Evidence suggests that large pre-trained language models (LMs) acquire some reasoning capacity, but this ability is difficult to control. Recently, it has been shown that Transformer-based models succeed in consistent reasoning over explicit symbolic facts, under a closed-world assumption. However, in an open-domain setup, it is desirable to tap into the vast reservoir of implicit knowledge already encoded in the parameters of pre-trained LMs. In this work, we provide a first demonstration that LMs can be trained to reliably perform systematic reasoning combining both implicit, pre-trained knowledge and explicit natural language statements. To do this, we describe a procedure for automatically generating datasets that teach a model new reasoning skills, and demonstrate that models learn to effectively perform inference which involves implicit taxonomic and world knowledge, chaining and counting. Finally, we show that teaching models to reason generalizes beyond the training distribution: they successfully compose the usage of multiple reasoning skills in single examples. Our work paves a path towards open-domain systems that constantly improve by interacting with users who can instantly correct a model by adding simple natural language statements.

Large Language Models (LLMs) have recently emerged as powerful tools for autoformalization. Despite their impressive performance, these models can still struggle to produce grounded and verifiable formalizations. Recent work in text-to-SQL, has revealed that LLMs can be sensitive to paraphrased natural language (NL) inputs, even when high degrees of semantic fidelity are preserved (Safarzadeh, Oroo-jlooyjadid, and Roth 2025). In this paper, we investigate this claim in the autoformalization domain. Specifically, we evaluate the robustness of LLMs generating formal proofs with semantically similar paraphrased NL statements by measuring semantic and compilation validity. Using the formal benchmarks MiniF2F (Zheng, Han, and Polu 2021) and Lean 4 version of ProofNet (Xin et al. 2024), and two modern LLMs, we generate paraphrased natural language statements and cross-evaluate these statements across both models. The results of this paper reveal performance variability across paraphrased inputs, demonstrating that minor shifts in NL statements can significantly impact model outputs.

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the A WS S3 bucket access policy code.

Evidence suggests that large pre-trained language models (LMs) acquire some reasoning capacity, but this ability is difficult to control.

In large-scale maintenance organizations, identifying subject matter experts and managing communications across complex entities relationships poses significant challenges -- including information overload and longer response times -- that traditional communication approaches fail to address effectively. We propose a novel framework that combines RDF graph databases with LLMs to process natural language queries for precise audience targeting, while providing transparent reasoning through a planning-orchestration architecture. Our solution enables communication owners to formulate intuitive queries combining concepts such as equipment, manufacturers, maintenance engineers, and facilities, delivering explainable results that maintain trust in the system while improving communication efficiency across the organization.

We introduce Goedel-Prover-V2, a series of open-source language models that set a new state-of-the-art in automated theorem proving. Built on the standard expert iteration and reinforcement learning pipeline, our approach incorporates three key innovations: (1) Scaffolded data synthesis: We generate synthetic tasks of increasing difficulty to train the model to master increasingly complex theorems; (2) Verifier-guided self-correction: We enable the model to iteratively revise its proofs by leveraging feedback from the Lean compiler; (3) Model averaging: We merge model checkpoints to mitigate the decrease in model output diversity in later stages of training. Our small model, Goedel-Prover-V2-8B, reaches 84.6% pass@32 on MiniF2F and outperforms DeepSeek-Prover-V2-671B under the same metric, despite being 80X smaller. Our flagship model, Goedel-Prover-V2-32B, achieves 88.1% on MiniF2F at pass@32 in standard mode and 90.4% in self-correction mode, outperforming prior SOTA by a large margin. Additionally, our flagship model solves 86 problems on PutnamBench at pass@184, securing the first place among open-source models on the leaderboard, surpassing DeepSeek-Prover-V2-671B's record of solving 47 problems by pass@1024 with a significantly smaller model size and compute budget. At the time of its release (July-August 2025), Goedel-Prover-V2 achieves the strongest overall performance among all open-source theorem provers. It also ranks among the top-performing models--including closed-source systems with publicly reported performance--under a constrained test-time compute budget. Our models, code, and data are released at https://github.com/Goedel-LM/Goedel-Prover-V2.

Autoformalization plays a crucial role in formal mathematical reasoning by enabling the automatic translation of natural language statements into formal languages. While recent advances using large language models (LLMs) have shown promising results, methods for automatically evaluating autoformalization remain underexplored. As one moves to more complex domains (e.g., advanced mathematics), human evaluation requires significant time and domain expertise, especially as the complexity of the underlying statements and background knowledge increases. LLM-as-a-judge presents a promising approach for automating such evaluation. However, existing methods typically employ coarse-grained and generic evaluation criteria, which limit their effectiveness for advanced formal mathematical reasoning, where quality hinges on nuanced, multi-granular dimensions. In this work, we take a step toward addressing this gap by introducing a systematic, automatic method to evaluate autoformalization tasks. The proposed method is based on an epistemically and formally grounded ensemble (EFG) of LLM judges, defined on criteria encompassing logical preservation (LP), mathematical consistency (MC), formal validity (FV), and formal quality (FQ), resulting in a transparent assessment that accounts for different contributing factors. We validate the proposed framework to serve as a proxy for autoformalization assessment within the domain of formal mathematics. Overall, our experiments demonstrate that the EFG ensemble of LLM judges is a suitable emerging proxy for evaluation, more strongly correlating with human assessments than a coarse-grained model, especially when assessing formal qualities. These findings suggest that LLM-as-judges, especially when guided by a well-defined set of atomic properties, could offer a scalable, interpretable, and reliable support for evaluating formal mathematical reasoning.

An agent's intention often remains hidden behind the black-box nature of embodied policies. Communication using natural language statements that describe the next action can provide transparency towards the agent's behavior. We aim to insert transparent behavior directly into the learning process, by transforming the problem of policy learning into a language generation problem and combining it with traditional autoregressive modelling. The resulting model produces transparent natural language statements followed by tokens representing the specific actions to solve long-horizon tasks in the Language-Table environment. Following previous work, the model is able to learn to produce a policy represented by special discretized tokens in an autoregressive manner. We place special emphasis on investigating the relationship between predicting actions and producing high-quality language for a transparent agent. We find that in many cases both the quality of the action trajectory and the transparent statement increase when they are generated simultaneously.

Evidence suggests that large pre-trained language models (LMs) acquire some reasoning capacity, but this ability is difficult to control. Recently, it has been shown that Transformer-based models succeed in consistent reasoning over explicit symbolic facts, under a "closed-world" assumption. However, in an open-domain setup, it is desirable to tap into the vast reservoir of implicit knowledge already encoded in the parameters of pre-trained LMs. In this work, we provide a first demonstration that LMs can be trained to reliably perform systematic reasoning combining both implicit, pre-trained knowledge and explicit natural language statements. To do this, we describe a procedure for automatically generating datasets that teach a model new reasoning skills, and demonstrate that models learn to effectively perform inference which involves implicit taxonomic and world knowledge, chaining and counting. Finally, we show that "teaching" models to reason generalizes beyond the training distribution: they successfully compose the usage of multiple reasoning skills in single examples.