Daily Papers

A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

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.

Spatial reasoning is an important component of human intelligence. We can imagine the shapes of 3D objects and reason about their spatial relations by merely looking at their three-view line drawings in 2D, with different levels of competence. Can deep networks be trained to perform spatial reasoning tasks? How can we measure their "spatial intelligence"? To answer these questions, we present the SPARE3D dataset. Based on cognitive science and psychometrics, SPARE3D contains three types of 2D-3D reasoning tasks on view consistency, camera pose, and shape generation, with increasing difficulty. We then design a method to automatically generate a large number of challenging questions with ground truth answers for each task. They are used to provide supervision for training our baseline models using state-of-the-art architectures like ResNet. Our experiments show that although convolutional networks have achieved superhuman performance in many visual learning tasks, their spatial reasoning performance on SPARE3D tasks is either lower than average human performance or even close to random guesses. We hope SPARE3D can stimulate new problem formulations and network designs for spatial reasoning to empower intelligent robots to operate effectively in the 3D world via 2D sensors. The dataset and code are available at https://ai4ce.github.io/SPARE3D.

Training large language models with data collected from various domains can improve their performance on downstream tasks. However, given a fixed training budget, the sampling proportions of these different domains significantly impact the model's performance. How can we determine the domain weights across different data domains to train the best-performing model within constrained computational resources? In this paper, we provide a comprehensive overview of existing data mixture methods. First, we propose a fine-grained categorization of existing methods, extending beyond the previous offline and online classification. Offline methods are further grouped into heuristic-based, algorithm-based, and function fitting-based methods. For online methods, we categorize them into three groups: online min-max optimization, online mixing law, and other approaches by drawing connections with the optimization frameworks underlying offline methods. Second, we summarize the problem formulations, representative algorithms for each subtype of offline and online methods, and clarify the relationships and distinctions among them. Finally, we discuss the advantages and disadvantages of each method and highlight key challenges in the field of data mixture.

Over the past decade, tremendous progress has been made in Recommender Systems (RecSys) for well-known tasks such as next-item and next-basket prediction. On the other hand, the recently proposed next-period recommendation (NPR) task is not covered as much. Current works about NPR are mostly based around distinct problem formulations, methods, and proprietary datasets, making solutions difficult to reproduce. In this article, we aim to fill the gap in RecSys methods evaluation on the NPR task using publicly available datasets and (1) introduce the TTRS, a large-scale financial transactions dataset suitable for RecSys methods evaluation; (2) benchmark popular RecSys approaches on several datasets for the NPR task. When performing our analysis, we found a strong repetitive consumption pattern in several real-world datasets. With this setup, our results suggest that the repetitive nature of data is still hard to generalize for the evaluated RecSys methods, and novel item prediction performance is still questionable.

Multi-component compounding is a prevalent phenomenon in Sanskrit, and understanding the implicit structure of a compound's components is crucial for deciphering its meaning. Earlier approaches in Sanskrit have focused on binary compounds and neglected the multi-component compound setting. This work introduces the novel task of nested compound type identification (NeCTI), which aims to identify nested spans of a multi-component compound and decode the implicit semantic relations between them. To the best of our knowledge, this is the first attempt in the field of lexical semantics to propose this task. We present 2 newly annotated datasets including an out-of-domain dataset for this task. We also benchmark these datasets by exploring the efficacy of the standard problem formulations such as nested named entity recognition, constituency parsing and seq2seq, etc. We present a novel framework named DepNeCTI: Dependency-based Nested Compound Type Identifier that surpasses the performance of the best baseline with an average absolute improvement of 13.1 points F1-score in terms of Labeled Span Score (LSS) and a 5-fold enhancement in inference efficiency. In line with the previous findings in the binary Sanskrit compound identification task, context provides benefits for the NeCTI task. The codebase and datasets are publicly available at: https://github.com/yaswanth-iitkgp/DepNeCTI

Face Restoration (FR) aims to restore High-Quality (HQ) faces from Low-Quality (LQ) input images, which is a domain-specific image restoration problem in the low-level computer vision area. The early face restoration methods mainly use statistical priors and degradation models, which are difficult to meet the requirements of real-world applications in practice. In recent years, face restoration has witnessed great progress after stepping into the deep learning era. However, there are few works to systematically study the deep learning based face restoration methods. Thus, in this paper, we provide a comprehensive survey of recent advances in deep learning techniques for face restoration. Specifically, we first summarize different problem formulations and analyze the characteristics of face images. Second, we discuss the challenges of face restoration. With regard to these challenges, we present a comprehensive review of recent FR methods, including prior-based methods and deep-learning methods. Then, we explore developed techniques in the task of FR covering network architectures, loss functions, and benchmark datasets. We also conduct a systematic benchmark evaluation on representative methods. Finally, we discuss the future directions including network designs, metrics, benchmark datasets, applications, etc. We also provide an open source repository for all the discussed methods, which is available at https://github.com/TaoWangzj/Awesome-Face-Restoration.

