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In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam&#39;s problem from projective geometryâ€”the long-standing problem of determining if a projective plane of order ten exists.  Both the original search and an independent verification in 2011 discovered no such projective plane.  However, these searches were each performed using highly specialized custom-written code and did not produce nonexistence certificates.  In this paper, we resolve Lam&#39;s problem by translating the problem into Boolean logic and use satisfiability (SAT) solvers to produce nonexistence certificates that can be verified by a third party.  Our work uncovered consistency issues in both previous searchesâ€”highlighting the difficulty of relying on special-purpose search code for nonexistence results.

AAAI 2021

A SAT-Based Resolution of Lam&#39;s Problem

### Welcome to The 63rd Annual Meeting of the Association for Computational Linguistics (ACL 2025)

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*It is my great pleasure and honor to welcome you to the 63rd Annual Meeting of the Association for Computational Linguistics (ACL 2025), held in beautiful Vienna, Austria, from July 27 to August 1, 2025. ACL2025continues our field’s tradition of excellence in scholarship, innovation, and inclusivity, and I am deeply grateful to the many volunteers who have worked tirelessly to bring this event to life.* 
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ACL 2025

Welcome to The 63rd Annual Meeting of the Association for Computational Linguistics (ACL 2025)

In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometryâ€”the long-standing problem of determining if a projective plane of order ten exists.  Both the original search and an independent verification in 2011 discovered no such projective plane.  However, these searches were each performed using highly specialized custom-written code and did not produce nonexistence certificates.  In this paper, we resolve Lam's problem by translating the problem into Boolean logic and use satisfiability (SAT) solvers to produce nonexistence certificates that can be verified by a third party.  Our work uncovered consistency issues in both previous searchesâ€”highlighting the difficulty of relying on special-purpose search code for nonexistence results.

A SAT-Based Resolution of Lam's Problem

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Deep neural networks (DNNs) have been widely applied to active learning. Despite of its effectiveness, the generalization ability of the discriminative classifier (the softmax classifier) is questionable when there is a significant distribution bias between the labeled set and the unlabeled set. In this paper, we attempt to replace the softmax classifier in deep neural network with a nearest neighbor classifier, considering its progressive generalization ability within the unknown sub-space. Our proposed active learning approach, termed nearest Neighbor Classifier Embedded network (NCE-Net), targets at reducing the risk of over-estimating unlabeled samples while improving the opportunity to query informative samples. NCE-Net is conceptually simple but surprisingly powerful, as justified from the perspective of the subset information, which defines a metric to quantify model generalization ability in active learning. Experimental results show that, with simple selection based on rejection or confusion confidence, NCE-Net improves state-of-the-arts on image classification and object detection tasks with significant margins.

Nearest Neighbor Classifier Embedded Network for Active Learning

Learning single-image 3D reconstruction with only 2D images supervision is a promising research topic. The main challenge in image-supervised 3D reconstruction is the shape-pose ambiguity, which means a 2D supervision can be explained by an erroneous 3D shape from an erroneous pose. It will introduce high uncertainty and mislead the learning process. Existed works rely on multi-view images or pose-aware annotations to resolve the ambiguity. In this paper, we propose to resolve the ambiguity without extra pose-aware labels or annotations. Our training data is single-view images from the same object category. To overcome the shape-pose ambiguity, we introduce a pose-independent GAN to learn the category-specific shape manifold from the image collections. With the learned shape space, we resolve the shape-pose ambiguity in original images by training a pseudo pose regressor. Finally, we learn a reconstruction network with both the common re-projection loss and a pose-independent discrimination loss, making the results plausible from all views. Through experiments on synthetic and real image datasets, we demonstrate that our method can perform comparably to existing methods while not requiring any extra pose-aware annotations, making it more applicable and adaptable.

