Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network’s output distribution to move closer to the symbolic constraints. While diffusion models have shown remarkable generative capability across various domains, we employ the powerful architecture to perform neuro-symbolic learning and solve logical puzzles. Our diffusion-based pipeline adopts a two-stage training strategy: the first stage focuses on cultivating basic reasoning abilities, while the second emphasizes systematic learning of logical constraints. To impose hard constraints on neural outputs in the second stage, we formulate the diffusion reasoner as a Markov decision process and innovatively fine-tune it with an improved proximal policy optimization algorithm. We utilize a rule-based reward signal derived from the logical consistency of neural outputs and adopt a flexible strategy to optimize the diffusion reasoner's policy. We evaluate our methodology on some classical symbolic reasoning benchmarks, including Sudoku, Maze, pathfinding and preference learning. Experimental results demonstrate that our approach achieves outstanding accuracy and logical consistency among neural networks.

Recent advances in model distillation show that data from advanced reasoning models can effectively train smaller student models.However, standard practices discard incorrect reasoning traces-valuable, yet underutilized data.This paper addresses the critical question: How can both positive and negative distilled reasoning traces be effectively leveraged to maximize LLM reasoning performance in an offline setting?We employ a two-stage training recipe: first, Supervised Fine-Tuning (SFT) on positive traces, followed by a refinement stage using both positive and negative traces.We find that a simple REINFORCE-style objective, which we term the Reinforcement Distillation (REDI) objective, outperforms established preference optimization methods like DPO and SimPO in this distillation context.Our empirical evaluations demonstrate the effectiveness of this approach.Notably, our Qwen-REDI-1.5Bmodel, trained on just 131k traces from the open Open-R1 dataset, achieves an 83.1% score on MATH-500.Its performance matches that of DeepSeek-R1-Distill-Qwen-1.5B, a model trained on 800k proprietary data.This result showcases the remarkable data efficiency of utilizing previously discarded negative traces.

Siming Huang, Tianhao Cheng, Jason Klein Liu, Weidi Xu, Jiaran Hao, Liuyihan Song, Yang Xu, Jian Yang, Jiaheng Liu, Chenchen Zhang, Linzheng Chai, Ruifeng Yuan, Xianzhen Luo, Qiufeng Wang, YuanTao Fan, Qingfu Zhu, Zhaoxiang Zhang, Yang Gao, Jie Fu, Qian Liu, Houyi Li, Ge Zhang, Yuan Qi, Xu Yinghui, Wei Chu, Zili Wang. Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2025.

Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP, which performs mean-field variational inference over a Markov Logic Network (MLN). It can be plugged into any off-the-shelf neural network to encode FOLCs while retaining modularity and efficiency. By exploiting the structure and symmetries in MLNs, we theoretically demonstrate that our well-designed, efficient mean-field iterations greatly mitigate the difficulty of MLN inference, reducing the inference from sequential calculation to a series of parallel tensor operations. Empirical results in three kinds of tasks over images, graphs, and text show that LogicMP outperforms advanced competitors in both performance and efficiency.

Simpson's paradox is a well-known statistical phenomenon that has captured the attention of statisticians, mathematicians, and philosophers for more than a century. The paradox often confuses people when it appears in data, and ignoring it may lead to incorrect decisions. Recent studies have found many examples of Simpson's paradox in social data and proposed a few methods to detect the paradox automatically. However, these methods suffer from many limitations, such as being only suitable for categorical variables or one specific paradox. To address these problems, we develop a learning-based approach to discover various Simpson's paradoxes. Firstly, we propose a framework from a statistical perspective that unifies multiple variants of Simpson's paradox currently known. Secondly, we present a novel loss function, Multi-group Pearson Correlation Coefficient (MPCC), to calculate the association strength of two variables of multiple subgroups. Then, we design a neural network model, coined SimNet, to automatically disaggregate data into multiple subgroups by optimizing the MPCC loss. Experiments on various datasets demonstrate that SimNet can discover various Simpson's paradoxes caused by discrete and continuous variables, even hidden variables. The code is available at https://github.com/ant-research/Learning-to-Discover-Various-Simpson-Paradoxes.

Recently, modeling temporal patterns of user-item interactions have attracted much attention in recommender systems. We argue that existing methods ignore the variety of temporal patterns of user behaviors. We define the subset of user behaviors that are ir- relevant to the target item as noises, which limits the performance of target-related time cycle modeling and affect the recommendation performance. In this paper, we propose Denoising Time Cycle Modeling (DiCycle), a novel approach to denoise user behaviors and select the subset of user behaviors that are highly related to the target item. DiCycle is able to explicitly model diverse time cycle patterns for recommendation. Extensive experiments are conducted on both public benchmarks and a real-world dataset, demonstrating the superior performance of DiCycle over the state-of-the-art recommendation methods.

