Mixed membership community detection is a challenging problem. In this paper, to detect mixed memberships, we propose a new method Mixed-SLIM which is a spectral clustering method on the symmetrized Laplacian inverse matrix under the degree-corrected mixed membership model. We provide theoretical bounds for the estimation error on the proposed algorithm and its regularized version under mild conditions. Meanwhile, we provide some extensions of the proposed method to deal with large networks in practice. These Mixed-SLIM methods outperform state-of-art methods in simulations and substantial empirical datasets for both community detection and mixed membership community detection problems.
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In this paper, we delve into several mechanisms employed by Transformer-based language models (LLMs) for factual recall tasks. We outline a pipeline consisting of three major steps: (1) Given a prompt ``The capital of France is,'' task-specific attention heads extract the topic token, such as ``France,'' from the context and pass it to subsequent MLPs. (2) As attention heads' outputs are aggregated with equal weight and added to the residual stream, the subsequent MLP acts as an ``activation,'' which either erases or amplifies the information originating from individual heads. As a result, the topic token ``France'' stands out in the residual stream. (3) A deep MLP takes ``France'' and generates a component that redirects the residual stream towards the direction of the correct answer, i.e., ``Paris.'' This procedure is akin to applying an implicit function such as ``get\_capital($X$),'' and the argument $X$ is the topic token information passed by attention heads. To achieve the above quantitative and qualitative analysis for MLPs, we proposed a novel analytic method aimed at decomposing the outputs of the MLP into components understandable by humans. Additionally, we observed a universal anti-overconfidence mechanism in the final layer of models, which suppresses correct predictions. We mitigate this suppression by leveraging our interpretation to improve factual recall confidence. The above interpretations are evaluated across diverse tasks spanning various domains of factual knowledge, using various language models from the GPT-2 families, 1.3B OPT, up to 7B Llama-2, and in both zero- and few-shot setups.
In this paper, we explore sampling from strongly log-concave distributions defined on convex and compact supports. We propose a general proximal framework that involves projecting onto the constrained set, which is highly flexible and supports various projection options. Specifically, we consider the cases of Euclidean and Gauge projections, with the latter having the advantage of being performed efficiently using a membership oracle. This framework can be seamlessly integrated with multiple sampling methods. Our analysis focuses on Langevin-type sampling algorithms within the context of constrained sampling. We provide nonasymptotic upper bounds on the W1 and W2 errors, offering a detailed comparison of the performance of these methods in constrained sampling.
The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify chain-of-thought reasoning, reward modeling, formal reasoning, data augmentation, and code interpreter in a unified seq2seq format and supervise our model to be a versatile math reasoner, verifier, prover, and augmenter. These abilities can be used to develop the next math LLMs or self-iteration. InternLM-Math obtains open-sourced state-of-the-art performance under the setting of in-context learning, supervised fine-tuning, and code-assisted reasoning in various informal and formal benchmarks including GSM8K, MATH, Hungary math exam, MathBench-ZH, and MiniF2F. Our pre-trained model achieves 30.3 on the MiniF2F test set without fine-tuning. We further explore how to use LEAN to solve math problems and study its performance under the setting of multi-task learning which shows the possibility of using LEAN as a unified platform for solving and proving in math. Our models, codes, and data are released at \url{//github.com/InternLM/InternLM-Math}.
In this paper, we introduce a data augmentation approach specifically tailored to enhance intersectional fairness in classification tasks. Our method capitalizes on the hierarchical structure inherent to intersectionality, by viewing groups as intersections of their parent categories. This perspective allows us to augment data for smaller groups by learning a transformation function that combines data from these parent groups. Our empirical analysis, conducted on four diverse datasets including both text and images, reveals that classifiers trained with this data augmentation approach achieve superior intersectional fairness and are more robust to ``leveling down'' when compared to methods optimizing traditional group fairness metrics.
Synergizing Spatial Optimization with Large Language Models for Open-Domain Urban Itinerary Planning
In this paper, we introduce the novel task of Open-domain Urban Itinerary Planning (OUIP), a paradigm designed to generate personalized urban itineraries from user requests articulated in natural language. This approach is different from traditional itinerary planning, which often restricts the granularity of user inputs, thus hindering genuine personalization. To this end, we present ItiNera, an OUIP system that synergizes spatial optimization with large language models (LLMs) to provide services that customize urban itineraries based on users' needs. Upon receiving the user's itinerary request, the LLM first decomposes it into detailed components, identifying key requirements, including preferences and dislikes. Then, we use these specifics to select candidate POIs from a large-scale collection using embedding-based Preference-aware POI Retrieval. Finally, a preference score-based Cluster-aware Spatial Optimization module clusters, filters, and orders these POIs, followed by the LLM for detailed POI selection and organization to craft a personalized, spatially coherent itinerary. Moreover, we created an LLM-based pipeline to update and personalize a user-owned POI database. This ensures up-to-date POI information, supports itinerary planning, pre-trip research, POI collection, recommendations, and more. To the best of our knowledge, this study marks the first integration of LLMs to innovate itinerary planning, with potential extensions for various urban travel and exploration activities. Offline and online evaluations demonstrate the capacity of our system to deliver more responsive, personalized, and spatially coherent itineraries than current solutions. Our system, deployed on an online platform, has attracted thousands of users for their urban travel planning.
Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.
Non-IID data present a tough challenge for federated learning. In this paper, we explore a novel idea of facilitating pairwise collaborations between clients with similar data. We propose FedAMP, a new method employing federated attentive message passing to facilitate similar clients to collaborate more. We establish the convergence of FedAMP for both convex and non-convex models, and propose a heuristic method to further improve the performance of FedAMP when clients adopt deep neural networks as personalized models. Our extensive experiments on benchmark data sets demonstrate the superior performance of the proposed methods.
In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.
We consider an interesting problem-salient instance segmentation in this paper. Other than producing bounding boxes, our network also outputs high-quality instance-level segments. Taking into account the category-independent property of each target, we design a single stage salient instance segmentation framework, with a novel segmentation branch. Our new branch regards not only local context inside each detection window but also its surrounding context, enabling us to distinguish the instances in the same scope even with obstruction. Our network is end-to-end trainable and runs at a fast speed (40 fps when processing an image with resolution 320x320). We evaluate our approach on a publicly available benchmark and show that it outperforms other alternative solutions. We also provide a thorough analysis of the design choices to help readers better understand the functions of each part of our network. The source code can be found at \url{//github.com/RuochenFan/S4Net}.
The key issue of few-shot learning is learning to generalize. In this paper, we propose a large margin principle to improve the generalization capacity of metric based methods for few-shot learning. To realize it, we develop a unified framework to learn a more discriminative metric space by augmenting the softmax classification loss function with a large margin distance loss function for training. Extensive experiments on two state-of-the-art few-shot learning models, graph neural networks and prototypical networks, show that our method can improve the performance of existing models substantially with very little computational overhead, demonstrating the effectiveness of the large margin principle and the potential of our method.
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