Token Homogenization in Theory & Applications

• Token homogenization is the process of converting heterogeneous inputs into uniform token spaces while preserving critical invariants like structural grammar, semantic consistency, and security features.
• It spans multiple domains—from formal language theory and transformer hidden-state convergence to cross-domain tokenization in recommendation systems and blockchain standardization.
• Its practical applications include enhancing model transferability, mitigating collapse in mixture-of-experts models, and standardizing asset representations across disparate systems.

Token homogenization is a research term used in several distinct but structurally related senses. In formal language theory, it denotes the structural alignment of character strings and token sequences through homomorphic decoding and canonical segmentation (Geng et al., 2024). In transformer analysis, it denotes the convergence of token representations toward low-rank, anisotropic, or nearly shared directions across depth, often under positional bias (Yusupov et al., 23 Aug 2025). In learned tokenization for tabular and recommender systems, it denotes the construction of shared, semantically stable token spaces across heterogeneous features or domains (Zhou et al., 2023, Hou et al., 17 Nov 2025). In sparse routing and alignment studies, it names collapse phenomena in which tokens, experts, or sampled responses become insufficiently diverse (Li et al., 2024, Liu, 25 Mar 2026). In blockchain and distributed infrastructure, it denotes the standardization of heterogeneous assets, cross-chain representations, or authorization claims into common token forms (Borjigin et al., 15 Aug 2025, Soureshjani et al., 6 Mar 2026, Bockelman et al., 31 Mar 2025). Across these usages, the common concern is the conversion of heterogeneous objects into more uniform token spaces while preserving the invariants that matter in each setting.

1. Formal-language interpretation of tokenization

In formal language theory, token homogenization is most naturally understood through the distinction between character space and token space. The formal setup uses a character alphabet $\Sigma$ with free monoid $\Sigma^*$, and a token-ID alphabet $\mathbb{N}=\{0,1,\dots,|V|-1\}$ with free monoid $\mathbb{N}^*$. Proper tokenization is a function $f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$ that maps each string to a unique token sequence and is injective but not surjective. Detokenization is the inverse string-level map $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$, satisfying $f_{\text{detok}}(f_{\text{tok}}(x))=x$ for all $x\in\Sigma^*$. The crucial step is the introduction of extended tokenization $F_{\text{tok}}$, which conceptually includes all valid segmentations of a string, and extended detokenization $F_{\text{detok}}$, which is defined on all token sequences that decode to valid strings (Geng et al., 2024).

The key proposition is that detokenization is homomorphic under concatenation:

$\Sigma^*$0

Accordingly, extended tokenization is an inverse homomorphism. If $\Sigma^*$1, then the tokenized language is the inverse homomorphic preimage

$\Sigma^*$2

This has a direct expressiveness consequence: if the source language $\Sigma^*$3 is regular or context-free, then $\Sigma^*$4 remains regular or context-free by closure under inverse homomorphism. In this sense, tokenization preserves the grammar-theoretic class of the source language rather than altering it.

The paper distinguishes three tokenization regimes. Proper tokenization $\Sigma^*$5 is the unique segmentation chosen by the tokenizer. Extended tokenization $\Sigma^*$6 is the set of all valid segmentations. Improper tokenizations are the remainder

$\Sigma^*$7

This makes proper tokenization a canonicalization procedure: it chooses one representative from many token sequences that decode to the same string. A plausible implication is that, in this formal setting, token homogenization means selecting a uniform representative in token space while preserving the concatenative structure of the source language.

Several caveats qualify the result. Tokenization itself is generally not homomorphic: in the GPT-3 tokenizer, [ and ] are individual token IDs, while [] is also a single token ID, so concatenation is not preserved by the tokenizer map. Byte-level tokenization requires an intermediate byte alphabet and finite-length encodings such as UTF-8; the homomorphism holds exactly at the byte level, and the context-free/regular status is then preserved through encoding. Practical schemes with leading-space tokens, as in T5 and LLaMA, can break pure homomorphism because the same token may decode differently at string-initial position; the formal repair proposed is to add regular pre- or post-processing so that the homomorphic characterization is restored. An open problem is whether the proper tokenization space $\Sigma^*$8 is regular, since that regularity would imply that the proper tokenization language $\Sigma^*$9 is context-free (Geng et al., 2024).

2. Hidden-state convergence in transformers

A second, now more literal, use of token homogenization appears in transformer representation analysis. Here the term denotes the process by which token hidden states in a sequence become progressively more similar as they pass through layers. For a sequence of $\mathbb{N}=\{0,1,\dots,|V|-1\}$0 tokens, layer-$\mathbb{N}=\{0,1,\dots,|V|-1\}$1 states are arranged as

$\mathbb{N}=\{0,1,\dots,|V|-1\}$2

and homogenization means that the rows $\mathbb{N}=\{0,1,\dots,|V|-1\}$3 lose distinctiveness and approach a low-dimensional, often nearly rank-1 structure (Yusupov et al., 23 Aug 2025).

