Daily Papers

Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs) based on Natural Language (NL) proofs. Similar methods have shown promising results in code generation. However, most modern LLMs exhibit suboptimal performance due to the scarcity of aligned NL and Formal Language (FL) theorem-proving data. This scarcity results in a paucity of methodologies for training LLMs and techniques to fully utilize their capabilities in composing formal proofs. To address the challenges, this paper proposes **TheoremLlama**, an end-to-end framework to train a general-purpose LLM to become a Lean4 expert. This framework encompasses NL-FL aligned dataset generation methods, training approaches for the LLM formal theorem prover, and techniques for LLM Lean4 proof writing. Using the dataset generation method, we provide *Open Bootstrapped Theorems* (OBT), an NL-FL aligned and bootstrapped dataset. A key innovation in this framework is the NL-FL bootstrapping method, where NL proofs are integrated into Lean4 code for training datasets, leveraging the NL reasoning ability of LLMs for formal reasoning. The **TheoremLlama** framework achieves cumulative accuracies of 36.48% and 33.61% on MiniF2F-Valid and Test datasets respectively, surpassing the GPT-4 baseline of 22.95% and 25.41%. We have also open-sourced our model checkpoints and generated dataset, and will soon make all the code publicly available.

Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods address this separately, first translating theorems and then generating proofs, creating a fundamental disconnect vis-a-vis true proof auto-formalization. This two-step process and its limitations were evident even in AlphaProof's silver-medal performance at the 2024 IMO, where problem statements needed manual translation before automated proof synthesis. We present ProofBridge, a unified framework for automatically translating entire NL theorems and proofs into Lean 4. At its core is a joint embedding model that aligns NL and FL (NL-FL) theorem-proof pairs in a shared semantic space, enabling cross-modal retrieval of semantically relevant FL examples to guide translation. Our training ensures that NL-FL theorems (and their proofs) are mapped close together in this space if and only if the NL-FL pairs are semantically equivalent. ProofBridge integrates retrieval-augmented fine-tuning with iterative proof repair, leveraging Lean's type checker and semantic equivalence feedback to ensure both syntactic correctness and semantic fidelity. Experiments show substantial improvements in proof auto-formalization over strong baselines (including GPT-5, Gemini-2.5, Kimina-Prover, DeepSeek-Prover), with our retrieval-augmented approach yielding significant gains in semantic correctness (SC, via proving bi-directional equivalence) and type correctness (TC, via type-checking theorem+proof) across pass@k metrics on miniF2F-Test-PF, a dataset we curated. In particular, ProofBridge improves cross-modal retrieval quality by up to 3.28x Recall@1 over all-MiniLM-L6-v2, and achieves +31.14% SC and +1.64% TC (pass@32) compared to the baseline Kimina-Prover-RL-1.7B.

Enhancing the mathematical reasoning capabilities of LLMs has garnered significant attention in both the mathematical and computer science communities. Recent works have made substantial progress in both Natural Language (NL) reasoning and Formal Language (FL) reasoning by leveraging the potential of pure Reinforcement Learning (RL) methods on base models. However, RL approaches struggle to impart new capabilities not presented in the base model, highlighting the need to integrate more knowledge like FL into NL math reasoning effectively. Yet, this integration is challenging due to inherent disparities in problem structure and reasoning format between NL and FL. To address these challenges, we introduce **NL-FL HybridReasoning**, an end-to-end framework designed to incorporate the FL expert into NL math problem-solving. To bridge the NL and FL input format gap, we propose the *NL-FL Problem Alignment* method, which reformulates the Question-Answering (QA) problems in NL as existence theorems in FL. Subsequently, the *Mixed Problem Input* technique we provide enables the FL reasoner to handle both QA and existence problems concurrently. Lastly, we mitigate the NL and FL output format gap in reasoning through an LLM-based *Answer Extraction* mechanism. Comprehensive experiments demonstrate that the **HybridReasoning** framework achieves **89.80%** and **84.34%** accuracy rates on the MATH-500 and the AMC benchmarks, surpassing the NL baseline by 4.60% and 4.82%, respectively. Notably, some problems resolved by our framework remain unsolved by the NL baseline model even under a larger number of trials.

Large language models (LLMs) are great at processing multiple natural language processing tasks, but their abilities are constrained by inferior performance with long context, slow inference speed, and the high cost of computing the results. Deploying LLMs with precise and informative context helps users process large-scale datasets more effectively and cost-efficiently. Existing works rely on compressing long prompt contexts into soft prompts. However, soft prompt compression encounters limitations in transferability across different LLMs, especially API-based LLMs. To this end, this work aims to compress lengthy prompts in the form of natural language with LLM transferability. This poses two challenges: (i) Natural Language (NL) prompts are incompatible with back-propagation, and (ii) NL prompts lack flexibility in imposing length constraints. In this work, we propose a Natural Language Prompt Encapsulation (Nano-Capsulator) framework compressing original prompts into NL formatted Capsule Prompt while maintaining the prompt utility and transferability. Specifically, to tackle the first challenge, the Nano-Capsulator is optimized by a reward function that interacts with the proposed semantics preserving loss. To address the second question, the Nano-Capsulator is optimized by a reward function featuring length constraints. Experimental results demonstrate that the Capsule Prompt can reduce 81.4% of the original length, decrease inference latency up to 4.5x, and save 80.1% of budget overheads while providing transferability across diverse LLMs and different datasets.

