Beyond Test-Time Training: Learning to Reason via Hardware-Efficient Optimal Control
This addresses the need for goal-directed reasoning in language models, offering a scalable architectural solution beyond incremental methods like test-time training.
The paper tackled the problem of enabling reasoning in language models by formulating it as optimal control and introducing a Test-Time Control layer that performs planning at inference time, resulting in up to +27.8% improvement on MATH-500 and 2-3x Pass@8 gains on AMC and AIME benchmarks.
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.