Write Back the $\Delta$: Revisiting the Same Tokens with Fresh Representations

arXiv:2609.32457v1 Announce Type: new Abstract: 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.

Abstract: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 this https URL.

Machine Learning (cs.LG)

arXiv:2609.32457 [cs.LG]

(or arXiv:2609.32457v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32457 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Write Back the $\Delta$: Revisiting the Same Tokens with Fresh Representations

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