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Isotropic Yet Undecodable: The Sequential Content-Sufficiency Gap in Latent-Predictive Text Representations

K. P. Santoso, N. Z. Fadil, F. P. Harsanti, R. V. H. Ginardi, G. N. Iyer

arXiv:2610.07906v1cs.AIcs.CLcs.LG

TL;DR

Sequential generation needs representations to preserve ordered target information, but agreement and geometric regularity do not establish that they do. The paper analyzes sufficiency, grounding, and readout constraints, and finds sharply different recovery despite nearly equal pooled ranks under natural corruption.

  • Problem

    It is unclear whether representations preserve the ordered target information available in text, even though downstream generation must recover intended content and order.

    Source: §1 · pp. 1–2

  • Method

    The paper analyzes content sufficiency and readout constraints, then uses CANOPE comparisons of latent agreement and canonical-token grounding under controlled and natural corruption.

    Source: §1 · p. 2

  • Results

    With natural severity 3 and oracle lengths, PL0/PL2 have pooled ranks of 15.76/15.82 but retrieval of 13.46%/98.80%, respectively.

    Source: §6.2 · p. 8

  • Takeaways & Limitations

    Agreement and geometric regularity alone do not guarantee recoverable sequential content, while canonical-token grounding supports accurate recovery in the studied settings.

    Source: §8 · p. 11

    Causal attribution is strongest in CL; PL compares complete recipes with different auxiliary losses and weights.

    Source: §7 · p. 11

Abstract

from arXiv · show

We study sequential content sufficiency by investigating whether a representation retains the ordered target information available in its input. An information-theoretic decomposition separates input ambiguity, representation loss, and readout mismatch. We construct recoverable views where perfect agreement and joint isotropic Gaussianity coexist with zero target information, and establish limits imposed by deterministic canonical anchors. Token log-loss provides a one-sided information-loss bound; a fixed-penalty ridge analysis shows why rank alone cannot determine prediction risk. These results motivate CANOPE, a nonautoregressive framework with ordered latent canvases, canonical-token supervision, and geometric regularization. On 40,000 validation sequences, latent-agreement (PL0) and token-grounded (PL2) have nearly identical pooled ranks but reach 13.5% and 98.8% positional Recall@1, respectively, under strong natural corruption when the correct target length is provided. On 3,930 LJSpeech validation utterances, frozen PL2 with a trained MatchaTTS readout yields 21.54% word error rate (WER) on corrupted text, versus 99.22% for frozen PL0, while end-to-end MatchaTTS reaches 10.93%. These results show that geometric regularity alone does not guarantee recoverable sequential content or effective downstream access in the text settings studied here.

1 INTRODUCTION

Sequential generation requires representations to retain target-specific content and order, even when surface details vary. The paper asks whether agreement and geometric regularity preserve that information, and examines how grounding and readout affect recovery.

1 INTRODUCTION

  • Sequential generation must recover the intended content and order, so distinctions treated as nuisance across views may still matter downstream.Canonicalization may discard surface variation only while preserving distinctions needed to recover a specified clean sequence.Source: §1 · p. 1
  • A favorable marginal geometry does not determine the conditional target distribution, so geometry alone does not establish that an encoder preserves target-identifying distinctions.The paper frames this as a question about agreement and isotropic Gaussian regularization, grounding, and readout.Source: §1 · p. 2
  • Controlled-length experiments use supplied target lengths and invertible corruption before natural corruption and predicted lengths test recovery under harder conditions.Trained speech readouts then assess downstream consequences.Source: §1 · p. 2
  • CANOPE comparisons report that latent agreement and token grounding can have sharply different recovery despite nearly equal pooled ranks, and that access contrasts persist with trained speech readouts.The introduction also identifies limits from deterministic canonical anchors, token log-loss bounds, and target-dependent ridge access.Source: §1 · p. 2

2 RELATED WORK

Related work spans view agreement and geometric constraints, task information and readout limits, latent prediction for language, and canonical or semantic text representations.

