Can Test-Time Memory Evolution Outperform Test-Time Training for Scientific Discovery?

Yepeng Liu; Shengmai Chen; Xuandong Zhao; Chengzhi Liu; Dawn Song; Xin Eric Wang; Yuheng Bu

cs.AIOct 23, 2026

Can Test-Time Memory Evolution Outperform Test-Time Training for Scientific Discovery?

Authors: Yepeng Liu, Shengmai Chen, Xuandong Zhao, Chengzhi Liu, Dawn Song, Xin Eric Wang, Yuheng Bu

Organizations: UC Santa Barbara · UC Berkeley

Abstract

Recent test-time training (TTT) frameworks have enabled open-weight large language models (LLMs) to outperform inference-only frameworks powered by frontier models on scientific discovery tasks. However, TTT introduces additional computational cost for online weight updates during the discovery process, making computational efficiency an important consideration when scaling to larger models. This motivates us to explore an efficient test-time adaptation method for scientific discovery. We introduce Test-Time Memory Evolution (TTME), a plug-and-play test-time adaptation method, as an alternative to TTT. TTME continually updates the external memory by distilling the experience to guide subsequent discovery without updating model weights. To have a clean comparison, we evaluate TTME and TTT under the same discovery framework, replacing only the test-time adaptation method. Our evaluation shows that TTME outperforms TTT on all five mathematical tasks, while reducing computational cost by $82.8$ - $84.6\%$ in FLOPs and $47.7$ - $58.4\%$ in runtime. These results establish TTME as an effective and computationally efficient alternative to TTT in the evaluated discovery settings.

Figures & tables

Figure 1: Best-found scores versus computational cost under the TTT-Discover framework [ 36 ] with Qwen3-8B. The three settings use the same discovery framework, with TTT, with TTME replacing TTT, or with neither method. TTME achieves the best scores at low computational cost across all three tasks.

Figure 2: Weight adaptation updates model parameters through test-time RL (top). Memory adaptation updates external memory that conditions generation while keeping model weights fixed (bottom). Both retain the same underlying discovery framework.

Method	Model	Erdős $\downarrow$	AC1 $\downarrow$	AC2 $\uparrow$
TTT-Discover (w/ TTT)	Qwen3-8B	0.380932	1.50525	0.9472
TTT-Discover (w/o TTT)	Qwen3-8B	0.380957	1.505242	0.944771
Ours (w/ TTME)	Qwen3-8B	0.380927	1.504329	0.949248
TTT-Discover (w/ TTT)	gpt-oss-120b	0.380876	1.50287	0.9591
TTT-Discover (w/o TTT)	gpt-oss-120b	0.380945	1.505966	0.953682
Ours (w/ TTME)	gpt-oss-120b	0.380862	1.502745	0.960784

Table 1: Results under the TTT-Discover framework for three settings: w/ TTT, w/o TTT, and w/ TTME. Results for w/ TTT are from Yuksekgonul et al. [36] over 50 search steps.

Method	Model	AC2 $\uparrow$	AC3 $\downarrow$	Hadamard $\uparrow$
ThetaEvolve (w/ TTT)	Distill-Qwen3-8B	0.9469	1.4930	0.5764
ThetaEvolve (w/o TTT)	Distill-Qwen3-8B	0.947375	1.519277	0.571085
Ours (w/ TTME)	Distill-Qwen3-8B	0.948148	1.464224	0.579938

Table 2: Results under the ThetaEvolve framework for three settings: w/ TTT, w/o TTT, and w/ TTME. Results for w/ TTT are from Wang et al. [33] over 65 search steps.

		Runtime excluding evaluation (h)			Computational cost (EFLOPs)
Task	Model	TTT	TTME	Reduction	TTT	TTME	Reduction
AC1	Qwen3-8B	11.76	5.36	54.5%	29.47	4.53	84.6%
AC2	Qwen3-8B	12.73	6.66	47.7%	33.09	5.69	82.8%
Erdős	Qwen3-8B	11.67	4.85	58.4%	26.21	4.15	84.2%

Table 3: Runtime (excluding evaluation) and computation under TTT-Discover with Qwen3-8B. TTME reduces runtime by 47.7–58.4% and FLOPs by 82.8–84.6%.

Figure 3: Best-found scores during search under TTT-Discover and ThetaEvolve frameworks. TTME achieves better final scores in every evaluated setting. Orange dots mark the first step at which TTME exceeds the corresponding final TTT score.

TTT-Discover framework: Qwen3-8B
TTT	TTME	AC2 $\uparrow$	Erdős $\downarrow$
✗	✗	0.944771	0.380957
✓	✗	0.9472	0.380932
✗	✓	0.949248	0.380927
✓	✓	0.944141	0.380944

Table 4: Comparison of TTT, TTME, and their combination against a baseline with neither. TTME alone achieves the best scores on both tasks; adding TTT reduces performance.

Configuration	AC1 $\downarrow$	AC2 $\uparrow$	Erdős $\downarrow$
TTT-Discover framework: gpt-oss-120b
Full TTME	1.502745	0.960784	0.380862
w/o Guideline Memory	1.505644	0.958506	0.380865
w/o Strategy Memory	1.505981	0.956493	0.380864
w/o TTME	1.505966	0.953682	0.380946

Table 5: Ablation of Guideline Memory and Strategy Memory. Full TTME achieves the best scores on all three tasks, demonstrating the benefit of combining both memory components.