This phenomenon is measured through several spectral and geometric diagnostics. Rapid singular-value decay indicates rank collapse. Maximum Explainable Variance is defined as

$\mathbb{N}=\{0,1,\dots,|V|-1\}$4

so high MEV indicates that most token variance lies in a single direction. Effective rank is defined by normalizing singular values into weights $\mathbb{N}=\{0,1,\dots,|V|-1\}$5, computing spectral entropy $\mathbb{N}=\{0,1,\dots,|V|-1\}$6, and setting

$\mathbb{N}=\{0,1,\dots,|V|-1\}$7

Homogenization corresponds to low effective rank. Additional metrics include Schatten norms, resultant length

$\mathbb{N}=\{0,1,\dots,|V|-1\}$8

for unit-normalized token vectors, and MAUVE between successive layers.

The empirical study uses LLaMA-3 8B, Gemma 7B, and Qwen-2.5 7B on a subsample of 1000 IMDB movie reviews. Three datasets are compared: original reviews, a front-biased paraphrase set with a GLM-identified important phrase moved to the beginning, and an end-biased set with that phrase moved to the end. Semantic preservation is validated by BERTScore, reported as 0.9008 for Front versus original and 0.8964 for End versus original. Across all three models, effective rank decreases with depth and stabilizes at low values, MEV increases and plateaus, resultant length rises, and front/end bias generally strengthens homogenization relative to the original dataset (Yusupov et al., 23 Aug 2025).

The mechanistic explanation centers on positional attention. The attention matrix is decomposed as

$\mathbb{N}=\{0,1,\dots,|V|-1\}$9

When positional attention strongly favors an extremal token, such as the first token, every position repeatedly mixes toward the same reference state. In the paper’s toy analysis, if $\mathbb{N}^*$0, then repeated application yields $\mathbb{N}^*$1 for all $\mathbb{N}^*$2, up to residual and multi-head effects. Attention-column sums show a strong first-token bias across layers and heads. In this literature, token homogenization is therefore a representation-space collapse driven by repeated attention mixing and amplified when content importance and positional bias align (Yusupov et al., 23 Aug 2025).

3. Shared token spaces for transfer across heterogeneous domains

In tabular learning and multi-domain recommendation, token homogenization denotes something different: not collapse of token distinctiveness, but deliberate construction of token spaces whose semantics are reusable across tasks or domains. In TabToken, a tabular model is decomposed into a feature tokenizer $\mathbb{N}^*$3 and a top-layer model $\mathbb{N}^*$4, with

$\mathbb{N}^*$5

Numerical features use learnable vectors $\mathbb{N}^*$6 and tokens $\mathbb{N}^*$7; categorical features use embedding tables $\mathbb{N}^*$8 and lookup tokens $\mathbb{N}^*$9. The central homogenizing move is to average feature tokens into an instance token

$f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$0

rather than concatenate them. Averaging is permutation-invariant and forces all feature dimensions to share a common semantic coordinate system. Contrastive Token Regularization then pulls $f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$1 toward its class center

$f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$2

using

$f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$3

This makes semantically similar tokens cluster within and across features, while noisy features cluster in a neutral region (Zhou et al., 2023).

The downstream transfer mechanism preserves this homogenized space. Tokens for overlapping features are reused and kept fixed; unseen features are initialized by averaging pretrained tokens and then fine-tuned. Experiments report improvements in 5-shot transfer on datasets such as Eye, Jannis, Elevators, Superconductivity, and Volume, and gains are also reported for standard tabular classification and regression without transfer. The theoretical claim is that the tokenizer alone does not increase model capacity; transferability arises only when explicit regularization imposes stable semantics on tokens (Zhou et al., 2023).

A parallel but larger-scale formulation appears in multi-domain LLM-based recommendation. UniTok projects items from multiple domains into a shared latent space through a common encoder, routes them through a TokenMoE architecture with domain-specific experts plus an always-active shared expert, and discretizes latents by residual quantization. Its token tuple combines code indices and expert IDs:

$f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$4

To avoid semantic imbalance across domains, it adds a mutual-information calibration objective based on HSIC estimates $f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$5:

$f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$6

This explicitly encourages comparable information retention across domains. The reported outcome is a unified tokenizer that improves recommendation performance by up to 51.89%, reduces trainable parameters by about $f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$7 relative to separate per-domain tokenizers, and exhibits zero-shot generalization to unseen domains such as Clothing, Health, and Sports (Hou et al., 17 Nov 2025).

