Hongyang R. Zhang

Haotian Ju, Dongyue Li, Aneesh Sharma et al.

Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the maximum degree. In this paper, we present generalization bounds that instead scale with the largest singular value of the graph neural network's feature diffusion matrix. These bounds are numerically much smaller than prior bounds for real-world graphs. We also construct a lower bound of the generalization gap that matches our upper bound asymptotically. To achieve these results, we analyze a unified model that includes prior works' settings (i.e., convolutional and message-passing networks) and new settings (i.e., graph isomorphism networks). Our key idea is to measure the stability of graph neural networks against noise perturbations using Hessians. Empirically, we find that Hessian-based measurements correlate with the observed generalization gaps of graph neural networks accurately. Optimizing noise stability properties for fine-tuning pretrained graph neural networks also improves test performance on several graph-level classification tasks.

Haotian Ju, Dongyue Li, Hongyang R. Zhang

We consider fine-tuning a pretrained deep neural network on a target task. We study the generalization properties of fine-tuning to understand the problem of overfitting, which has often been observed (e.g., when the target dataset is small or when the training labels are noisy). Existing generalization measures for deep networks depend on notions such as distance from the initialization (i.e., the pretrained network) of the fine-tuned model and noise stability properties of deep networks. This paper identifies a Hessian-based distance measure through PAC-Bayesian analysis, which is shown to correlate well with observed generalization gaps of fine-tuned models. Theoretically, we prove Hessian distance-based generalization bounds for fine-tuned models. We also describe an extended study of fine-tuning against label noise, where overfitting remains a critical problem. We present an algorithm and a generalization error guarantee for this algorithm under a class conditional independent noise model. Empirically, we observe that the Hessian-based distance measure can match the scale of the observed generalization gap of fine-tuned models in practice. We also test our algorithm on several image classification tasks with noisy training labels, showing gains over prior methods and decreases in the Hessian distance measure of the fine-tuned model.

Dongyue Li, Huy L. Nguyen, Hongyang R. Zhang

Multitask learning is widely used in practice to train a low-resource target task by augmenting it with multiple related source tasks. Yet, naively combining all the source tasks with a target task does not always improve the prediction performance for the target task due to negative transfers. Thus, a critical problem in multitask learning is identifying subsets of source tasks that would benefit the target task. This problem is computationally challenging since the number of subsets grows exponentially with the number of source tasks; efficient heuristics for subset selection do not always capture the relationship between task subsets and multitask learning performances. In this paper, we introduce an efficient procedure to address this problem via surrogate modeling. In surrogate modeling, we sample (random) subsets of source tasks and precompute their multitask learning performances. Then, we approximate the precomputed performances with a linear regression model that can also predict the multitask performance of unseen task subsets. We show theoretically and empirically that fitting this model only requires sampling linearly many subsets in the number of source tasks. The fitted model provides a relevance score between each source and target task. We use the relevance scores to perform subset selection for multitask learning by thresholding. Through extensive experiments, we show that our approach predicts negative transfers from multiple source tasks to target tasks much more accurately than existing task affinity measures. Additionally, we demonstrate that for several weak supervision datasets, our approach consistently improves upon existing optimization methods for multitask learning.

Dongyue Li, Haotian Ju, Aneesh Sharma et al.

Predicting node labels on a given graph is a widely studied problem with many applications, including community detection and molecular graph prediction. This paper considers predicting multiple node labeling functions on graphs simultaneously and revisits this problem from a multitask learning perspective. For a concrete example, consider overlapping community detection: each community membership is a binary node classification task. Due to complex overlapping patterns, we find that negative transfer is prevalent when we apply naive multitask learning to multiple community detection, as task relationships are highly nonlinear across different node labeling. To address the challenge, we develop an algorithm to cluster tasks into groups based on a higher-order task affinity measure. We then fit a multitask model on each task group, resulting in a boosting procedure on top of the baseline model. We estimate the higher-order task affinity measure between two tasks as the prediction loss of one task in the presence of another task and a random subset of other tasks. Then, we use spectral clustering on the affinity score matrix to identify task grouping. We design several speedup techniques to compute the higher-order affinity scores efficiently and show that they can predict negative transfers more accurately than pairwise task affinities. We validate our procedure using various community detection and molecular graph prediction data sets, showing favorable results compared with existing methods. Lastly, we provide a theoretical analysis to show that under a planted block model of tasks on graphs, our affinity scores can provably separate tasks into groups.

Dongyue Li, Aneesh Sharma, Hongyang R. Zhang

Multitask learning is a widely used paradigm for training models on diverse tasks, with applications ranging from graph neural networks to language model fine-tuning. Since tasks may interfere with each other, a key notion for modeling their relationships is task affinity. This includes pairwise task affinity, computed among pairs of tasks, and higher-order affinity, computed among subsets of tasks. Naively computing either of them requires repeatedly training on data from various task combinations, which is computationally intensive. We present a new algorithm Grad-TAG that can estimate task affinities without this repeated training. The key idea of Grad-TAG is to train a "base" model for all tasks and then use a linearization technique to estimate the loss of the model for a specific task combination. The linearization works by computing a gradient-based approximation of the loss, using low-dimensional projections of gradients as features in a logistic regression to predict labels for the task combination. We show that the linearized model can provably approximate the loss when the gradient-based approximation is accurate, and also empirically verify that on several large models. Then, given the estimated task affinity, we design a semi-definite program for clustering similar tasks by maximizing the average density of clusters. We evaluate Grad-TAG's performance across seven datasets, including multi-label classification on graphs, and instruction fine-tuning of language models. Our task affinity estimates are within 2.7% distance to the true affinities while needing only 3% of FLOPs in full training. On our largest graph with 21M edges and 500 labeling tasks, our algorithm delivers estimates within 5% distance to the true affinities, using only 112 GPU hours. Our results show that Grad-TAG achieves excellent performance and runtime tradeoffs compared to existing approaches.