Joint embeddings and geometry

  • Joint-embedding methods combine cross-view agreement with representation constraints, while I-JEPA and data2vec use latent prediction across regions or modalities.LeJEPA and VISReg target isotropic Gaussian geometry under explicit assumptions.Source: §2 · pp. 2–3

Task information and readouts

  • Task-information work studies view preservation and identifiability, while usable-information frameworks and RankMe address predictive constraints and empirical rank diagnostics.The passage names InfoMin, augmentation-based identifiability, the Decodable Information Bottleneck, and RankMe.Source: §2 · p. 3

Latent prediction for language

  • Language latent-prediction studies combine embedding objectives, masked-token reconstruction, and analyses of concentration, downstream geometry, and sequential prediction.This paper focuses on ordered canonical content under controlled invertible corruption and fixed-readout constraints.Source: §2 · p. 3

Canonical and semantic representations

  • Noisy-to-clean methods and typo-robust retrieval address canonical representations, while embedding, negation, lexical-overlap, and token-interaction work supplies semantic references.The passage names BART, TSDAE, ByT5, Sentence-BERT, SimCSE, Qwen3, NegMPNet, SemAntoNeg, PAWS, and ColBERT.Source: §2 · p. 3

3 SEQUENTIAL CONTENT SUFFICIENCY

The section separates target information available in the input from what a representation preserves and a readout can access. It shows that agreement and isotropic Gaussianity do not by themselves guarantee ordered target content.

3.1 WHAT IS PRESERVED, AND WHAT CAN A READOUT ACCESS?

  • When the input channel is recoverable, the sufficiency gap is representation loss; low population token log-loss upper-bounds that gap, while high loss may also reflect readout limits or fitting error.The decomposition distinguishes input ambiguity, representation loss, and readout mismatch.Source: §3.1 · p. 4

3.2 WHY AGREEMENT AND ISOTROPY DO NOT GUARANTEE CONTENT

  • Even perfect agreement and joint Gaussianity can coexist with zero target information when recoverable views share independent Gaussian content that the encoder outputs instead of the target.Exact continuous Gaussianity is unavailable to deterministic finite-string encoders, though finite-string counterparts can approximate it in Wasserstein-2 distance.Source: §3.2 · p. 4
  • A deterministic canonical anchor forces the representation to be a function of the target, but a nonconstant code can still merge distinct sequences.The anchor rules out the zero-information construction except for a constant representation; token supervision specifies which distinctions must survive.Source: §3.2 · p. 4

4 READOUT CONSTRAINTS AND TARGET-DEPENDENT GEOMETRY

The section connects token supervision to retained distinctions, then analyzes how representation geometry affects access through a fixed readout. It shows that rank changes alone do not establish a universal prediction-risk ordering.

4.1 WHAT CANONICAL TOKEN SUPERVISION CONSTRAINS

  • 58. Token probabilities under a fixed head are unchanged exactly along the null space of its logit-difference map, leaving d − r_W latent directions unobserved.Low population loss over every target position bounds the content gap but does not constrain all latent directions.Source: §4.1 · p. 5
  • A local token head can fail even when a full-canvas readout recovers the sequence, so failure of a fixed linear head alone does not prove information loss.For the stated swapped-bit example, each local prediction is at chance while swapping positions recovers the target.Source: §4.1 · p. 5

4.2 WHY HIGHER EFFECTIVE RANK CAN HELP OR HURT A FIXED READOUT

  • Higher effective rank lowers fixed-ridge risk below the target-alignment threshold and raises it above, with the two-dimensional example showing opposite risk changes for different targets.The analysis rescales information-preserving directions at fixed total variance to isolate geometry–readout interaction.Source: §4.2 · pp. 5–6
  • The rank comparison is local, depends on target alignment, and excludes penalty retuning; small-variance target directions also incur stronger coefficient penalties.Thus rank need not reflect information change or predict a universal risk ordering.Source: §4.2 · p. 6

5 CANOPE FRAMEWORK

CANOPE makes sequential content sufficiency testable by mapping corrupted text to ordered latent canvases, while separating predictive target, regularization location, and readout.

