Cross-Linguistic Top-K Ambiguity
and Reasoning Emergence

I The Problem

When the current LLM research community discusses multilingual model performance, attention focuses on three areas: vocabulary design and tokenization efficiency, the proportions and quality of multilingual training data, and score differences across language-specific benchmarks. However, a more fundamental structural question has been entirely overlooked—the probability distribution shapes at each token position during model inference already exhibit systematic differences across languages.

This blind spot is not accidental. Among the world’s top 20% of AI researchers, 47% are of Chinese origin, while 18% are from the United States^[1]. In leading U.S. AI institutions, researchers of Chinese origin account for 38%, slightly exceeding the 37% of U.S. natives^[2]. Among the global top 100 AI experts, 50 are of Chinese origin^[3]. Yet the dominant LLM research paradigm still defaults to English-language corpora, English-language publications, and English-language benchmarks as the reference frame. This research ecosystem may cause the structural impact of non-English languages on model next-token prediction distributions to be systematically underestimated—even when the researchers themselves are native speakers of those very languages.

II Core Hypotheses

2.1 A Critical Distinction: Linguistic Ambiguity vs. Model Prediction Ambiguity

Before developing the hypotheses, three levels of concepts must be strictly distinguished: (a) linguistic ambiguity—the polysemy, ellipsis, and boundary fuzziness inherent in human language structures; (b) model prediction ambiguity—the density of legitimate candidates when the model predicts the next token given context; and (c) reasoning emergence—the model’s generalization performance on non-linguistic tasks. The core assumption of this paper is that a causal transmission chain exists among these three levels:

This paper acknowledges that every jump from the first step to the last has yet to be empirically verified. High linguistic ambiguity does not necessarily mean the model’s prediction distribution is flatter—the model may learn to disambiguate through sufficient training data. However, our hypothesis is that even as the model progressively reduces its perplexity on high-ambiguity languages during training, the stronger disambiguation capacity required by this very process is itself the source of reasoning emergence.

2.2 Mathematical Formalization: Conditional Entropy and Disambiguation Load

Define the conditional entropy of the token distribution for language L given context C:

The core assumption of this paper can be formalized as: for semantically equivalent contexts C_zh and C_en, the average conditional entropy in Chinese is significantly higher than in English:

This leads to the concept of “Disambiguation Load”: when predicting the next token in a high-ambiguity language, the model must maintain more “semantic parallel paths” within its internal attention layers—simultaneously tracking multiple plausible continuation possibilities until sufficient contextual information accumulates to converge on the correct candidate. This cognitive pressure of parallel disambiguation is precisely the mechanism we hypothesize drives “reasoning muscle” growth.

2.3 The Top-K Divergence Hypothesis

During the autoregressive generation process of LLM inference, at each token position the model computes a probability distribution over the entire vocabulary. The Top-P sampling strategy selects the smallest set of tokens whose cumulative probability reaches threshold P. We propose that the shapes of probability distributions produced by different languages within the same model exhibit systematic differences—high-ambiguity languages produce flatter distributions (high entropy), while low-ambiguity languages produce steeper distributions (low entropy)^[4].

When the distribution is steep (e.g., English “I went to the ___”), the top 2–3 candidates can cover 90% of the probability mass. When the distribution is flat (e.g., Chinese “我到了___”), potentially hundreds of candidates may be needed to reach the same threshold.

2.4 The Ambiguity–Reasoning Emergence Hypothesis

More importantly, this distributional difference affects not only the computational cost during inference but produces a fundamental impact during the training phase. During training, the model optimizes via cross-entropy loss on next-token prediction. For high-ambiguity language corpora, there are more legitimate candidates at each position, and the model cannot effectively reduce perplexity by relying solely on surface-level pattern matching. Early research has shown that language models processing multi-character Chinese tokens can reduce perplexity by 20.94% compared to character-level baselines^[15], hinting at the impact of Chinese tokens’ rich semantic structure on model learning. The model is forced to develop deeper semantic understanding and contextual reasoning capabilities—analogous to athletes training at high altitude being forced to develop greater oxygen-carrying capacity.

III The Linguistic Ambiguity Index Framework

To quantify the ambiguity level of different languages, we construct a multi-dimensional Linguistic Ambiguity Index (LAI) covering the following eight dimensions. The weights in V4 are heuristically assigned and can be calibrated in future work by regressing against actual model average prediction entropy. It should be noted that “semantic density” strictly measures information compression efficiency rather than ambiguity—we deliberately include it in the LAI to maintain framework completeness while acknowledging the conceptual tension between this dimension and the other seven. This tension itself merits further investigation in future research:

The “Ellipsis Rate” dimension deserves particularly detailed discussion. Chinese and Japanese exhibit extremely high rates of zero anaphora—subjects and objects are frequently omitted, and the model must recover the missing entities through long-range dependency tracking within context. This forces the model to develop stronger logical coherence tracking capabilities and is one of the key pressure sources for reasoning emergence.