Large Reasoning Models like DeepSeek-R1 mark a fundamental shift in how LLMs approach complex problems. Instead of directly producing an answer for a given input, DeepSeek-R1 creates detailed multi-step reasoning chains, seemingly "thinking" about a problem before providing an answer. This reasoning process is publicly available to the user, creating endless opportunities for studying the reasoning behaviour of the model and opening up the field of Thoughtology. Starting from a taxonomy of DeepSeek-R1's basic building blocks of reasoning, our analyses on DeepSeek-R1 investigate the impact and controllability of thought length, management of long or confusing contexts, cultural and safety concerns, and the status of DeepSeek-R1 vis-\`a-vis cognitive phenomena, such as human-like language processing and world modelling. Our findings paint a nuanced picture. Notably, we show DeepSeek-R1 has a 'sweet spot' of reasoning, where extra inference time can impair model performance. Furthermore, we find a tendency for DeepSeek-R1 to persistently ruminate on previously explored problem formulations, obstructing further exploration. We also note strong safety vulnerabilities of DeepSeek-R1 compared to its non-reasoning counterpart, which can also compromise safety-aligned LLMs.

Reinforcement learning has proven its effectiveness in enhancing the reasoning capabilities of large language models. Recent research efforts have progressively extended this paradigm to multimodal reasoning tasks. Due to the inherent complexity and diversity of multimodal tasks, especially in semantic content and problem formulations, existing models often exhibit unstable performance across various domains and difficulty levels. To address these limitations, we propose VL-Cogito, an advanced multimodal reasoning model trained via a novel multi-stage Progressive Curriculum Reinforcement Learning (PCuRL) framework. PCuRL systematically guides the model through tasks of gradually increasing difficulty, substantially improving its reasoning abilities across diverse multimodal contexts. The framework introduces two key innovations: (1) an online difficulty soft weighting mechanism, dynamically adjusting training difficulty across successive RL training stages; and (2) a dynamic length reward mechanism, which encourages the model to adaptively regulate its reasoning path length according to task complexity, thus balancing reasoning efficiency with correctness. Experimental evaluations demonstrate that VL-Cogito consistently matches or surpasses existing reasoning-oriented models across mainstream multimodal benchmarks spanning mathematics, science, logic, and general understanding, validating the effectiveness of our approach.

In this paper, we give an in-depth analysis on the mathematical problem formulations and the probabilistic optimization explorations for some of the key components in Transformer model [33] in the field of generative AI. We explore and discuss some potential further enhancement for current state of the art methods for some key underlying technologies of generative AI models from algorithmic and probabilistic optimization perspective. In particular, we present an optimal solution for sub-word encoding (SWE) based on similar initial settings as that of byte-pair encoding (BPE) algorithm in [9] with similar objectives as that of WordPiece approach in [28, 31] to maximize the likelihood of the training data. We also present cross entropy optimization method to optimize hyperparameters for word2vec model [17]. In addition, we propose a factored combination of rotary positional encoding (RoPE) [32] and attention with linear biases (ALiBi) [23] with a harmonic series. We also present a probabilistic FlashAttention [6, 7] (PrFlashAttention) method with a probability distribution over block distances in the matrix to decide which block is likely to participate in a given round of attention computation while maintaining the lower triangle shape of the tensor for autoregressive language models by re-shaping the tensors. Finally, we present staircase adaptive quantization (SAQ) of key-value (KV) cache for multi-query attention (MQA) based on the framework presented in [16] to have gradual quantization degradation while achieving reasonable model quality and cost savings.

