Pseudo-Unification in Multimodal Models

• Pseudo-unification is the mismatch between an apparent unified architecture and distinct internal processing regimes, notably in models combining language and vision.
• In unified multimodal models, shared parameters mask divergent objectives, leading to failures in transferring reasoning from text generation to image synthesis.
• An information-theoretic probing framework using matrix-based Rényi entropy quantifies encoding asymmetries and response splits, providing actionable diagnostic insights.

Searching arXiv for the cited papers to ground the article and confirm the relevant literature. arXiv Search Query: id:(Yang et al., 13 Apr 2026) OR id:(Beklemishev, 2024) OR id:(Alanne, 2016) Pseudo-unification most directly denotes a mismatch between the apparent architectural unity of a system and its actual internal unification. In the most explicit current usage, it describes unified multimodal models whose language and vision components share parameters or a common backbone yet retain divergent information-processing and response-generation regimes, so that language-like reasoning does not reliably transfer into image synthesis (Yang et al., 13 Apr 2026). Related literature makes the notion relevant, in a broader technical sense, to structurally nonclassical unification phenomena in logic and symbolic computation, and to partial high-energy unification schemes in which the “pseudo” qualifier attaches to a pseudo-Goldstone mechanism rather than to a fully unified gauge group (Beklemishev, 2024, Alanne, 2016).

1. Terminological scope and conceptual profile

In the multimodal-model literature, pseudo-unification is introduced as a diagnosis of a specific failure mode of so-called unified multimodal models. These systems are architecturally presented as joint models of language and vision, but they often do not exhibit a unified internal information-processing logic. A model may correctly reason in text about a prompt, retrieve the right concept, and articulate it verbally, yet fail to synthesize an image that reflects the same reasoning. The term therefore names a gap between shared architecture and cross-modal reasoning transfer (Yang et al., 13 Apr 2026).

In a broader technical sense, the expression is relevant to research on generalized or nonclassical unification. Beklemishev’s study of $GLP$ isolates a canonical pathology in which a natural provability logic has unifiers that cannot be organized by maximal elements, even though unifiability remains decidable in the relevant fragment (Beklemishev, 2024). A plausible implication is that pseudo-unification can serve as an umbrella description for cases where the formal structure of unifiers departs from the classical expectation of finitely generated maximal bases.

A different adjacent use appears in particle physics. The framework of "Radiatively induced Fermi scale and unification" is not a full simple-group grand unified theory, but a minimal Pati–Salam-type construction combined with an elementary Goldstone Higgs sector. In that setting, the “pseudo” aspect refers primarily to the Higgs being a pseudo-Goldstone boson, while the gauge structure itself is only partially unified rather than embedded into a single simple GUT group (Alanne, 2016). This distinction is central to any encyclopedic treatment of the term, because it separates pseudo-unification as a property of internal mechanism from unification as a claim about global architecture or gauge embedding.

2. Pseudo-unification in unified multimodal models

The explicit contemporary formulation of pseudo-unification concerns unified multimodal models (UMMs) designed to combine the reasoning ability of LLMs with the generation capability of vision models. The motivating question is why UMMs fail to transfer LLM-like reasoning into image synthesis even when text and image tasks are placed inside one shared model. The proposed answer is that architectural co-location does not imply multimodal synergy, because LLMs and text-to-image systems inherit different generative objectives and therefore different uncertainty profiles (Yang et al., 13 Apr 2026).

The multimodal formulation treats a UMM as implicitly modeling a joint distribution

$P(\mathbf{X}, \mathbf{Y}),$

where $\mathbf{X}$ denotes visual inputs and $\mathbf{Y}$ denotes text inputs. Under this view, multimodal tasks appear as conditionals of the shared distribution, including $P(\mathbf{X}\mid \mathbf{Y})$ for text-to-image generation and $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$ for text response with image context. The central claim is that true unification should be assessed not by parameter sharing alone, but by whether information flows through the model in a unified way across modalities and across prompt-to-response processing (Yang et al., 13 Apr 2026).

The paper identifies the practical symptom of pseudo-unification through a contrast between BAGEL and Harmon on an “American flag” reasoning prompt. BAGEL’s text output identifies the target concept, but its image generation misses it, whereas the smaller Harmon better aligns its text and image outputs around the same concept. The paper therefore frames pseudo-unification as a failure of reasoning-grounded transfer rather than as a failure of text competence or image competence in isolation (Yang et al., 13 Apr 2026).

This diagnosis is explicitly historical as well as architectural. LLMs were trained in a next-token prediction regime that supports open-ended, context-sensitive, high-variance continuation, whereas text-to-image systems were trained toward prompt fidelity, often suppressing uncertainty to produce a single visually aligned output. UMMs were supposed to merge these strengths, but the paper argues that most current systems instead preserve the split internally. The direct conclusion is that real multimodal unification requires consistency in information flow, not just shared parameters (Yang et al., 13 Apr 2026).