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted mathematical and computer science communities. State-of-the-art methods utilize single Large Language Models (LLMs) as agents or provers to either generate complete proof or perform tree searches. However, single-agent methods inherently lack a structured way to combine high-level reasoning in Natural Language (NL) with Formal Language (FL) verification feedback. To solve these issues, we propose MA-LoT: Multi-Agent Lean-based Long Chain-of-Thought framework, (to the best of our knowledge), the first multi-agent framework for Lean4 theorem proving that balance high-level NL reasoning and FL verification in Long CoT. Using this structured interaction, our approach enables deeper insights and long-term coherence in proof generation, with which past methods struggle. We do this by leveraging emergent formal reasoning ability in Long CoT using our novel LoT-Transfer Learning training-inference pipeline. Extensive experiments show that our framework achieves 54.51% accuracy rate on the Lean4 version of MiniF2F-Test dataset, largely outperforming GPT-4 (22.95%), single-agent tree search (InternLM-Step-Prover, 50.70%), and whole-proof generation (DeepSeek-Prover-v1.5, 48.36%) baselines. Furthermore, our findings highlight the potential of combining Long CoT with formal verification for a more insightful generation in a broader perspective.

Will a Visual Language Model (VLM)-based bot warn us about slipping if it detects a wet floor? Recent VLMs have demonstrated impressive capabilities, yet their ability to infer outcomes and causes remains underexplored. To address this, we introduce NL-Eye, a benchmark designed to assess VLMs' visual abductive reasoning skills. NL-Eye adapts the abductive Natural Language Inference (NLI) task to the visual domain, requiring models to evaluate the plausibility of hypothesis images based on a premise image and explain their decisions. NL-Eye consists of 350 carefully curated triplet examples (1,050 images) spanning diverse reasoning categories: physical, functional, logical, emotional, cultural, and social. The data curation process involved two steps - writing textual descriptions and generating images using text-to-image models, both requiring substantial human involvement to ensure high-quality and challenging scenes. Our experiments show that VLMs struggle significantly on NL-Eye, often performing at random baseline levels, while humans excel in both plausibility prediction and explanation quality. This demonstrates a deficiency in the abductive reasoning capabilities of modern VLMs. NL-Eye represents a crucial step toward developing VLMs capable of robust multimodal reasoning for real-world applications, including accident-prevention bots and generated video verification.

Abstraction is a core tenet of human cognition and communication. When composing natural language instructions, humans naturally evoke abstraction to convey complex procedures in an efficient and concise way. Yet, interpreting and grounding abstraction expressed in NL has not yet been systematically studied in NLP, with no accepted benchmarks specifically eliciting abstraction in NL. In this work, we set the foundation for a systematic study of processing and grounding abstraction in NLP. First, we deliver a novel abstraction elicitation method and present Hexagons, a 2D instruction-following game. Using Hexagons we collected over 4k naturally-occurring visually-grounded instructions rich with diverse types of abstractions. From these data, we derive an instruction-to-execution task and assess different types of neural models. Our results show that contemporary models and modeling practices are substantially inferior to human performance, and that models' performance is inversely correlated with the level of abstraction, showing less satisfying performance on higher levels of abstraction. These findings are consistent across models and setups, confirming that abstraction is a challenging phenomenon deserving further attention and study in NLP/AI research.

Traditional POI recommendation systems often lack transparency, interpretability, and scrutability due to their reliance on dense vector-based user embeddings. Furthermore, the cold-start problem -- where systems have insufficient data for new users -- limits their ability to generate accurate recommendations. Existing methods often address this by leveraging similar trajectories from other users, but this approach can be computationally expensive and increases the context length for LLM-based methods, making them difficult to scale. To address these limitations, we propose a method that generates natural language (NL) user profiles from large-scale, location-based social network (LBSN) check-ins, utilizing robust personality assessments and behavioral theories. These NL profiles capture user preferences, routines, and behaviors, improving POI prediction accuracy while offering enhanced transparency. By incorporating NL profiles as system prompts to LLMs, our approach reduces reliance on extensive historical data, while remaining flexible, easily updated, and computationally efficient. Our method is not only competitive with other LLM-based and complex agentic frameworks but is also more scalable for real-world scenarios and on-device POI recommendations. Results demonstrate that our approach consistently outperforms baseline methods, offering a more interpretable and resource-efficient solution for POI recommendation systems. Our source code is available at: https://github.com/w11wo/GenUP.

