Implicit Neural Representations (INRs) have emerged as a powerful framework for representing continuous signals. However, generating diverse INR weights remains challenging due to limited training data. We introduce Few-shot Implicit Function Generation, a new problem setup that aims to generate diverse yet functionally consistent INR weights from only a few examples. This is challenging because even for the same signal, the optimal INRs can vary significantly depending on their initializations. To tackle this, we propose EquiGen, a framework that can generate new INRs from limited data. The core idea is that functionally similar networks can be transformed into one another through weight permutations, forming an equivariance group. By projecting these weights into an equivariant latent space, we enable diverse generation within these groups, even with few examples. EquiGen implements this through an equivariant encoder trained via contrastive learning and smooth augmentation, an equivariance-guided diffusion process, and controlled perturbations in the equivariant subspace. Experiments on 2D image and 3D shape INR datasets demonstrate that our approach effectively generates diverse INR weights while preserving their functional properties in few-shot scenarios.

The ubiquity and value of tables as semi-structured data across various domains necessitate advanced methods for understanding their complexity and vast amounts of information. Despite the impressive capabilities of large language models (LLMs) in advancing the natural language understanding frontier, their application to large-scale tabular data presents significant challenges, specifically regarding table size and complex intricate relationships. Existing works have shown promise with small-scale tables but often flounder when tasked with the complex reasoning required by larger, interconnected tables found in real-world scenarios. To address this gap, we introduce "Tree-of-Table", a novel approach designed to enhance LLMs' reasoning capabilities over large and complex tables. Our method employs Table Condensation and Decomposition to distill and reorganize relevant data into a manageable format, followed by the construction of a hierarchical Table-Tree that facilitates tree-structured reasoning. Through a meticulous Table-Tree Execution process, we systematically unravel the tree-structured reasoning chain to derive the solutions. Experiments across diverse datasets, including WikiTQ, TableFact, FeTaQA, and BIRD, demonstrate that Tree-of-Table sets a new benchmark with superior performance, showcasing remarkable efficiency and generalization capabilities in large-scale table reasoning.

Graphs are a fundamental data structure for representing relationships in real-world scenarios. With the success of Large Language Models (LLMs) across various natural language processing (NLP) tasks, there has been growing interest in integrating LLMs for graph learning. However, applying LLMs to graph-related tasks poses significant challenges, as these models are not inherently designed to capture the complex structural information present in graphs. Existing approaches address this challenge through two strategies: the chain of tasks approach, which uses Graph Neural Networks (GNNs) to encode the graph structure so that LLMs are relieved from understanding spatial positions; and Graph-to-Text Conversion, which translates graph structures into semantic text representations that LLMs can process. Despite their progress, these methods often struggle to fully preserve the topological information of graphs or require extensive computational resources, limiting their practical applicability. In this work, we introduce Node Tokenizer for Large Language Models (NT-LLM), a novel framework that efficiently encodes graph structures by selecting key nodes as anchors and representing each node based on its relative distance to these anchors. This position-anchored encoding effectively captures the graph topology, enabling enhanced reasoning capabilities in LLMs over graph data. Additionally, we implement a task-specific tuning procedure to further improve structural understanding within LLMs. Through extensive empirical evaluations, NT-LLM demonstrates significant performance improvements across a variety of graph-related tasks.

The innovative Federated Multi-Task Learning (FMTL) approach consolidates the benefits of Federated Learning (FL) and Multi-Task Learning (MTL), enabling collaborative model training on multi-task learning datasets. However, a comprehensive evaluation method, integrating the unique features of both FL and MTL, is currently absent in the field. This paper fills this void by introducing a novel framework, FMTL-Bench, for systematic evaluation of the FMTL paradigm. This benchmark covers various aspects at the data, model, and optimization algorithm levels, and comprises seven sets of comparative experiments, encapsulating a wide array of non-independent and identically distributed (Non-IID) data partitioning scenarios. We propose a systematic process for comparing baselines of diverse indicators and conduct a case study on communication expenditure, time, and energy consumption. Through our exhaustive experiments, we aim to provide valuable insights into the strengths and limitations of existing baseline methods, contributing to the ongoing discourse on optimal FMTL application in practical scenarios. The source code can be found on https://github.com/youngfish42/FMTL-Benchmark .

Federated Learning (FL) enables joint training across distributed clients using their local data privately. Federated Multi-Task Learning (FMTL) builds on FL to handle multiple tasks, assuming model congruity that identical model architecture is deployed in each client. To relax this assumption and thus extend real-world applicability, we introduce a novel problem setting, Hetero-Client Federated Multi-Task Learning (HC-FMTL), to accommodate diverse task setups. The main challenge of HC-FMTL is the model incongruity issue that invalidates conventional aggregation methods. It also escalates the difficulties in accurate model aggregation to deal with data and task heterogeneity inherent in FMTL. To address these challenges, we propose the FedHCA$^2$ framework, which allows for federated training of personalized models by modeling relationships among heterogeneous clients. Drawing on our theoretical insights into the difference between multi-task and federated optimization, we propose the Hyper Conflict-Averse Aggregation scheme to mitigate conflicts during encoder updates. Additionally, inspired by task interaction in MTL, the Hyper Cross Attention Aggregation scheme uses layer-wise cross attention to enhance decoder interactions while alleviating model incongruity. Moreover, we employ learnable Hyper Aggregation Weights for each client to customize personalized parameter updates. Extensive experiments demonstrate the superior performance of FedHCA$^2$ in various HC-FMTL scenarios compared to representative methods. Our code will be made publicly available.