5 CANOPE FRAMEWORK

  • CANOPE maps corrupted text to ordered latent canvases and separates predictive target, regularization location, and readout.Its common architecture supports comparisons among these design choices.Source: §5 · p. 6

5.1 ARCHITECTURE AND CANVAS LENGTH

  • A Transformer encodes UTF-8 bytes, a resampler forms an ordered canvas, and a noncausal decoder predicts all positions in parallel.Oracle routing sets canvas length to target length; predicted routing uses a learned length head, while input routing sets it to input length.Source: §5.1 · p. 6

5.2 OBJECTIVES AND THE CL/PL COMPARISONS

  • Controlled-Length compares canonical-byte grounding with latent-view agreement and pooled versus sampled-token regularization.The sampled-token variant constrains a position mixture rather than the joint canvas; VISReg constrains coordinate means, scales, and projected shapes without certifying exact Gaussianity.Source: §5.2 · p. 7
  • Parametrized-Length recipes add length, surface-invariance, and premise–negation objectives; PL0 instead uses detached-anchor latent agreement with token loss training only the head.The token-grounded recipe combines canonical-byte and PAD supervision with length, invariance, negation, and VISReg losses.Source: §5.2 · p. 7

5.3 READOUTS: IDENTITY RETRIEVAL AND TOKEN RECONSTRUCTION

  • Retrieval compares corrupted queries with canonical targets using canvas-level or relative-position cosine scores, while native reconstruction uses per-position argmax until PAD.These diagnostics fit no new probes; each measures access through its specified readout, not information loss itself.Source: §5.3 · p. 7

6 EXPERIMENTS AND RESULTS

The experiments compare canonical-token grounding with latent agreement under controlled and natural corruption, then test whether their access differences carry over to speech. Across these settings, grounding supports stronger recovery, though retrieval does not establish full reconstruction or broad semantic equivalence.

6.1 CONTROLLED CONTENT RECOVERY

  • 99.985%/99.980% retrieval for CL-GP/GT versus 0.52%/0.75% for CL-LP/LT under recoverable severity 3 and oracle lengths.Grounding also yields 98.97%/98.78% exact reconstruction for CL-GP/GT; with input-length routing, CL-GP/GT retrieval is 97.48%/16.53%.Source: §6.1 · p. 7

6.2 NATURAL CORRUPTION

  • 13.46%/98.80% positional retrieval for PL0/PL2 despite pooled ranks of 15.76/15.82 under natural severity 3 and oracle lengths.Predicted lengths and centering leave the contrast intact, but PL2’s 23.09% CER and 12.64% exact match limit what retrieval establishes; PL7’s positional gain also shows readout choice matters.Source: §6.2 · p. 8

6.3 EXTERNAL IDENTITY AND SEMANTIC TRANSFER

  • On LexNorm, PL3 leads on original queries while PL2 leads under whitespace perturbation; relative positions improve both, but external semantic results remain weak.Strong synthetic-foil results indicate sensitivity to specified changes rather than general semantic equivalence.Source: §6.3 · p. 8

6.4 SPEECH FROM FROZEN CANVASES

  • 21.54% corrupted WER for frozen PL2 versus 99.22% for frozen PL0, while end-to-end MatchaTTS reaches 10.93%.The comparison uses trained MatchaTTS readouts on frozen predicted-length canvases.Source: §6.4 · p. 9

7 DISCUSSION

The discussion distinguishes what an encoder preserves from what a readout can access: jointly learned latent targets may agree without preserving every canonical distinction. Centering and ridge analyses further show why low disagreement or favorable pooled geometry does not guarantee target-specific recovery.

