# Text Generation Beyond Discrete Token Sampling

arXiv: https://arxiv.org/abs/2505.14827 · HTML: https://mlsanity.com/paper/2505.14827/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 30 of 34)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Learning How to Ask: Querying LMs with Mixtures of Soft Prompts](https://mlsanity.com/paper/2104.06599/) (2021)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Good Debt or Bad Debt: Detecting Semantic Orientations in Economic Texts](https://mlsanity.com/paper/1307.5336/) (2013)
- [LLMLingua: Compressing Prompts for Accelerated Inference of Large Language Models](https://mlsanity.com/paper/2310.05736/) (2023)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [On the Origins of Linear Representations in Large Language Models](https://mlsanity.com/paper/2403.03867/) (2024)
- [It's MBR All the Way Down: Modern Generation Techniques Through the Lens of Minimum Bayes Risk](https://mlsanity.com/paper/2310.01387/) (2023)
- [On Linear Representations and Pretraining Data Frequency in Language Models](https://mlsanity.com/paper/2504.12459/) (2025)

## Built on by (most cited first, 21 of 21)

- [Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.16782/) (2025)
- [LLM Latent Reasoning as Chain of Superposition](https://mlsanity.com/paper/2510.15522/) (2025)
- [LLMs are Single-threaded Reasoners: Demystifying the Working Mechanism of Soft Thinking](https://mlsanity.com/paper/2508.03440/) (2025)
- [SofT-GRPO: Surpassing Discrete-Token LLM Reinforcement Learning via Gumbel-Reparameterized Soft-Thinking Policy Optimization](https://mlsanity.com/paper/2511.06411/) (2025)
- [Generative Recursive Reasoning](https://mlsanity.com/paper/2605.19376/) (2026)
- [Soft-Masked Diffusion Language Models](https://mlsanity.com/paper/2510.17206/) (2025)
- [Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decoding](https://mlsanity.com/paper/2603.13366/) (2026)
- [Latent-GRPO: Group Relative Policy Optimization for Latent Reasoning](https://mlsanity.com/paper/2604.27998/) (2026)
- [Loopholing Discrete Diffusion: Deterministic Bypass of the Sampling Wall](https://mlsanity.com/paper/2510.19304/) (2025)
- [Quantifying the Necessity of Chain of Thought through Opaque Serial Depth](https://mlsanity.com/paper/2603.09786/) (2026)
- [T^2MLR: Transformer with Temporal Middle-Layer Recurrence](https://mlsanity.com/paper/2607.15178/) (2026)
- [Beyond Hard Masks: Progressive Token Evolution for Diffusion Language Models](https://mlsanity.com/paper/2601.07351/) (2026)
- [Do Large Language Models (Really) Need Statistical Foundations?](https://mlsanity.com/paper/2505.19145/) (2025)
- [LEPO: Latent Reasoning Policy Optimization for Large Language Models](https://mlsanity.com/paper/2604.17892/) (2026)
- [Learning to Reason with Mixture of Tokens](https://mlsanity.com/paper/2509.21482/) (2025)
- [Lightweight Latent Reasoning for Narrative Tasks](https://mlsanity.com/paper/2512.02240/) (2025)
- [Multi-Path Collaborative Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2512.01485/) (2025)
- [SuperThoughts: Reasoning Tokens in Superposition](https://mlsanity.com/paper/2606.13862/) (2026)
- [Efficient Chain-of-Modality Reasoning via Progressive Compression for Spoken Language Models](https://mlsanity.com/paper/2607.19932/) (2026)
- [RECLAIM: Can Agents Reproduce the Claims of Machine Learning Papers?](https://mlsanity.com/paper/2609.28850/) (2026)
- [Pretraining Latent Information Feedback Transformers with Teacher Supervision](https://mlsanity.com/paper/2609.38149/) (2026)

## Abstract (arXiv)

In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.