Improving Implicit Regularization of SGD with Preconditioning for Least Square Problems

Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice and plays an important role in the generalization of modern machine learning. However, prior research has revealed instances where the generalization performance of SGD is worse than ridge regression due to uneven optimization along different dimensions. Preconditioning offers a natural solution to this issue by rebalancing optimization across different directions. Yet, the extent to which preconditioning can enhance the generalization performance of SGD and whether it can bridge the existing gap with ridge regression remains uncertain. In this paper, we study the generalization performance of SGD with preconditioning for the least squared problem. We make a comprehensive comparison between preconditioned SGD and (standard \& preconditioned) ridge regression. Our study makes several key contributions toward understanding and improving SGD with preconditioning. First, we establish excess risk bounds (generalization performance) for preconditioned SGD and ridge regression under an arbitrary preconditions matrix. Second, leveraging the excessive risk characterization of preconditioned SGD and ridge regression, we show that (through construction) there exists a simple preconditioned matrix that can outperform (standard \& preconditioned) ridge regression. Finally, we show that our proposed preconditioning matrix is straightforward enough to allow robust estimation from finite samples while maintaining a theoretical advantage over ridge regression. Our empirical results align with our theoretical findings, collectively showcasing the enhanced regularization effect of preconditioned SGD.

BG-HGNN: Toward Scalable and Efficient Heterogeneous Graph Neural Network

Many computer vision and machine learning problems are modelled as learning tasks on heterogeneous graphs, featuring a wide array of relations from diverse types of nodes and edges. Heterogeneous graph neural networks (HGNNs) stand out as a promising neural model class designed for heterogeneous graphs. Built on traditional GNNs, existing HGNNs employ different parameter spaces to model the varied relationships. However, the practical effectiveness of existing HGNNs is often limited to simple heterogeneous graphs with few relation types. This paper first highlights and demonstrates that the standard approach employed by existing HGNNs inevitably leads to parameter explosion and relation collapse, making HGNNs less effective or impractical for complex heterogeneous graphs with numerous relation types. To overcome this issue, we introduce a novel framework, Blend&Grind-HGNN (BG-HGNN), which effectively tackles the challenges by carefully integrating different relations into a unified feature space manageable by a single set of parameters. This results in a refined HGNN method that is more efficient and effective in learning from heterogeneous graphs, especially when the number of relations grows. Our empirical studies illustrate that BG-HGNN significantly surpasses existing HGNNs in terms of parameter efficiency (up to 28.96 $\times$), training throughput (up to 8.12 $\times$), and accuracy (up to 1.07 $\times$).

On the Topology Awareness and Generalization Performance of Graph Neural Networks

Many computer vision and machine learning problems are modelled as learning tasks on graphs, where graph neural networks (GNNs) have emerged as a dominant tool for learning representations of graph-structured data. A key feature of GNNs is their use of graph structures as input, enabling them to exploit the graphs' inherent topological properties-known as the topology awareness of GNNs. Despite the empirical successes of GNNs, the influence of topology awareness on generalization performance remains unexplored, particularly for node-level tasks that diverge from the assumption of data being independent and identically distributed (I.I.D.). The precise definition and characterization of the topology awareness of GNNs, especially concerning different topological features, are still unclear. This paper introduces a comprehensive framework to characterize the topology awareness of GNNs across any topological feature. Using this framework, we investigate the effects of topology awareness on GNN generalization performance. Contrary to the prevailing belief that enhancing the topology awareness of GNNs is always advantageous, our analysis reveals a critical insight: improving the topology awareness of GNNs may inadvertently lead to unfair generalization across structural groups, which might not be desired in some scenarios. Additionally, we conduct a case study using the intrinsic graph metric, the shortest path distance, on various benchmark datasets. The empirical results of this case study confirm our theoretical insights. Moreover, we demonstrate the practical applicability of our framework by using it to tackle the cold start problem in graph active learning.

LLM-PQ: Serving LLM on Heterogeneous Clusters with Phase-Aware Partition and Adaptive Quantization

Recent breakthroughs in Large-scale language models (LLMs) have demonstrated impressive performance on various tasks. The immense sizes of LLMs have led to very high resource demand and cost for running the models. Though the models are largely served using uniform high-caliber GPUs nowadays, utilizing a heterogeneous cluster with a mix of available high- and low-capacity GPUs can potentially substantially reduce the serving cost. There is a lack of designs to support efficient LLM serving using a heterogeneous cluster, while the current solutions focus on model partition and uniform compression among homogeneous devices. This paper proposes LLM-PQ, a system that advocates adaptive model quantization and phase-aware partition to improve LLM serving efficiency on heterogeneous GPU clusters. We carefully decide on mixed-precision model quantization together with phase-aware model partition and micro-batch sizing in distributed LLM serving with an efficient algorithm, to greatly enhance inference throughput while fulfilling user-specified model quality targets. Extensive experiments on production inference workloads in 11 different clusters demonstrate that LLM-PQ achieves up to 2.88x (2.26x on average) throughput improvement in inference, showing great advantages over state-of-the-art works.

