A parameter-free clustering algorithm for missing datasets

Missing datasets, in which some objects have missing values in certain dimensions, are prevalent in the Real-world. Existing clustering algorithms for missing datasets first impute the missing values and then perform clustering. However, both the imputation and clustering processes require input parameters. Too many input parameters inevitably increase the difficulty of obtaining accurate clustering results. Although some studies have shown that decision graphs can replace the input parameters of clustering algorithms, current decision graphs require equivalent dimensions among objects and are therefore not suitable for missing datasets. To this end, we propose a Single-Dimensional Clustering algorithm, i.e., SDC. SDC, which removes the imputation process and adapts the decision graph to the missing datasets by splitting dimension and partition intersection fusion, can obtain valid clustering results on the missing datasets without input parameters. Experiments demonstrate that, across three evaluation metrics, SDC outperforms baseline algorithms by at least 13.7%(NMI), 23.8%(ARI), and 8.1%(Purity).

Question Translation Training for Better Multilingual Reasoning

Large language models show compelling performance on reasoning tasks but they tend to perform much worse in languages other than English. This is unsurprising given that their training data largely consists of English text and instructions. A typical solution is to translate instruction data into all languages of interest, and then train on the resulting multilingual data, which is called translate-training. This approach not only incurs high cost, but also results in poorly translated data due to the non-standard formatting of chain-of-thought and mathematical reasoning instructions. In this paper, we explore the benefits of question alignment, where we train the model to translate reasoning questions into English by finetuning on X-English question data. In this way we perform targetted, in-domain language alignment which makes best use of English instruction data to unlock the LLMs' multilingual reasoning abilities. Experimental results on LLaMA2-13B show that question alignment leads to consistent improvements over the translate-training approach: an average improvement of 11.3\% and 16.1\% accuracy across ten languages on the MGSM and MSVAMP maths reasoning benchmarks (The project will be available at: https://github.com/NJUNLP/QAlign).

MAPO: Advancing Multilingual Reasoning through Multilingual Alignment-as-Preference Optimization

Though reasoning abilities are considered language-agnostic, existing LLMs exhibit inconsistent reasoning abilities across different languages, e.g., reasoning in a pivot language is superior to other languages due to the imbalance of multilingual training data.To enhance reasoning abilities in non-pivot languages, we propose an alignment-as-preference optimization framework. Specifically, we adopt an open-source translation model to estimate the consistency between answers in non-pivot and pivot languages. We further adopt the answer consistency as the preference for DPO or PPO thus optimizing the lesser reasoning. Experiments show that our method significantly improves the model's multilingual reasoning, with better reasoning consistency across languages. Our framework achieved a 13.7% accuracy improvement on out-of-domain datasets MSVAMP while preserving the competitive performance on MGSM. Moreover, we find that iterative DPO is helpful for further alignment and improvement of the model's multilingual mathematical reasoning ability, further pushing the improvement to 16.7%

PMNN:Physical Model-driven Neural Network for solving time-fractional differential equations

In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which effectively combines deep neural networks (DNNs) with interpolation approximation of fractional derivatives. Specifically, once the fractional differential operator is discretized, DNNs are employed as a bridge to integrate interpolation approximation techniques with differential equations. On the basis of this integration, we construct a neural-based iteration scheme. Subsequently, by training DNNs to learn this temporal iteration scheme, approximate solutions to the differential equations can be obtained. The proposed method aims to preserve the intrinsic physical information within the equations as far as possible. It fully utilizes the powerful fitting capability of neural networks while maintaining the efficiency of the difference schemes for fractional differential equations. Moreover, we validate the efficiency and accuracy of PMNN through several numerical experiments.

Extrapolating Large Language Models to Non-English by Aligning Languages

Due to the unbalanced training data distribution, the language ability of large language models (LLMs) is often biased towards English. In this paper, we propose to empower pre-trained LLMs on non-English languages by building semantic alignment across languages. We perform instruction-tuning on LLaMA with both translation task data and cross-lingual general task data to obtain cross-lingual models (x-LLaMA). Experiment results on cross-lingual benchmark XQUAD and MLQA show that x-LLaMA models outperform the English instruction-tuned counterpart (Alpaca) by 42.50% on average on six non-English languages. Further experiments on Chinese benchmark C-Eval show that x-LLaMA achieves significant improvement on Chinese humanities tasks, outperforming Alpaca by 8.2%. We also discover that incorporating non-English text on the target side of translation data is particularly effective for boosting non-English ability. Besides, we find that semantic alignment within LLM can be further strengthened as translation task data scales up and we present the formulation of the underlying scaling law. Evaluation results on translation dataset Flores-101 show that \method outperforms previous LLaMA-based models in all evaluated directions. Code and data will be available at: https://github.com/OwenNJU/x-LLM.

