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Understanding the Role of Training Data in Test-Time Scaling

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Language modelsLearning theoryChains-of-ThoughtInference computeTest error
Abstract:

Test-time scaling improves the reasoning capabilities of large language models (LLMs) by allocating extra compute to generate longer Chains-of-Thoughts (CoTs). This enables models to tackle more complex problem by breaking them down into additional steps, backtracking, and correcting mistakes. Despite its strong performance--demonstrated by OpenAI's o1 and DeepSeek R1, the conditions in the training data under which long CoTs emerge, and when such long CoTs improve the performance, remain unclear. In this paper, we study the performance of test-time scaling for transformers trained on an in-context weight prediction task for linear regression. Our analysis provides a theoretical explanation for several intriguing observations: First, at any fixed test error, increasing test-time compute allows us to reduce the number of in-context examples (context length) in training prompts. Second, if the skills required to solve a downstream task are not sufficiently present in the training data, increasing test-time compute can harm performance. Finally, we characterize task hardness via the smallest eigenvalue of its feature covariance matrix and show that training on a diverse, relevant, and hard set of tasks results in best performance for test-time scaling. We confirm our findings with experiments on large, nonlinear transformer architectures.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper provides a theoretical analysis of test-time scaling for transformers trained on in-context weight prediction tasks, examining how training data characteristics influence the emergence and effectiveness of long chains-of-thought. It resides in the Training Data Requirements and Diversity leaf, which contains only three papers total. This is a relatively sparse research direction within the broader taxonomy of 38 papers across the field, suggesting the specific intersection of training data theory and test-time scaling remains underexplored compared to more crowded areas like verification-guided scaling or model size scaling laws.

The taxonomy reveals that this work sits at the boundary between Training Paradigms and Efficiency (its parent branch) and Test-Time Compute Scaling Mechanisms. Neighboring leaves include Model Size and Compute Scaling Laws (five papers examining empirical relationships between model size and performance) and Data-Efficient Learning Strategies (three papers on architectural biases and training objectives). The scope note for the parent leaf explicitly focuses on how training data characteristics affect test-time scaling performance, distinguishing it from test-time adaptation methods and general scaling laws that lack this training-inference interplay focus.

Among 18 candidates examined across three contributions, no clearly refuting prior work was identified. The theoretical analysis of test-time scaling examined three candidates with no refutations; the task hardness measure based on feature covariance examined five candidates with no refutations; and the optimal task selection strategy examined ten candidates with no refutations. This limited search scope—focused on top-K semantic matches—suggests that within the examined literature, the specific theoretical framework connecting training data diversity to test-time scaling effectiveness appears relatively unexplored, though the analysis cannot claim exhaustiveness.

Based on the limited search of 18 candidates, the work appears to occupy a distinct position connecting training data theory to test-time scaling dynamics. The sparse population of its taxonomy leaf and absence of refuting work among examined candidates suggest novelty, though the restricted search scope means potentially relevant theoretical work in adjacent areas (e.g., in-context learning theory, curriculum learning) may not have been captured by semantic similarity alone.

Taxonomy

Core-task Taxonomy Papers
38
3
Claimed Contributions
18
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: test-time scaling and training data requirements in transformers. The field has organized itself around four main branches that capture distinct but interrelated concerns. Test-Time Compute Scaling Mechanisms explores how additional inference-time computation—through iterative refinement, search, or verification—can improve model outputs, as seen in works like Inference Compute Theory[7] and Scaling Without Verification[9]. Training Paradigms and Efficiency examines how models learn from data, including questions of data diversity, curriculum design, and efficient training strategies, with contributions such as Diversity-Aware Scaling[6] and Data Efficient Scaling[24]. Domain-Specific Applications investigates scaling behaviors in specialized contexts like vision, medical reasoning (m1 Medical Reasoning[5]), motion forecasting (Motion Forecasting Laws[15]), and code generation (CodeChemist[31]). Implementation and Systems Considerations addresses practical deployment challenges, including memory optimization (KV Cache Compression[3]) and system-level trade-offs that arise when scaling transformers in production environments. Within the training efficiency landscape, a central tension emerges between scaling model capacity versus curating high-quality, diverse training data. Some lines of work emphasize that careful data selection and diversity can yield better performance than simply increasing dataset size, as explored in Diversity-Aware Scaling[6] and LIMOPro[33]. Others investigate how training and inference dynamics interact, examining whether test-time adaptation can compensate for limited training resources (Test-Time Training Transformers[4], Training Inference Dynamics[35]). Training Data Role[0] sits squarely in this conversation, focusing on the interplay between training data characteristics and test-time scaling potential. It aligns closely with neighbors like s1 Scaling[29], which examines scaling laws under constrained data regimes, and LIMOPro[33], which explores data efficiency in multimodal settings. The emphasis in Training Data Role[0] appears to be on understanding how training data quality and diversity shape the effectiveness of test-time compute, bridging the training efficiency and test-time scaling branches.

Claimed Contributions

Theoretical analysis of test-time scaling for transformers on in-context weight prediction

The authors provide a theoretical framework analyzing how transformers trained on in-context weight prediction for linear regression perform test-time scaling. They show that with chain-of-thought prompting at test time, the transformer effectively implements multi-step pseudo-Newton's method for loss optimization, extending prior work to accommodate general feature covariance and CoT dynamics at test time.

3 retrieved papers
Task hardness measure based on feature covariance spectrum

The authors introduce a measure of task hardness defined by the ratio of the smallest eigenvalue of the feature covariance matrix to its trace. They interpret eigenvectors as representing different skills required for a task, with eigenvalues indicating skill strength, where hard tasks have long-tailed skill spectra and easy tasks have few well-balanced skills.

5 retrieved papers
Optimal task selection strategy for multi-task training

The authors develop a quadratic optimization framework for selecting training tasks in a multi-task setting. They prove that optimal task selection favors diverse tasks covering all relevant directions, tasks relevant to the target distribution, and sufficiently hard tasks with small minimum eigenvalues, leading to best test-time scaling performance.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Theoretical analysis of test-time scaling for transformers on in-context weight prediction

The authors provide a theoretical framework analyzing how transformers trained on in-context weight prediction for linear regression perform test-time scaling. They show that with chain-of-thought prompting at test time, the transformer effectively implements multi-step pseudo-Newton's method for loss optimization, extending prior work to accommodate general feature covariance and CoT dynamics at test time.

Contribution

Task hardness measure based on feature covariance spectrum

The authors introduce a measure of task hardness defined by the ratio of the smallest eigenvalue of the feature covariance matrix to its trace. They interpret eigenvectors as representing different skills required for a task, with eigenvalues indicating skill strength, where hard tasks have long-tailed skill spectra and easy tasks have few well-balanced skills.

Contribution

Optimal task selection strategy for multi-task training

The authors develop a quadratic optimization framework for selecting training tasks in a multi-task setting. They prove that optimal task selection favors diverse tasks covering all relevant directions, tasks relevant to the target distribution, and sufficiently hard tasks with small minimum eigenvalues, leading to best test-time scaling performance.

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