Compute Aligned Training: Optimizing for Test Time Inference
Authors: Adam Ousherovitch, Ambuj Tewari
Organizations: Department of Statistics University of Michigan
Abstract
Scaling test-time compute has emerged as a powerful mechanism for enhancing Large Language Model (LLM) performance. However, standard post-training paradigms, Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), optimize the likelihood of individual samples under a base policy, creating a misalignment with test time procedures that rely on aggregated or filtered outputs. In this work, we propose Compute Aligned Training, which aligns training objectives with test-time strategies. By conceptualizing inference strategies as operators on the base policy, we derive new loss functions that maximize performance when said strategies are applied. We instantiate such loss functions for SFT and RL across common test time strategies. Finally, we provide empirical evidence that this training method substantially improves test time scaling over standard training.
Test-time compute scaling, the practice of spending extra computation during inference via repeated sampling, search, or extended reasoning, has become a powerful lever for improving large language model performance. Yet deploying these techniques under finite inference budgets requires a decision that current systems largely ignore: which inputs deserve more compute, and which can be answered cheaply? We formalize this as a constrained optimization problem (maximize expected accuracy subject to an average compute budget) and solve it with a two-stage Solve-then-Learn pipeline. In the solve stage, Lagrangian relaxation decomposes the global constraint into per-instance sub-problems, each admitting a closed-form oracle action that optimally prices accuracy against cost. We prove that the induced cost is monotone in the dual variable, enabling exact budget targeting via binary search. In the learn stage, a lightweight classifier is trained to predict oracle actions from cheap input features, amortizing the allocation rule for real-time deployment. We establish that the task-level regret of the learned policy is bounded by its imitation error times the worst-case per-instance gap, yielding a clean reduction from constrained inference to supervised classification. Experiments on MATH and GSM8K with three LLMs (DeepSeek-V3, GPT-4o-mini, Qwen2.5-7B) show that our method consistently outperforms uniform and heuristic allocation baselines, achieving up to 12.8% relative accuracy improvement on MATH under matched budget constraints, while closely tracking the Lagrangian oracle upper bound with over 91% imitation accuracy.
Large language models (LLMs) are typically deployed with fixed parameters, and their performance is often improved by allocating more computation at inference time. While such test-time scaling can be effective, it cannot correct model misconceptions or adapt the model to the specific structure of an individual query. Test-time optimization addresses this limitation by enabling parameter updates during inference, but existing approaches either rely on external data or optimize generic self-supervised objectives that lack query-specific alignment. In this work, we propose Query-Conditioned Test-Time Self-Training (QueST), a framework that adapts model parameters during inference using supervision derived directly from the input query. Our key insight is that the input query itself encodes latent signals sufficient for constructing structurally related problem--solution pairs. Based on this, QueST generates such query-conditioned pairs and uses them as supervision for parameter-efficient fine-tuning at test time. The adapted model is then used to produce the final answer, enabling query-specific adaptation without any external data. Across seven mathematical reasoning benchmarks and the GPQA-Diamond scientific reasoning benchmark, QueST consistently outperforms strong test-time optimization baselines. These results demonstrate that query-conditioned self-training is an effective and practical paradigm for test-time adaptation in LLMs. Code is available at https://chssong.github.io/Query-Conditioned-TTST/.
Test-time compute (TTC) scaling has emerged as a powerful paradigm for improving large language model (LLM) reasoning by allocating additional compute during inference, e.g., via multi-sample generation and verifier-based reranking. Existing TTC scaling strategies and reasoning scorers remain fragmented, evaluated under inconsistent protocols, and are rarely analyzed through the lens of quality-cost trade-offs. We introduce ThinkBooster, a unified framework for seamless test-time compute scaling of LLM reasoning, which consists of (i) a modular Python library implementing state-of-the-art TTC scaling strategy and scorer families, (ii) a benchmark that jointly evaluates performance and computational efficiency, and (iii) a deployable OpenAI-compatible proxy service that enables drop-in integration of adaptive reasoning into real-world applications. We further provide a demo visual debugger for inspecting the reasoning trajectories, intermediate selection decisions, and alternative reasoning paths. Empirical results on mathematical and coding tasks reveal the performance-compute trade-offs of TTC scaling strategies and scoring methods and demonstrate that ThinkBooster provides practical gains in real-world tasks. The code is available online under an MIT license.