Beyond Generic: Enhancing Image Captioning with Real-World Knowledge using Vision-Language Pre-Training Model

Current captioning approaches tend to generate correct but "generic" descriptions that lack real-world knowledge, e.g., named entities and contextual information. Considering that Vision-Language Pre-Training (VLP) models master massive such knowledge from large-scale web-harvested data, it is promising to utilize the generalizability of VLP models to incorporate knowledge into image descriptions. However, using VLP models faces challenges: zero-shot inference suffers from knowledge hallucination that leads to low-quality descriptions, but the generic bias in downstream task fine-tuning hinders the VLP model from expressing knowledge. To address these concerns, we propose a simple yet effective method called Knowledge-guided Replay (K-Replay), which enables the retention of pre-training knowledge during fine-tuning. Our approach consists of two parts: (1) a knowledge prediction task on automatically collected replay exemplars to continuously awaken the VLP model's memory about knowledge, thus preventing the model from collapsing into the generic pattern; (2) a knowledge distillation constraint to improve the faithfulness of generated descriptions hence alleviating the knowledge hallucination. To evaluate knowledge-enhanced descriptions, we construct a novel captioning benchmark KnowCap, containing knowledge of landmarks, famous brands, special foods and movie characters. Experimental results show that our approach effectively incorporates knowledge into descriptions, outperforming strong VLP baseline by 20.9 points (78.7->99.6) in CIDEr score and 20.5 percentage points (34.0%->54.5%) in knowledge recognition accuracy. Our code and data is available at https://github.com/njucckevin/KnowCap.

SIFTER: A Task-specific Alignment Strategy for Enhancing Sentence Embeddings

The paradigm of pre-training followed by fine-tuning on downstream tasks has become the mainstream method in natural language processing tasks. Although pre-trained models have the advantage of generalization, their performance may still vary significantly across different domain tasks. This is because the data distribution in different domains varies. For example, the different parts of the sentence 'He married Smt. Dipali Ghosh in 1947 and led a very happy married life' may have different impact for downstream tasks. For similarity calculations, words such as 'led' and 'life' are more important. On the other hand, for sentiment analysis, the word 'happy' is crucial. This indicates that different downstream tasks have different levels of sensitivity to sentence components. Our starting point is to scale information of the model and data according to the specifics of downstream tasks, enhancing domain information of relevant parts for these tasks and reducing irrelevant elements for different domain tasks, called SIFTER. In the experimental part, we use the SIFTER to improve SimCSE by constructing positive sample pairs based on enhancing the sentence stem and reducing the unimportant components in the sentence, and maximize the similarity between three sentences. Similarly, SIFTER can improve the gate mechanism of the LSTM model by short-circuiting the input gate of important words so that the LSTM model remembers the important parts of the sentence. Our experiments demonstrate that SIFTER outperforms the SimCSE and LSTM baselines.

INK: Injecting kNN Knowledge in Nearest Neighbor Machine Translation

Neural machine translation has achieved promising results on many translation tasks. However, previous studies have shown that neural models induce a non-smooth representation space, which harms its generalization results. Recently, kNN-MT has provided an effective paradigm to smooth the prediction based on neighbor representations during inference. Despite promising results, kNN-MT usually requires large inference overhead. We propose an effective training framework INK to directly smooth the representation space via adjusting representations of kNN neighbors with a small number of new parameters. The new parameters are then used to refresh the whole representation datastore to get new kNN knowledge asynchronously. This loop keeps running until convergence. Experiments on four benchmark datasets show that \method achieves average gains of 1.99 COMET and 1.0 BLEU, outperforming the state-of-the-art kNN-MT system with 0.02x memory space and 1.9x inference speedup.

On Structural Expressive Power of Graph Transformers

Graph Transformer has recently received wide attention in the research community with its outstanding performance, yet its structural expressive power has not been well analyzed. Inspired by the connections between Weisfeiler-Lehman (WL) graph isomorphism test and graph neural network (GNN), we introduce \textbf{SEG-WL test} (\textbf{S}tructural \textbf{E}ncoding enhanced \textbf{G}lobal \textbf{W}eisfeiler-\textbf{L}ehman test), a generalized graph isomorphism test algorithm as a powerful theoretical tool for exploring the structural discriminative power of graph Transformers. We theoretically prove that the SEG-WL test is an expressivity upper bound on a wide range of graph Transformers, and the representational power of SEG-WL test can be approximated by a simple Transformer network arbitrarily under certain conditions. With the SEG-WL test, we show how graph Transformers' expressive power is determined by the design of structural encodings, and present conditions that make the expressivity of graph Transformers beyond WL test and GNNs. Moreover, motivated by the popular shortest path distance encoding, we follow the theory-oriented principles and develop a provably stronger structural encoding method, Shortest Path Induced Subgraph (\textit{SPIS}) encoding. Our theoretical findings provide a novel and practical paradigm for investigating the expressive power of graph Transformers, and extensive synthetic and real-world experiments empirically verify the strengths of our proposed methods.

Hierarchical Transformer for Scalable Graph Learning

Graph Transformer is gaining increasing attention in the field of machine learning and has demonstrated state-of-the-art performance on benchmarks for graph representation learning. However, as current implementations of Graph Transformer primarily focus on learning representations of small-scale graphs, the quadratic complexity of the global self-attention mechanism presents a challenge for full-batch training when applied to larger graphs. Additionally, conventional sampling-based methods fail to capture necessary high-level contextual information, resulting in a significant loss of performance. In this paper, we introduce the Hierarchical Scalable Graph Transformer (HSGT) as a solution to these challenges. HSGT successfully scales the Transformer architecture to node representation learning tasks on large-scale graphs, while maintaining high performance. By utilizing graph hierarchies constructed through coarsening techniques, HSGT efficiently updates and stores multi-scale information in node embeddings at different levels. Together with sampling-based training methods, HSGT effectively captures and aggregates multi-level information on the hierarchical graph using only Transformer blocks. Empirical evaluations demonstrate that HSGT achieves state-of-the-art performance on large-scale benchmarks with graphs containing millions of nodes with high efficiency.