3.1 Ambiguity Index Ranking of Eight Major Languages

IV Three-Layer Effect of a Single Property

This paper proposes a unified theoretical framework: a single property of language—its ambiguity level—simultaneously produces three distinct effects across three different layers, and these three effects are inseparable.

These three-layer effects are driven by the same underlying property and cannot be independently adjusted. You cannot enjoy the reasoning capability gains from Chinese-language training while avoiding the increased computational cost of Chinese-language inference—they are two sides of the same coin.

V Temperature Amplification Effect

The Temperature parameter’s amplification of the Chinese–English Top-K gap exhibits nonlinear growth. Low Temperature (T≤0.7) compresses probability distributions, driving all languages toward deterministic outputs and narrowing the gap. At T=1.0, the gap becomes apparent. At T≥1.2, the gap explodes—because when Temperature flattens distributions, the already-flat Chinese distribution becomes even less convergent. The table below is an illustrative simulation based on Zipf distributions; the absolute values should not be interpreted as empirical measurements, but the directional trends are robust:

VI Illustrative Case: DeepSeek and the Chinese Training Pressure Hypothesis

The DeepSeek series offers an illustrative case consistent with the hypothesis of this paper—but cannot alone prove causation. DeepSeek-V4 (released April 2026) was pretrained on over 32T tokens^[6], with 1.6 trillion total parameters (49B activated per token), achieving a Codeforces rating of 3206—becoming the first open-source model to match closed-source models in competitive programming^[7]. Notably, DeepSeek’s pretraining corpus is described as “a multilingual corpus primarily composed of English and Chinese,” but the specific language proportions have never been disclosed^[8]. Therefore, this paper does not assume DeepSeek is a “Chinese-corpus-dominant” model, but treats it merely as a case study of a model that grew within the Chinese technology ecosystem, exhibits strong Chinese capabilities, and demonstrates exceptional reasoning ability.

Conventional explanations attribute DeepSeek’s success to its MoE architecture, hybrid attention mechanisms (CSA/HCA), reinforcement learning, synthetic data distillation, and engineering optimization. Chinese online communities have discussed how the higher information density of Chinese training data contributes to its logical capabilities, but that discussion remains at the surface level of “information density,” without touching the deeper mechanism of “ambiguity-driven reasoning emergence” proposed in this paper. Our framework offers a possible complementary explanation (note: this is one of multiple possible factors, not the sole factor):

This provides a supplementary explanation for a more general question: why might bilingual/multilingual models with strong Chinese capabilities also exhibit strong reasoning performance on English, mathematical, and coding tasks? Our answer is that this may not be a matter of “English performance being good too,” but rather that the underlying reasoning capability is strong, and English is merely a beneficiary of that capability. Just as an athlete who trains at high altitude carries their enhanced oxygen capacity to sea-level competitions, their advantage holds at any elevation.

This framework also yields a testable corollary: if Chinese-language training indeed develops stronger disambiguation capacity, then using Chinese as the “thinking language” during Chain-of-Thought (CoT) reasoning may trigger deeper search than using English. Notably, DeepSeek-R1 exhibits performance degradation when forced into language consistency^[16], while free language mixing (code-switching) correlates positively with stronger reasoning performance—this can be interpreted as the model switching between different languages’ ambiguity spaces to find optimal reasoning paths.

VII Industry Blind Spots and the Pricing Paradox

The framework of this paper reveals four structural issues in the current AI industry that may be underestimated:

VIII Verifiable Experimental Designs

The hypotheses proposed in this paper can be verified through the following experimental designs:

Experiment 1: Empirical Top-K Distribution Measurement

For a given model, input semantically equivalent texts in eight languages (e.g., using parallel corpora), record the complete probability distribution and effective Top-K values at each token position under identical Temperature and Top-P settings. Compare the Top-K distributions across the eight languages horizontally to verify whether they correlate positively with the linguistic ambiguity index.

Experiment 2: Training Language Causal Experiment

A controlled-variable experiment—same model architecture, same parameter count, same number of training tokens—train four models separately on pure Chinese, pure English, pure Japanese, and pure German corpora, then compare their performance on entirely language-independent tasks (mathematical reasoning, abstract logic, symbolic operations). If the Chinese-trained model leads on non-linguistic reasoning tasks, this would provide causal evidence for the training pressure hypothesis.

Experiment 3: Temperature Response Curve Experiment

Measure the entropy growth curve, K_eff growth curve, and output quality degradation curve for each language as Temperature varies continuously from 0.1 to 2.0. This paper does not presuppose that the “quality collapse point” for high-ambiguity languages is necessarily higher or lower than for low-ambiguity languages—a high baseline entropy could mean earlier collapse (being closer to uniform distribution) or greater structural resilience (the model having already learned to maintain coherence in high-ambiguity environments). Which prediction is correct should be determined by empirical measurement. Recommended metrics include: H(T), K_eff@0.9(T), dH/dT (entropy sensitivity to Temperature), and dK_eff/dT (effective Top-K expansion rate). We recommend using bits-per-byte (BPB) as a cross-linguistic, cross-tokenizer normalization metric to avoid incomparability caused by different tokenization schemes.

