CodePDE: An Inference Framework for LLM-driven PDE Solver Generation

Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge. Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while neural-network-based solvers require large training datasets and often lack interpretability. In this work, we frame PDE solving as a code generation task and introduce CodePDE, the first inference framework for generating PDE solvers using large language models (LLMs). Leveraging advanced inference-time algorithms and scaling strategies, CodePDE unlocks critical capacities of LLM for PDE solving: reasoning, debugging, selfrefinement, and test-time scaling -- all without task-specific tuning. CodePDE achieves superhuman performance across a range of representative PDE problems. We also present a systematic empirical analysis of LLM generated solvers, analyzing their accuracy, efficiency, and numerical scheme choices. Our findings highlight the promise and the current limitations of LLMs in PDE solving, offering a new perspective on solver design and opportunities for future model development. Our code is available at https://github.com/LithiumDA/CodePDE.

Direct Retrieval-augmented Optimization: Synergizing Knowledge Selection and Language Models

Retrieval-augmented generation (RAG) integrates large language models ( LLM s) with retrievers to access external knowledge, improving the factuality of LLM generation in knowledge-grounded tasks. To optimize the RAG performance, most previous work independently fine-tunes the retriever to adapt to frozen LLM s or trains the LLMs to use documents retrieved by off-the-shelf retrievers, lacking end-to-end training supervision. Recent work addresses this limitation by jointly training these two components but relies on overly simplifying assumptions of document independence, which has been criticized for being far from real-world scenarios. Thus, effectively optimizing the overall RAG performance remains a critical challenge. We propose a direct retrieval-augmented optimization framework, named DRO, that enables end-to-end training of two key components: (i) a generative knowledge selection model and (ii) an LLM generator. DRO alternates between two phases: (i) document permutation estimation and (ii) re-weighted maximization, progressively improving RAG components through a variational approach. In the estimation step, we treat document permutation as a latent variable and directly estimate its distribution from the selection model by applying an importance sampling strategy. In the maximization step, we calibrate the optimization expectation using importance weights and jointly train the selection model and LLM generator. Our theoretical analysis reveals that DRO is analogous to policy-gradient methods in reinforcement learning. Extensive experiments conducted on five datasets illustrate that DRO outperforms the best baseline with 5%-15% improvements in EM and F1. We also provide in-depth experiments to qualitatively analyze the stability, convergence, and variance of DRO.

Replication and Exploration of Generative Retrieval over Dynamic Corpora

Generative retrieval (GR) has emerged as a promising paradigm in information retrieval (IR). However, most existing GR models are developed and evaluated using a static document collection, and their performance in dynamic corpora where document collections evolve continuously is rarely studied. In this paper, we first reproduce and systematically evaluate various representative GR approaches over dynamic corpora. Through extensive experiments, we reveal that existing GR models with \textit{text-based} docids show superior generalization to unseen documents. We observe that the more fine-grained the docid design in the GR model, the better its performance over dynamic corpora, surpassing BM25 and even being comparable to dense retrieval methods. While GR models with \textit{numeric-based} docids show high efficiency, their performance drops significantly over dynamic corpora. Furthermore, our experiments find that the underperformance of numeric-based docids is partly due to their excessive tendency toward the initial document set, which likely results from overfitting on the training set. We then conduct an in-depth analysis of the best-performing GR methods. We identify three critical advantages of text-based docids in dynamic corpora: (i) Semantic alignment with language models' pretrained knowledge, (ii) Fine-grained docid design, and (iii) High lexical diversity. Building on these insights, we finally propose a novel multi-docid design that leverages both the efficiency of numeric-based docids and the effectiveness of text-based docids, achieving improved performance in dynamic corpus without requiring additional retraining. Our work offers empirical evidence for advancing GR methods over dynamic corpora and paves the way for developing more generalized yet efficient GR models in real-world search engines.

LLM4Ranking: An Easy-to-use Framework of Utilizing Large Language Models for Document Reranking

Utilizing large language models (LLMs) for document reranking has been a popular and promising research direction in recent years, many studies are dedicated to improving the performance and efficiency of using LLMs for reranking. Besides, it can also be applied in many real-world applications, such as search engines or retrieval-augmented generation. In response to the growing demand for research and application in practice, we introduce a unified framework, \textbf{LLM4Ranking}, which enables users to adopt different ranking methods using open-source or closed-source API-based LLMs. Our framework provides a simple and extensible interface for document reranking with LLMs, as well as easy-to-use evaluation and fine-tuning scripts for this task. We conducted experiments based on this framework and evaluated various models and methods on several widely used datasets, providing reproducibility results on utilizing LLMs for document reranking. Our code is publicly available at https://github.com/liuqi6777/llm4ranking.

CO-Bench: Benchmarking Language Model Agents in Algorithm Search for Combinatorial Optimization

Although LLM-based agents have attracted significant attention in domains such as software engineering and machine learning research, their role in advancing combinatorial optimization (CO) remains relatively underexplored. This gap underscores the need for a deeper understanding of their potential in tackling structured, constraint-intensive problems-a pursuit currently limited by the absence of comprehensive benchmarks for systematic investigation. To address this, we introduce CO-Bench, a benchmark suite featuring 36 real-world CO problems drawn from a broad range of domains and complexity levels. CO-Bench includes structured problem formulations and curated data to support rigorous investigation of LLM agents. We evaluate multiple agent frameworks against established human-designed algorithms, revealing key strengths and limitations of current approaches and identifying promising directions for future research. CO-Bench is publicly available at https://github.com/sunnweiwei/CO-Bench.