Shape-Pose Ambiguity in Learning 3D Reconstruction from Images

Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of the best-known theoretical models to explain patterns as a reminiscent of those observed in nature. Over the years, concerted efforts have been made to align theoretical models to explain patterns in real systems. The apparent difficulty in identifying the specific dynamics of the RD system makes the problem particularly challenging. Interestingly, we observe Turing-like patterns in a system of neurons with adversarial interaction. In this study, we establish the involvement of Turing instability to create such patterns. By theoretical and empirical studies, we present a \textit{pseudo-reaction-diffusion} model to explain the mechanism that may underlie these phenomena. While supervised learning attains homogeneous equilibrium, this paper suggests that the introduction of an adversary helps break this homogeneity to create non-homogeneous patterns at equilibrium. Further, we prove that randomly initialized gradient descent with over-parameterization can converge exponentially fast to an $\epsilon$-stationary point even under adversarial interaction. In addition, different from sole supervision, we show that the solutions obtained under adversarial interaction are not limited to a tiny subspace around initialization.

Why Adversarial Interaction Creates Non-Homogeneous Patterns: A Pseudo-Reaction-Diffusion Model for Turing Instability

This paper proposes a method to disentangle and quantify interactions among words that are encoded inside a DNN for natural language processing. We construct a tree to encode salient interactions extracted by the DNN. Six metrics are proposed to analyze properties of interactions between constituents in a sentence. The interaction is defined based on Shapley values of words, which are considered as an unbiased estimation of word contributions to the network prediction. Our method is used to quantify word interactions encoded inside the BERT, ELMo, LSTM, CNN, and Transformer networks. Experimental results have provided a new perspective to understand these DNNs, and have demonstrated the effectiveness of our method.

Building Interpretable Interaction Trees for Deep NLP Models

In classical planning as search, duplicate state pruning is a standard method to avoid unnecessarily handling the same state multiple times. In decoupled search, similar to symbolic search approaches, search nodes, called decoupled states, do not correspond to individual states, but to sets of states. Therefore, duplicate state pruning is less effective in decoupled search, and dominance pruning is employed, taking into account the state sets. We observe that the time required for dominance checking dominates the overall runtime, and propose two ways to tackle this issue. Our main contribution is a stronger variant of dominance checking for optimal planning, where efficiency and pruning power are most crucial. The new variant greatly improves the latter, without incurring a computational overhead. Moreover, we develop three methods that make the dominance check more efficient: exact duplicate checking, which, albeit resulting in weaker pruning, can pay off due to the use of hashing; avoiding the dominance check in non-optimal planning if leaf state spaces are invertible; and exploiting the transitivity of the dominance relation to only check against the relevant subset of visited decoupled states. We show empirically that all our improvements are indeed beneficial in many standard benchmarks.

Revisiting Dominance Pruning in Decoupled Search

Neural abstractive summarization has been studied in many pieces of literature and achieves great success with the aid of large corpora. However, when encountering novel tasks, one may not always benefit from transfer learning due to the domain shifting problem, and overfitting could happen without adequate labeled examples. Furthermore, the annotations of abstractive summarization are costly, which often demand domain knowledge to ensure the ground-truth quality. Thus, there are growing appeals for Low-Resource Abstractive Summarization, which aims to leverage past experience to improve the performance with limited labeled examples of target corpus. In this paper, we propose to utilize two knowledge-rich sources to tackle this problem, which are large pre-trained models and diverse existing corpora. The former can provide the primary ability to tackle summarization tasks; the latter can help discover common syntactic or semantic information to improve the generalization ability. We conduct extensive experiments on various summarization corpora with different writing styles and forms. The results demonstrate that our approach achieves the state-of-the-art on 6 corpora in low-resource scenarios, with only 0.7% of trainable parameters compared to previous work.

