We study the convergence rate of first-order methods for rectangular matrix factorization, which is a canonical nonconvex optimization problem. Specifically, given a rank-$r$ matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, we prove that gradient descent (GD) can find a pair of $\epsilon$-optimal solutions $\mathbf{X}_T\in\mathbb{R}^{m\times d}$ and $\mathbf{Y}_T\in\mathbb{R}^{n\times d}$, where $d\geq r$, satisfying $\lVert\mathbf{X}_T\mathbf{Y}_T^\top-\mathbf{A}\rVert_\mathrm{F}\leq\epsilon\lVert\mathbf{A}\rVert_\mathrm{F}$ in $T=O(\kappa^2\log\frac{1}{\epsilon})$ iterations with high probability, where $\kappa$ denotes the condition number of $\mathbf{A}$. Furthermore, we prove that Nesterov's accelerated gradient (NAG) attains an iteration complexity of $O(\kappa\log\frac{1}{\epsilon})$, which is the best-known bound of first-order methods for rectangular matrix factorization. Different from small balanced random initialization in the existing literature, we adopt an unbalanced initialization, where $\mathbf{X}_0$ is large and $\mathbf{Y}_0$ is $0$. Moreover, our initialization and analysis can be further extended to linear neural networks, where we prove that NAG can also attain an accelerated linear convergence rate. In particular, we only require the width of the network to be greater than or equal to the rank of the output label matrix. In contrast, previous results achieving the same rate require excessive widths that additionally depend on the condition number and the rank of the input data matrix.

In the field of Recommender Systems (RS), neural collaborative filtering represents a significant milestone by combining matrix factorization and deep neural networks to achieve promising results. Traditional methods like matrix factorization often rely on linear models, limiting their capability to capture complex interactions between users, items, and contexts. This limitation becomes particularly evident with high-dimensional datasets due to their inability to capture relationships among users, items, and contextual factors. Unsupervised learning and dimension reduction tasks utilize autoencoders, neural network-based models renowned for their capacity to encode and decode data. Autoencoders learn latent representations of inputs, reducing dataset size while capturing complex patterns and features. In this paper, we introduce a framework that combines neural contextual matrix factorization with autoencoders to predict user ratings for items. We provide a comprehensive overview of the framework's design and implementation. To evaluate its performance, we conduct experiments on various real-world datasets and compare the results against state-of-the-art approaches. We also extend the concept of conformal prediction to prediction rating and introduce a Conformal Prediction Rating (CPR). For RS, we define the nonconformity score, a key concept of conformal prediction, and demonstrate that it satisfies the exchangeability property.

The rapid advancement of Multimodal Large Language Models (MLLMs) has significantly impacted various multimodal tasks. However, these models face challenges in tasks that require spatial understanding within 3D environments. Efforts to enhance MLLMs, such as incorporating point cloud features, have been made, yet a considerable gap remains between the models' learned representations and the inherent complexity of 3D scenes. This discrepancy largely stems from the training of MLLMs on predominantly 2D data, which restricts their effectiveness in comprehending 3D spaces. To address this issue, in this paper, we propose a novel generalist model, i.e., Video-3D LLM, for 3D scene understanding. By treating 3D scenes as dynamic videos and incorporating 3D position encoding into these representations, our Video-3D LLM aligns video representations with real-world spatial contexts more accurately. Additionally, we have implemented a maximum coverage sampling technique to optimize the balance between computational costs and performance efficiency. Extensive experiments demonstrate that our model achieves state-of-the-art performance on several 3D scene understanding benchmarks, including ScanRefer, Multi3DRefer, Scan2Cap, ScanQA, and SQA3D.

Instruction tuning has underscored the significant potential of large language models (LLMs) in producing more human-controllable and effective outputs in various domains. In this work, we focus on the data selection problem for task-specific instruction tuning of LLMs. Prevailing methods primarily rely on the crafted similarity metrics to select training data that aligns with the test data distribution. The goal is to minimize instruction tuning loss on the test data, ultimately improving performance on the target task. However, it has been widely observed that instruction tuning loss (i.e., cross-entropy loss for next token prediction) in LLMs often fails to exhibit a monotonic relationship with actual task performance. This misalignment undermines the effectiveness of current data selection methods for task-specific instruction tuning. To address this issue, we introduce ROSE, a novel Reward-Oriented inStruction data sElection method which leverages pairwise preference loss as a reward signal to optimize data selection for task-specific instruction tuning. Specifically, ROSE adapts an influence formulation to approximate the influence of training data points relative to a few-shot preference validation set to select the most task-related training data points. Experimental results show that by selecting just 5% of the training data using ROSE, our approach can achieve competitive results compared to fine-tuning with the full training dataset, and it surpasses other state-of-the-art data selection methods for task-specific instruction tuning. Our qualitative analysis further confirms the robust generalizability of our method across multiple benchmark datasets and diverse model architectures.

