# Delayed Supervision for Test-Time Language Models

arXiv: https://arxiv.org/abs/2609.32312 · HTML: https://mlsanity.com/paper/2609.32312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 12 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [BABILong: Testing the Limits of LLMs with Long Context Reasoning-in-a-Haystack](https://mlsanity.com/paper/2406.10149/) (2024)
- [RWKV-7 "Goose" with Expressive Dynamic State Evolution](https://mlsanity.com/paper/2503.14456/) (2025)
- [Test-Time Training Done Right](https://mlsanity.com/paper/2505.23884/) (2025)
- [Reinforced Fast Weights with Next-Sequence Prediction](https://mlsanity.com/paper/2602.16704/) (2026)

## Abstract (arXiv)

Test-time language models adapt a compact memory while processing the input sequence. This perspective encompasses nonlinear fast-weight learning in LaCT, associative delta-rule updates in DeltaNet, and generalized delta-rule state updates in RWKV-7. Training these models to predict the next token does not explicitly require a fact to remain accessible after many subsequent memory updates. We study delayed supervision for this test-time memory: during post-training, ask a simulator-grounded question only after a long interval of unrelated events, and supervise its answer alongside ordinary next-token prediction. Questions are evaluated on disposable branches, so their answers never enter the continuing event stream. The construction distinguishes retention from revision: a retained fact must remain valid throughout the delay, whereas a revised fact must be answered with its latest value. We evaluate this approach on LaCT-760M and plain DeltaNet-1.3B using TextWorld training trajectories and shared BABILong and RULER evaluation panels, and include a separately reported RWKV-7 comparison. Relative to event-only training, delayed QA improves BABILong by 5.48 percentage points for LaCT and 1.32 points for DeltaNet, and single-needle RULER by 1.45 and 3.27 points, respectively. The RWKV-7 comparison reports gains of 4.60 and 7.00 points on its own panels. These results support delayed semantic supervision as a practical outer training objective for usable test-time memory, while leaving open how much of the benefit derives specifically from delay rather than general question-answering and answer-termination supervision.