted map, not its identity with the encoder's mechanism. Fresh shared-protocol semantic transfer remains **[needs to be run]**. [PDF](figures/fig3-composition.pdf) · [PNG](figures/fig3-composition.png) · [Numeric data and provenance](figures/data.json).

### 5.2 Reading a property is not a selective editing handle [existing result]

A more recent SONAR study tests the nine-dimensional subspace of a query-conditioned order reader [S02]. On fresh stimuli, the reader achieves AUC 0.977–0.980 by construction family. Swapping the coordinates of this subspace changes decoded order in 0.140 of edits, compared with 0.124 and 0.110 for two energy-matched structured controls. The study reports no resolved selective advantage in its primary paired comparison. Transferring the complete counterfactual difference achieves 0.995 order swaps, establishing a strong target-latent capability reference in this setting.

This result separates a readable description from a selective manipulation mechanism. It concerns the tested reader/subspaces, doses, and distribution; it does not rule out every compact causal handle. Large interventions that lose nouns do not count as successful role or order editing.

The plotted swap and noun-retention means and the primary paired point difference have now been reproduced from retained output rows. The primary comparison subtracts the **best control separately for each proposition**, then averages: −0.00104, with saved noun-cluster interval [−0.0395, 0.0359]. Choosing one best control for the whole dataset instead gives +0.015625, with saved interval [−0.0213, 0.0523]. This difference in estimand explains why the primary result is not the subtraction of the displayed aggregate rates. Neither comparison establishes equivalence.

**[existing result]** The B1 absence cells give the same lesson from the reading side. Linear, MLP and mean-difference readers trained on active sentences to answer "is A the agent" score .92 within construction and .13 [.08, .21] on passives, at mean confidence .93; asked "is A first-mentioned" the same readers score .87 on passives. What they read is position. All three overclaim under the benchmark's rule, and the inversion is exact by label construction (.13 = 1 − .87 up to noise). On the L2 organisms the corresponding designated-name label reads at chance while 100-way agent identity reads at 1.00, the known name-comparison artefact of that label; the binding reader there is the identity one.

**[needs to be improved]** N06b must connect these outcomes to the benchmark's prediction/control panels. The saved bootstrap intervals have not been recomputed here; N05 supplies the shared-protocol evaluation. This is the default second case study because a controlled result already exists.

[![SONAR order reader AUC is approximately 0.98 across three construction families. Order swaps occur in 0.140 of reader-subspace edits, 0.124 and 0.110 for structured controls, 0.024 for isotropic controls, and 0.995 for full-target differences. Noun retention is shown separately.](figures/fig4-read-control.svg)](figures/fig4-read-control.svg)

**Figure 4 — readability and control are different endpoints. [existing result]** A: saved query-conditioned reader AUC. B: order-swap means with saved 95% noun-cluster bootstrap intervals; hollow diamonds show noun-retention point estimates. The latter is a partial preservation check, not complete semantic fidelity. Non-oracle controls match the reader edit's energy, not its subspace dimension. The full target difference is a privileged reference. Edit means and the paired point contrast were checked against retained rows; intervals are imported from the original analysis. [PDF](figures/fig4-read-control.pdf) · [PNG](figures/fig4-read-control.png) · [Numeric data and provenance](figures/data.json).

### 5.3 An open question: what remains beyond the words?

One possible explanation of the gap is that simple descriptions omit context-dependent sentence information. In E01, the tested linear lexical/bag model explains approximately 0.233 of pooled-z variance on a document-disjoint natural-text split [S03]. Token-state analyses and the follow-up broadcast model also leave substantial unexplained variance [S07]. A tested bigram instrument captures only about 4% of a planted generic bilinear interaction, so its small real-data gain is not evidence that interactions are absent.

The remainder r(x) = E(x) − Ê(x) is therefore an object for investigation, not a known meaning vector. Future tests should measure lexical leftovers, generalizable relational information, and the effects of transferring matched residual components. Restoring the exact residual merely reconstructs the original vector by definition; the discovery would be a reusable prediction or selective intervention on unfamiliar cases. A remainder decoded alone may be outside the native distribution, allowing the decoder's prior to dominate.

**[needs to be run]** N07 is a bounded optional residual pilot. Its outcome is not a prerequisite for the broad benchmark paper. A residual SAE or new decomposition family is justified only if this pilot identifies a reproducible target. Keep this subsection short or move it to discussion when typesetting.