Experiment 4: Optimal Mixed Corpus Ratio

Systematically vary the ratio of high-ambiguity languages (Chinese/Japanese) to low-ambiguity languages (English/German) in the training corpus, measure the impact curve on downstream reasoning task performance, and identify the optimal mixing ratio.

Experiment 5: Minimum Viable Experiment (No Model Training Required)

The above experiments are costly. The following design can be executed immediately on existing open-source models: select multi-architecture models such as Qwen, Llama, Gemma, and DeepSeek; use parallel corpora (e.g., Flores-200) to obtain semantically equivalent multilingual inputs; for each sentence, perform token-by-token teacher forcing and record the complete logits at each step; compute entropy, K_eff@0.9, K_eff@0.95, top-1 probability, and distribution Gini coefficient at each position; compare language differences horizontally. This experiment requires no GPU cluster—a single GPU suffices—and can provide preliminary verification or falsification of this paper’s core hypothesis within one week.

Experiment 6: CoT Language Selection Experiment

If Chinese-language training indeed develops stronger disambiguation capacity, then allowing models to freely select their thinking language (code-switching) during Chain-of-Thought reasoning may outperform enforcing a single language. An experiment can be designed where the model is forced to use pure Chinese CoT, pure English CoT, and free mixed-language CoT on the same reasoning task, comparing accuracy differences on mathematical and logical tasks.

Experiment 7: Reasoning Type Decomposition Experiment

Different linguistic properties may have different effects on different types of reasoning. We recommend decomposing “reasoning” into subtypes: causal reasoning, mathematical reasoning, spatial reasoning, temporal reasoning, abstract symbolic operations, and others, then separately measuring the performance differences of models trained on high-ambiguity languages across each subtype. Chinese’s high ellipsis rate may particularly enhance causal tracking ability (requiring recovery of dropped subjects), but the improvement in pure mathematical reasoning may be limited.

Experiment 8: Context Window Semantic Coverage Experiment

If each Chinese token carries more semantic content, then a context window of the same token length covers a broader semantic range in Chinese. This factor could independently explain better reasoning performance apart from ambiguity. We recommend measuring: under an identical token-count context window, the performance differences of models across languages on long-document comprehension and multi-hop reasoning tasks, in order to disentangle the “semantic density effect” from the “ambiguity effect.”

IX The AI Interaction Advantage of Multilingual Users

One corollary of this paper’s framework is that multilingual users—especially those who span different ambiguity gradients—hold a structural advantage in AI interaction. This corollary is supported by neuroscience evidence: bilinguals and multilinguals demonstrate enhanced cognitive capabilities in task-switching accuracy, cognitive flexibility, and abstract symbolic thinking^[9][10][11]. Research has found that the cognitive flexibility required for language switching makes the brain more adept at exploring different and novel perspectives^[12]. Furthermore, Chinese-specific causal ordering preferences are internalized and rigidly applied by models, with reasoning accuracy declining when input structures deviate from standard expressions^[13], further confirming that structural processing path differences exist across languages within models.

However, this paper highlights a dimension not previously discussed: multilingual users possess not only more flexible thinking but also the ability to choose which language to use to trigger different response modes in the AI. Using a high-ambiguity language as input forces the model to search across a larger probability space, potentially producing deeper responses. This is a “linguistic weapon selection” capability that monolingual users do not possess.

X Counterexamples and Alternative Explanations

To strengthen the credibility of this paper’s hypothesis framework, the following lists counterexamples and alternative explanations that could weaken or overturn the core propositions. Any serious follow-up research should prioritize ruling out these alternative hypotheses:

This paper positions itself as proposing hypotheses worthy of verification, not as providing verified conclusions. If any of the above alternative explanations is confirmed as the primary factor, it would weaken the core propositions of this paper. This is precisely the embodiment of falsifiability.

XI Conclusion

The core contributions of this paper are three interrelated original propositions:

Proposition One (Top-K Divergence Proposition): Under identical Temperature and Top-P settings, the effective Top-K values across different languages exhibit order-of-magnitude differences that correlate positively with the language’s ambiguity index.

Proposition Two (Training Pressure Proposition): High-ambiguity languages used as training corpora may constitute a higher conditional-entropy learning environment that drives models to develop stronger contextual integration and disambiguation capabilities; whether such capabilities transfer across languages to non-linguistic reasoning tasks requires verification through controlled-variable experiments.

Proposition Three (Three-Layer Unification Proposition): Language ambiguity produces homologous yet directionally distinct effects across three layers—human communication efficiency, LLM training capability emergence, and LLM inference computational cost—and the three are inseparable.

All numerical values in this paper are theoretical estimates requiring verification through actual model experiments. However, we believe the theoretical framework and testable hypotheses proposed herein offer a fundamentally new perspective for understanding how linguistic properties deeply influence LLM reasoning capabilities.

XII External Data Annotations