Airborne multichannel high-resolution radar (HRR)-ground moving target indication (GMTI) is of great significance to wide-area surveillance, traffic monitoring and target recognition. The Aerospace Information Research Institute, Chinese Academy of Sciences, produced an advanced airborne digital array radar with high resolution and conducted an experiment with slow and weak cooperative moving targets in 2021. In this paper, an overall processing framework for target detection, parameter estimation and target tracking using this system is introduced. For HRR detection, the echo energy of targets is spread into multiple range units, so-called range-spread targets; thus, using detectors designed for point-like targets will severely degrade the detection performance, especially for slow and weak targets. To address the adaptive detection of such range-spread targets embedded in Gaussian clutter with an unknown covariance matrix, a novel two-step generalized space-time adaptive processing (GSTAP) algorithm is proposed, which offers an enhanced clutter suppression capability compared with natural competitors. Moreover, a tracking method is implemented in the range-Doppler domain to avoid track loss caused by azimuth relocation error and reject discrete false alarms. Both simulation and experimental results are presented to demonstrate the effectiveness of the proposed method and provide a paradigm for further research.

With the exploration of synthetic aperture radar (SAR), the requirements for its functionality, precision, and response time are inevitably increasing, in which the technical core is the generation, reception, and processing of wideband signals with low time cost. Owing to the excellent performance of modern photonics, such as the ultra-wide bandwidth (UWB), flat response, low transmission loss, fast analog signal processing, and microwave photonics (MWP) promises to be an appropriate solution to improve the capability of SAR in resolution, coverage, and efficiency. However, on the one hand, due to the high sensitivity of optical fiber, moisture, temperature, or physical vibration can produce an unknown extra propagation delay. On the other hand, the wavelength shift effect should be taken into consideration for the UWB system. Thereby, under very high resolution (VHR) circumstance, two-dimensional (2-D) defocus including migration through resolution cells (MTRC) and azimuth phase error (APE) becomes a challenge for MWP SAR imaging. Unfortunately, existing 2-D autofocus approaches concerning motion errors inherently fail for the commonly underlying assumption that the prominent nonsystematic residual range cell migration (RCM) is global in the azimuth time domain. In this article, we analyze the effects of the above-mentioned negative factors in the image processing of range migration algorithm (RMA) and reveal the structural characteristics of the 2-D phase errors. A novel two-step postprocessing compensation strategy is developed, and experiments on real data acquired by an airborne MWP SAR system demonstrate its effectiveness.

Synthetic aperture radar (SAR) installed on unmanned aerial vehicles (UAVs) has drawn increasing attention in the area of remote sensing due to its high spatial resolution and low energy consumption. However, due to the sensitivity toward atmospheric turbulences, strong motion errors can defocus the image in both azimuth and range directions. In this article, based on symmetric triangular linear frequency-modulation continuous microwave (STLFMCW) signals, a novel motion error estimation method is proposed. The core concept is to eliminate the effect of residual range cell migration (RCM) and investigate the motion parameters from azimuth phase history by range-frequency-domain interferometry between the up-ramp and down-ramp chirp sections. With preknowledge of the structural characteristics of the differential signal, we first obtain the high-order component, then estimate the quadratic term with an azimuth profile width minimization (APWM) algorithm on the basis of bisection search, and subsequently remove the linear part through phase gradient matching and joining. Consequently, the desired motion errors can be achieved purely based on raw data. Simulations demonstrate that our proposed algorithm can achieve high accuracy with or without standard prominent point targets. Experimental results on a W-band UAV SAR system in strip-map mode indicate that this approach also outperforms other existing postprocessing autofocus methods.

The frequency modulation continuous wave (FMCW) Laser radar (Ladar) inevitably suffers from vibration and nonlinear modulation, which will reduce ranging accuracy and imaging resolution. We propose a vibration and nonlinearity compensation method using particle filtering (PF) for one- period triangular frequency modulation continuous wave (T-FMCW) signals. We first extend the traditional ranging model to an instantaneous ranging model by a second-order synchro-squeezing transform (SST) which can characterize the local distributions of time-varying signals. We then eliminate the nonlinearity errors from the instantaneous measurement ranges by setting an auxiliary channel. Finally, we built a particle filtering (PF) model using the instantaneous ranges to compensate for the vibration and the residual nonlinearity errors, and estimate the range of target by using the triangular relations of T -FMCW. Experimental tests prove that the proposed method can accurately estimate the range of target by simultaneously compensating for the vibration and nonlinearity errors in one-period T -FMCW.