LoRA Meets Dropout under a Unified Framework

With the remarkable capabilities, large language models (LLMs) have emerged as essential elements in numerous NLP applications, while parameter-efficient finetuning, especially LoRA, has gained popularity as a lightweight approach for model customization. Meanwhile, various dropout methods, initially designed for full finetuning with all the parameters updated, alleviates overfitting associated with excessive parameter redundancy. Hence, a possible contradiction arises from negligible trainable parameters of LoRA and the effectiveness of previous dropout methods, which has been largely overlooked. To fill this gap, we first confirm that parameter-efficient LoRA is also overfitting-prone. We then revisit transformer-specific dropout methods, and establish their equivalence and distinctions mathematically and empirically. Building upon this comparative analysis, we introduce a unified framework for a comprehensive investigation, which instantiates these methods based on dropping position, structural pattern and compensation measure. Through this framework, we reveal the new preferences and performance comparisons of them when involved with limited trainable parameters. This framework also allows us to amalgamate the most favorable aspects into a novel dropout method named HiddenKey. Extensive experiments verify the remarkable superiority and sufficiency of HiddenKey across multiple models and tasks, which highlights it as the preferred approach for high-performance and parameter-efficient finetuning of LLMs.

PRoLoRA: Partial Rotation Empowers More Parameter-Efficient LoRA

With the rapid scaling of large language models (LLMs), serving numerous LoRAs concurrently has become increasingly impractical, leading to unaffordable costs and necessitating more parameter-efficient finetuning methods. In this work, we introduce Partially Rotation-enhanced Low-Rank Adaptation (PRoLoRA), an intra-layer sharing mechanism comprising four essential components: broadcast reduction, rotation enhancement, partially-sharing refinement, and rectified initialization strategy. As a superset of LoRA, PRoLoRA pertains its advantages, and effectively circumvent the drawbacks of peer parameter-sharing methods with superior model capacity, practical feasibility, and broad applicability. Empirical experiments demonstrate the remarkably higher parameter efficiency of PRoLoRA in both specific parameter budget and performance target scenarios, and its scalability to larger LLMs. Notably, with one time less trainable parameters, PRoLoRA still outperforms LoRA on multiple instruction tuning datasets. Subsequently, an ablation study is conducted to validate the necessity of individual components and highlight the superiority of PRoLoRA over three potential variants. Hopefully, the conspicuously higher parameter efficiency can establish PRoLoRA as a resource-friendly alternative to LoRA.

MSPipe: Efficient Temporal GNN Training via Staleness-aware Pipeline

Memory-based Temporal Graph Neural Networks (MTGNNs) are a class of temporal graph neural networks that utilize a node memory module to capture and retain long-term temporal dependencies, leading to superior performance compared to memory-less counterparts. However, the iterative reading and updating process of the memory module in MTGNNs to obtain up-to-date information needs to follow the temporal dependencies. This introduces significant overhead and limits training throughput. Existing optimizations for static GNNs are not directly applicable to MTGNNs due to differences in training paradigm, model architecture, and the absence of a memory module. Moreover, they do not effectively address the challenges posed by temporal dependencies, making them ineffective for MTGNN training. In this paper, we propose MSPipe, a general and efficient framework for MTGNNs that maximizes training throughput while maintaining model accuracy. Our design addresses the unique challenges associated with fetching and updating node memory states in MTGNNs by integrating staleness into the memory module. However, simply introducing a predefined staleness bound in the memory module to break temporal dependencies may lead to suboptimal performance and lack of generalizability across different models and datasets. To solve this, we introduce an online pipeline scheduling algorithm in MSPipe that strategically breaks temporal dependencies with minimal staleness and delays memory fetching to obtain fresher memory states. Moreover, we design a staleness mitigation mechanism to enhance training convergence and model accuracy. We provide convergence analysis and prove that MSPipe maintains the same convergence rate as vanilla sample-based GNN training. Experimental results show that MSPipe achieves up to 2.45x speed-up without sacrificing accuracy, making it a promising solution for efficient MTGNN training.

Towards Robust Graph Incremental Learning on Evolving Graphs

Incremental learning is a machine learning approach that involves training a model on a sequence of tasks, rather than all tasks at once. This ability to learn incrementally from a stream of tasks is crucial for many real-world applications. However, incremental learning is a challenging problem on graph-structured data, as many graph-related problems involve prediction tasks for each individual node, known as Node-wise Graph Incremental Learning (NGIL). This introduces non-independent and non-identically distributed characteristics in the sample data generation process, making it difficult to maintain the performance of the model as new tasks are added. In this paper, we focus on the inductive NGIL problem, which accounts for the evolution of graph structure (structural shift) induced by emerging tasks. We provide a formal formulation and analysis of the problem, and propose a novel regularization-based technique called Structural-Shift-Risk-Mitigation (SSRM) to mitigate the impact of the structural shift on catastrophic forgetting of the inductive NGIL problem. We show that the structural shift can lead to a shift in the input distribution for the existing tasks, and further lead to an increased risk of catastrophic forgetting. Through comprehensive empirical studies with several benchmark datasets, we demonstrate that our proposed method, Structural-Shift-Risk-Mitigation (SSRM), is flexible and easy to adapt to improve the performance of state-of-the-art GNN incremental learning frameworks in the inductive setting.

Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models

Diffusion models have gained attention in text processing, offering many potential advantages over traditional autoregressive models. This work explores the integration of diffusion models and Chain-of-Thought (CoT), a well-established technique to improve the reasoning ability in autoregressive language models. We propose Diffusion-of-Thought (DoT), allowing reasoning steps to diffuse over time through the diffusion process. In contrast to traditional autoregressive language models that make decisions in a left-to-right, token-by-token manner, DoT offers more flexibility in the trade-off between computation and reasoning performance. Our experimental results demonstrate the effectiveness of DoT in multi-digit multiplication and grade school math problems. Additionally, DoT showcases promising self-correction abilities and benefits from existing reasoning-enhancing techniques like self-consistency decoding. Our findings contribute to the understanding and development of reasoning capabilities in diffusion language models.