Traffic incident detection plays a key role in intelligent transportation systems, which has gained great attention in transport engineering. In the past, traditional machine learning (ML) based detection methods achieved good performance under a centralised computing paradigm, where all data are transmitted to a central server for building ML models therein. Nowadays, deep neural networks based federated learning (FL) has become a mainstream detection approach to enable the model training in a decentralised manner while warranting local data governance. Such neural networks-centred techniques, however, have overshadowed the utility of well-established ML-based detection methods. In this work, we aim to explore the potential of potent conventional ML-based detection models in modern traffic scenarios featured by distributed data. We leverage an elegant but less explored distributed optimisation framework named Network Lasso, with guaranteed global convergence for convex problem formulations, integrate the potent convex ML model with it, and compare it with centralised learning, local learning, and federated learning methods atop a well-known traffic incident detection dataset. Experimental results show that the proposed network lasso-based approach provides a promising alternative to the FL-based approach in data-decentralised traffic scenarios, with a strong convergence guarantee while rekindling the significance of conventional ML-based detection methods.

We study the Levine hat problem, a classic combinatorial puzzle introduced by Lionel Levine in 2010. This problem involves a game in which n geq 2 players, each seeing an infinite stack of hats on each of their teammates' heads but not on their own, must simultaneously guess the index of a black hat on their own stack. If one of the players fails to do so, the team loses collectively. The players must therefore come up with a good strategy before the game starts. While the optimal winning probability V_{n} remains unknown even for n=2, we make three key advances. First, we develop a novel geometric framework for representing strategies through measurable functions, providing a new expression of V_{n} and a unified treatment of the game for finite and for infinite stacks via integral formulations. Secondly, we construct a new strategy K_{5} that reaches the conjectured optimal probability of victory : 0.35. We also show that K_{5} is part of a larger class of strategies that allow us to improve current bounds and resolve conjectured inequalities. Finally, we introduce and entirely solve a continuous generalization of the problem, demonstrating that extending to uncountable hat stacks increases the optimal winning probability to exactly 1/2. This generalization naturally leads to a broader and smoother strategic framework, within which we also describe how to compute optimal responses to a range of strategies.

Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM), spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expert-inspired framework that decomposes mathematical modeling into four stages: open-ended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88\% improvement over human expert solutions while requiring only 15 minutes and \$0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (top 2.0\% among 27,456 teams) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot. Our code is available at https://github.com/usail-hkust/LLM-MM-Agent

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.

Variational auto-encoders are powerful probabilistic models in generative tasks but suffer from generating low-quality samples which are caused by the holes in the prior. We propose the Coupled Variational Auto-Encoder (C-VAE), which formulates the VAE problem as one of Optimal Transport (OT) between the prior and data distributions. The C-VAE allows greater flexibility in priors and natural resolution of the prior hole problem by enforcing coupling between the prior and the data distribution and enables flexible optimization through the primal, dual, and semi-dual formulations of entropic OT. Simulations on synthetic and real data show that the C-VAE outperforms alternatives including VAE, WAE, and InfoVAE in fidelity to the data, quality of the latent representation, and in quality of generated samples.

Accurately modeling protein 3D structure is essential for the design of functional proteins. An important sub-task of structure modeling is protein side-chain packing: predicting the conformation of side-chains (rotamers) given the protein's backbone structure and amino-acid sequence. Conventional approaches for this task rely on expensive sampling procedures over hand-crafted energy functions and rotamer libraries. Recently, several deep learning methods have been developed to tackle the problem in a data-driven way, albeit with vastly different formulations (from image-to-image translation to directly predicting atomic coordinates). Here, we frame the problem as a joint regression over the side-chains' true degrees of freedom: the dihedral chi angles. We carefully study possible objective functions for this task, while accounting for the underlying symmetries of the task. We propose Holographic Packer (H-Packer), a novel two-stage algorithm for side-chain packing built on top of two light-weight rotationally equivariant neural networks. We evaluate our method on CASP13 and CASP14 targets. H-Packer is computationally efficient and shows favorable performance against conventional physics-based algorithms and is competitive against alternative deep learning solutions.

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of COPs, while preserving problem structure. Our approach introduces three key ideas: (i) constraint-aware shrinking that prevents merges that will likely violate problem-specific feasibility constraints, (ii) a verification-and-repair pipeline to correct infeasible solutions post-optimization, and (iii) adaptive strategies for recalculating correlations and controlling the graph shrinking process. We apply our approach to three standard benchmark problems: Multidimensional Knapsack (MDKP), Maximum Independent Set (MIS), and the Quadratic Assignment Problem (QAP). Empirical results show that our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances. These findings demonstrate a scalable pathway for applying near-term quantum algorithms to classically challenging constrained optimization problems.