3. Information-theoretic probing framework

To diagnose pseudo-unification internally, the multimodal paper proposes an information-theoretic probing framework for Transformer-based UMMs. The framework jointly analyzes two stages: input encoding and output generation. The first examines how text prompts and image prompts are represented across layers; the second examines how response representations depend on prompt representations across layers, for both text generation and image synthesis. The framework is explicitly designed to address two stated limitations of prior work: benchmark evaluations reveal whether a model succeeds or fails but not why, while many internal analyses inspect prompt representations without modeling prompt–response dependency (Yang et al., 13 Apr 2026).

For an embedding sequence $\mathbf{Z}$, entropy $H(\mathbf{Z})$ is interpreted as measuring uncertainty, isotropy, and effective dimensionality of the representation. Higher entropy corresponds to a richer, more isotropic embedding geometry. For prompt–response behavior, if $\mathbf{Z_p}$ is a prompt embedding sequence and $\mathbf{Z_r}$ a response embedding sequence, conditional entropy $P(\mathbf{X}, \mathbf{Y}),$0 is interpreted as residual output uncertainty given the input. Low conditional entropy indicates a faithful, deterministic mapping, while high conditional entropy indicates a more open-ended response pattern (Yang et al., 13 Apr 2026).

Because explicit density estimation is impractical for hidden states in Transformers, the paper uses matrix-based Rényi entropy in an RKHS. For

$P(\mathbf{X}, \mathbf{Y}),$1

it constructs a Gaussian-kernel Gram matrix

$P(\mathbf{X}, \mathbf{Y}),$2

normalizes it by trace,

$P(\mathbf{X}, \mathbf{Y}),$3

and defines the $P(\mathbf{X}, \mathbf{Y}),$4-order matrix-based Rényi entropy as

$P(\mathbf{X}, \mathbf{Y}),$5

In practice, $P(\mathbf{X}, \mathbf{Y}),$6 is used to approximate Shannon entropy while remaining numerically stable (Yang et al., 13 Apr 2026).

The conditional-entropy proxy is built from

$P(\mathbf{X}, \mathbf{Y}),$7

with prompt kernel $P(\mathbf{X}, \mathbf{Y}),$8, joint block kernel

$P(\mathbf{X}, \mathbf{Y}),$9

and proxy

$\mathbf{X}$0

The paper does not claim that this is exact Shannon conditional entropy; it interprets the quantity as the additional structural complexity introduced by the response beyond the prompt. Validation experiments in controlled synthetic settings show monotonic behavior both for representation diversity and for prompt–response dependence, which is then used as the basis for model-internal diagnosis (Yang et al., 13 Apr 2026).

The empirical study covers ten representative UMMs: BAGEL (14B), BAGEL-RecA (14B), Harmon (1.5B), Harmon-RecA (1.5B), Janus-Pro (1B), Janus-Pro (7B), JanusFlow (1.3B), Show-o (1.3B), Show-o2 (7B), and OmniGen2 (7B). Text prompts come from T2I-CoReBench with 1,080 prompts spanning composition plus deductive, inductive, and abductive reasoning. Image prompts come from MMBench with 3,217 images spanning reasoning-heavy and perception-heavy categories (Yang et al., 13 Apr 2026).

4. Dual divergence: encoding asymmetry and response split

The first empirical signature of pseudo-unification is Modality-Asymmetric Encoding. Within a modality, prompt type has relatively little effect on entropy trajectories. Across modalities, however, text and image prompts follow systematically different entropy trajectories inside the same model. The paper therefore concludes that most UMMs are structure-agnostic within modality while sharply distinguishing between modalities in their encoding geometry (Yang et al., 13 Apr 2026).

Several model families exemplify this asymmetry. In the BAGEL series, text prompts undergo early-layer entropy collapse and recover only later to a moderate plateau around $\mathbf{X}$1, whereas image prompts start high, around $\mathbf{X}$2, and remain stable. In the Harmon series, text entropy rises quickly and stabilizes around $\mathbf{X}$3, while image entropy starts lower and climbs gradually to the same region. In the Show-o and Janus families, both modalities saturate early but with different absolute entropy levels, such as text around $\mathbf{X}$4 and image around $\mathbf{X}$5. OmniGen2 shows text entropy rising slowly toward a high plateau while image entropy begins high and stays flat, with final values close across modalities (Yang et al., 13 Apr 2026).

The paper also reports explicit cross-modality entropy gaps. BAGEL’s text prompt entropies are around $\mathbf{X}$6–$\mathbf{X}$7, while its image prompt entropies are around $\mathbf{X}$8–$\mathbf{X}$9. Show-o and Show-o2 are especially asymmetric: text prompt entropies are around $\mathbf{Y}$0–$\mathbf{Y}$1, while image prompt entropies are around $\mathbf{Y}$2–$\mathbf{Y}$3. Janus and BAGEL show large image-over-text entropy offsets, while Harmon is much more balanced. These quantitative differences are presented as one of the paper’s strongest signatures of pseudo-unification (Yang et al., 13 Apr 2026).

