Artificial intelligence is advancing across a wide range of fields, with one of the most important developments being its growing capacity for reasoning. This capability could help AI becomes a reliable partner in critical domains like scientific research and healthcare.
To support this progress, we’ve identified three primary strategies to strengthen reasoning capabilities in both small and large language models: improve architectural design to boost performance in smaller models; incorporate mathematical reasoning techniques to increase reliability; and build stronger generalization capabilities to enable reasoning across a variety of fields.
Smarter reasoning in smaller models
While language models trained on broad world knowledge hold great potential, they lack the ability to learn continuously and refine their understanding. This limitation becomes especially pronounced in smaller models, where limited capacity makes strong reasoning even harder.
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The problem stems from how current language models operate. They rely on fast, pattern recognition-based responses that break down in complex scenarios. In contrast, people use deliberate, step-by-step reasoning, test different approaches, and evaluate outcomes. To address this gap, we’re building methods to enable stronger reasoning in smaller systems.
rStar-Math is a method that uses Monte Carlo Tree Search (MCTS) to simulate deeper, more methodical reasoning in smaller models. It uses a three-step, self-improving cycle:
- Problem decomposition breaks down complex mathematical problems into manageable steps, creating a thorough and accurate course of reasoning.
- Process preference model (PPM) trains small models to predict reward labels for each step, improving process-level supervision.
- Iterative refinement applies a four-round, self-improvement cycle in which updated strategy models and PPMs guide MCTS to improve performance.
When tested on four small language models ranging from 1.5 billion to 7 billion parameters, rStar-Math achieved an average accuracy of 53% on the American Invitational Mathematics Examination (AIME)—performance that places it among the top 20% of high school competitors in the US.
Logic-RL is a reinforcement learning framework that strengthens logical reasoning through a practical system prompt and a structured reward function. By training models on logic puzzles, Logic-RL grants rewards only when both the reasoning process and the final answer meet strict formatting requirements. This prevents shortcuts and promotes analytical rigor.
Language models trained with Logic-RL demonstrate strong performance beyond logic puzzles, generalizing effectively to mathematical competition problems. On the AIME and AMC (American Mathematics Competitions) datasets, 7-billion-parameter models improved accuracy by 125% and 38%, respectively, compared with baseline models.
Building reliable mathematical reasoning
Mathematics poses a unique challenge for language models, which often struggle to meet its precision and rigor using natural language. To address this, we’re creating formal and symbolic methods to enable language models to adopt structured mathematical tools. The goal is to convert language model outputs into code based on the fundamental rules of arithmetic, like 1 + 1 = 2, allowing us to systematically verify accuracy.
LIPS (LLM-based Inequality Prover with Symbolic Reasoning) is a system that combines LLMs’ pattern recognition capabilities with symbolic reasoning. LIPS draws on the strategies participants in math competitions use in order to distinguish between tasks best suited to symbolic solvers (e.g., scaling) and those better handled by language models (e.g., rewriting). On 161 Olympiad-level problems, LIPS achieved state-of-the-art results without additional training data.
However, translating natural-language math problems into precise, machine-readable formats is a challenge. Our goal is to bridge the gap between the one-pass success rate, where the top-ranked generated result is correct, and the k-pass success rate, where at least one of the top k generated results is correct.
We developed a new framework using two evaluation methods. Symbolic equivalence checks whether outputs are logically identical, while semantic consistency uses embedding similarity to detect subtle differences missed by symbolic checks.
When we evaluated this approach on the MATH and miniF2F datasets, which include problems from various math competitions, it improved accuracy by up to 1.35 times over baseline methods.
To address the shortage of high-quality training data, we developed a neuro-symbolic framework that automatically generates diverse, well-structured math problems. Symbolic solvers create the problems, while language models translate them into natural language. This approach not only broadens training resources but also supports more effective instruction and evaluation of mathematical reasoning in language models.
Boosting generalization across domains
A key indicator of advanced AI is its ability to generalize—the ability to transfer reasoning skills across different domains. We found that training language models on math data significantly improved performance in coding, science, and other areas, revealing unexpected cross-domain benefits.
This discovery motivated us to develop Chain-of-Reasoning (CoR), an approach that unifies reasoning across natural language, code, and symbolic forms. CoR lets models blend these formats using natural language to frame context, code for precise calculations, and symbolic representations for abstraction. By adjusting prompts, CoR adapts both reasoning depth and paradigm diversity to match specific problem requirements.
Tests of CoR across five math datasets showed its ability to tackle both computational and proof-based problems, demonstrating strong general mathematical problem-solving skills.
Current language models often rely on domain-specific solutions, limiting their flexibility across different types of problems. To move beyond this constraint, we developed Critical Plan Step Learning (CPL), an approach focused on high-level abstract planning that teaches models to identify key knowledge, break down problems, and make strategic decisions.
The technique draws on how people solve problems, by breaking them down, identifying key information, and recalling relevant knowledge—strategies we want language models to learn.
CPL combines two key components: plan-based MCTS, which searches multi-step solution paths and constructs planning trees, and step-APO, which learns preferences for strong intermediate steps while filtering out weak ones. This combination enhances reasoning and improves generalization across tasks, moving AI systems closer to the flexible thinking that characterizes human intelligence.
Looking ahead: Next steps in AI reasoning
From building reliable math solvers to unifying reasoning approaches, researchers are redefining how language models approach complex tasks. Their work sets the stage for more capable and versatile AI systems—applicable to education, science, healthcare, and beyond. Despite these advances, hallucinations and imprecise logic continue to pose risks in critical fields like medicine and scientific research, where accuracy is essential.
These challenges are driving the team’s exploration of additional tools and frameworks to improve language model reasoning. This includes AutoVerus for automated proof generation in Rust code, SAFE for addressing data scarcity in Rust formal verification, and Alchemy, which uses symbolic mutation to improve neural theorem proving.
Together, these technologies represent important progress toward building trustworthy, high-performing reasoning models and signal a broader shift toward addressing some of AI’s current limitations.