Object pose estimation is a fundamental computer vision problem with broad applications in augmented reality and robotics. Over the past decade, deep learning models, due to their superior accuracy and robustness, have increasingly supplanted conventional algorithms reliant on engineered point pair features. Nevertheless, several challenges persist in contemporary methods, including their dependency on labeled training data, model compactness, robustness under challenging conditions, and their ability to generalize to novel unseen objects. A recent survey discussing the progress made on different aspects of this area, outstanding challenges, and promising future directions, is missing. To fill this gap, we discuss the recent advances in deep learning-based object pose estimation, covering all three formulations of the problem, i.e., instance-level, category-level, and unseen object pose estimation. Our survey also covers multiple input data modalities, degrees-of-freedom of output poses, object properties, and downstream tasks, providing the readers with a holistic understanding of this field. Additionally, it discusses training paradigms of different domains, inference modes, application areas, evaluation metrics, and benchmark datasets, as well as reports the performance of current state-of-the-art methods on these benchmarks, thereby facilitating the readers in selecting the most suitable method for their application. Finally, the survey identifies key challenges, reviews the prevailing trends along with their pros and cons, and identifies promising directions for future research. We also keep tracing the latest works at https://github.com/CNJianLiu/Awesome-Object-Pose-Estimation.

In real-world applications where confidence is key, like autonomous driving, the accurate detection and appropriate handling of classes differing from those used during training are crucial. Despite the proposal of various unknown object detection approaches, we have observed widespread inconsistencies among them regarding the datasets, metrics, and scenarios used, alongside a notable absence of a clear definition for unknown objects, which hampers meaningful evaluation. To counter these issues, we introduce two benchmarks: a unified VOC-COCO evaluation, and the new OpenImagesRoad benchmark which provides clear hierarchical object definition besides new evaluation metrics. Complementing the benchmark, we exploit recent self-supervised Vision Transformers performance, to improve pseudo-labeling-based OpenSet Object Detection (OSOD), through OW-DETR++. State-of-the-art methods are extensively evaluated on the proposed benchmarks. This study provides a clear problem definition, ensures consistent evaluations, and draws new conclusions about effectiveness of OSOD strategies.

Multi-Agent Large Language Models (LLMs) are gaining significant attention for their ability to harness collective intelligence in complex problem-solving, decision-making, and planning tasks. This aligns with the concept of the wisdom of crowds, where diverse agents contribute collectively to generating effective solutions, making it particularly suitable for educational settings. Senior design projects, also known as capstone or final year projects, are pivotal in engineering education as they integrate theoretical knowledge with practical application, fostering critical thinking, teamwork, and real-world problem-solving skills. In this paper, we explore the use of Multi-Agent LLMs in supporting these senior design projects undertaken by engineering students, which often involve multidisciplinary considerations and conflicting objectives, such as optimizing technical performance while addressing ethical, social, and environmental concerns. We propose a framework where distinct LLM agents represent different expert perspectives, such as problem formulation agents, system complexity agents, societal and ethical agents, or project managers, thus facilitating a holistic problem-solving approach. This implementation leverages standard multi-agent system (MAS) concepts such as coordination, cooperation, and negotiation, incorporating prompt engineering to develop diverse personas for each agent. These agents engage in rich, collaborative dialogues to simulate human engineering teams, guided by principles from swarm AI to efficiently balance individual contributions towards a unified solution. We adapt these techniques to create a collaboration structure for LLM agents, encouraging interdisciplinary reasoning and negotiation similar to real-world senior design projects. To assess the efficacy of this framework, we collected six proposals of engineering and computer science of...

Language models (LMs) have demonstrated their capability in possessing commonsense knowledge of the physical world, a crucial aspect of performing tasks in everyday life. However, it remains unclear whether they have the capacity to generate grounded, executable plans for embodied tasks. This is a challenging task as LMs lack the ability to perceive the environment through vision and feedback from the physical environment. In this paper, we address this important research question and present the first investigation into the topic. Our novel problem formulation, named G-PlanET, inputs a high-level goal and a data table about objects in a specific environment, and then outputs a step-by-step actionable plan for a robotic agent to follow. To facilitate the study, we establish an evaluation protocol and design a dedicated metric, KAS, to assess the quality of the plans. Our experiments demonstrate that the use of tables for encoding the environment and an iterative decoding strategy can significantly enhance the LMs' ability in grounded planning. Our analysis also reveals interesting and non-trivial findings.

