# JTok: On Token Embedding as another Axis of Scaling Law via Joint Token Self-modulation

arXiv: https://arxiv.org/abs/2602.00800 · HTML: https://mlsanity.com/paper/2602.00800/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 50 of its 59 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 50)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [CMMLU: Measuring massive multitask language understanding in Chinese](https://mlsanity.com/paper/2306.09212/) (2023)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [Byte Latent Transformer: Patches Scale Better Than Tokens](https://mlsanity.com/paper/2412.09871/) (2024)

## Built on by (most cited first, 3 of 3)

- [xHC: Expanded Hyper-Connections](https://mlsanity.com/paper/2607.14530/) (2026)
- [MoME: Mixture-of-Memory Embeddings for Context-Aware Sparse Lookup](https://mlsanity.com/paper/2609.15126/) (2026)
- [STAPLE: Static Sparse Upcycling of Pretrained Checkpoints via Embedding Modules](https://mlsanity.com/paper/2610.12599/) (2026)

## Abstract (arXiv)

LLMs have traditionally scaled along dense dimensions, where performance is coupled with near-linear increases in computational cost. While MoE decouples capacity from compute, it introduces large memory overhead and hardware efficiency challenges. To overcome these, we propose token-indexed parameters as a novel, orthogonal scaling axis that decouple model capacity from FLOPs. Specifically, we introduce Joint-Token (JTok) and Mixture of Joint-Token (JTok-M), which augment Transformer layers with modulation vectors retrieved from auxiliary embedding tables. These vectors modulate the backbone via lightweight, element-wise operations, incurring negligible FLOPs overhead. Extensive experiments on both dense and MoE backbones, spanning from 650M (190M + 460M embedding) to 61B (17B + 44B embedding) total parameters, demonstrate that our approach consistently reduces validation loss and significantly improves downstream task performance (e.g., +4.1 on MMLU, +8.3 on ARC, +8.9 on CEval). Rigorous isoFLOPs analysis further confirms that JTok-M fundamentally shifts the quality-compute Pareto frontier, achieving comparable model quality with 35% less compute relative to vanilla MoE architectures, and we validate that token-indexed parameters exhibit a predictable power-law scaling behavior. Moreover, our efficient implementation ensures that the overhead introduced by JTok and JTok-M remains marginal.