# Write Back the Delta: Revisiting the Same Tokens with Fresh Representations

arXiv: https://arxiv.org/abs/2609.32457 · HTML: https://mlsanity.com/paper/2609.32457/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 64 of its 73 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 64)

- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Efficient Attentions for Long Document Summarization](https://mlsanity.com/paper/2104.02112/) (2021)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)

## Abstract (arXiv)

Transformers process information strictly forward through depth, preventing deeper computation from revisiting and refining earlier representations. To augment the standard forward pass, existing approaches either re-execute depth, incurring additional computation, or modify the residual stream using predefined directions, limiting their instance-level adaptation. Recently, inference-time feedback offers a direct mechanism for recycling endogenously produced computation by writing deeper residual states back to earlier layers, yet what should be fed back remains unclear. We argue that the depth increment Delta, capturing newly accumulated computation between two layers, provides a more effective, composable, and scalable feedback signal than the full state. Building on this observation, we introduce ReFlux, a learnable feedback graph that dynamically selects and composes increment-carrying routes. ReFlux supports synchronous feedback to the same token and streaming feedback to subsequent tokens. Extensive experiments across various models, corpora, and benchmarks show that synchronous ReFlux consistently reduces perplexity across ten language-modeling corpora, and improves accuracy by 2.1-2.3 points, with gains reaching 4.7 points on multi-hop reasoning. Streaming ReFlux further retains most of these gains while preserving the base model's 1x theoretical backbone FLOPs. These results establish ReFlux as an efficient paradigm for unlocking the latent computational potential of LLMs, allowing them to revisit the same tokens with fresh representations. Code implementation can be found at https://github.com/gooogleshanghai/reflux.