In this paper, we introduce Jointist, an instrument-aware multi-instrument framework that is capable of transcribing, recognizing, and separating multiple musical instruments from an audio clip. Jointist consists of the instrument recognition module that conditions the other modules: the transcription module that outputs instrument-specific piano rolls, and the source separation module that utilizes instrument information and transcription results. The instrument conditioning is designed for an explicit multi-instrument functionality while the connection between the transcription and source separation modules is for better transcription performance. Our challenging problem formulation makes the model highly useful in the real world given that modern popular music typically consists of multiple instruments. However, its novelty necessitates a new perspective on how to evaluate such a model. During the experiment, we assess the model from various aspects, providing a new evaluation perspective for multi-instrument transcription. We also argue that transcription models can be utilized as a preprocessing module for other music analysis tasks. In the experiment on several downstream tasks, the symbolic representation provided by our transcription model turned out to be helpful to spectrograms in solving downbeat detection, chord recognition, and key estimation.

Pretrained language models (PTLMs) are typically learned over a large, static corpus and further fine-tuned for various downstream tasks. However, when deployed in the real world, a PTLM-based model must deal with data distributions that deviate from what the PTLM was initially trained on. In this paper, we study a lifelong language model pretraining challenge where a PTLM is continually updated so as to adapt to emerging data. Over a domain-incremental research paper stream and a chronologically-ordered tweet stream, we incrementally pretrain a PTLM with different continual learning algorithms, and keep track of the downstream task performance (after fine-tuning). We evaluate PTLM's ability to adapt to new corpora while retaining learned knowledge in earlier corpora. Our experiments show distillation-based approaches to be most effective in retaining downstream performance in earlier domains. The algorithms also improve knowledge transfer, allowing models to achieve better downstream performance over the latest data, and improve temporal generalization when distribution gaps exist between training and evaluation because of time. We believe our problem formulation, methods, and analysis will inspire future studies towards continual pretraining of language models.

Optimization problems are prevalent across various scenarios. Formulating and then solving optimization problems described by natural language often requires highly specialized human expertise, which could block the widespread application of optimization-based decision making. To automate problem formulation and solving, leveraging large language models (LLMs) has emerged as a potential way. However, this kind of approach suffers from the issue of optimization generalization. Namely, the accuracy of most current LLM-based methods and the generality of optimization problem types that they can model are still limited. In this paper, we propose a unified learning-based framework called LLMOPT to boost optimization generalization. Starting from the natural language descriptions of optimization problems and a pre-trained LLM, LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. Then, LLMOPT employs the multi-instruction tuning to enhance both problem formalization and solver code generation accuracy and generality. After that, to prevent hallucinations in LLMs, such as sacrificing solving accuracy to avoid execution errors, the model alignment and self-correction mechanism are adopted in LLMOPT. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets covering roughly 20 fields such as health, environment, energy and manufacturing, etc. Extensive experiment results show that LLMOPT is able to model various optimization problem types such as linear/nonlinear programming, mixed integer programming, and combinatorial optimization, and achieves a notable 11.08% average solving accuracy improvement compared with the state-of-the-art methods. The code is available at https://github.com/caigaojiang/LLMOPT.

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet expressive inputs, e.g., multi-digit images and image fragments, through a neural sorting network. To learn a mapping from a high-dimensional input to an ordinal variable, the differentiability of sorting networks needs to be guaranteed. In this paper we define a softening error by a differentiable swap function, and develop an error-free swap function that holds a non-decreasing condition and differentiability. Furthermore, a permutation-equivariant Transformer network with multi-head attention is adopted to capture dependency between given inputs and also leverage its model capacity with self-attention. Experiments on diverse sorting benchmarks show that our methods perform better than or comparable to baseline methods.

We study the problem of classification with a reject option for a fixed predictor, applicable in natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss function. We provide a complete theoretical analysis of the surrogate loss function with a strong H-consistency guarantee. For evaluation, we choose the decontextualization task, and provide a manually-labelled dataset of 2mathord,000 examples. Our algorithm significantly outperforms the baselines considered, with a sim!!25% improvement in coverage when halving the error rate, which is only sim!! 3 % away from the theoretical limit.