Figure 4: Implementation validity rate and final performance under the TTT-Discover framework with Qwen3-8B across three tasks. Bars show mean validity rates over 50 steps (left axes); markers show best-found scores (right axes), with better scores plotted higher.

Figure 5: Combination of ideas in subsequent search under TTT-Discover with Qwen3-8B. TTME has a higher combination share on both tasks, with and without the

10^{-5}

improvement requirement.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Task	Score	Best-found
AC1 ( $\downarrow$ )	Upper bound	Minimum
AC2 ( $\uparrow$ )	Lower bound	Maximum
AC3 ( $\downarrow$ )	Upper bound	Minimum
Erdős ( $\downarrow$ )	Upper bound	Minimum
Hadamard ( $\uparrow$ )	Normalized determinant	Maximum

Appendix

Table 6: Evaluation metrics. Arrows indicate the direction of improvement. We compute best-found scores over all valid candidates evaluated up to the current search step.

Setting	Original ThetaEvolve	Ours
	w/o TTT	w/o TTT	w/ TTME
Search budget and archive
Search steps	65	65	65
Parents $\times$ candidates per parent	$32\times 16=512$	$32\times 16=512$	$32\times 16=512$
Primary candidates per run	33,280	33,280	33,280
Random seeds	42, 1234, 3407	3407	3407

Appendix

Table 7: Settings for fixed-weight Distill-Qwen3-8B on AC2, AC3, and Hadamard. Original denotes ThetaEvolve’s 65-step early inference-only setting [ 33 ] . Counts are per task and seed.

Setting	Original TTT-Discover	Ours
	w/ TTT	w/o TTT	w/ TTME
Search budget and reuse buffer
Search steps	50	50	50
Parents $\times$ candidates per parent	$8\times 64=512$	$8\times 64=512$	$8\times 64=512$
Primary candidates per run	25,600	25,600	25,600
Buffer capacity / PUCT coefficient $c$	1,000 / 1.0	1,000 / 1.0	1,000 / 1.0

Appendix

Table 8: Settings for gpt-oss-120b on AC1, AC2, and Erdős. Original denotes TTT-Discover with reinforcement learning [ 36 ] ; both of our conditions use frozen weights. Counts are per run.

Aspect	Guideline Memory	Strategy Memory
Input evidence	Valid outcomes and execution or validity failures collected across parents.	Evaluated parent–child pairs in which the child is valid and improves on the parent.
Model input	Outcome summaries and the current guidelines.	Parent and child code, their diff, and evaluation results.
Extracted content	An operational lesson: a trigger, a mechanism, and a concrete action.	An experience note: the algorithmic idea expressed by a change and its application conditions.
Memory update	Merge new lessons with current guidelines, combine duplicates, and retain at most 24.	Group notes into strategy families. Create an entry for a new family, or consolidate new notes with the existing entry.
Use during generation	Include current guidelines in the prompt for both generation branches.	Select a strategy for the parent, then adapt its entry into a modification instruction for Strategy-Guided Generation.

Appendix

Table 9: Construction and use of the two memories. We update both from evaluated search outcomes every

K=2

steps.

Setting	TTT-Discover	ThetaEvolve
Joint memory update interval, $K$ (steps)	2	2
Maximum stored guidelines	24	24
Maximum proposed guidelines per update	3	3
Guideline expiry window (search steps)	20	20
Guideline matching threshold (Jaccard)	0.5	0.5
Display budget per guideline (characters)	240	240

Appendix

Table 10: Memory hyperparameters and candidate allocation. We measure

K

in search steps;

N

is the number of modification instructions per parent. Character budgets apply to prompt-visible text.

Panel of Figure 6 — Figure 6: Discovered constructions for AC1–AC3 and Erdős. The AC1 inset shows normalized heights 0–0.06. Arrows indicate the direction of improvement.

Figure 7: Discovered constructions (continued). Panel (e) preserves the original row and column order of the Hadamard construction.

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Test-time scaling (TTS) has become an effective approach for improving large language model performance by allocating additional computation during inference. However, existing TTS strategies are largely hand-crafted: researchers manually design reasoning patterns and tune heuristics by intuition, leaving much of the computation-allocation space unexplored. We propose an environment-driven framework, AutoTTS, that changes what researchers design: from individual TTS heuristics to environments where TTS strategies can be discovered automatically. The key to AutoTTS lies in environment construction: the discovery environment must make the control space tractable and provide cheap, frequent feedback for TTS search. As a concrete instantiation, we formulate width--depth TTS as controller synthesis over pre-collected reasoning trajectories and probe signals, where controllers decide when to branch, continue, probe, prune, or stop and can be evaluated cheaply without repeated LLM calls. We further introduce beta parameterization to make the search tractable and fine-grained execution trace feedback to improve discovery efficiency by helping the agent diagnose why a TTS program fails. Experiments on mathematical reasoning benchmarks show that the discovered strategies improve the overall accuracy--cost tradeoff over strong manually designed baselines. The discovered strategies generalize to held-out benchmarks and model scales, while the entire discovery costs only $39.9 and 160 minutes. Our data, and code will be open-source at https://github.com/zhengkid/AutoTTS.

Abstract

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