A quantitative analysis of semantic information in deep representations of text and images
Pith reviewed 2026-05-22 14:33 UTC · model grok-4.3
The pith
Deep representations of text and images align on shared semantic information across languages, modalities, and model architectures, with directed predictability peaking in middle layers and showing asymmetries by language and scale.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Measurements of Information Imbalance between representations show that semantic information is distributed across many tokens and reaches peak predictability in a set of central layers for language models, in middle layers for autoregressive vision models, and in final layers for encoder vision models; those same layers produce the strongest cross-modal links to textual caption representations, with English representations more predictive than others and larger-model representations more predictive of smaller-model ones.
What carries the argument
Information Imbalance, the asymmetric rank-based measure that quantifies how well one high-dimensional representation can predict another as a proxy for cross-entropy.
If this is right
- Semantic information spreads across many tokens rather than concentrating in a few.
- Predictability between representations is strongest in central layers for text models and varies by layer type in vision models.
- English representations are systematically more predictive of other languages than the reverse.
- Larger models predict smaller-model representations more effectively than the smaller models predict the larger ones.
- The layers holding the most semantic content within each modality also yield the strongest cross-modal predictability.
Where Pith is reading between the lines
- The observed convergence may point to an underlying shared semantic geometry that different training regimes approximate.
- Layer-specific predictability patterns could be used to select which activations to align when building multimodal systems.
- The English-centric asymmetry raises the question of how much the convergence depends on training-data language balance.
- Similar analyses on models trained from scratch on balanced multilingual data could test whether the asymmetries persist.
Load-bearing premise
The Information Imbalance metric faithfully captures semantic predictability without substantial distortion from the high-dimensional rank approximation or from the particular models and inputs chosen.
What would settle it
A new experiment applying the same Information Imbalance analysis to models trained on entirely non-overlapping data distributions or to a fresh modality such as audio would show no layer-wise concentration or cross-modal alignment if the central claim is incorrect.
Figures
read the original abstract
It was recently observed that the representations of different models that process identical or semantically related inputs tend to align. We analyze this phenomenon using the Information Imbalance, an asymmetric rank-based measure that quantifies the capability of a representation to predict another, providing a proxy of the cross-entropy which can be computed efficiently in high-dimensional spaces. By measuring the Information Imbalance between representations generated by DeepSeek-V3 processing translations, we find that semantic information is spread across many tokens, and that semantic predictability is strongest in a set of central layers of the network, robust across six language pairs. We measure clear information asymmetries: English representations are systematically more predictive than those of other languages, and DeepSeek-V3 representations are more predictive of those in a smaller model such as Llama3-8b than the opposite. In the visual domain, we observe that semantic information concentrates in middle layers for autoregressive models and in final layers for encoder models, and these same layers yield the strongest cross-modal predictability with textual representations of image captions. Our results support the hypothesis of semantic convergence across languages, modalities, and architectures, while showing that directed predictability between representations varies strongly with layer-depth, model scale, and language.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript analyzes semantic convergence in deep representations using the Information Imbalance, an asymmetric rank-based proxy for cross-entropy between model outputs. On text, it reports that semantic information is distributed across tokens in DeepSeek-V3, with strongest directed predictability in central layers across six language pairs; English representations are more predictive than those of other languages, and DeepSeek-V3 representations predict Llama3-8b outputs better than the reverse. On images, semantic information concentrates in middle layers for autoregressive models and final layers for encoders, with peak cross-modal predictability to caption text occurring in the same layers. The central claim is that these patterns support semantic convergence across languages, modalities, and architectures while showing that directed predictability varies systematically with layer depth, model scale, and language.