7 DISCUSSION

  • A jointly learned latent target can merge canonical sequences even when views agree exactly; token grounding instead penalizes lost distinctions at supervised positions.The difference is the fixed content target versus the jointly learned latent target, not cross-entropy versus squared loss.Source: §7 · p. 10
  • With invertible corruption and oracle lengths, input ambiguity is zero, but failed latent retrieval still cannot distinguish representation loss from readout mismatch.Grounded reconstruction and low empirical token loss are consistent with a population token-loss bound on the sufficiency gap.Source: §7 · p. 10
  • A large common mean and tiny residual variance let small absolute disagreement coexist with unstable content distinctions; mean removal barely helps corrupted views.The passage attributes this to residual shrinkage without improved separation relative to corruption.Source: §7 · p. 11
  • Favorable worst-target geometry and poor access to a particular target are compatible; matched pooled ranks motivate target-specific evaluation but do not certify joint Gaussianity.The ridge comparison holds information loss at zero through invertibility, isolating fixed-penalty access effects.Source: §7 · p. 11
  • Causal attribution is strongest in controlled-length experiments; natural-corruption comparisons vary complete recipes, and speech WER measures lexical fidelity rather than naturalness.Bootstrap intervals omit seed variation, and speech validation data had pretraining exposure with frontend, freezing, and alignment differences.Source: §7 · p. 11

8 CONCLUSION

The conclusion is that agreement and geometric regularity do not by themselves ensure recoverable ordered content, while canonical-token grounding supports accurate recovery and downstream speech benefits. The accompanying theoretical results separate input uncertainty, representation loss, and readout limitations, and examine Gaussian constructions, anchored codes, token heads, and ridge access.

8 CONCLUSION

  • Agreement and geometric regularity alone do not guarantee recoverable sequential content, while canonical-token grounding supports accurate recovery with benefits extending to downstream speech.The paper motivates evaluating ordered-content recovery alongside geometric diagnostics for sequential generation.Source: §8 · p. 11

A.1 INFORMATION DECOMPOSITION AND READOUT MISMATCH

  • The information decomposition separates representation loss from readout-family approximation limits and fitted-predictor excess; token log-loss bounds the information gap from above.Zero representation loss is equivalent to preserving the input-conditioned target posterior almost surely.Source: §A.1 · p. 16

A.2 FROM TARGET PRESERVATION TO SQUARED PREDICTION RISK

  • For squared loss, the risk identity separates input Bayes risk, its increase after encoding, and readout error; geometry can affect access while encoding can discard target information.For a one-hot finite target, the middle term vanishes exactly when input- and representation-conditioned posteriors agree.Source: §A.2 · pp. 16–17

A.3 INVARIANT GAUSSIAN COUNTEREXAMPLE

  • A recoverable input can yield exact view agreement and joint isotropic Gaussianity while the representation carries zero target information; every readout then has error at least 1 − max_c p(c).This is a population existence result, not a claim that finite-batch regularization or optimization produces that encoder.Source: §A.3 · p. 17

A.4 FINITE-STRING CONSTRUCTION

  • A finite-string construction achieves zero target information and identity covariance while approximating a Gaussian in Wasserstein-2, not total variation or KL.The construction shares a finite index across views and retains exact agreement; its diagnostic convergence is a population result.Source: §A.4 · pp. 17–18

A.5 CANONICAL ANCHORS AND CONDITIONALLY INDEPENDENT VIEWS

  • Under deterministic canonical anchoring, exact agreement forces the representation to be a function of the target; a nonconstant code retains information but can merge targets.With conditionally independent views, zero disagreement forces zero conditional variance; shared nuisance violates that premise.Source: §A.5 · p. 18

A.6 FIXED TOKEN HEADS AND LOCAL READOUTS

  • A fixed token head’s population log-loss upper-bounds the information gap, while local token factors can miss dependencies recoverable by a sequence readout.For the swapped independent-bit example, the full canvas determines the sequence, but the local optimum is 2 log 2.Source: §A.6 · pp. 18–19

A.7 POPULATION RIDGE RISK

  • With invertible representations, ridge excess risk comes from the fixed penalty rather than information loss, and depends on target alignment with the representation geometry.The comparison fixes the target in factor coordinates; changing representation-coordinate coefficients would change the target.Source: §A.7 · p. 19

A.8 EFFECTIVE-RANK THRESHOLD WITH ALL INTERMEDIATE STEPS

The analysis shows that increasing effective rank can raise or lower fixed-readout ridge risk, depending on how the target aligns with the changing variance. A local threshold determines the direction of the risk change, while the accompanying minimax discussion bounds when Gaussian results apply.

