Computer Science > Machine Learning
arXiv:2603.09221 (cs)
[Submitted on 10 Mar 2026]
Title:Beyond Test-Time Training: Learning to Reason via Hardware-Efficient Optimal Control
Authors:Peihao Wang, Shan Yang, Xijun Wang, Tesi Xiao, Xin Liu, Changlong Yu, Yu Lou, Pan Li, Zhangyang Wang, Ming Lin, René Vidal
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Abstract:Associative memory has long underpinned the design of sequential models. Beyond recall, humans reason by projecting future states and selecting goal-directed actions, a capability that modern language models increasingly require but do not natively encode. While prior work uses reinforcement learning or test-time training, planning remains external to the model architecture. We formulate reasoning as optimal control and introduce the Test-Time Control (TTC) layer, which performs finite-horizon LQR planning over latent states at inference time, represents a value function within neural architectures, and leverages it as the nested objective to enable planning before prediction. To ensure scalability, we derive a hardware-efficient LQR solver based on a symplectic formulation and implement it as a fused CUDA kernel, enabling parallel execution with minimal overhead. Integrated as an adapter into pretrained LLMs, TTC layers improve mathematical reasoning performance by up to +27.8% on MATH-500 and 2-3x Pass@8 improvements on AMC and AIME, demonstrating that embedding optimal control as an architectural component provides an effective and scalable mechanism for reasoning beyond test-time training.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2603.09221 [cs.LG] |
| (or arXiv:2603.09221v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.09221
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View a PDF of the paper titled Beyond Test-Time Training: Learning to Reason via Hardware-Efficient Optimal Control, by Peihao Wang and 10 other authors
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