Knowledge Flow: Scaling Reasoning Beyond the Context Limit

TL;DR

Knowledge Flow is a training-free test-time-scaling paradigm that maintains a persistent, model-edited knowledge list across independent rollouts: each iteration consumes the prior list as part of the prompt, answers the question, and emits one edit (add / drop / both) to the list before the next rollout. The authors frame this as an AR-LM simulation of diffusion/flow-matching inference — recursive denoising of a fixed-size “knowledge state” rather than expanding context. Reported result: gpt-oss-120b and Qwen3-235B-A22B-Thinking-2507 both reach 100% accuracy on AIME25 with pure-text reasoning, no tools, no external feedback. The mechanism is distinct from parallel-thinking baselines (independent rollouts + majority vote) because information flows between attempts via the edited list rather than being aggregated post-hoc.

Key claims

Knowledge Flow reaches 100% accuracy on AIME25 with both gpt-oss-120b and Qwen3-235B-A22B-Thinking-2507, using only pure-text reasoning — no tools, no external feedback, no training [§TL;DR, §Experiments setup].
The edit operation is constrained to three primitives — add one item, drop one item, or both — keeping the knowledge list bounded across iterations so test-time compute is not bottlenecked by an ever-growing context window [Fig. 2].
The paradigm is positioned as an AR-LM simulation of diffusion/flow-matching inference: a recursive denoising trajectory on a fixed-size knowledge state, rather than an expanding sequence of tokens [§Knowledge flow mirrors the iterative refinement…, Fig. 1].
Distinct from parallel-thinking-with-aggregation baselines that either train an aggregator, train a cross-attention module, or use a recurrent-depth diffusion-forcing model — Knowledge Flow needs no training and works with off-the-shelf SOTA models [§Recent work in parallel thinking…].
Distinct from vanilla parallel thinking (independent traces + majority vote): static aggregation cannot exchange knowledge between attempts, whereas Knowledge Flow’s prompt-mediated list is the explicit channel for inter-attempt knowledge transfer [Fig. 4, §parallel thinking approaches…].
Motivation framing: long-runtime frontier results (Gemini’s 11.3-hour ICPC-WF solve) imply a level of test-time scaling a fixed context window cannot sustain — Knowledge Flow is offered as the compute-scaling primitive that breaks the context-window ceiling [§Introduction].

Method

A knowledge list K is initialized empty. At iteration t, the prompt to the LM is (question, K_{t-1}, edit instructions). The LM produces both (a) an answer attempt and (b) an edit to K: add one new knowledge item, drop one old item, or both. K_t is the updated list, and iteration t+1 reuses it. Because the list size is bounded by the cumulative cap on additions minus drops, the prompt never exceeds the model’s context window even as test-time compute grows. The post explicitly draws an analogy to flow-matching inference (Dieleman 2025): repeated refinement of a state under a learned update rule, with knowledge items playing the role of latent coordinates and the LM playing the role of the velocity field.

Experiments use gpt-oss-120b and Qwen3-235B-A22B-Thinking-2507 off-the-shelf — no fine-tuning. Evaluation is on AIME24 and AIME25; the post highlights AIME25 100% as the headline.

Results

AIME25: 100% accuracy with gpt-oss-120b; 100% accuracy with Qwen3-235B-A22B-Thinking-2507. Both with pure-text reasoning, no tools, no external feedback [§TL;DR].
AIME24 results are referenced but not summarized in the post body excerpt; the post points at the experiment section as the source of detail.
No direct head-to-head accuracy numbers vs. independent-sampling majority vote at matched compute are reproduced in the body excerpt — the comparison is structural (Fig. 4), not numerical, at the level of detail surfaced.

Why it’s interesting

This is a new, training-free axis on top of the inference-time-scaling concept page (Inference-Time Scaling). The wiki’s existing six axes are: scaffold-side / REPL sub-LM dispatch (Recursive Language Models), interaction-depth tool-use (MiroThinker: Pushing the Performance Boundaries of Open-Source Research Agents via Model, Context, and Interactive Scaling), KV-cache compression at fixed memory (Inference-Time Hyper-Scaling with KV Cache Compression), learned parallel-agent orchestration (Kimi K2.5: Visual Agentic Intelligence), per-step iterative refinement on a generator (Self-Refining Video Sampling), and test-time weight updates (End-to-End Test-Time Training for Long Context). Knowledge Flow adds a seventh: a bounded, model-edited scratchpad shared across independent rollouts, where the extra compute lands as more rollout iterations rather than as more tokens within one rollout, more parallel chains, or more weight updates. The mechanism is closer to parallel-thinking-with-aggregation (cf. Zhao 2025, Dong 2025, Geiping 2025) but trades the learned aggregator for a prompt-mediated, model-emitted edit channel — which is precisely the surface that lets it run on frontier models off-the-shelf. The 100% AIME25 claim is also a useful datapoint for the wiki’s reasoning-rl page (Reasoning RL): it suggests a non-trivial fraction of single-pass reasoning gaps on competition math are recoverable by structured iterative refinement without any policy training, which complements rather than substitutes for RLVR-style approaches and reinforces a recurring theme on that page that the inference-time-scaling story is at least as important as the RL story.