A.8 EFFECTIVE-RANK THRESHOLD WITH ALL INTERMEDIATE STEPS

  • The analysis uses an invertible analytical covariance path, not a spectrum assumed to describe a trained model.As ρ approaches 1, the threshold tends to r/d; the local derivative claim is not asserted at ρ = 1.Source: §A.8 · pp. 19–20
  • The variance shift raises the first block’s risk contribution and lowers the second’s, with their balance determining the local risk direction.The derivation holds the target and basis fixed as ρ varies.Source: §A.8 · pp. 19–20
  • Higher effective rank lowers ridge risk when η < η∗ and raises it when η > η∗; the threshold depends on ρ, so the comparison is local.At equality, the local derivative is zero.Source: §A.8 · p. 20
  • For d = 2, r = 1, μ = q0 = 1, and zero observation noise, increasing ρ raises ridge risk for a first-direction target but lowers it for a second-direction target.The map remains invertible for every 0 < ρ < 1, so both targets remain fully represented.Source: Figure 4 · p. 21

A.9 MINIMAX COMPATIBILITY AND SCOPE RELATIVE TO LEJEPA

  • The minimax uniqueness claim applies within the assumed Gaussian family; deterministic string encoders do not automatically satisfy LeJEPA’s density assumptions.The paper distinguishes target-retention analysis from ridge analysis, which preserves information and isolates geometry–readout interaction.Source: §A.9 · p. 21

B.1 READOUT IMPLEMENTATION

The appendix specifies retrieval and reconstruction readouts, training objectives, and evaluation protocols, then reports a gap between controlled identity discrimination and semantic equivalence. It also documents the length, corruption, and evaluation conditions that constrain interpretation.

B.1 READOUT IMPLEMENTATION

  • Retrieval compares corrupted queries with canonical targets using pooled cosine or 16 relative positions; the positional score preserves coarse order but neither certifies word-order understanding nor every detail.Native reconstruction uses per-position argmax and stops at PAD; diagnostics measure specified readout access, not Δinfo itself.Source: §B.1 · pp. 21–22

B.2 ARCHITECTURE AND LENGTH POLICIES

  • The application resamples encoder states into ordered canvases, while length policies route queries using predicted, input, or oracle lengths; underestimated canvases supervise only a target prefix.Capacity violations fail explicitly rather than truncate, and inference does not use the true query length for the training content mask.Source: §B.2 · p. 22, §B.5 · p. 24

B.3 RECOVERABLE CHANNEL AND VISREG

  • The recoverable channel’s inverse removes insertion markers and reverses escaping without the corruption seed, preserving canonical bytes; natural spelling errors are separate because unique recovery may fail.VISReg is assessed through separate geometry diagnostics, which are not calibrated p-values or tests of joint-canvas Gaussianity.Source: §B.3 · pp. 22–23

B.4 APPLICATION OBJECTIVE AND REGULARIZATION

  • The application objective combines token cross-entropy, empty-tail, length, invariance, negation, and geometry terms, with configurations differing in their weights and gradient paths.The negation ranking objective favors positive views over negations and unrelated anchors without a semantic teacher; invariance alone does not enforce order.Source: §B.4 · pp. 23–24, §B.5 · p. 24

B.5 APPLICATION LOSSES AND GRADIENT PATHS

  • Underestimated-canvas cross-entropy cannot certify full-target sufficiency, and the reported retrieval protocols use fixed candidate identities and paired queries across severities.The evaluation reports validation-cohort analyses, and the PL evaluation does not rerun a complete train/validation content-overlap audit.Source: §B.5 · p. 24, §B.6 · pp. 24–26

C ADDITIONAL EMPIRICAL RESULTS

  • CANOPE diagnostics use UTF-8 text bytes rather than the corpus’s phoneme modality, while the downstream MatchaTTS baseline uses its own phonemizer.The frozen PL0/PL2 systems condition a trained speech generator through trainable adapters while keeping CANOPE backbones frozen.Source: §B.6 · p. 25

B.6 EXECUTED RETRIEVAL AND SEMANTIC PROTOCOLS

  • The protocols evaluate canonical retrieval alongside semantic benchmarks and synthetic controls, but the template controls do not establish open-domain semantic equivalence or isolate word order from every other cue.The reported synthetic controls cover negation, number, entity, and role swap; benchmark tasks use their specified splits and metrics.Source: §B.6 · p. 26