Dongyue Li, Ziniu Zhang, Lu Wang et al.

We study the problem of fine-tuning a language model (LM) for a target task by optimally using the information from $n$ auxiliary tasks. This problem has broad applications in NLP, such as targeted instruction tuning and data selection in chain-of-thought fine-tuning. The key challenge of this problem is that not all auxiliary tasks are beneficial in improving the performance of the target task. Thus, selecting the right subset of auxiliary tasks is crucial. Conventional subset selection methods, such as forward and backward stepwise selection, are unsuitable for LM fine-tuning because they require repeated training on subsets of auxiliary tasks. This paper introduces a new algorithm for estimating model fine-tuning performance without requiring repeated training. Our algorithm first performs multitask training using data from all tasks to obtain a meta initialization. Then, we approximate the model fine-tuning loss of a subset using functional values and gradients from the meta initialization. Empirically, we find that this gradient-based approximation holds with remarkable accuracy for twelve transformer-based LMs. Thus, we can now estimate fine-tuning performances on CPUs within a few seconds. Finally, we fine-tune the pretrained base model once on the selected subset of tasks. We conduct extensive experiments to validate this approach, delivering a speedup of $30\times$ over conventional subset selection while incurring only $1\%$ error of the true fine-tuning performances. In downstream evaluations involving both instruction tuning and chain-of-thought fine-tuning, this loss-based selection approach improves over prior gradient or representation similarity-based methods for subset selection by up to $3.8\%$.

Dongyue Li, Zhenshuo Zhang, Minxuan Duan et al.

Algorithmic reasoning -- the ability to perform step-by-step logical inference -- has become a core benchmark for evaluating reasoning in graph neural networks (GNNs) and large language models (LLMs). Ideally, one would like to design a single model capable of performing well on multiple algorithmic reasoning tasks simultaneously. However, this is challenging when the execution steps of algorithms differ from one another, causing negative interference when they are trained together. We propose branching neural networks, a principled architecture for multitask algorithmic reasoning. Searching for the optimal $k$-ary tree with $L$ layers over $n$ algorithmic tasks is combinatorial, requiring exploration of up to $k^{nL}$ possible structures. We develop AutoBRANE, an efficient algorithm that reduces this search to $O(nL)$ time by solving a convex relaxation at each layer to approximate an optimal task partition. The method clusters tasks using gradient-based affinity scores and can be used on top of any base model, including GNNs and LLMs. We validate AutoBRANE on a broad suite of graph-algorithmic and text-based reasoning benchmarks. We show that gradient features estimate true task performance within 5% error across four GNNs and four LLMs (up to 34B parameters). On the CLRS benchmark, it outperforms the strongest single multitask GNN by 3.7% and the best baseline by 1.2%, while reducing runtime by 48% and memory usage by 26%. The learned branching structures reveal an intuitively reasonable hierarchical clustering of related algorithms. On three text-based graph reasoning benchmarks, AutoBRANE improves over the best non-branching multitask baseline by 3.2%. Finally, on a large graph dataset with 21M edges and 500 tasks, AutoBRANE achieves a 28% accuracy gain over existing multitask and branching architectures, along with a 4.5$\times$ reduction in runtime.

Dongyue Li, Ziniu Zhang, Lu Wang et al.

This paper develops an ensemble method for fine-tuning a language model to multiple datasets. Existing methods, such as quantized LoRA (QLoRA), are efficient when adapting to a single dataset. When training on multiple datasets of different tasks, a common setup in practice, it remains unclear how to design an efficient adaptation for fine-tuning language models. We propose to use an ensemble of multiple smaller adapters instead of a single adapter per task. We design an efficient algorithm that partitions $n$ datasets into $m$ groups, where $m$ is typically much smaller than $n$ in practice, and train one adapter for each group before taking a weighted combination to form the ensemble. The algorithm leverages a first-order approximation property of low-rank adaptation to quickly obtain the fine-tuning performances of dataset combinations since methods like LoRA stay close to the base model. Hence, we use the gradients of the base model to estimate its behavior during fine-tuning. Empirically, this approximation holds with less than $1\%$ error on models with up to $34$ billion parameters, leading to an estimation of true fine-tuning performances under $5\%$ error while speeding up computation compared to base fine-tuning by $105$ times. When applied to fine-tune Llama and GPT models on ten text classification tasks, our approach provides up to $10\%$ higher average test accuracy over QLoRA, with only $9\%$ more FLOPs. On a Llama model with $34$ billion parameters, an ensemble of QLoRA increases test accuracy by $3\%$ compared to QLoRA, with only $8\%$ more FLOPs.