Deep learning (DL) has proven to be a highly effective approach for developing models in diverse contexts, including visual perception, speech recognition, and machine translation. However, the end-to-end process for applying DL is not trivial. It requires grappling with problem formulation and context understanding, data engineering, model development, deployment, continuous monitoring and maintenance, and so on. Moreover, each of these steps typically relies heavily on humans, in terms of both knowledge and interactions, which impedes the further advancement and democratization of DL. Consequently, in response to these issues, a new field has emerged over the last few years: automated deep learning (AutoDL). This endeavor seeks to minimize the need for human involvement and is best known for its achievements in neural architecture search (NAS), a topic that has been the focus of several surveys. That stated, NAS is not the be-all and end-all of AutoDL. Accordingly, this review adopts an overarching perspective, examining research efforts into automation across the entirety of an archetypal DL workflow. In so doing, this work also proposes a comprehensive set of ten criteria by which to assess existing work in both individual publications and broader research areas. These criteria are: novelty, solution quality, efficiency, stability, interpretability, reproducibility, engineering quality, scalability, generalizability, and eco-friendliness. Thus, ultimately, this review provides an evaluative overview of AutoDL in the early 2020s, identifying where future opportunities for progress may exist.

Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One is to do an alternative optimization of both the dictionary and the sparse code; the other way is to optimize the dictionary by restricting it over the orthogonal group. The latter one is called orthogonal dictionary learning which has a lower complexity implementation, hence, it is more favorable for lowcost devices. However, existing schemes on orthogonal dictionary learning only work with batch data and can not be implemented online, which is not applicable for real-time applications. This paper proposes a novel online orthogonal dictionary scheme to dynamically learn the dictionary from streaming data without storing the historical data. The proposed scheme includes a novel problem formulation and an efficient online algorithm design with convergence analysis. In the problem formulation, we relax the orthogonal constraint to enable an efficient online algorithm. In the algorithm design, we propose a new Frank-Wolfe-based online algorithm with a convergence rate of O(ln t/t^(1/4)). The convergence rate in terms of key system parameters is also derived. Experiments with synthetic data and real-world sensor readings demonstrate the effectiveness and efficiency of the proposed online orthogonal dictionary learning scheme.

Agents in the real world must make not only logical but also timely judgments. This requires continuous awareness of the dynamic environment: hazards emerge, opportunities arise, and other agents act, while the agent's reasoning is still unfolding. Despite advances in language model reasoning, existing approaches fail to account for this dynamic nature. We introduce real-time reasoning as a new problem formulation for agents in evolving environments and build Real-Time Reasoning Gym to demonstrate it. We study two paradigms for deploying language models in agents: (1) reactive agents, which employ language models with bounded reasoning computation for rapid responses, and (2) planning agents, which allow extended reasoning computation for complex problems. Our experiments show that even state-of-the-art models struggle with making logical and timely judgments in either paradigm. To address this limitation, we propose AgileThinker, which simultaneously engages both reasoning paradigms. AgileThinker consistently outperforms agents engaging only one reasoning paradigm as the task difficulty and time pressure rise, effectively balancing reasoning depth and response latency. Our work establishes real-time reasoning as a critical testbed for developing practical agents and provides a foundation for research in temporally constrained AI systems, highlighting a path toward real-time capable agents.

We introduce a new method for extracting structured threat behaviors from threat intelligence text. Our method is based on a multi-stage ranking architecture that allows jointly optimizing for efficiency and effectiveness. Therefore, we believe this problem formulation better aligns with the real-world nature of the task considering the large number of adversary techniques and the extensive body of threat intelligence created by security analysts. Our findings show that the proposed system yields state-of-the-art performance results for this task. Results show that our method has a top-3 recall performance of 81\% in identifying the relevant technique among 193 top-level techniques. Our tests also demonstrate that our system performs significantly better (+40\%) than the widely used large language models when tested under a zero-shot setting.