NoKSR: Kernel-Free Neural Surface Reconstruction via Point Cloud Serialization

We present a novel approach to large-scale point cloud surface reconstruction by developing an efficient framework that converts an irregular point cloud into a signed distance field (SDF). Our backbone builds upon recent transformer-based architectures (i.e., PointTransformerV3), that serializes the point cloud into a locality-preserving sequence of tokens. We efficiently predict the SDF value at a point by aggregating nearby tokens, where fast approximate neighbors can be retrieved thanks to the serialization. We serialize the point cloud at different levels/scales, and non-linearly aggregate a feature to predict the SDF value. We show that aggregating across multiple scales is critical to overcome the approximations introduced by the serialization (i.e. false negatives in the neighborhood). Our frameworks sets the new state-of-the-art in terms of accuracy and efficiency (better or similar performance with half the latency of the best prior method, coupled with a simpler implementation), particularly on outdoor datasets where sparse-grid methods have shown limited performance.

Phonetic Reconstruction of the Consonant System of Middle Chinese via Mixed Integer Optimization

This paper is concerned with phonetic reconstruction of the consonant system of Middle Chinese. We propose to cast the problem as a Mixed Integer Programming problem, which is able to automatically explore homophonic information from ancient rhyme dictionaries and phonetic information from modern Chinese dialects, the descendants of Middle Chinese. Numerical evaluation on a wide range of synthetic and real data demonstrates the effectiveness and robustness of the new method. We apply the method to information from Guangyun and 20 modern Chinese dialects to obtain a new phonetic reconstruction result. A linguistically-motivated discussion of this result is also provided.

Improving Retrieval-Augmented Generation through Multi-Agent Reinforcement Learning

Retrieval-augmented generation (RAG) is extensively utilized to incorporate external, current knowledge into large language models, thereby minimizing hallucinations. A standard RAG pipeline may comprise several components, such as query rewriting, document retrieval, document filtering, and answer generation. However, these components are typically optimized separately through supervised fine-tuning, which can lead to misalignments between the objectives of individual modules and the overarching aim of generating accurate answers in question-answering (QA) tasks. Although recent efforts have explored reinforcement learning (RL) to optimize specific RAG components, these approaches often focus on overly simplistic pipelines with only two components or do not adequately address the complex interdependencies and collaborative interactions among the modules. To overcome these challenges, we propose treating the RAG pipeline as a multi-agent cooperative task, with each component regarded as an RL agent. Specifically, we present MMOA-RAG, a Multi-Module joint Optimization Algorithm for RAG, which employs multi-agent reinforcement learning to harmonize all agents' goals towards a unified reward, such as the F1 score of the final answer. Experiments conducted on various QA datasets demonstrate that MMOA-RAG improves the overall pipeline performance and outperforms existing baselines. Furthermore, comprehensive ablation studies validate the contributions of individual components and the adaptability of MMOA-RAG across different RAG components and datasets. The code of MMOA-RAG is on https://github.com/chenyiqun/MMOA-RAG.

Accelerating Quantum Emitter Characterization with Latent Neural Ordinary Differential Equations

Deep neural network models can be used to learn complex dynamics from data and reconstruct sparse or noisy signals, thereby accelerating and augmenting experimental measurements. Evaluating the quantum optical properties of solid-state single-photon emitters is a time-consuming task that typically requires interferometric photon correlation experiments, such as Photon correlation Fourier spectroscopy (PCFS) which measures time-resolved single emitter lineshapes. Here, we demonstrate a latent neural ordinary differential equation model that can forecast a complete and noise-free PCFS experiment from a small subset of noisy correlation functions. By encoding measured photon correlations into an initial value problem, the NODE can be propagated to an arbitrary number of interferometer delay times. We demonstrate this with 10 noisy photon correlation functions that are used to extrapolate an entire de-noised interferograms of up to 200 stage positions, enabling up to a 20-fold speedup in experimental acquisition time from $\sim$3 hours to 10 minutes. Our work presents a new approach to greatly accelerate the experimental characterization of novel quantum emitter materials using deep learning.

MAIR: A Massive Benchmark for Evaluating Instructed Retrieval

Recent information retrieval (IR) models are pre-trained and instruction-tuned on massive datasets and tasks, enabling them to perform well on a wide range of tasks and potentially generalize to unseen tasks with instructions. However, existing IR benchmarks focus on a limited scope of tasks, making them insufficient for evaluating the latest IR models. In this paper, we propose MAIR (Massive Instructed Retrieval Benchmark), a heterogeneous IR benchmark that includes 126 distinct IR tasks across 6 domains, collected from existing datasets. We benchmark state-of-the-art instruction-tuned text embedding models and re-ranking models. Our experiments reveal that instruction-tuned models generally achieve superior performance compared to non-instruction-tuned models on MAIR. Additionally, our results suggest that current instruction-tuned text embedding models and re-ranking models still lack effectiveness in specific long-tail tasks. MAIR is publicly available at https://github.com/sunnweiwei/Mair.