C.1 SEMANTIC GENERALIZATION AND SYNTHETIC CONTROLS

  • PL3 reaches 100% accuracy on synthetic role-swap controls but only 9.11% SemAntoNeg accuracy, so controlled content-change discrimination does not establish general semantic-equivalence recognition.The authors interpret the evidence as supporting canonical identity matching while revealing limitations in how the evaluated similarity functions expose semantic relationships.Source: §C.1 · p. 27

C.2 RAW GEOMETRY AND ITS INTERPRETATION

The geometry and readout analyses show that concentrated or well-shaped representations do not by themselves establish robust content access. Comparisons of centering, positional scoring, and frozen speech conditioning are reported under specified corruption, length, and validation settings.

C.2 RAW GEOMETRY AND ITS INTERPRETATION

  • CL-GT has lower token characteristic-function discrepancy than CL-GP (0.00280 versus 0.15207), yet its covariance deviation from identity is 1.375 and effective rank is 194.47.The paper cautions that improved projected-shape diagnostics do not establish exact isotropy.Source: §C.2 · p. 28, Table 11 · p. 28
  • CL-LT centering raises clean retrieval from 0.76% to 100%, but severity-3 retrieval only from 0.75% to 1.58%, despite its highly concentrated geometry.Its pooled mean norm is 543.35, coordinate variance 3.79 × 10−4, effective rank 3.68, and raw cross-view MSE 6.67 × 10−7.Source: §C.2 · p. 29, Figure 5 · p. 29
  • As the scale factor ε decreases, absolute disagreement and inter-target separation shrink together; a fixed common mean can also drive uncentered cosine similarities toward one.This is an explanatory illustration, not evidence that learned residuals follow this path or that it is an optimizer’s global optimum.Source: §C.2 · p. 29

C.3 PAIRED 3D VIEWS AND DISTRIBUTION GEOMETRY

  • The 3D panels show selected matched identities and PCA projections, not full-gallery retrieval accuracy; short trajectories can coexist with poor retrieval.PCA bases are fit separately by model, and the visualizations use a fixed 4,096-item subset.Source: §C.3 · p. 29, Figure 6 · p. 30

C.4 CORRUPTION SENSITIVITY AND POSITIONAL ACCESS

  • Within-checkpoint comparisons find the largest benefit from relative-position scoring under the strongest whitespace perturbation, without showing recovery of every byte or all semantic relations.The figure compares pooled states with 16 relative positions; PL2/PL3 gain 36.89/21.54 points at maximum whitespace perturbation.Source: §C.4 · p. 31, Figure 7 · p. 31, Figure 9 · p. 32

C.5 SUPPORTING READOUT CONTROLS

  • The supporting controls contrast centered and raw CL-LT retrieval across severity and compare pooled states with relative-position scores on the same query-target sets.Figure 8 uses 40,000 targets and a clean mean from 1,024 disjoint calibration examples.Source: Figure 8 · p. 32, Figure 9 · p. 32

D.1 DATA, TRAINING, AND THE FROZEN INTERFACE

  • The speech experiment evaluates 3,930 LJSpeech validation utterances with stored corrupted text targeting the same recordings as clean text.The augmentation is a string-similarity heuristic, not a certified information-preserving channel or a Levenshtein-error bound.Source: §D.1 · p. 33
  • Frozen PL0 and PL2 condition a trained MatchaTTS generator through trainable adapters, use predicted canvas lengths, and receive UTF-8 bytes without oracle lengths or a canonical-token prefix.Their CANOPE backbones remain frozen, making this a latent-conditioning experiment rather than text correction followed by an unchanged TTS model.Source: §D.1 · p. 33

D.2 RECOMPUTED WORD ERROR RATES AND PAIRED UNCERTAINTY

The section reports paired WER contrasts and bounds their interpretation, then distinguishes information loss, readout mismatch, and length uncertainty. Its examples and evaluation details clarify which conclusions apply to the tested settings.