Creating programs to correctly manipulate data is a difficult task, as the underlying programming languages and APIs can be challenging to learn for many users who are not skilled programmers. Large language models (LLMs) demonstrate remarkable potential for generating code from natural language, but in the data manipulation domain, apart from the natural language (NL) description of the intended task, we also have the dataset on which the task is to be performed, or the "data context". Existing approaches have utilized data context in a limited way by simply adding relevant information from the input data into the prompts sent to the LLM. In this work, we utilize the available input data to execute the candidate programs generated by the LLMs and gather their outputs. We introduce semantic reranking, a technique to rerank the programs generated by LLMs based on three signals coming the program outputs: (a) semantic filtering and well-formedness based score tuning: do programs even generate well-formed outputs, (b) semantic interleaving: how do the outputs from different candidates compare to each other, and (c) output-based score tuning: how do the outputs compare to outputs predicted for the same task. We provide theoretical justification for semantic interleaving. We also introduce temperature mixing, where we combine samples generated by LLMs using both high and low temperatures. We extensively evaluate our approach in three domains, namely databases (SQL), data science (Pandas) and business intelligence (Excel's Power Query M) on a variety of new and existing benchmarks. We observe substantial gains across domains, with improvements of up to 45% in top-1 accuracy and 34% in top-3 accuracy.

This paper introduces a novel approach to Dialogue State Tracking (DST) that leverages Large Language Models (LLMs) to generate natural language descriptions of dialogue states, moving beyond traditional slot-value representations. Conventional DST methods struggle with open-domain dialogues and noisy inputs. Motivated by the generative capabilities of LLMs, our Natural Language DST (NL-DST) framework trains an LLM to directly synthesize human-readable state descriptions. We demonstrate through extensive experiments on MultiWOZ 2.1 and Taskmaster-1 datasets that NL-DST significantly outperforms rule-based and discriminative BERT-based DST baselines, as well as generative slot-filling GPT-2 DST models, in both Joint Goal Accuracy and Slot Accuracy. Ablation studies and human evaluations further validate the effectiveness of natural language state generation, highlighting its robustness to noise and enhanced interpretability. Our findings suggest that NL-DST offers a more flexible, accurate, and human-understandable approach to dialogue state tracking, paving the way for more robust and adaptable task-oriented dialogue systems.

Information retrieval involves selecting artifacts from a corpus that are most relevant to a given search query. The flavor of retrieval typically used in classical applications can be termed as homogeneous and relaxed, where queries and corpus elements are both natural language (NL) utterances (homogeneous) and the goal is to pick most relevant elements from the corpus in the Top-K, where K is large, such as 10, 25, 50 or even 100 (relaxed). Recently, retrieval is being used extensively in preparing prompts for large language models (LLMs) to enable LLMs to perform targeted tasks. These new applications of retrieval are often heterogeneous and strict -- the queries and the corpus contain different kinds of entities, such as NL and code, and there is a need for improving retrieval at Top-K for small values of K, such as K=1 or 3 or 5. Current dense retrieval techniques based on pretrained embeddings provide a general-purpose and powerful approach for retrieval, but they are oblivious to task-specific notions of similarity of heterogeneous artifacts. We introduce Adapted Dense Retrieval, a mechanism to transform embeddings to enable improved task-specific, heterogeneous and strict retrieval. Adapted Dense Retrieval works by learning a low-rank residual adaptation of the pretrained black-box embedding. We empirically validate our approach by showing improvements over the state-of-the-art general-purpose embeddings-based baseline.

Despite the recent progresses, particularly in developing Language Models, there are fundamental challenges and unanswered questions about how such models can continually learn/memorize, self-improve, and find effective solutions. In this paper, we present a new learning paradigm, called Nested Learning (NL), that coherently represents a machine learning model with a set of nested, multi-level, and/or parallel optimization problems, each of which with its own context flow. Through the lenses of NL, existing deep learning methods learns from data through compressing their own context flow, and in-context learning naturally emerges in large models. NL suggests a philosophy to design more expressive learning algorithms with more levels, resulting in higher-order in-context learning and potentially unlocking effective continual learning capabilities. We advocate for NL by presenting three core contributions: (1) Expressive Optimizers: We show that known gradient-based optimizers, such as Adam, SGD with Momentum, etc., are in fact associative memory modules that aim to compress the gradients' information (by gradient descent). Building on this insight, we present other more expressive optimizers with deep memory and/or more powerful learning rules; (2) Self-Modifying Learning Module: Taking advantage of NL's insights on learning algorithms, we present a sequence model that learns how to modify itself by learning its own update algorithm; and (3) Continuum Memory System: We present a new formulation for memory system that generalizes the traditional viewpoint of long/short-term memory. Combining our self-modifying sequence model with the continuum memory system, we present a continual learning module, called Hope, showing promising results in language modeling, knowledge incorporation, and few-shot generalization tasks, continual learning, and long-context reasoning tasks.

Research on generative models to produce human-aligned / human-preferred outputs has seen significant recent contributions. Between text and image-generative models, we narrowed our focus to text-based generative models, particularly to produce captions for images that align with human preferences. In this research, we explored a potential method to amplify the performance of the Deep Neural Network Model to generate captions that are preferred by humans. This was achieved by integrating Supervised Learning and Reinforcement Learning with Human Feedback (RLHF) using the Flickr8k dataset. Also, a novel loss function that is capable of optimizing the model based on human feedback is introduced. In this paper, we provide a concise sketch of our approach and results, hoping to contribute to the ongoing advances in the field of human-aligned generative AI models.