## 6. Discussion, related work, and limitations [needs to be improved]

TAEs expose a useful middle ground between authored codes and opaque internal reasoning states. Their linguistic endpoints permit counterfactual construction and semantic evaluation; their learned vectors still require interpretation. The benchmark asks which capabilities a proposed explanation supports, rather than declaring a representation understood because one metric is high. Transfer from a reconstruction bottleneck to a model's reasoning, planning, or inter-agent communication remains an empirical question.

SONAR supplies the principal encoder–decoder substrate [R1]. ROLE is relevant prior work on learning compositional approximations to neural representations [R2]. Earlier exploratory SONAR work demonstrates token-replacement and position-dependent edits, with dependence on surrounding text and decoder behavior [R3]. Our intended contribution is a shared, calibrated evaluation connecting several such capabilities, not the first discovery that sentence vectors can be probed or edited. **[needs to be improved]** Complete primary-source positioning against interpretability benchmarks, automated explanation evaluation, and SAE evaluation before novelty claims are finalized.

The present empirical material is heterogeneous, with several results on small lexical banks or a single model. The proposed common evaluation, calibration, independent semantic audit, and final comparison remain unfinished. A second trained substrate would strengthen generality; natural-text transfer is necessary before template results are described as broadly linguistic. Approximate reconstruction does not identify a unique basis, and observed output effects do not uniquely identify an encoder mechanism. Decoder priors, off-distribution interventions, supervision differences, and compute budgets must remain visible.

The open challenges are broad: reusable composition rules, context-dependent content, interpretable residual information, descriptions that predict collateral effects, and explanations that remain useful under distribution shift. A complete algebra of meaning or a universally better SAE is not required to make these questions measurable.

**[needs to be improved]** Write the final conclusion from N05/N06 outcomes. The current project establishes the manuscript and planned contract, not a completed benchmark release or new empirical finding.

## References and evidence — outside page budget

- **[R1]** Duquenne et al. *SONAR: Sentence-Level Multimodal and Language-Agnostic Representations.* [Primary paper](https://arxiv.org/abs/2308.11466).
- **[R2]** Soulos et al. *Discovering the Compositional Structure of Vector Representations with Role Learning Networks.* [Primary paper](https://arxiv.org/abs/1910.09113).
- **[R3]** antonghawthorne and Samuel Nellessen. *Investigating Representations in the Embedding in SONAR Text Autoencoders.* Exploratory project report, September 2025. [Post](https://www.lesswrong.com/posts/hNBzHC7RADt3ERuqo/investigating-representations-in-the-embedding-in-sonar-text).
- **[R4]** Samuel Nellessen and antonghawthorne. *Investigating Internal Representations of Correctness in SONAR Text Autoencoders.* Exploratory project report, August 2025. Logistic probes on SONAR z: code validity .96, grammaticality .93 (cross-lingual), addition .76, multiplication and chess at chance; no interventions. [Post](https://www.lesswrong.com/posts/NNGB77BipWpHn4vRW/investigating-internal-representations-of-correctness-in).
- **[S01–S08]** Local research reports, with dated snapshots, exact original paths, hashes, and scope notes in the [evidence register](evidence.html). These are internal evidence records, not independent publications.

**[needs to be improved]** Complete bibliographic metadata and venue formatting; add only primary sources actually checked for the associated claims. Related-work coverage is incomplete.

## Appendix plan — outside page budget

A. Task definitions, supervision, splits, query budgets, and scorers (N01/N02). B. Known-code controls and sensitivity curves (N03). C. Checkpoint/inference manifest and per-item reproducibility (N04/N05). D. Per-family outcomes, uncertainty, failed gates, and natural-text audit. E. Case-study provenance and optional residual pilot. F. Release smoke commands and example submissions (N08). G. Pilot shortfall tables in full (B1 SONAR: read, edit at three doses, DAS per k, SAE calibration; B2 organisms: all checkpoints, seed spread, untrained copies; B5 LCM transfer: coverage breakdown, read and edit transfer) — `experiments/B1-sonar-shortfall/results/TABLE.md`, `B2-organism-shortfall/results/TABLE.md`, `B5-l4-lcm-transfer/results/TABLE_L4.md`. H. Breaker report on the pilot (ten attacks, swings, wording changes) — `experiments/B3-breaker/REPORT.md`. I. Training and generalisation of the L2 organisms (architecture, corpus, tokens seen and non-repeated tokens per parameter, held-out splits) — [appendix_organisms.html](appendix_organisms.html). J. Discovery-track pilots as they land (activation-space stochastic decomposition, B7; parameter decomposition on the organisms). Appendix material is provisional and will be pruned; inclusion here does not promote a run to the main text.


The [experiment plan](experiments.html) and [evidence register](evidence.html) currently hold this working material. Do not import the full campaign history into the main nine pages.