Beyond Test-Time Training: Learning to Reason via Hardware-Efficient Optimal Control
arXiv:2603.09221v1 Announce Type: new 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 mathemat
arXiv:2603.09221v1 Announce Type: new 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.
Executive Summary
This article introduces the Test-Time Control (TTC) layer, a novel architecture that embeds optimal control as a component for reasoning in deep learning models. The TTC layer enables planning before prediction by performing finite-horizon LQR planning over latent states at inference time. The authors derive a hardware-efficient LQR solver and integrate it as an adapter into pre-trained large language models (LLMs). The proposed approach demonstrates significant improvements in mathematical reasoning performance and scalability. The article showcases the potential of incorporating optimal control into neural architectures, offering a promising direction for future research in AI and deep learning.
Key Points
- ▸ The TTC layer formulates reasoning as optimal control and performs finite-horizon LQR planning over latent states at inference time.
- ▸ The authors derive a hardware-efficient LQR solver based on a symplectic formulation and implement it as a fused CUDA kernel.
- ▸ The proposed approach improves mathematical reasoning performance by up to +27.8% on MATH-500 and 2-3x Pass@8 improvements on AMC and AIME.
Merits
Strength in Scalability
The proposed approach demonstrates significant improvements in scalability, making it a promising direction for future research in AI and deep learning.
Embedding Optimal Control
The TTC layer embeds optimal control as a component for reasoning in deep learning models, offering a novel and effective mechanism for planning before prediction.
Demerits
Limited Training Dataset
The proposed approach requires a large and diverse training dataset to effectively learn the optimal control policy, which may limit its applicability in real-world scenarios.
Hardware Requirements
The proposed approach requires significant computational resources and specialized hardware, which may limit its adoption in certain applications or environments.
Expert Commentary
The proposed approach offers a novel and effective mechanism for planning before prediction, which can be applied in various domains where mathematical reasoning is required. However, the limited training dataset and hardware requirements may limit its applicability in real-world scenarios. The proposed approach also raises interesting questions about the explainability of deep learning models and the potential implications for policy-making. Overall, the article showcases the potential of incorporating optimal control into neural architectures, offering a promising direction for future research in AI and deep learning.
Recommendations
- ✓ Further research is needed to explore the applicability of the proposed approach in real-world scenarios and to develop more efficient and scalable hardware solutions.
- ✓ The proposed approach should be evaluated on a wider range of datasets and tasks to demonstrate its generalizability and robustness.