The second signature is Pattern-Split Response. Nearly every model except Harmon exhibits higher prompt-conditioned entropy for text generation than for image generation. High conditional entropy in text generation is interpreted as broad semantic continuation and creative openness; low conditional entropy in image generation is interpreted as narrow deterministic mapping that emphasizes fidelity and suppresses variance. The same nominally unified system therefore behaves like an LLM for text and like a fidelity-constrained image generator for vision (Yang et al., 13 Apr 2026).

Harmon is treated as the strongest counterexample to pseudo-unification. It has 1.5B parameters, much smaller than BAGEL’s 14B, yet its image-generation conditional entropy is initially higher than its text-generation conditional entropy in early layers, and the two curves later converge. The authors attribute this to contextual prediction, meaning that both text and image generation are trained under the same basic inductive bias of predicting missing content from visible context. For language this is next-token or future-token prediction; for images in Harmon, the visual side is based on a masked autoencoder, where missing patches are reconstructed from visible patches (Yang et al., 13 Apr 2026).

The broader interpretation is presented carefully. Directly supported findings are that prompt type matters less than modality, architecture, and scale; that text and image prompts follow systematically different entropy trajectories in most UMMs; that text generation generally has higher prompt-conditioned entropy than image synthesis; and that Harmon shows stronger cross-modal convergence. The stronger causal claim—that pseudo-unification is primarily caused by misaligned inductive biases between language modeling and image generation—is explicitly an interpretation rather than an interventionally established result (Yang et al., 13 Apr 2026).

5. Generalized unification phenomena in logic and symbolic computation

Outside multimodal modeling, the literature relevant to pseudo-unification is dominated by nonclassical unifier spaces, restricted higher-order formalisms, and unification-adjacent generalization procedures.

Area	Representative formulation	Reported result
Provability logic	Unifiers of $\mathbf{Y}$4 in $\mathbf{Y}$5	Nullary unification type for $\mathbf{Y}$6, $\mathbf{Y}$7
Context and higher-order fragments	Context unification; SOGU/ASOGU	Context unification in PSPACE; ASOGU undecidable
Calculus and equational settings	Delayed unification; GP 2 AU-unification	First-order superposition remains complete; GP 2 algorithm terminating, sound, complete

Beklemishev shows that the polymodal provability logic $\mathbf{Y}$8, in a language with at least two modalities and one variable, has nullary unification type. The focal formula is $\mathbf{Y}$9. It is unifiable, for example by $P(\mathbf{X}\mid \mathbf{Y})$0, but it has no maximal unifiers. The paper constructs canonical substitutions

$P(\mathbf{X}\mid \mathbf{Y})$1

and

$P(\mathbf{X}\mid \mathbf{Y})$2

and proves that a substitution $P(\mathbf{X}\mid \mathbf{Y})$3 is a unifier of $P(\mathbf{X}\mid \mathbf{Y})$4 iff $P(\mathbf{X}\mid \mathbf{Y})$5 for some $P(\mathbf{X}\mid \mathbf{Y})$6. Since $P(\mathbf{X}\mid \mathbf{Y})$7 whenever $P(\mathbf{X}\mid \mathbf{Y})$8, no maximal unifier exists. The same paper also states that the unification problem for $P(\mathbf{X}\mid \mathbf{Y})$9 is decidable and formulates arithmetical analogues of unification and admissibility (Beklemishev, 2024).

Restricted higher-order variants display a different landscape. "One is all you need: Second-order Unification without First-order Variables" introduces Second-Order Ground Unification (SOGU), where only one second-order variable is allowed and first-order variables do not occur. Its associative variant ASOGU is shown undecidable by reduction from Hilbert’s $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$0 problem, and the reduction still works under power associativity

$P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$1

By contrast, context unification, where context variables range over one-hole contexts, is shown to be in PSPACE under the usual assumption that the first-order signature is finite, using recompression and uncrossing operations that compress solutions without materializing them explicitly (Cerna et al., 2024, Jeż, 2013).

A proof-theoretic reorganization appears in "Superposition with Delayed Unification". There, first-order superposition remains complete when part of unification is moved to the calculus level, with unification steps represented by explicit inference rules such as Decompose, Bind, and ReflDel, and residual obligations represented by negative equality literals. In an application-specific equational setting, "A Unification Algorithm for GP 2" studies sorted AU-unification for list labels modulo associativity and unit,

$P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$2

and proves termination, soundness, and completeness for the fragment induced by simple left-hand expressions and left-linearity (Bhayat et al., 2024, Hristakiev et al., 2017).