Scientific Machine Learning (SciML) has advanced recently across many different areas in computational science and engineering. The objective is to integrate data and physics seamlessly without the need of employing elaborate and computationally taxing data assimilation schemes. However, preprocessing, problem formulation, code generation, postprocessing and analysis are still time consuming and may prevent SciML from wide applicability in industrial applications and in digital twin frameworks. Here, we integrate the various stages of SciML under the umbrella of ChatGPT, to formulate MyCrunchGPT, which plays the role of a conductor orchestrating the entire workflow of SciML based on simple prompts by the user. Specifically, we present two examples that demonstrate the potential use of MyCrunchGPT in optimizing airfoils in aerodynamics, and in obtaining flow fields in various geometries in interactive mode, with emphasis on the validation stage. To demonstrate the flow of the MyCrunchGPT, and create an infrastructure that can facilitate a broader vision, we built a webapp based guided user interface, that includes options for a comprehensive summary report. The overall objective is to extend MyCrunchGPT to handle diverse problems in computational mechanics, design, optimization and controls, and general scientific computing tasks involved in SciML, hence using it as a research assistant tool but also as an educational tool. While here the examples focus in fluid mechanics, future versions will target solid mechanics and materials science, geophysics, systems biology and bioinformatics.

Reinforcement learning from human feedback (RLHF) has become an important technical and storytelling tool to deploy the latest machine learning systems. In this book, we hope to give a gentle introduction to the core methods for people with some level of quantitative background. The book starts with the origins of RLHF -- both in recent literature and in a convergence of disparate fields of science in economics, philosophy, and optimal control. We then set the stage with definitions, problem formulation, data collection, and other common math used in the literature. The core of the book details every optimization stage in using RLHF, from starting with instruction tuning to training a reward model and finally all of rejection sampling, reinforcement learning, and direct alignment algorithms. The book concludes with advanced topics -- understudied research questions in synthetic data and evaluation -- and open questions for the field.

Accurate plant counting provides valuable information for agriculture such as crop yield prediction, plant density assessment, and phenotype quantification. Vision-based approaches are currently the mainstream solution. Prior art typically uses a detection or a regression model to count a specific plant. However, plants have biodiversity, and new cultivars are increasingly bred each year. It is almost impossible to exhaust and build all species-dependent counting models. Inspired by class-agnostic counting (CAC) in computer vision, we argue that it is time to rethink the problem formulation of plant counting, from what plants to count to how to count plants. In contrast to most daily objects with spatial and temporal invariance, plants are dynamic, changing with time and space. Their non-rigid structure often leads to worse performance than counting rigid instances like heads and cars such that current CAC and open-world detection models are suboptimal to count plants. In this work, we inherit the vein of the TasselNet plant counting model and introduce a new extension, TasselNetV4, shifting from species-specific counting to cross-species counting. TasselNetV4 marries the local counting idea of TasselNet with the extract-and-match paradigm in CAC. It builds upon a plain vision transformer and incorporates novel multi-branch box-aware local counters used to enhance cross-scale robustness. Two challenging datasets, PAC-105 and PAC-Somalia, are harvested. Extensive experiments against state-of-the-art CAC models show that TasselNetV4 achieves not only superior counting performance but also high efficiency.Our results indicate that TasselNetV4 emerges to be a vision foundation model for cross-scene, cross-scale, and cross-species plant counting.

Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for post-training large language models (LLMs), achieving state-of-the-art performance on tasks with structured, verifiable answers. Applying RLVR to Multimodal LLMs (MLLMs) presents significant opportunities but is complicated by the broader, heterogeneous nature of vision-language tasks that demand nuanced visual, logical, and spatial capabilities. As such, training MLLMs using RLVR on multiple datasets could be beneficial but creates challenges with conflicting objectives from interaction among diverse datasets, highlighting the need for optimal dataset mixture strategies to improve generalization and reasoning. We introduce a systematic post-training framework for Multimodal LLM RLVR, featuring a rigorous data mixture problem formulation and benchmark implementation. Specifically, (1) We developed a multimodal RLVR framework for multi-dataset post-training by curating a dataset that contains different verifiable vision-language problems and enabling multi-domain online RL learning with different verifiable rewards; (2) We proposed a data mixture strategy that learns to predict the RL fine-tuning outcome from the data mixture distribution, and consequently optimizes the best mixture. Comprehensive experiments showcase that multi-domain RLVR training, when combined with mixture prediction strategies, can significantly boost MLLM general reasoning capacities. Our best mixture improves the post-trained model's accuracy on out-of-distribution benchmarks by an average of 5.24% compared to the same model post-trained with uniform data mixture, and by a total of 20.74% compared to the pre-finetuning baseline.