Class Incremental Learning (CIL) aims to handle the scenario where data of novel classes occur continuously and sequentially. The model should recognize the sequential novel classes while alleviating the catastrophic forgetting. In the self-supervised manner, it becomes more challenging to avoid the conflict between the feature embedding spaces of novel classes and old ones without any class labels. To address the problem, we propose a self-supervised CIL framework CPPF, meaning Combining Past, Present and Future. In detail, CPPF consists of a prototype clustering module (PC), an embedding space reserving module (ESR) and a multi-teacher distillation module (MTD). 1) The PC and the ESR modules reserve embedding space for subsequent phases at the prototype level and the feature level respectively to prepare for knowledge learned in the future. 2) The MTD module maintains the representations of the current phase without the interference of past knowledge. One of the teacher networks retains the representations of the past phases, and the other teacher network distills relation information of the current phase to the student network. Extensive experiments on CIFAR100 and ImageNet100 datasets demonstrate that our proposed method boosts the performance of self-supervised class incremental learning. We will release code in the near future.

Federated Learning (FL) has emerged as a promising approach to enable collaborative learning among multiple clients while preserving data privacy. However, cross-domain FL tasks, where clients possess data from different domains or distributions, remain a challenging problem due to the inherent heterogeneity. In this paper, we present UNIDEAL, a novel FL algorithm specifically designed to tackle the challenges of cross-domain scenarios and heterogeneous model architectures. The proposed method introduces Adjustable Teacher-Student Mutual Evaluation Curriculum Learning, which significantly enhances the effectiveness of knowledge distillation in FL settings. We conduct extensive experiments on various datasets, comparing UNIDEAL with state-of-the-art baselines. Our results demonstrate that UNIDEAL achieves superior performance in terms of both model accuracy and communication efficiency. Additionally, we provide a convergence analysis of the algorithm, showing a convergence rate of O(1/T) under non-convex conditions.

Data-efficient learning on graphs (GEL) is essential in real-world applications. Existing GEL methods focus on learning useful representations for nodes, edges, or entire graphs with ``small'' labeled data. But the problem of data-efficient learning for subgraph prediction has not been explored. The challenges of this problem lie in the following aspects: 1) It is crucial for subgraphs to learn positional features to acquire structural information in the base graph in which they exist. Although the existing subgraph neural network method is capable of learning disentangled position encodings, the overall computational complexity is very high. 2) Prevailing graph augmentation methods for GEL, including rule-based, sample-based, adaptive, and automated methods, are not suitable for augmenting subgraphs because a subgraph contains fewer nodes but richer information such as position, neighbor, and structure. Subgraph augmentation is more susceptible to undesirable perturbations. 3) Only a small number of nodes in the base graph are contained in subgraphs, which leads to a potential ``bias'' problem that the subgraph representation learning is dominated by these ``hot'' nodes. By contrast, the remaining nodes fail to be fully learned, which reduces the generalization ability of subgraph representation learning. In this paper, we aim to address the challenges above and propose a Position-Aware Data-Efficient Learning framework for subgraph neural networks called PADEL. Specifically, we propose a novel node position encoding method that is anchor-free, and design a new generative subgraph augmentation method based on a diffused variational subgraph autoencoder, and we propose exploratory and exploitable views for subgraph contrastive learning. Extensive experiment results on three real-world datasets show the superiority of our proposed method over state-of-the-art baselines.

The message-passing scheme is the core of graph representation learning. While most existing message-passing graph neural networks (MPNNs) are permutation-invariant in graph-level representation learning and permutation-equivariant in node- and edge-level representation learning, their expressive power is commonly limited by the 1-Weisfeiler-Lehman (1-WL) graph isomorphism test. Recently proposed expressive graph neural networks (GNNs) with specially designed complex message-passing mechanisms are not practical. To bridge the gap, we propose a plug-in Equivariant Distance ENcoding (EDEN) for MPNNs. EDEN is derived from a series of interpretable transformations on the graph's distance matrix. We theoretically prove that EDEN is permutation-equivariant for all level graph representation learning, and we empirically illustrate that EDEN's expressive power can reach up to the 3-WL test. Extensive experiments on real-world datasets show that combining EDEN with conventional GNNs surpasses recent advanced GNNs.

In this paper, we propose two novel multi-dimensional tensor sparse coding (MDTSC) schemes using the t-linear combination. Based on the t-linear combination, the shifted versions of the bases are used for the data approximation, but without need to store them. Therefore, the dictionaries of the proposed schemes are more concise and the coefficients have richer physical explanations. Moreover, we propose an efficient alternating minimization algorithm, including the tensor coefficient learning and the tensor dictionary learning, to solve the proposed problems. For the tensor coefficient learning, we design a tensor-based fast iterative shrinkage algorithm. For the tensor dictionary learning, we first divide the problem into several nearly-independent subproblems in the frequency domain, and then utilize the Lagrange dual to further reduce the number of optimization variables. Experimental results on multi-dimensional signals denoising and reconstruction (3DTSC, 4DTSC, 5DTSC) show that the proposed algorithms are more efficient and outperform the state-of-the-art tensor-based sparse coding models.