Chun Cao

Shuo Xu, Jiakun Zhang, Junyu Lai et al.

Automated theorem proving with large language models in Lean 4 is commonly approached through either step-level tactic prediction with tree search or whole-proof generation. These two paradigms represent opposite granularities for constructing supervised training data: the former provides dense local signals but may fragment coherent proof processes, while the latter preserves global structure but requires complex end-to-end generation. In this paper, we revisit supervision granularity as a training set construction problem over proof trajectories and propose segment-level supervision, a training data construction strategy that extracts locally coherent proof segments for training policy models. We further reuse the same strategy at inference time to trigger short rollouts for existing step-level models. When trained with segment-level supervision on STP, LeanWorkbook, and NuminaMath-LEAN, the resulting policy models achieve proof success rates of 64.84%, 60.90%, and 66.31% on miniF2F, respectively, consistently outperforming both step-level and whole-proof baselines. Goal-aware rollout further improves existing step-level provers while reducing inference costs. It increases the proof success rate of BFS-Prover-V2-7B from 68.77% to 70.74% and that of InternLM2.5-StepProver from 59.59% to 60.33%, showing that appropriate supervision granularity better aligns model learning with proof structure and search. Code and models are available at https://github.com/NJUDeepEngine/SEG-ATP.

Yuchen Zhang, Hanyue Du, Chun Cao et al.

Low-Rank Adaptation (LoRA) has become a widely adopted parameter-efficient fine-tuning (PEFT) technique for adapting large language models (LLMs) to downstream tasks. While prior work has explored strategies for integrating LLM training and serving, there still remains a gap in unifying fine-tuning and inference for LoRA-based models. We present Loquetier, a virtualized multi-LoRA framework that seamlessly integrates LoRA fine-tuning and serving within a single runtime. Loquetier introduces two key components: (1) a Virtualized Module that isolates PEFT-based modifications and supports multiple adapters on a shared base model, and (2) an optimized computation flow with a kernel design that merges fine-tuning and inference paths in forward propagation, enabling efficient batching and minimizing kernel invocation overhead. Extensive experiments across three task settings show that Loquetier consistently outperforms existing baselines in both performance and flexibility, achieving up to $3.0\times$ the throughput of the state-of-the-art co-serving system on inference-only tasks and $46.4\times$ higher SLO attainment than PEFT on unified fine-tuning and inference tasks. The implementation of Loquetier is publicly available at https://github.com/NJUDeepEngine/Loquetier.

Zenan Li, Zhi Zhou, Yuan Yao et al. · microsoft-research

A critical question about Large Language Models (LLMs) is whether their apparent deficiency in mathematical reasoning is inherent, or merely a result of insufficient exposure to high-quality mathematical data. To explore this, we developed an automated method for generating high-quality, supervised mathematical datasets. The method carefully mutates existing math problems, ensuring both diversity and validity of the newly generated problems. This is achieved by a neuro-symbolic data generation framework combining the intuitive informalization strengths of LLMs, and the precise symbolic reasoning of math solvers along with projected Markov chain Monte Carlo sampling in the highly-irregular symbolic space. Empirical experiments demonstrate the high quality of data generated by the proposed method, and that the LLMs, specifically LLaMA-2 and Mistral, when realigned with the generated data, surpass their state-of-the-art counterparts.

Zenan Li, Yuan Yao, Taolue Chen et al.

Neuro-symbolic learning generally consists of two separated worlds, i.e., neural network training and symbolic constraint solving, whose success hinges on symbol grounding, a fundamental problem in AI. This paper presents a novel, softened symbol grounding process, bridging the gap between the two worlds, and resulting in an effective and efficient neuro-symbolic learning framework. Technically, the framework features (1) modeling of symbol solution states as a Boltzmann distribution, which avoids expensive state searching and facilitates mutually beneficial interactions between network training and symbolic reasoning;(2) a new MCMC technique leveraging projection and SMT solvers, which efficiently samples from disconnected symbol solution spaces; (3) an annealing mechanism that can escape from %being trapped into sub-optimal symbol groundings. Experiments with three representative neuro symbolic learning tasks demonstrate that, owining to its superior symbol grounding capability, our framework successfully solves problems well beyond the frontier of the existing proposals.

Junyu Lai, Jiakun Zhang, Shuo Xu et al.

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of $60.74\%$ on MiniF2F and $21.18\%$ on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.

Siyuan Yan, Guo-Qing Jiang, Yuchen Zhang et al.