4. Routing collapse and expert specialization in mixture-of-experts models

In sparse MoE architectures, token homogenization refers to routing collapse: many tokens are sent through effectively the same experts, causing expert representations to become redundant and the model to degenerate toward dense computation. The Expert-Token Resonance framework defines the problem in terms of low routing diversity, overloaded and idle experts, and poor specialization. Its formal metric is training success rate, defined as the probability that a class-discriminative token is routed to the correct expert. The paper also uses the Calinski–Harabasz index

$f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$8

to measure clustering quality of tokens by expert, as well as per-expert load histograms and token-feature correlation matrices (Li et al., 2024).

The theoretical account separates early and late training. In early phases, token-choice routing is preferable because expert-choice routing is confounded by high false-positive rates from class-irrelevant tokens. In later phases, once experts have become discriminative, expert-choice routing becomes superior and can achieve high success rate with much lower capacity. This yields a two-phase strategy: token-choice routing early, expert-choice routing later. The paper states that the dynamic bidirectional approach can reduce the expert-capacity lower bound by up to 40%.

The routing mechanism itself is affinity-based. Grouped Average Pooling reduces router complexity from $f_{\text{tok}}:\Sigma^*\to\mathbb{N}^*$9 to $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$0, and affinity scores are cosine similarities between token features and expert vectors. A block-diagonal affinity structure is used to maintain near-orthogonality among experts, preventing the gating vectors from collapsing to similar directions. Empirically, this yields stronger token clustering, more balanced token loads, and clear block structure in token correlation after training. On Ascend NPU clusters, the reported end-to-end training efficiency gain over baseline MoE implementations ranges from 5.4% to 46.6%, with downstream performance gains of 9.7% to 14.5% on GDAD, GPQA, HumanEval, and TeleQnA (Li et al., 2024).

5. Alignment-induced response homogenization

A more recent line of work shifts the focus from hidden states to sampled outputs. Here the relevant notion is response homogenization: repeated stochastic decoding from an aligned LLM yields the same semantic answer across samples, even at nonzero temperature. For a query $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$1 with $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$2 sampled responses clustered into semantic clusters $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$3, the number of distinct semantic clusters is $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$4, and the alignment tax is defined as

$f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$5

The maximal practical case is the single-cluster regime $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$6, where all samples collapse onto one semantic answer (Liu, 25 Mar 2026).

The reported empirical effect is substantial. On TruthfulQA with $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$7 questions and 10 i.i.d. samples, RLHF-aligned models yield single-cluster rates between 40% and 79%, depending on the clustering method. On affected questions, sampling-based uncertainty estimators have zero discriminative power, with AUROC = 0.500, while free token entropy retains signal at 0.603. The same paper reports that this alignment tax is task-dependent: on GSM8K with $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$8, token entropy achieves AUROC 0.724 with Cohen’s $f_{\text{detok}}:\mathbb{N}^*\to\Sigma^*$9. Cross-dataset validation on WebQuestions shows a 58.0% single-cluster rate, indicating that the effect is not confined to TruthfulQA (Liu, 25 Mar 2026).

The causal role of alignment is established by ablations. A base-versus-instruct comparison reports a 1.0% single-cluster rate for the base model versus 28.5% for the instruct model, with $f_{\text{detok}}(f_{\text{tok}}(x))=x$0. A training-stage ablation localizes the effect primarily to preference optimization rather than supervised fine-tuning: Base 0.0% $f_{\text{detok}}(f_{\text{tok}}(x))=x$1 SFT 1.5% $f_{\text{detok}}(f_{\text{tok}}(x))=x$2 DPO 4.0% single-cluster rate in one model family. Cross-family replication on four model families and three scales from 3B to 14B shows that severity varies substantially by family and scale.

A notable result is the decoupling between response-level and token-level uncertainty. Even when semantic entropy collapses because all samples belong to one cluster, token-level next-token entropy

$f_{\text{detok}}(f_{\text{tok}}(x))=x$3

and its sequence-level summaries remain informative. This indicates that alignment can narrow the distribution over semantic outcomes without forcing token distributions to become degenerate in the same way. In this literature, homogenization therefore refers primarily to semantic-output collapse rather than to zero token entropy (Liu, 25 Mar 2026).

6. Standardization of assets, cross-chain representations, and authorization claims

In digital asset research, token homogenization denotes the conversion of heterogeneous assets into standardized token units. One explicit formulation is the two-tier architecture of Element Tokens and Everything Tokens. Element Tokens $f_{\text{detok}}(f_{\text{tok}}(x))=x$4 represent standardized, fully collateralized components such as 1 MWh of electricity, 1 CO$f_{\text{detok}}(f_{\text{tok}}(x))=x$5 credit, a unit of water usage right, or a permit right. An Everything Token $f_{\text{detok}}(f_{\text{tok}}(x))=x$6 represents the entire asset as a fixed bundle

$f_{\text{detok}}(f_{\text{tok}}(x))=x$7

The associated net asset value relation is

$f_{\text{detok}}(f_{\text{tok}}(x))=x$8

Two-way convertibility enforces minting and redemption between the basket of elements and the composite token, and arbitrage keeps the composite token aligned with the value of its constituents. The architecture is presented for solar plants, hydropower projects, mining projects, and other alternative assets, with the stated aim of converting heterogeneous resource bundles into standardized, fungible claims (Borjigin et al., 15 Aug 2025).