The unification-adjacent landscape is equally relevant. "Implementing Anti-Unification Modulo Equational Theory" develops E-anti-unification with regular tree grammars; "Algebraic anti-unification" replaces syntactic instantiation with semantic image inclusion in arbitrary algebras; "Anti-unification of Unordered Goals" and "Anti-unification in Constraint Logic Programming" study generalization of unordered goals and CLP goals, proving that some exact optimization problems are NP-complete while polynomial-time abstractions remain available; and "Automating the Derivation of Unification Algorithms" synthesizes an environment-relative first-order unification procedure $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$3 whose output is a most-general idempotent reducing unifier extending the environment substitution (Burghardt et al., 2014, Antić, 2024, Yernaux et al., 2021, Yernaux et al., 2019, Waldinger, 15 Aug 2025).

Taken together, these results indicate that broader pseudo-unification phenomena are typically organized around one of three departures from classical first-order unification: non-maximal or nullary unifier spaces, restricted but expressive higher-order or equational fragments, and procedures that replace exact common-instance search by controlled common generalization.

6. Partial unification and pseudo-Goldstone mechanisms in particle physics

In high-energy physics, the paper "Radiatively induced Fermi scale and unification" is relevant to pseudo-unification because it links a Pati–Salam-type unification scale to electroweak symmetry breaking through a pseudo-Goldstone Higgs, while explicitly avoiding the claim of full simple-group grand unification. The symmetry structure is

$P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$4

where $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$5 is the leptocolor group of Pati–Salam type and $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$6 is a global symmetry acting on the scalar sector. The Standard Model Higgs sector is replaced by an $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$7-symmetric scalar sector (Alanne, 2016).

The desired breaking pattern is generated by two scalar multiplets: $P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$8 with

$P(\mathbf{Y_r}\mid \mathbf{X}, \mathbf{Y_p})$9

The elementary pseudo-Goldstone Higgs arises from

$\mathbf{Z}$0

which produces five Goldstone bosons, one of which becomes the observed Higgs after explicit symmetry breaking from electroweak gauging and Yukawa couplings. The scalar $\mathbf{Z}$1 is parameterized as

$\mathbf{Z}$2

The electroweak embedding is specified by

$\mathbf{Z}$3

The vacuum is misaligned according to

$\mathbf{Z}$4

This relation is the paper’s hierarchy mechanism: radiative corrections favor $\mathbf{Z}$5, so the observed Fermi scale can be much smaller than the underlying scalar-sector scale even when the scalar vacuum expectation values are of order the unification scale (Alanne, 2016).

The model is minimal and renormalizable, with scalar potential

$\mathbf{Z}$6

Radiative generation of the Fermi scale is analyzed through the one-loop Coleman–Weinberg effective potential

$\mathbf{Z}$7

The electroweak gauge interactions and top Yukawa coupling lift the flat direction and select a preferred vacuum with small $\mathbf{Z}$8. The paper fixes the renormalization scale by requiring

$\mathbf{Z}$9

while the leptocolor vacuum expectation value $H(\mathbf{Z})$0 and the angle $H(\mathbf{Z})$1 are determined by minimizing the full one-loop potential (Alanne, 2016).

Phenomenologically, the high scale is the Pati–Salam leptocolor-breaking scale rather than a conventional GUT unification scale. The paper reviews the lower bound

$H(\mathbf{Z})$2

on the leptoquark mass from processes such as

$H(\mathbf{Z})$3

and hence

$H(\mathbf{Z})$4

Its explicit benchmark is

$H(\mathbf{Z})$5

For this choice, viable points cluster around

$H(\mathbf{Z})$6

with the electroweak scale reproduced only if $H(\mathbf{Z})$7 is very small. The quartic scalar couplings are generally very small, with no strong hierarchy among them, and in the limit of equal self-couplings and $H(\mathbf{Z})$8 the minimization conditions imply

$H(\mathbf{Z})$9

Three fields have Higgs-like quantum numbers,

$\mathbf{Z_p}$0

and therefore mix, with the observed Higgs mostly the pseudo-Goldstone boson $\mathbf{Z_p}$1 and only a small admixture of $\mathbf{Z_p}$2 (Alanne, 2016).

The significance of this example for pseudo-unification is sharply delimited by the paper itself. The model is a “minimal Pati–Salam framework” rather than a complete gauge unification into one simple group. The “pseudo” aspect refers to the pseudo-Goldstone nature of the Higgs and to radiative vacuum misalignment, not to a pseudo-unified gauge structure. This suggests a broader encyclopedic pattern: across domains, pseudo-unification names situations in which an appearance of unity is qualified by a deeper structural distinction—between modalities, between unifier spaces, or between gauge organization and the mechanism that generates observed low-energy scales (Alanne, 2016).