Meta-Transfer Learning for Low-Resource Abstractive Summarization

A video-grounded dialogue system referred to as the Structured Co-reference Graph Attention (SCGA) is presented for decoding the answer sequence to a question regarding a given video while keeping track of the dialogue context. Although recent efforts have made great strides in improving the quality of the response, performance is still far from satisfactory. The two main challenging issues are as follows: (1) how to deduce co-reference among multiple modalities and (2) how to reason on the rich underlying semantic structure of video with complex spatial and temporal dynamics. To this end, SCGA is based on (1) Structured Co-reference Resolver that performs dereferencing via building a structured graph over multiple modalities, (2) Spatio-temporal Video Reasoner that captures local-to-global dynamics of video via gradually neighboring graph attention. SCGA makes use of pointer network to dynamically replicate parts of the question for decoding the answer sequence. The validity of the proposed SCGA is demonstrated on AVSD@DSTC7 and AVSD@DSTC8 datasets, a challenging video-grounded dialogue benchmarks, and TVQA dataset, a large-scale videoQA benchmark. Our empirical results show that SCGA outperforms other state-of-the-art dialogue systems on both benchmarks, while extensive ablation study and qualitative analysis reveal performance gain and improved interpretability.

Structured Co-Reference Graph Attention for Video-Grounded Dialogue

Magnetic resonance (MR) image acquisition is an inherently prolonged process, whose acceleration by obtaining multiple undersampled images simultaneously through parallel imaging has always been the subject of research. In this paper, we propose the Dual-Octave Convolution (Dual-OctConv), which is capable of learning multi-scale spatial-frequency features from both real and imaginary components, for fast parallel MR image reconstruction. By reformulating the complex operations using octave convolutions, our model shows a strong ability to capture richer representations of MR images, while at the same time greatly reducing the spatial redundancy. More specifically, the input feature maps and convolutional kernels are first split into two components (i.e., real and imaginary), which are then divided into four groups according to their spatial frequencies. Then, our Dual-OctConv conducts intra-group information updating and inter-group information exchange to aggregate the contextual information across different groups. Our framework provides two appealing benefits: (i) it encourages interactions between real and imaginary components at various spatial frequencies to achieve richer representational capacity, and (ii) it enlarges the receptive field by learning multiple spatial-frequency features of both the real and imaginary components. We evaluate the performance of the proposed model on the acceleration of multi-coil MR image reconstruction. Extensive experiments are conducted on an {in vivo} knee dataset under different undersampling patterns and acceleration factors. The experimental results demonstrate the superiority of our model in accelerated parallel MR image reconstruction.
Our code is available at: github.com/chunmeifeng/Dual-OctConv.

Dual-Octave Convolution for Accelerated Parallel MR Image Reconstruction

Knowledge distillation (KD) is one of the most useful techniques for light-weight neural networks. Although neural networks have a clear purpose of embedding datasets into the low-dimensional space, the existing knowledge was quite far
from this purpose and provided only limited information. We argue that good knowledge should be able to interpret the embedding procedure. This paper proposes a method of generating interpretable embedding procedure (IEP) knowledge based on principal component analysis, and distilling it based on a message passing neural network. Experimental results show that the student network trained by the proposed KD method improves 2.28% in the CIFAR100 dataset, which is a higher performance than the state-of-the-art (SOTA) method. We also demonstrate that the embedding procedure knowledge is interpretable via visualization of the proposed KD process. The implemented code is available at https://github.com/sseung0703/IEPKT.

Interpretable Embedding Procedure Knowledge Transfer via Stacked Principal Component Analysis and Graph Neural Network

The maximum quasi-clique problem (MQCP) is an important extension of maximum clique problem with wide applications. Recent heuristic MQCP algorithms can hardly solve large and hard graphs effectively. This paper develops an efficient local search algorithm named NuQClq for the MQCP, which has two main ideas. First, we propose a novel vertex selection strategy, which utilizes cumulative saturation information to be a selection criterion when the candidate vertices have equal values on the primary scoring function. Second, a variant of configuration checking named BoundedCC is designed by setting an upper bound for the threshold of forbidding strength. When the threshold value of vertex exceeds the upper bound, we reset its threshold value to increase the diversity of search process. Experiments on a broad range of classic benchmarks and sparse instances show that NuQClq significantly outperforms the state-of-the-art MQCP algorithms for most instances.

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