D.2 RECOMPUTED WORD ERROR RATES AND PAIRED UNCERTAINTY

  • 10,000 paired bootstrap samples of 3,930 utterance IDs estimate sampling variation conditional on fitted checkpoints and realized synthesis/ASR outputs, not variation across seeds, ASR engines, or domains.Each draw retains all systems and views for selected IDs and recomputes the word numerator and denominator.Source: §D.2 · p. 34
  • 7.94 points [7.43, 8.44] was PL2’s corruption increment, versus 8.71 [8.26, 9.18] for the baseline and 0.09 [−1.03, 1.21] for PL0; PL2 had 10.62 points more augmented WER than the baseline.These contrasts describe evaluated runs and are not multiple-comparison-adjusted hypothesis tests.Source: §D.2 · p. 34

D.3 SCOPE OF THE DOWNSTREAM EVIDENCE

  • The baseline uses a pretrained phoneme encoder, whereas CANOPE uses frozen byte-based states and a newly trained adapter, so this comparison does not isolate freezing or the CANOPE objective.PL2’s smaller corruption increment is conditional on its higher clean error and this perturbation mixture, not a general robustness guarantee.Source: §D.3 · p. 34
  • The LJSpeech items are held out from acoustic fine-tuning but are not shown to be unseen during pretraining; Whisper WER measures ASR-mediated lexical fidelity, not human intelligibility or naturalness.The authors report no pretraining-overlap audit or original-recording Whisper WER.Source: §D.3 · p. 34

D.4 REPRODUCIBILITY AND WAVEFORM DISPLAYS

  • The ten archived sample pages are illustrative, not a random cohort sample, and their plots expose timing and spectral differences without establishing spoken words or audio naturalness.The displays use shared magnitude scaling and mark time after a waveform ends as absent audio.Source: §D.4 · p. 35

E.1 RANDOM VARIABLES, EXPECTATIONS, AND CONDITIONAL DISTRIBUTIONS

  • C ⊥ Z | (X, S) means Z adds no target information once X and S are known; deterministic Z = F(X, S) satisfies this condition.The appendix distinguishes population information identities from finite-cohort diagnostics.Source: §E.1 · p. 36, E PROBABILITY AND INFORMATION… · p. 36

E.2 ENTROPY, LOG-LOSS, AND THE INFORMATION GAP

  • A swapped two-bit representation preserves all information but defeats position-local heads, separating readout mismatch from encoder loss and uncertainty already present in the input.An input containing only one of two independent target bits leaves irreducible uncertainty even when the encoder preserves that input.Source: §E.2 · p. 36

E.3 WHY LENGTH IS A SEPARATE INFORMATION VARIABLE

  • Length is a separate information variable: CL supplies L, whereas PL must infer length from X; source entropy-rate asymptotics do not imply fixed information per natural-language token.The entropy-rate statement does not imply that arbitrary variable-length sentences contain exactly h units of information per token.Source: §E.3 · p. 37

E.4 COVARIANCE, EIGENVALUES, AND THE QUANTITY CALLED RANK

Covariance rank summarizes variance structure but does not specify a full distribution or determine task performance. The appendix’s diagnostics therefore pair geometric views with identity retrieval and cohort-level measures.

E.4 COVARIANCE, EIGENVALUES, AND THE QUANTITY CALLED RANK

  • Both example covariance matrices have algebraic rank two, yet their effective ranks are 1.3841 and 1.9601; effective rank responds to spectral unevenness, not the full distribution.Isotropic covariance and effective rank do not determine whether a law is Gaussian.Source: §E.4 · p. 37

E.5 POPULATION GUARANTEES AND MEASURED DIAGNOSTICS

  • Recall@1 is stricter than a positive cosine margin against one random negative; stability in three plotted components must be considered with retained variance, identity correspondence, and full-gallery retrieval.Paired bootstrap intervals describe cohort uncertainty conditional on the checkpoint, while empirical token-loss averages estimate population quantities.Source: §E.5 · p. 37

