You Can Learn Tokenization End-to-End with Reinforcement Learning

Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that decomposes scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step $T$, data-scale $D$, and model-scale $M$ axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.

Small models are made more capable through distillation from a larger one that shares their tokenization scheme. However, do distilled byte and token models behave similarly in terms of scaling trends as compute and data increases? To enable this comparison, we introduce two variants to efficiently convert token logits to Byte Logits: 1) approximate: Marginalize-It, and 2) exact: End-Of-Token. We then present the first large scale study of overtraining decoder-only dense transformer models varying two dimensions simultaneously: the tokenization scheme (Tokens, Bytes, Bytes w/ eot) and the training objective (Distillation vs. Cross-Entropy), sweeping layer-parameter-matched models with roughly 1 billion parameters up to 1 trillion bytes of data. Across eight benchmarks spanning three categories: Multiple Choice QA, Language Generation, and Machine Translation, we find that Token-1B models outperform byte models (End-Of-Token-1B and Bytes-1B) in the low-FLOP regime but eventually plateau; byte models start worse yet surpass Token-1B models with more compute, reaching a higher downstream task performance ceiling. Extrapolating the average top-1 error vs. validation BPB scaling laws predicts that, asymptotically, distilled End-Of-Token-1B outperforms distilled Token-1B by up to 4%. They are also far more data efficient, matching the performance of distilled Token-1B using only one-sixth of the training data. Moreover, by operating over a small vocabulary of 256 bytes instead of on the order of 100K tokens, they circumvent the need for top-k truncation during logit dumping, while also reducing logit storage costs to roughly one-fifth. Finally, our downstream performance scaling laws predict that our distilled End-Of-Token-1B models asymptotically surpass the Llama 3.2-1B, Gemma-3-1B-pt, and Gemma 2B models on averaged downstream tasks by up to 6.5%, 8.1%, and 2.1%, respectively.

Tokenization is a necessary component within the current architecture of many language mod-els, including the transformer-based large language models (LLMs) of Generative AI, yet its impact on the model's cognition is often overlooked. We argue that LLMs demonstrate that the Distributional Hypothesis (DH) is sufficient for reasonably human-like language performance (particularly with respect to inferential lexical competence), and that the emergence of human-meaningful linguistic units among tokens and current structural constraints motivate changes to existing, linguistically-agnostic tokenization techniques, particularly with respect to their roles as (1) vehicles for conveying salient distributional patterns from human language to the model and as (2) semantic primitives. We explore tokenizations from a BPE tokenizer; extant model vocabularies obtained from Hugging Face and tiktoken; and the information in exemplar token vectors as they move through the layers of a RoBERTa (large) model. Besides creating suboptimal semantic building blocks and obscuring the model's access to the necessary distributional patterns, we describe how tokens and pretraining can act as a backdoor for bias and other unwanted content, which current alignment practices may not remediate. Additionally, we relay evidence that the tokenization algorithm's objective function impacts the LLM's cognition, despite being arguably meaningfully insulated from the main system intelligence. Finally, we discuss implications for architectural choices, meaning construction, the primacy of language for thought, and LLM cognition. [First uploaded to arXiv in December, 2024.]