Pretokenization Curriculum in Language Models

• Pretokenization curriculum is a dynamic process that refines tokenization by updating vocabularies based on entropy and frequency criteria.
• It alternates between model optimization and vocabulary merging, leading to improved pretraining efficiency and enhanced model compression.
• The approach supports multilingual robustness and domain adaptation, ensuring accurate token boundaries and effective scaling in diverse settings.

Pretokenization curriculum refers to the systematic, often staged, process of evolving the segmentation and vocabulary (tokenization) used for LLM (LM) pretraining in a data-driven, adaptive manner. Unlike static vocabulary approaches, pretokenization curriculum methods dynamically refine the atomic units of representation during pretraining, typically guided by information-theoretic, statistical, or linguistic criteria. This strategy yields measurable improvements in pretraining efficiency, language modeling compression, and downstream performance by aligning the tokenization process with emergent linguistic, computational, and domain-specific patterns.

1. Adaptive Vocabulary Curriculum: Objectives and Learning Paradigm

Vocabulary curriculum learning deviates from the conventional practice of fixing the tokenizer and vocabulary prior to model pretraining. Instead, it alternates between two phases:

• Model optimization using the current vocabulary;
• Vocabulary refinement/expansion based on model-driven signals such as token entropy.

The process is formalized as follows: At each stage $k$, the LLM $f_{\theta_k}$ is optimized on tokenized sequences $s_{1:n} = e(x_{1:m}|\V_k)$ by minimizing the cross-entropy objective:

$\L_k(\theta_k) = -\sum_{x_{1:m}\in\D}\sum_{t=1}^n\log p_{\theta_k}(s_t|s_{1:t-1};\V_k).$

After model update steps, the curriculum computes conditional token entropies and merges highly predictable multigram sequences (subword, word, or phrase) into new tokens, subject to entropy and frequency criteria. Embedding and output matrices are expanded as new vocabulary items are added. This loop repeats, allowing the vocabulary to evolve in tandem with model capacity and learned representations (Yu, 25 Feb 2025).

A central motivation is to mimic the adaptive vocabulary acquisition observed in human language learning, facilitating the learning of transferable representations across diverse tokenization granularities and allocation of modeling capacity.

2. Entropy-Guided Merging and Statistical Criteria

A defining feature of advanced pretokenization curricula is the use of entropy and other information-theoretic measures to determine eligible vocabulary expansions. The model quantifies the conditional entropy

$H(s_t|s_{1:t-1}) = -\sum_{v\in\V_k} p(v|s_{1:t-1})\,\log p(v|s_{1:t-1})$

for each token prediction step. Candidate subsequences $v = (s_i, ..., s_j)$ are assessed for "mergeability" based on two requirements at each position $t > i$:

• Strictly decreasing entropy: $H(s_t|s_{i:t-1}) < H(s_{t-1}|s_{i:t-2})$.
• Entropy threshold: $H(s_t|s_{i:t-1}) < \epsilon$, with typical $\epsilon \approx 0.3$ bits.

Only sequences meeting these criteria are bundled as new lexical entries. This scheme allocates tokens to maximize predictability (ease of modeling), bundling frequent and locally predictable patterns, while maintaining finer granularity for irregular or context-sensitive constructs (Yu, 25 Feb 2025).

In cross-boundary curricula such as SupraTok, additional metrics such as pointwise mutual information (PMI), context entropy, and lightweight LM-based statistical predictors modulate the acceptance of merge candidates, especially for complex or multi-word phrase patterns. Phase transitions in the curriculum control the complexity of permissible merges and loss functions adapt to balance frequency, predictability, and context-specificity (Tănase et al., 16 Aug 2025).

3. Vocabulary Growth Schedules and Scaling Laws

Pretokenization curricula are characterized by controlled, scheduled vocabulary expansion. Notable parameters include:

• Initialization from a minimal alphabet (e.g., character or byte);
• Per-iteration cap on tokens added (e.g., $\Delta V_\text{max} = 3\,000$);
• Number of training steps per curriculum phase.