Foundation models (FMs), such as GPT-4 and AlphaFold, are reshaping the landscape of scientific research. Beyond accelerating tasks such as hypothesis generation, experimental design, and result interpretation, they prompt a more fundamental question: Are FMs merely enhancing existing scientific methodologies, or are they redefining the way science is conducted? In this paper, we argue that FMs are catalyzing a transition toward a new scientific paradigm. We introduce a three-stage framework to describe this evolution: (1) Meta-Scientific Integration, where FMs enhance workflows within traditional paradigms; (2) Hybrid Human-AI Co-Creation, where FMs become active collaborators in problem formulation, reasoning, and discovery; and (3) Autonomous Scientific Discovery, where FMs operate as independent agents capable of generating new scientific knowledge with minimal human intervention. Through this lens, we review current applications and emerging capabilities of FMs across existing scientific paradigms. We further identify risks and future directions for FM-enabled scientific discovery. This position paper aims to support the scientific community in understanding the transformative role of FMs and to foster reflection on the future of scientific discovery. Our project is available at https://github.com/usail-hkust/Awesome-Foundation-Models-for-Scientific-Discovery.

Artificial Intelligence (AI) is starting to transform the research process as we know it by automating the discovery of new solutions. Given a task, the typical AI-driven approach is (i) to generate a set of diverse solutions, and then (ii) to verify these solutions and select one that solves the problem. Crucially, this approach assumes the existence of a reliable verifier, i.e., one that can accurately determine whether a solution solves the given problem. We argue that systems research, long focused on designing and evaluating new performance-oriented algorithms, is particularly well-suited for AI-driven solution discovery. This is because system performance problems naturally admit reliable verifiers: solutions are typically implemented in real systems or simulators, and verification reduces to running these software artifacts against predefined workloads and measuring performance. We term this approach as AI-Driven Research for Systems (ADRS), which iteratively generates, evaluates, and refines solutions. Using penEvolve, an existing open-source ADRS instance, we present case studies across diverse domains, including load balancing for multi-region cloud scheduling, Mixture-of-Experts inference, LLM-based SQL queries, and transaction scheduling. In multiple instances, ADRS discovers algorithms that outperform state-of-the-art human designs (e.g., achieving up to 5.0x runtime improvements or 50% cost reductions). We distill best practices for guiding algorithm evolution, from prompt design to evaluator construction, for existing frameworks. We then discuss the broader implications for the systems community: as AI assumes a central role in algorithm design, we argue that human researchers will increasingly focus on problem formulation and strategic guidance. Our results highlight both the disruptive potential and the urgent need to adapt systems research practices in the age of AI.

Major search engine providers are rapidly incorporating Large Language Model (LLM)-generated content in response to user queries. These conversational search engines operate by loading retrieved website text into the LLM context for summarization and interpretation. Recent research demonstrates that LLMs are highly vulnerable to jailbreaking and prompt injection attacks, which disrupt the safety and quality goals of LLMs using adversarial strings. This work investigates the impact of prompt injections on the ranking order of sources referenced by conversational search engines. To this end, we introduce a focused dataset of real-world consumer product websites and formalize conversational search ranking as an adversarial problem. Experimentally, we analyze conversational search rankings in the absence of adversarial injections and show that different LLMs vary significantly in prioritizing product name, document content, and context position. We then present a tree-of-attacks-based jailbreaking technique which reliably promotes low-ranked products. Importantly, these attacks transfer effectively to state-of-the-art conversational search engines such as perplexity.ai. Given the strong financial incentive for website owners to boost their search ranking, we argue that our problem formulation is of critical importance for future robustness work.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

Event argument extraction (EAE) identifies event arguments and their specific roles for a given event. Recent advancement in generation-based EAE models has shown great performance and generalizability over classification-based models. However, existing generation-based EAE models mostly focus on problem re-formulation and prompt design, without incorporating additional information that has been shown to be effective for classification-based models, such as the abstract meaning representation (AMR) of the input passages. Incorporating such information into generation-based models is challenging due to the heterogeneous nature of the natural language form prevalently used in generation-based models and the structured form of AMRs. In this work, we study strategies to incorporate AMR into generation-based EAE models. We propose AMPERE, which generates AMR-aware prefixes for every layer of the generation model. Thus, the prefix introduces AMR information to the generation-based EAE model and then improves the generation. We also introduce an adjusted copy mechanism to AMPERE to help overcome potential noises brought by the AMR graph. Comprehensive experiments and analyses on ACE2005 and ERE datasets show that AMPERE can get 4% - 10% absolute F1 score improvements with reduced training data and it is in general powerful across different training sizes.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.