F COMPLETE DISTRIBUTION AND PAIRED-VIEW COMPARISONS

  • Some PL views stay visually close despite poor full-gallery retrieval; CL-GP/GT spread most variance beyond the displayed axes, while CL-LP/LT concentrate it there.The grids compare clean, severity-3, and Gaussian-reference distributions, and paired panels follow identities through corruption; compact clouds alone do not establish content preservation.Source: Figure 10 · p. 38, F COMPLETE DISTRIBUTION AND… · pp. 38, 40, Figure 11 · p. 39

E.4 COVARIANCE, EIGENVALUES, AND THE QUANTITY CALLED RANK

  • 83.32% and 88.44% of clean pooled CL-LP and CL-LT variance, versus 59.56% and 37.50% in corresponding token projections, are retained by the first three principal components.These projections expose different subspaces and scales, not a shared coordinate system for cross-model distances.Source: F COMPLETE DISTRIBUTION AND… · p. 40

G DOWNSTREAM SPEECH SAMPLES

This section presents downstream speech samples and documents the empirical setup, including computational budgets, training and workflow details, and dataset and software provenance. It also clarifies that bootstrap intervals reflect sampled evaluation cohorts rather than variation across retraining seeds.

G DOWNSTREAM SPEECH SAMPLES

H.1 COMPUTATIONAL PROPERTIES AND SAMPLE BUDGET

  • The dense forward-pass cost accounts for encoder and decoder projections and attention, Gaussian resampling, and token logits; parallel decoding still leaves attention quadratic in sequence length.Backpropagation has the same asymptotic arithmetic order, and the resampling computation is counted even when an equal-length identity branch replaces its result.Source: §H.1 · p. 64
  • Parameter storage scales as O((Le + Ld)d^2 + Kd), while the conservative dense training-activation bound includes attention and token-logit terms.Gradients and AdamW states have the same asymptotic parameter-storage order.Source: §H.1 · p. 64
  • Chunking resampling positions at 256 bounds temporary weight storage, while VISReg projection chunks bound forward workspace and token regularization samples one state per sentence and view.The default VISReg projection and chunk sizes are both 256; pooling and dense cross-view agreement still require O(BV Md) operations.Source: §H.1 · p. 64
  • PL and CL use five-epoch budgets with nominal batch size 36; evaluation uses 40,000 targets, and TTS uses 9,170 training and 3,930 validation utterances.The prepared PL and CL training sets contain 8,635,993 and 8,656,553 rows, respectively. Bootstrap intervals describe the sampled evaluation cohort, while theoretical results concern information retention and population risk.Source: §H.1 · p. 64

H.2 EXECUTABLE DEFAULTS AND TRAINING DETAILS

The appendix records executable training and evaluation defaults, a reproduction workflow, and data-use context. It specifies variant settings and makes clear that component data retain their own terms and content context.

H.2 EXECUTABLE DEFAULTS AND TRAINING DETAILS

  • PL defaults specify seed 42, a 512-wide four-encoder/two-decoder model, five epochs, and AdamW; PL variants alter objective weights and related settings.The recipe also specifies augmentation views, optimizer schedule, checkpointing, and probe settings.Source: §H.2 · pp. 64–65
  • CL uses oracle lengths and recoverable corruption; its four primary arms combine latent agreement or token grounding with pooled or sampled-token regularization.The arms use VISReg weight 0.01 and share the stated model and training budget.Source: §H.2 · p. 65
  • The MatchaTTS recipe trains for 1,000 epochs, and evaluation uses ten flow steps plus Whisper large-v3 with English normalization and beam size five.The appendix distinguishes executable bootstrap defaults from the retrospective 10,000-replicate WER audit.Source: §H.2 · p. 65

H.3 REPRODUCTION WORKFLOW

  • The companion workflow covers data preparation, PL/CL training, feature extraction, speech training, evaluation, and figure generation, with pinned dependencies and configurable cluster fields.The environment record lists Python, PyTorch, CUDA, and system prerequisites.Source: §H.3 · pp. 65–66, §H.2 · p. 65

H.4 ATTRIBUTION, LICENSES, CONSENT, AND SENSITIVE CONTENT

  • Component datasets retain their original license terms; the study reuses public corpora without new participant recruitment, while individual examples may contain identifying or sensitive material.Reuse should follow source terms and account for the original content context.Source: §H.4 · p. 66
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