The application of miniature unmanned aerial platforms has been growing in popularity whether in military reconnaissance or in civilian monitoring systems over the past few years. Installation of synthetic aperture radar (SAR) on board of unmanned aerial vehicle (UAV) is a high-efficient but low-cost remote sensing technology. However, UAV is sensitive to atmospheric turbulences and it may not carry high-accuracy inertial navigation systems (INS) and global positioning system (GPS). These make Mini SAR imagery a challenge, and motion compensation (MoCo) a crucial task. This paper is aimed at studying on the MoCo technology for Mini SAR mounted on UAV. Practical data processing is presented to primarily demonstrate the validity of our proposed approach.

Product query classification is the basic component for query understanding, which aims to classify the user queries into multiple categories under a predefined product category taxonomy for the E-commerce search engine. It is a challenging task due to the tremendous amount of product categories. And a slight modification to a query will change its corresponding categories entirely, e.g., appending the "button" to the query "shirt". The problem is more severe for the tail queries which lack enough supervision information from customers. Motivated by this phenomenon, this paper proposes to model the contrasting/similar relationships between such similar queries. Our framework is composed of a base model and an across-context attention module. The across-context attention module plays the role of deriving and extracting external information from these variant queries by predicting their categories. We conduct both offline and online experiments on the real-world E-commerce search engine. Experimental results demonstrate the effectiveness of our across-context attention module.

Chinese Spelling Check (CSC) is a task to detect and correct spelling errors in Chinese natural language.Existing methods have made attempts to incorporate the similarity knowledge between Chinese characters.However, they take the similarity knowledge as either an external input resource or just heuristic rules.This paper proposes to incorporate phonological and visual similarity knowledge into language models for CSC via a specialized graph convolutional network (SpellGCN).The model builds a graph over the characters, and SpellGCN is learned to map this graph into a set of inter-dependent character classifiers.These classifiers are applied to the representations extracted by another network, such as BERT, enabling the whole network to be end-to-end trainable.Experiments 1 are conducted on three human-annotated datasets.Our method achieves superior performance against previous models by a large margin.

Learning powerful discriminative features is a challenging task in Semi-Supervised Learning, as the estimation of the feature space is more likely to be wrong with scarcer labeled data. Previous methods utilize a relation graph with edges representing 'similarity' or 'dissimilarity' between nodes. Similar nodes are forced to output consistent features, while dissimilar nodes are forced to be inconsistent. However, since unlabeled data may be wrongly labeled, the judgment of edges may be unreliable. Besides, the nodes connected by edges may already be well fitted, thus contributing little to the model training. We propose Reliable Edge Mining (REM), which forms a reliable graph by only selecting reliable and useful edges. Guided by the graph, the feature extractor is able to learn discriminative features in a data-efficient way, and consequently boosts the accuracy of the learned classifier. Visual analyses show that the features learned are more discriminative and better reveals the underlying structure of the data. REM can be combined with perturbation-based methods like Pi-model, TempEns and Mean Teacher to further improve accuracy. Experiments prove that our method is data-efficient on simple tasks like SVHN and CIFAR-10, and achieves state-of-the-art results on the challenging CIFAR-100.

Kunlong Chen, Weidi Xu, Xingyi Cheng, Zou Xiaochuan, Yuyu Zhang, Le Song, Taifeng Wang, Yuan Qi, Wei Chu. Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP). 2020.

The ability of semantic reasoning over the sentence pair is essential for many natural language understanding tasks, e.g., natural language inference and machine reading comprehension. A recent significant improvement in these tasks comes from BERT. As reported, the next sentence prediction (NSP) in BERT is of great significance for downstream problems with sentence-pair input. Despite its effectiveness, NSP still lacks the essential signal to distinguish between entailment and shallow correlation. To remedy this, we propose to augment the NSP task to a multi-class categorization task, which includes previous sentence prediction (PSP). This task encourages the model to learn the subtle semantics, thereby improves the ability of semantic understanding. Furthermore, by using a smoothing technique, the scopes of NSP and PSP are expanded into a broader range which includes close but nonsuccessive sentences. This simple method yields remarkable improvement against vanilla BERT. Our method consistently improves the performance on the NLI and MRC benchmarks by a large margin, including the challenging HANS dataset.