Cross-chain token standards pursue a related but narrower goal: making a token deployed on multiple blockchains behave as one logically unified asset. The common invariant is a unified total supply model

$f_{\text{detok}}(f_{\text{tok}}(x))=x$9

with cross-chain transfers preserving $x\in\Sigma^*$0. The comparative analysis covers xERC20/ERC-7281, OFT, NTT, CCT, and SuperchainERC20/ERC-7802. All aim at seamless cross-chain fungibility, but they differ in architecture, message-passing mechanism, trust model, and interoperability scope. Burn-and-mint constructions come closest to strict supply homogenization, whereas lock-and-mint and adapter-based constructions retain a distinction between native and synthetic representations. The paper concludes that present systems achieve only local homogenization pockets within particular interoperability frameworks or superchains, not a universally homogeneous multi-chain asset model (Soureshjani et al., 6 Mar 2026).

Wrapped-token research makes the same limitation explicit. Wrapped assets refit tokens to local standards such as ERC-20 or SNIP-20 and thereby enable interface-level interoperability, but different wrappers of the same underlying asset remain non-fungible with each other because they are redeemable only through their own custodians or bridges. WBTC, renBTC, synthetic sBTC, and other BTC-derived representations are therefore economically similar but not homogeneous in trust, redemption, or risk. In this context, token homogenization is partial and superficial: it standardizes contract interfaces and DeFi usability, not underlying trust assumptions (Caldarelli, 2021).

A non-financial but technically parallel usage appears in distributed scientific computing. In the CMS/WLCG transition from X.509 certificates and VOMS attributes to bearer tokens, token homogenization means replacing a heterogeneous, site-specific authorization environment with a common capability-based token model under the WLCG Common JWT profile. INDIGO IAM serves as the issuer, HashiCorp Vault stores and refreshes tokens, a token bastion pushes credentials to HTCondor CredMon, and Credd maintains fresh access tokens in long-running jobs. The intended result is a single authorization fabric in which compute elements, storage services, transfer services, and batch infrastructure interpret the same claims and scopes with common semantics (Bockelman et al., 31 Mar 2025).

7. Recurring themes and open questions

Across these literatures, token homogenization has no single definition, but its recurrent structure is stable. It always concerns a map from heterogeneous inputs to a more regular token space, together with a claim that some invariant is preserved. In formal language theory, the invariant is language class under inverse homomorphism. In transformer analysis, the relevant quantities are rank, anisotropy, and positional mixing. In transfer learning and recommendation, the invariant is semantic comparability across features or domains. In MoE routing, it is expert specialization under sparse computation. In blockchain and authorization, it is unified supply, capability semantics, or standardized collateralization.

Several common misconceptions are explicitly contradicted by the literature. First, homogenization is not necessarily an increase in expressive power: the inverse-homomorphism analysis shows that tokenization does not alter the regular/context-free language class recognized by a fixed architecture (Geng et al., 2024). Second, homogenization is not always equivalent to reduced token-level uncertainty: aligned LLMs can exhibit severe response-level collapse while still retaining informative token entropy (Liu, 25 Mar 2026). Third, a unified interface does not imply a unified trust model: wrapped tokens and cross-chain standards can standardize representation while remaining heterogeneous in custody, verifier assumptions, and redemption semantics (Caldarelli, 2021, Soureshjani et al., 6 Mar 2026).

The open problems are correspondingly domain-specific. In formal language theory, the regularity of the proper tokenization space remains unresolved. In transformer studies, mitigation of positional bias and preservation of representational diversity remain open design questions (Yusupov et al., 23 Aug 2025). In alternative-asset tokenization, governance rights, oracle risk, and the standardization of taxonomies for element tokens remain unsettled (Borjigin et al., 15 Aug 2025). In cross-chain systems, protocol-agnostic token semantics and formally verified supply invariants remain outstanding goals (Soureshjani et al., 6 Mar 2026). In aligned LLMs, diversity-preserving alignment methods are needed if sampling-based uncertainty estimation is to remain meaningful under response homogenization (Liu, 25 Mar 2026).

Taken together, the term denotes a family of problems rather than a single doctrine. Its uses range from canonical segmentation in tokenizers, to low-rank convergence in hidden states, to semantically transferable discrete codes, to the standardization of economic or authorization claims. What unifies the family is the attempt to make token spaces more uniform without losing the structural, semantic, or security properties on which the surrounding system depends.