This paper presents DynRank, a novel framework for enhancing passage retrieval in open-domain question-answering systems through dynamic zero-shot question classification. Traditional approaches rely on static prompts and pre-defined templates, which may limit model adaptability across different questions and contexts. In contrast, DynRank introduces a dynamic prompting mechanism, leveraging a pre-trained question classification model that categorizes questions into fine-grained types. Based on these classifications, contextually relevant prompts are generated, enabling more effective passage retrieval. We integrate DynRank into existing retrieval frameworks and conduct extensive experiments on multiple QA benchmark datasets.

The success of most federated learning (FL) methods heavily depends on label quality, which is often inaccessible in real-world scenarios, such as medicine, leading to the federated label-noise (F-LN) problem. In this study, we observe that the global model of FL memorizes the noisy labels slowly. Based on the observations, we propose a novel approach dubbed Global Reviser for Federated Learning with Noisy Labels (FedGR) to enhance the label-noise robustness of FL. In brief, FedGR employs three novel modules to achieve noisy label sniffing and refining, local knowledge revising, and local model regularization. Specifically, the global model is adopted to infer local data proxies for global sample selection and refine incorrect labels. To maximize the utilization of local knowledge, we leverage the global model to revise the local exponential moving average (EMA) model of each client and distill it into the clients' models. Additionally, we introduce a global-to-local representation regularization to mitigate the overfitting of noisy labels. Extensive experiments on three F-LNL benchmarks against seven baseline methods demonstrate the effectiveness of the proposed FedGR.

Representations learned by self-supervised approaches are generally considered to possess sufficient generalizability and discriminability. However, we disclose a nontrivial mutual-exclusion relationship between these critical representation properties through an exploratory demonstration on self-supervised learning. State-of-the-art self-supervised methods tend to enhance either generalizability or discriminability but not both simultaneously. Thus, learning representations jointly possessing strong generalizability and discriminability presents a specific challenge for self-supervised learning. To this end, we revisit the learning paradigm of self-supervised learning from the perspective of evolutionary game theory (EGT) and outline the theoretical roadmap to achieve a desired trade-off between these representation properties. EGT performs well in analyzing the trade-off point in a two-player game by utilizing dynamic system modeling. However, the EGT analysis requires sufficient annotated data, which contradicts the principle of self-supervised learning, i.e., the EGT analysis cannot be conducted without the annotations of the specific target domain for self-supervised learning. Thus, to enhance the methodological generalization, we propose a novel self-supervised learning method that leverages advancements in reinforcement learning to jointly benefit from the general guidance of EGT and sequentially optimize the model to chase the consistent improvement of generalizability and discriminability for specific target domains during pre-training. Theoretically, we establish that the proposed method tightens the generalization error upper bound of self-supervised learning. Empirically, our method achieves state-of-the-art performance on various benchmarks.

Message passing plays a vital role in graph neural networks (GNNs) for effective feature learning. However, the over-reliance on input topology diminishes the efficacy of message passing and restricts the ability of GNNs. Despite efforts to mitigate the reliance, existing study encounters message-passing bottlenecks or high computational expense problems, which invokes the demands for flexible message passing with low complexity. In this paper, we propose a novel dynamic message-passing mechanism for GNNs. It projects graph nodes and learnable pseudo nodes into a common space with measurable spatial relations between them. With nodes moving in the space, their evolving relations facilitate flexible pathway construction for a dynamic message-passing process. Associating pseudo nodes to input graphs with their measured relations, graph nodes can communicate with each other intermediately through pseudo nodes under linear complexity. We further develop a GNN model named $\mathtt{\mathbf{N^2}}$ based on our dynamic message-passing mechanism. $\mathtt{\mathbf{N^2}}$ employs a single recurrent layer to recursively generate the displacements of nodes and construct optimal dynamic pathways. Evaluation on eighteen benchmarks demonstrates the superior performance of $\mathtt{\mathbf{N^2}}$ over popular GNNs. $\mathtt{\mathbf{N^2}}$ successfully scales to large-scale benchmarks and requires significantly fewer parameters for graph classification with the shared recurrent layer.

A robotic arm that can automatically turn cockroaches into controllable cyborgs could be used to create swarms of biological robots for search missions. Hirotaka Sato at Nanyang Technological University in Singapore and his colleagues have previously shown that groups of up to 20 Madagascar hissing cockroaches (Gromphadorhina portentosa) equipped with electronic backpacks can be steered across desert-like terrain. However, to be used in a real-world search-and-rescue mission, the team calculates that hundreds or thousands of cyborg insects would be needed.

Welcome to our monthly digest, where you can catch up with any AIhub stories you may have missed, peruse the latest news, recap recent events, and more. This month, we hear from AfriClimate AI co-founder Amal Nammouchi, learn about the kidney exchange problem, and find out how to improve the interpretability of logistic regression models. This month, we had the pleasure of chatting to Amal Nammouchi, co-founder of AfriClimate AI, a grassroots community focused on using artificial intelligence to tackle climate challenges in Africa. Amal told us about the inspiration behind the initiative, some of their activities and projects, and plans for the future. In this blog post, Danial Dervovic writes about work presented at IJCAI 2024 on improving the interpretability of logistic regression models.