Empirical analysis reveals that bits-per-character (BPC) scales according to a log-linear law with vocabulary size:

$\mathrm{BPC}(|\V|) \approx c_0 - \alpha \log_{10}|\V|, \;\; \alpha > 0.$

Curriculum-based expansion exhibits a steeper negative slope (e.g., $-0.147$ for curriculum vs. $-0.109$ for static vocabulary), implying that each 10× vocabulary increase yields larger BPC reductions under the curriculum approach. These findings establish that staged, entropy-driven vocabulary expansion outperforms compute-matched static baselines in scaling efficiency (Yu, 25 Feb 2025).

Three-phase schedules in cross-boundary curricula (SupraTok) further demonstrate that staged complexity—morphological subwords, high-PMI multi-word units, and formulaic/domain-specific tokens—are required to guarantee robust convergence and optimal tokenization efficiency (Tănase et al., 16 Aug 2025).

Schedule Phase	Merge Criterion & Objective	Example Approach
Initial	Frequency (e.g., BPE within words)	Token frequency
Intermediate	Statistical association (e.g., PMI + frequency)	PMI/frequency threshold
Advanced/Final	Context entropy + LM-based predictability	Composite loss

4. Emergent Compute Allocation and Representation Hierarchies

Pretokenization curricula induce self-organized specialization of tokens. Longer, merged tokens absorb highly predictable content (morphemes, frequent words/phrases) and result in low-entropy, nearly “solved” prediction steps. Shorter tokens persist in high-entropy contexts (surface forms, ambiguous or rare terms), ensuring model computation is concentrated on at-risk or difficult regions. This mechanism reduces the number of forward-softmax calls and concentrates cross-entropy loss on unresolved ambiguities, yielding a hierarchical structure in both vocabulary and model attention (Yu, 25 Feb 2025).

Token-level BPC analysis demonstrates that newly merged long tokens achieve BPC near 0.76 bits/char, while unmerged or atomized tokens exhibit rising BPC—reflecting the intentionally uneven allocation of modeling capacity justified by the entropy-aware merge algorithm.

5. Robust Multilingual Pretokenization and Constrained Merging

In multilingual settings, pretokenization curricula must further address token integrity and fairness across scripts. The SCRIPT scheme proposes encoding each Unicode character via a pair of tokens: a script supercategory block and an index within the block, ensuring that merges never produce partial code points or cross-character fragments. Merge eligibility is explicitly restricted to preserve Unicode boundaries. Comparisons between byte-based BPE and SCRIPT-BPE demonstrate that the latter eliminates the “byte premium” for non-Latin scripts and uniformly prevents encoding errors, while achieving compression within 2–5% of highly tuned regex-based approaches (Land et al., 30 May 2025).

Method	Tokens/Char (English)	Tokens/Char (Chinese)	Partial-UTF8 Tokens?
Bytes-BPE	0.215	0.626	Yes
SCRIPT-BPE	0.218	0.654	No

This approach guarantees deterministic, script-respecting, and regex-free pretokenization, simplifies downstream model implementation, and is well-suited for curriculum integration and instructional purposes.

6. Extensions, Applications, and Empirical Outcomes

Pretokenization curricula generalize to different LM architectures, larger models, and diverse domains:

• Model-size scaling can target optimal vocabulary sizes proportional to the number of parameters, as supported by vocabulary scaling laws.
• The curriculum framework applies to other modalities, such as byte sequences in vision or audio, by merging statistically predictable patterns at each step.
• Domain adaptation via curriculum-based fine-tuning rapidly acquires domain-specific lexical units, improving both compression and downstream task performance.
• Adaptive stopping, based on validation BPC delta per new token, prevents unnecessary curriculum expansion.

Empirical results from controlled experiments indicate:

• 5–6% BPC reduction vs. static tokenization in small GPT models trained on enwiki8 (Yu, 25 Feb 2025).
• 8.4% and 9.5% gains on HellaSWAG and MMLU (GPT-2 scale, SupraTok (Tănase et al., 16 Aug 2025)).
• Near-elimination of encoding-based penalties and partial tokens in robust multilingual settings (Land et al., 30 May 2025).

A plausible implication is that as curriculum methods continue to mature, they will become an integral part of LLM architectures, serving not only as a compression and efficiency lever but also as a means of aligning model tokenization behavior with evolving domain- or task-specific requirements.