Significance. If the metric faithfully captures semantic predictability, the work supplies quantitative evidence for cross-lingual and cross-modal alignment in neural representations and identifies layer-specific loci of semantic content. The efficient, parameter-free nature of the rank-based measure in high dimensions is a methodological strength that enables the reported comparisons without additional fitting. The patterns are falsifiable through replication on other models or inputs.
major comments (1)
- [Methods (Information Imbalance definition and application)] The load-bearing assumption that Information Imbalance provides an undistorted asymmetric proxy for semantic predictability and cross-entropy must be validated against high-dimensional rank-estimation artifacts (nearest-neighbor sensitivity to local density, embedding norm, or k). The abstract and methods description give no sign of such controls or comparisons to direct entropy estimates; without them the reported asymmetries (English > other languages; DeepSeek-V3 > Llama3-8b) and layer-wise peaks cannot be confidently attributed to semantic content rather than metric bias. This directly affects the central claims.
minor comments (2)
- [Experimental setup] Clarify the exact token sampling and exclusion rules used for the multilingual translation experiments; the abstract mentions 'many tokens' but does not specify how inputs were prepared or whether length normalization was applied.
- [Visual domain experiments] Add a brief statement on the number of image-caption pairs and the precise visual models employed; this would help readers assess the scope of the cross-modal results.
Simulated Author's Rebuttal
We thank the referee for their constructive feedback and for recognizing the methodological strengths of the Information Imbalance approach. We address the major comment on metric validation below and will incorporate additional controls in the revision.
read point-by-point responses
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Referee: The load-bearing assumption that Information Imbalance provides an undistorted asymmetric proxy for semantic predictability and cross-entropy must be validated against high-dimensional rank-estimation artifacts (nearest-neighbor sensitivity to local density, embedding norm, or k). The abstract and methods description give no sign of such controls or comparisons to direct entropy estimates; without them the reported asymmetries (English > other languages; DeepSeek-V3 > Llama3-8b) and layer-wise peaks cannot be confidently attributed to semantic content rather than metric bias. This directly affects the central claims.
Authors: We agree that explicit checks for rank-estimation artifacts would increase confidence in attributing the observed asymmetries and layer-wise patterns to semantic content. The current manuscript does not report dedicated sensitivity analyses or direct entropy comparisons, relying instead on the parameter-free nature of the rank-based proxy and the consistency of results across six language pairs, multiple models, and both text and image modalities. In the revised version we will add: (i) robustness tests varying the neighbor parameter k across a range of values, (ii) results after L2-normalizing all embeddings to control for norm effects, and (iii) mutual-information estimates on PCA-reduced representations for a representative subset of layers as a proxy comparison to direct entropy. These additions should help confirm that the reported English > other-language and DeepSeek-V3 > Llama3-8b directed predictabilities, as well as the central-layer peaks, are not driven by local-density or norm biases. revision: yes
Circularity Check
Minor self-citation for Information Imbalance metric but central empirical claims remain independent
full rationale
The paper introduces the Information Imbalance as an asymmetric rank-based proxy for cross-entropy between high-dimensional representations and applies it to measure predictability across layers, models (DeepSeek-V3, Llama3-8b), languages, and modalities. The reported patterns of semantic convergence and directed asymmetries are direct empirical outputs of this metric applied to fixed model activations on translations and image captions. No equation or result reduces to a fitted parameter or input definition by construction, and any self-citation for the metric definition is not load-bearing for the convergence hypothesis. The derivation chain is therefore self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Information Imbalance provides an efficient proxy for cross-entropy between high-dimensional representations.
Lean theorems connected to this paper
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IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We employ here the Information Imbalance (Glielmo et al., 2022), a statistical measure which is a proxy of the cross-entropy... Δ(X→Y) = 2/(N−1) * 1/N ∑ r^Y_{i,j} where r^X_{ij}=1
What do these tags mean?
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- supports
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- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Forward citations
Cited by 1 Pith paper
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The Wittgensteinian Representation Hypothesis: Is Language the Attractor of Multimodal Convergence?
Language representations serve as the asymptotic attractor for convergence in independently trained multimodal neural networks due to feature density asymmetry.
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A Misalignment of translations erases semantic similarity As a consistency check, Fig 7 shows the Information Imbalance for DeepSeek-V3 and Llama3.1-8b represen- tations using misaligned translations, namely performing a batch-shuffle in one of the datasets. Since the semantic correspondence between sentences is destroyed, the representations are not info...
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