Large language models (LLMs) now support context windows of hundreds of thousands to millions of tokens, enabling applications such as long-document summarization, large-scale code synthesis, multi-document question answering and persistent multi-turn dialogue. However, such extended contexts exacerbate the quadratic cost of self-attention, leading to severe latency in autoregressive decoding. Existing sparse attention methods alleviate these costs but rely on heuristic patterns that struggle to recall critical key-value (KV) pairs for each query, resulting in accuracy degradation. We introduce Adamas, a lightweight yet highly accurate sparse attention mechanism designed for long-context inference. Adamas applies the Hadamard transform, bucketization and 2-bit compression to produce compact representations, and leverages Manhattan-distance estimation for efficient top-k selections. Experiments show that Adamas matches the accuracy of full attention with only a 64-token budget, achieves near-lossless performance at 128, and supports up to 8x higher sparsity than prior state-of-the-art (SOTA) methods while delivering up to 4.4x self-attention and 1.5x end-to-end speedups on 32K-length sequences. Remarkably, Adamas attains comparable or even lower perplexity than full attention, underscoring its effectiveness in maintaining accuracy under aggressive sparsity.

Tao Bu, Qiangang Wang, Bowen Zeng et al.

Transformer-based large language models (LLMs) have achieved remarkable success, yet their standard attention mechanism incurs quadratic computation and memory costs with respect to sequence length, posing a major bottleneck for long-context training. Prior work tackles this challenge along two directions: (1) kernel-level optimizations, which accelerate dense and sparse attention operators; and (2) module-level strategies, often referred to as distributed attention or context parallel training, which scale attention across multiple devices. However, systematic evaluation still remains limited: operator-level comparisons are often incomplete, while context parallel strategies are typically framework-specific, with unclear performance analysis across contexts. To address these gaps, we propose a unified benchmark that integrates representative attention kernels and context parallel mechanisms with a modular and extensible interface for evaluation. The benchmark evaluates methods along two critical dimensions: (1) attention mask patterns, which strongly affect efficiency, scalability, and usability, and (2) sequence length and distributed scale, which determine performance under extreme long-context training. Through comprehensive experiments on the cluster of up to 96 GPUs, our benchmark enables reproducible comparisons, highlights method-specific trade-offs, and provides practical guidance for designing and deploying attention mechanisms in long-context LLM training.

Zenan Li, Xiaoxing Ma, Chang Xu et al.

Trained DNN models are increasingly adopted as integral parts of software systems, but they often perform deficiently in the field. A particularly damaging problem is that DNN models often give false predictions with high confidence, due to the unavoidable slight divergences between operation data and training data. To minimize the loss caused by inaccurate confidence, operational calibration, i.e., calibrating the confidence function of a DNN classifier against its operation domain, becomes a necessary debugging step in the engineering of the whole system. Operational calibration is difficult considering the limited budget of labeling operation data and the weak interpretability of DNN models. We propose a Bayesian approach to operational calibration that gradually corrects the confidence given by the model under calibration with a small number of labeled operation data deliberately selected from a larger set of unlabeled operation data. The approach is made effective and efficient by leveraging the locality of the learned representation of the DNN model and modeling the calibration as Gaussian Process Regression. Comprehensive experiments with various practical datasets and DNN models show that it significantly outperformed alternative methods, and in some difficult tasks it eliminated about 71% to 97% high-confidence (>0.9) errors with only about 10\% of the minimal amount of labeled operation data needed for practical learning techniques to barely work.

Zenan Li, Xiaoxing Ma, Chang Xu et al.

With the increasing adoption of Deep Neural Network (DNN) models as integral parts of software systems, efficient operational testing of DNNs is much in demand to ensure these models' actual performance in field conditions. A challenge is that the testing often needs to produce precise results with a very limited budget for labeling data collected in field. Viewing software testing as a practice of reliability estimation through statistical sampling, we re-interpret the idea behind conventional structural coverages as conditioning for variance reduction. With this insight we propose an efficient DNN testing method based on the conditioning on the representation learned by the DNN model under testing. The representation is defined by the probability distribution of the output of neurons in the last hidden layer of the model. To sample from this high dimensional distribution in which the operational data are sparsely distributed, we design an algorithm leveraging cross entropy minimization. Experiments with various DNN models and datasets were conducted to evaluate the general efficiency of the approach. The results show that, compared with simple random sampling, this approach requires only about a half of labeled inputs to achieve the same level of precision.