Semisupervised text classification has attracted much attention from the research community. In this paper, a novel model, the semisupervised sequential variational autoencoder (SSVAE), is proposed to tackle this problem. By treating the categorical label of unlabeled data as a discrete latent variable, the proposed model maximizes the variational evidence lower bound of the data likelihood, which implicitly derives the underlying label distribution for the unlabeled data. Analytical work indicates that the autoregressive nature of the sequential model is the crucial issue that renders the vanilla model ineffective. To remedy this, two types of decoders are investigated in the SSVAE model and verified. In addition, a reweighting approach is proposed to circumvent the credit assignment problem that occurs during the reconstruction procedure, which can further improve performance for sparse text data. Experimental results show that our method significantly improves the classification accuracy compared with other modern methods.

Aspect-term sentiment analysis (ATSA) is a long-standing challenge in natural language processing.It requires fine-grained semantical reasoning about a target entity appeared in the text.As manual annotation over the aspects is laborious and time-consuming, the amount of labeled data is limited for supervised learning.This paper proposes a semisupervised method for the ATSA problem by using the Variational Autoencoder based on Transformer.The model learns the latent distribution via variational inference.By disentangling the latent representation into the aspect-specific sentiment and the lexical context, our method induces the underlying sentiment prediction for the unlabeled data, which then benefits the ATSA classifier.Our method is classifier-agnostic, i.e., the classifier is an independent module and various supervised models can be integrated.Experimental results are obtained on the SemEval 2014 task 4 and show that our method is effective with different five specific classifiers and outperforms these models by a significant margin.

Fireworks algorithm (FWA) is a newly proposed swarm intelligence optimization method. It simulates the fireworks explosion process to search for the best location of sparks and has demonstrated good performance in many continuous optimization problems. In this paper, we apply FWA to the travel salesman problem (TSP), a classical discrete optimization problem. We propose a discrete fireworks algorithm for TSP by combining the general framework of FWA and current ideas for solving the TSP. We call it DFWA-TSP. In DFWA-TSP, 2-opt and 3-opt edge exchange heuristic are implemented as the basic explosion operation in FWA. An adaptive strategy is designed to decide the explosion amplitude. A particular mutation method based on insertion is also used to cover the shortage of edge exchange and a new selection method based on the quality of fireworks is adopted to pick up good fireworks efficiently. Various experiments on both TSPLIB and synthetic data have been made to compare the performance of our algorithm with current heuristic methods for TSP, such as genetic algorithm and ant colony system algorithm. We conclude that our algorithm out-performs these algorithms, especially on large-scale cases.

Conditional text generation is a fundamental task in natural language generation. Traditional conditional generative models build conditional probability distributions over the given labels. However, categorical label information is usually very abstract, e.g., sentiment, and it is difficult to be disentangled from the content. Therefore, instead of generating text by modeling conditional probability distribution, we propose a novel text generation method TextDream through searching in the semantic space. Specifically, in this method, a random text seed is initially given and the new text is generated by local search operation. The generation procedure is guided by a fitness function, typically a classification model. Text with higher fitness will be preserved. This procedure loops until the qualified solution is found. Experimental results show that our method is able to generate more diverse text compared with advanced conditional generative models.

Although semi-supervised variational autoencoder (SemiVAE) works in image classification task, it fails in text classification task if using vanilla LSTM as its decoder. From a perspective of reinforcement learning, it is verified that the decoder's capability to distinguish between different categorical labels is essential. Therefore, Semi-supervised Sequential Variational Autoencoder (SSVAE) is proposed, which increases the capability by feeding label into its decoder RNN at each time-step. Two specific decoder structures are investigated and both of them are verified to be effective. Besides, in order to reduce the computational complexity in training, a novel optimization method is proposed, which estimates the gradient of the unlabeled objective function by sampling, along with two variance reduction techniques. Experimental results on Large Movie Review Dataset (IMDB) and AG's News corpus show that the proposed approach significantly improves the classification accuracy compared with pure-supervised classifiers, and achieves competitive performance against previous advanced methods. State-of-the-art results can be obtained by integrating other pretraining-based methods.

In the field of deep neural networks, several generative methods have been proposed to address the challenges from generative and discriminative tasks, e.g., natural language process, image caption and image generation. In this paper, a conditional recurrent variational autoencoder is proposed for multi-digit image synthesis. This model is capable of generating multi-digit images from the given number sequences and retaining the generalisation ability to recover different types of background. Our method is evaluated on SVHN dataset and the experimental results show it succeeds to generate multi-digit images with various styles according to the given sequential inputs. The generated images can also be easily identified by both human beings and convolutional neural networks for digit classification.